Proceedings of Sinn und Bedeutung 21

Edinburgh Research Explorer Proceedings of Sinn und Bedeutung 21 Citation for published version: Truswell, R, Cummins, C, Heycock, C, Rabern, B & Rohde, H (eds) 2018, Proceedings of Sinn und Bedeutung 21. vol. 21. <https://semanticsarchive.net/Archive/DRjNjViN/SuB21.pdf> Link: Link to publication record in Edinburgh Research Explorer Document Version: Publisher's PDF, also known as Version of record General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 30. Nov. 2022 21    –        Editorial matter and compilation c 2018 Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde. The chapters c 2018 their authors. This collection is distributed under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are credited. See http://creativecommons.org/licenses/by/4.0/. ii TABLE OF C ONTENTS VOLUME 1 Sam Alxatib & Natasha Ivlieva: Van Benthem’s problem, exhaustivity, and distributivity 1 Pranav Anand & Maziar Toosarvandani: Unifying the canonical, historical, and play-by-play present 19 Curt Anderson: Kinds, epistemic indefinites, and some-exclamatives 35 Nicholas Asher, Julie Hunter, & Soumya Paul: Games in linguistics 53 Nadine Bade: Obligatory additives in the antecedent of conditionals 73 Gemma Barberà & Patricia Cabredo Hofherr: Two indefinite pronouns in Catalan Sign Language (LSC) 89 Toni Bassaganyas-Bars: H AVE as a relation between individuals and properties 107 Itai Bassi & Moshe E. Bar-Lev A unified existential semantics for bare conditionals 125 Sigrid Beck & Sonja Tiemann: Towards a model of incremental composition 143 Anton Benz & Nicole Gotzner: Embedded disjunctions and the best response paradigm 163 Marı́a Biezma & Arno Goebel: The pragmatic ingredients to get perfect biscuits 179 M. Ryan Bochnak & Eva Csipak: Reportative deontic modality in English and German 199 Elizabeth Bogal-Allbritten & Keir Moulton: Nominalized clauses and reference to propositional content 215 iii Brian Buccola & Andreas Haida: A surface-scope analysis of authoritative readings of modified numerals 233 Thuy Bui: The Vietnamese perfect 249 Sam Carter: Loose talk, negation and commutativity: A hybrid static-dynamic theory 267 Ivano Ciardelli, Elizabeth Coppock, & Floris Roelofsen: Implicatures of modified numerals: Quality or quantity? 283 Eva Csipak: Discourse-structuring conditionals and past tense 301 Amy Rose Deal & Julia Nee: Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec 317 Emilie Destruel, David Beaver, & Elizabeth Coppock: Clefts: Quite the contrary! 335 Joseph P. De Veaugh-Geiss, Swantje Tönnis, Edgar Onea, & Malte Zimmermann: An experimental investigation of (non-)exhaustivity in es-clefts 347 Kajsa Djärv, Jérémy Zehr, & Florian Schwarz: Cognitive vs. emotive factives: An experimental differentiation 367 Mojmı́r Dočekal & Jakub Dotlačil: When is not-believing believing that not? 387 Michael Yoshitaka Erlewine & Hadas Kotek: Focus association by movement: Evidence from binding and parasitic gaps 399 Huilin Fang: Subjective standard-setting in gradable predicates: On the Mandarin hen structure 409 Jovana Gajić: Coordination and focus particles (re?)united 427 Francesco Paolo Gentile & Bernhard Schwarz: A uniqueness puzzle: How many-questions and non-distributive predication 445 Jonathan Ginzburg, Robin Cooper, Julian Hough, & David Schlangen: Incrementality and clarification/sluicing potential 463 Thomas Grano & Samson Lotven: Control, logophoricity, and harmonic modality in Gengbe desire reports 481 Yael Greenberg: Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles: Evidence from Modern Hebrew 499 Mira Grubic: Two strategies of reopening QUDs — evidence from German auch and noch 517 Daniel Hardt: Internal and external readings of same: Evidence for a uniform account 535 iv Aron Hirsch, Jérémy Zehr, & Florian Schwarz: Presupposition projection from disjunction in online processing 547 Hsin-Lun Huang: On the role of classifiers in licensing Mandarin existential wh-phrases 567 Julie Hunter & Nicholas Asher: Composing discourse parenthetical reports 587 Michela Ippolito: Constraints on the embeddability of epistemic modals 605 Rudmila-Rodica Ivan & Deniz Özyıldız: The temporal presuppositions of Somali definite determiners 623 Peter Jenks, Andrew Koontz-Garboden, & Emmanuel-Moselly Makasso: On the lexical semantics of property concept nouns in Basaá 643 Magdalena Kaufmann & Stefan Kaufmann: Stativity and progressive: The case of Japanese tokoro-da 661 Todor Koev: Parentheticality, assertion strength, and discourse 679 VOLUME 2 David Krassnig: Simple even hypothesis: NPIs and differences in question bias 695 Margaret Kroll: Polarity reversals under sluicing 713 Peter Lasersohn: Common nouns as variables: Evidence from conservativity and the temperature paradox 731 Daniel Lassiter Bayes nets and the dynamics of probabilistic language 747 Sven Lauer & Prerna Nadathur: Quantified indicative conditionals and the relative reading of most 767 Jess H. K. Law: The number sensitivity of modal indefinites 785 Haoze Li: Event-related relative measurement 801 Mingming Liu: Mandarin dou: The common core of distributivity, maximality, and EVEN 819 Matthew Mandelkern: A solution to Karttunen’s problem 827 Daniel Margulis: Expletive negation and the decomposition of only 845 v Clemens Mayr: Predicting polar question embedding 863 A. Marlijn Meijer & Sophie Repp: Modal subordination of propositional anaphora: On the role of tense and the modal particle ook in contextual counterfactuals in Dutch 881 Mioko Miyama: The proper treatment of the wide scope or reading of the English either . . . or . . . construction 899 Charlie O’Hara: Hillary Clinton is not Mitt Romney rich: Nouns modifying degree and dimension of adjectives 915 Doris Penka: One many, many readings 933 Milo Phillips-Brown: I want to, but. . . 951 Kilu von Prince: Paradigm-induced implicatures of TAM markers: The case of the Daakaka distal 969 Dee Ann Reisinger: Saving monotonic modals with ranked ordering sources 985 Floris Roelofsen & Wataru Uegaki: The distributive ignorance puzzle 999 Jacopo Romoli & Matthew Mandelkern: Hierarchical structure and local contexts 1017 Moria Ronen, Yael Greenberg, & Galit Sassoon: A lexical marker of degrees of answerhood 1035 Mats Rooth & Dorit Absuch: Picture descriptions and centered content 1051 Uli Sauerland & Kazuko Yatsushiro: The acquisition of disjunctions: Evidence from German children 1065 Julian J. Schlöder, Antoine Venant, & Nicholas Asher: Aligning intentions: Acceptance and rejection in dialogue 1073 Viola Schmitt & Frank Sode: An anti-intellectualist treatment of German wissen (‘know’) 1091 Per Erik Solberg: Perspectival reflexives and event semantics 1109 Stephanie Solt: Proportional comparatives and relative scales 1123 Alexandra Anna Spalek & Barbara Maria Tomaszewicz: Complement coercion in Polish and the role of selectional restrictions revealed in a self-paced reading study 1141 William B. Starr: Conjoining imperatives and declaratives 1159 vi Tammi Stout: Let’s talk about the future: An investigation of temporal reference in Kaqchikel 1177 Peter Sutton & Hana Filip: Restrictions on subkind coercion in object mass nouns 1195 Satoru Suzuki: Bounded rationality and logic for epistemic modals 1215 Ai Taniguchi: Positive vs. negative inversion exclamatives 1225 Ye Tian & Jonathan Ginzburg: “No, I AM”: What are you saying “no” to? 1241 Wataru Uegaki: Japanese alternative questions and a unified in-situ semantics for ka 1253 Ekaterina Vostrikova: On the similarity between unless and only-if-not 1271 Andrew Weir: Cointensional questions, fragment answers, and structured meanings 1289 Matthijs Westera: An attention-based explanation for some exhaustivity operators 1307 Aaron Steven White & Kyle Rawlins Question agnosticism and change of state 1325 Katsuhiko Yabushita: Only meets vagueness 1343 Dan Zeman: Perspectival plurality, relativism, and multiple indexing 1353 Linmin Zhang: Modified numerals revisited: The cases of fewer than 4 and between 4 and 8 1371 vii viii Foreword The present volume contains a collection of papers presented at the 21st annual meeting “Sinn und Bedeutung” of the Gesellschaft für Semantik, which was held at the University of Edinburgh on September 4th–6th, 2016. 239 abstracts were submitted to SuB21; of the 72 talks and 30 posters on the program, 82 were elaborated into the papers in this collection. The editors of the present volume would like to thank the authors for their contributions and all the anonymous reviewers for their collaboration. We also wish to thank Ede Zimmermann for patient and helpful advice; our fellow organizers Nikolas Gisborne and Marieke Schouwstra; our administrative team Julie Anderson, Steven McGauley, Sylvia Rennie, and Davy Wilkinson for invaluable help in the background; our student volunteers Michela Bonfieni, Kiera Davidson, Jim Donaldson, Sorcha Gilroy, E Jamieson, and Schuyler Laparle; the invited speakers Nicholas Asher, Sigrid Beck, and Peter Lasersohn; Sarah Meyer Truswell for designing the front cover; and everyone else who contributed to the success of the conference. Edinburgh, September 2018 Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde ix x Van Benthem’s problem, exhaustification, and distributivity1 Sam ALXATIB — CUNY GC Natasha IVLIEVA — HSE Moscow Abstract. We discuss the problem of deriving upper-bounded meanings of few, fewer than, and related expressions, in treatments where they are taken to denote predicates of individuals. In such analyses, the determiner-like uses of these expressions are derived by existentiallyclosing their predicate denotations, but this is known to give rise to problems (van Benthem, 1986). We show that the needed upper bound can be derived by applying an exhaustification operator above existential closure. Crucially, this exhaustification operator is insensitive to the distributive properties of the predicates in the sentence, an assumption that we see as consistent with recent work supporting the blindness view of implicatures (Fox and Hackl, 2006; Magri, 2009). We also discuss some similarities and differences between our analysis and Buccola and Spector’s (2016) maximality-based approach. Keywords: Modified numerals, exhaustification, distributivity, maximality. 1. Introduction It is known that the expressions many and few, along with morphosyntactic derivatives like fewer than 3, show adjectival as well as determiner-like uses. Examples are shown in (1). (1) a. b. c. The many/few people who smiled were smiling broadly (The) people who smiled were many/few Many/few people smiled It is also known that, in the case of many, these multiple uses can be accommodated in a uniformly adjectival treatment, if it is complemented with an operation of Existential Closure (EC). The idea would be that many denotes a predicate of individuals, holding of those plural entities that reach a contextually-set cardinality, and in cases like (1c) where many behaves like a determiner, the truth conditions result from existentially closing the predicate. But (as is also known), EC generates problematic results in the case of few. Suppose that, analogously to many, few denotes a predicate of (plural) individuals, holding of just those pluralities that fall below a certain cardinality threshold. If the determiner-like reading is to be derived from EC, the resulting truth conditions will require that some ‘small’ plurality exist that has whatever other properties appear in the given sentence. But these predicted conditions are inaccurate, because (i) they incorrectly require existence, and (ii) they fail to set a desired upper bound. The unwanted existence requirement comes from EC: under EC, and following standard ontological assumptions, sentences like (1c) where few behaves like a determiner cannot be true unless the given predicate(s) are verified by some existing plurality. But as is generally agreed in the literature, such sentences are intuitively true even if no individuals 1 We are grateful to Brian Buccola, Danny Fox, Rick Nouwen, Benjamin Spector, Eytan Zweig, and the audience at the 21st Sinn und Bedeutung in the University of Edinburgh. All errors are our own. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 1 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity verify the predicate(s).2 The second problem, the upper bound problem, is that the existence of small pluralities is compatible with the existence of larger ones; any large plurality of e.g. smiling people will have a small sub-plurality that satisfies the condition of fewness, which means that scenarios where a great number of people smiled will be predicted (incorrectly) to verify the truth conditions of few people smiled. In this paper we will have little to say about the existence problem (problem (i) above). Our focus will be on the upper bound problem, known in current literature as van Benthem’s problem (van Benthem 1986). We propose an exhaustification mechanism that correctly sets the needed upper bound, thus circumventing van Benthem’s problem. The key detail in the proposal is that exhaustification applies without any sensitivity to the distributive/collective properties of the predicates appearing in the given construction. This assumption builds on recent work promoting the ‘blindness’ view of implicatures. We explain the details of our proposal in Section 2, and discuss some of its consequences in Section 3. In Section 4 we turn our attention to Buccola and Spector’s (2016) discussion of these issues, and provide a brief (and at the moment inconclusive) comparison between one of their proposals and ours. In the remaining parts of the current section, we elaborate on the details of van Benthem’s problem, taking note in particular of how it interacts with distributive predicates, and with non-distributive ones. 1.1. Van Benthem’s problem and distributive/non-distributive predicates To keep things simple we will assume that EC is the product of an unpronounced existential determiner, E, defined in (2). (2) J EK = [λ Phe,ti . λ Qhe,ti . ∃x(P(x)=Q(x)=1)] We will also focus our attention on comparative phrases like more than 4 and fewer than 4, instead of many and few, in order to sidestep the vagueness of the latter’s semantics. To keep the presentation simple we assume that more than 4 and fewer then 4 denote predicates of individuals:3 (3) a. b. Jmore than 4K = [λ xe . |x| > 4] Jfewer than 4K = [λ xe . |x| < 4] If predicates of type he,ti can compose by Predicate Modification, then more/fewer than 4 people will denote another set/predicate of plural entities, namely entities of size greater (or less) than four that consist of people. Applying E to these predicates will produce an existential quantifier that maps a given predicate Q to True iff Q holds of some plurality of people that contains more than (or less than) four atoms. The LFs and truth conditions for the two sentences are shown below. 2 Though sentences like few students smiled license existence inferences by default, the inference is thought to be extra-semantic, given its disappearance in DE contexts, and cancellability in in fact continuations. 3 As far as we can see, this assumption can be replaced with a more complex syntax/semantics for comparatives without affecting the tenability of the overall proposal. See Alxatib (2013), Chapter 7. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 2 S. Alxatib & N. Ivlieva (4) a. b. (5) a. b. Van Benthem’s problem, exhaustivity, and distributivity [[E more than 4 people] smiled] ∃x(JpeopleK(x)=1 & |x|>4 & JsmiledK(x)=1) [[E fewer than 4 people] smiled] ∃x(JpeopleK(x)=1 & |x|<4 & JsmiledK(x)=1) As remarked above, the conditions in (5b) are less informative than desired: they hold even in situations where more than four people smiled, because if (say) five people smiled, there is guaranteed to be a smiling sub-group whose size is lower than four. In fact, if we look more closely we can see that the truth conditions of (5a) are identical to those that result when 4 is replaced with any other numeral. To see this, consider the minimally different fewer than 5 people smiled: (6) a. b. [[E fewer than 5 people] smiled] ∃x(JpeopleK(x)=1 & |x|<5 & JsmiledK(x)=1) If the conditions in (5b) hold, then there is a smiling plurality of size less than four, and therefore less than five, which means that (5a) entails (6a). Conversely, if (6b) holds, i.e. if there is a plurality of smilers of size less than five, then by the distributivity of the predicate smiled it follows that there is a smiling sub-plurality of size less than four. Therefore, (6a) entails (5a). This makes (5a) and (6a) equivalent, and the numeral in them semantically irrelevant. At this point it is crucial to highlight the role of distributivity, of the predicate smiled in this case, in making (6)/(5) equivalent. In the case of non-distributive predicates like lifted the piano (together), only one of the two entailments noted above will hold. Consider the LFs and truth conditions in (7) and (8). (7) a. b. (8) a. b. [[E fewer than 4 people] lifted the piano] ∃x(JpeopleK(x)=1 & |x|<4 & Jlifted the pianoK(x)=1) [[E fewer than 5 people] lifted the piano] ∃x(JpeopleK(x)=1 & |x|<5 & Jlifted the pianoK(x)=1) (7b) says that there is a person-plurality of size less than four that lifted the piano. When this holds, the conditions in (8b) must also hold; if there is a piano-lifting plurality of size less than four, then that same plurality makes it true that there is one of size less than five. (7a) therefore entails (8a), in parallel to the entailment from (5a) to (6a). But the reverse entailment does not hold here; if there is a piano-lifting group of size less than five (=(8b)), it does not follow that there is one of size less than four (=(7b)): Suppose exactly four people lifted the piano together. The size of this group falls below five, but not below four, and there is no guarantee that some sub-group of the four lifters also lifted the piano, because the lifting is true of them collectively, not individually. We therefore see that van Benthem’s problem (the problem of the upper bound) causes numerals to be semantically redundant in the case of distributive predicates, though as we pointed out, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 3 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity this is not the case for non-distributive predicates. We will now explain what this redundancy means for attempts to derive the upper bound by pragmatic strengthening (or exhaustification): because (under distributivity) all alternatives of the form fewer than n are equivalent, there will be no way of selecting the right alternatives for exhaustification, and of using those alternatives to generate the desired upper bound at the correct n. We expand on this next. From this point on, we will write ‘E>few constructions’ to refer to sentences where EC outscopes few and similar expressions. We also write ‘distributive/non-distributive E>few constructions’ to refer to E>few constructions that contain (or do not contain) distributive predicates. 1.2. Van Benthem’s problem and pragmatic strengthening? Our current truth conditions for distributive E>few constructions only require existence, and appear to make no use of the numeral modified by fewer than.4 But what if the truth conditions were complemented with the negation of other, more informative alternatives? In (Neo-) Gricean pragmatics, a sentence S that is uttered in a certain context licenses not only the inferences that result from its literal meaning, but also the inference that alternative sentences which (i) were not uttered, (ii) would have been as relevant in that context, and (iii) are stronger than S, are false. It may seem that pragmatic principles along these lines can be used to derive the upper bound of E>few sentences, but as we now explain, pragmatic strengthening of distributive E>few LFs is either vacuous, or excessive. The first of these two outcomes results if the only relevant alternatives to an E>few sentence are those where the numeral/degree is substituted for another. In the case of our example (5a), repeated below as (9a), this assumption limits the alternatives to those in (9b). (9) a. b. [[E fewer than 4 people] smiled] {[[E fewer than 3 people] smiled], [[ E fewer than 5 people] smiled], [[ E fewer than 6 people] smiled], · · ·} The problem is that none of the alternatives in (9b) are stronger than (9a); they are all equivalent. This gives the strengthening mechanism nothing to negate (or ‘exclude’) in strengthening (9a), and leaves it vacuous. Now, suppose we enrich our set of alternatives and add constructions of the form [[n people] smiled], i.e. where fewer than is removed: 4 We will return to the existence requirement in Section 4. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 4 S. Alxatib & N. Ivlieva (10) a. b. c. Van Benthem’s problem, exhaustivity, and distributivity [[E fewer than 4 people] smiled] {[[E fewer than 3 people] smiled], [[ E fewer than 5 people] smiled], [[ E fewer than 6 people] smiled], [[ E 2 people] smiled], [[ E 3 people] smiled], [[ E 4 people] smiled], [[ E 5 people] smiled], · · · } Each alternative in (10c) requires that there be an n-sized plurality of smiling people, and hence they each asymmetrically entail the weak existence truth conditions of (10a). It follows, by the simple pragmatic recipe described above, that an utterance of (10a) will semantically require existence, and via pragmatic strengthening will imply that no group of four or five smilers exists—so far correctly—but also that no group of three smilers exists, and no group of two smilers exists. By nullfying the semantic contribution of the numeral in the original utterance, the strengthening mechanism described above will not help recover the correct upper bound, because there will be no way to correctly identify its location. In the next section, we will present a modified strengthening mechanism that bypasses van Benthem’s problem. We will first introduce the mechanism’s two key components, Innocent Exclusion and blindness, and show how they interact to produce the correct upper bound for distributive E>few constructions. We will then discuss our predictions for non-distributive cases, and finally, compare our analysis to the analysis offered in Buccola and Spector (2016). 2. Reconsidering Pragmatic Strengthening 2.1. Innocent Excludability, Blindness, and Implicature Calculation We will assume that the strengthened meaning of a sentence S is derived by applying an exhaustification operator Exh to the denotation of S (along the lines of Fox 2007a, following proposals by Groenendijk and Stokhof 1984; Krifka 1995; Landman 1998; van Rooy 2002). Exh may be viewed as a covert variant of only. Its semantics is defined below: (11) JExhKw (Ahst,ti )(phs,ti )=1 iff p(w)=1 & ∀q(q∈ EXCL (p, A) → q(w)=0) The exhaustification operator takes a proposition p, its ‘prejacent’, and a set of alternatives A, and asserts that p is true and that all its excludable alternatives (from A) are false. The set of excludable alternatives EXCL (p, A) is a subset of A. Different versions of Exh proposed in the literature differ with respect to how this set of excludable alternatives is defined. One possibility is to define EXCL (p, A) as that subset of A that contains all (and only) propositions that are not entailed by p: (12) EXCL (p, A) = {q : q∈A & p 2 q} But we will now show why (12) is problematic, and why (following Fox and others) we adopt Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 5 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity the notion of ‘Innocent Excludability’ instead of it. 2.2. Innocent Excludability It was argued in Sauerland (2004) that disjunctive constructions should have not only their conjunctive counterparts as alternatives, but also the disjuncts. This is based on cases like (13). (13) John needs to talk to Mary or Sue. (13) naturally implies that John does not need to talk to Mary specifically, nor to Sue. If this is to be derived as an implicature, then the mechanism that generates implicatures must have access to the alternatives seen in (14), where the disjunction is replaced with its disjuncts. The alternatives are shown together with the conjunctive alternative to (13), but in this example the conjunctive alternative will not play an important role. (14) a. b. c. John needs to talk to Mary John needs to talk to Sue John needs to talk to Mary and Sue Note that each of (14a) and (14b) is logically stronger than the original (13), which means that, if they are included in the set of alternatives, they will count as excludable by the definition in (12) and consequently be negated by the strengthening mechanism. Here, this seems to be a good result.5 But in the case of unembedded disjunctions like (15), the same ingredients make strengthening contradictory. (15) John saw Mary or Sue. (16) a. b. c. John saw Mary. John saw Sue. John saw Mary and Sue. Under the assumption that disjunction has its disjuncts among its alternatives, the application of Exh to (15) is predicted to assert (15) and negate both of (16a) and (16b) (in addition to negating (16c)). But this leads to the contradiction in (17): (17) John saw Mary or Sue and he didn’t see Mary and he didn’t see Sue. The conclusion from this result is that (12), our current definition of excludable alternatives, must be revised in a way that allows the alternatives in (14) to participate in strengthening (13), but blocks (16a–b) from participating in strengthening (15). The revision we adopt is Fox’s (2007a), who defines excludability as ‘innocent’ excludability. 5 Negating the conjunctive alternative in (14c) is vacuous here, since it follows from negating either of the disjuncts. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 6 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity Our formulation of Innocent Excludability (IE) is the following: given a proposition p and a set of propositions A, the IE-alternatives (EXCL (p, A)) are those that remain in A after the noninnocent subsets of A are removed from A. The non-innocent sets, in turn, are those whose ‘set-negation’ contradicts p, and that have no proper subsets whose set-negation contradicts p. The set negation of a set A is the conjunction of the negations of A’s elements. These definitions are summarized below: (18) EXCL (p, A) = A − a. b. S {B : B⊆A and B is non-innocent w.r.t. p} B is non-innocent w.r.t. p iff (i) B¬  ¬p, and (ii) ¬∃B′ (B′ ⊂B & B′¬  ¬p). V ¬ B = {¬q : q∈B} This revised definition of EXCL in (18) successfully distinguishes the case of (13) from (15). Let us represent the disjunction in (15) as p ∨ q, and its alternatives as p, q, and p ∧ q: (19) A = {p, q, p ∧ q} Now, given the definition in (18), what subsets of A are non-innocent with respect to p ∨ q? It is clear that negating all of the propositions in A will jointly contradict the disjunctive p ∨ q, so A itself satisfies condition (i) in (18a). But A fails condition (ii) in (18b) because there is a proper subset of A whose set negation also contradicts p ∨q. This is the set {p, q}. And because {p, q} does not have proper subsets whose set negations contradict p ∨ q, it follows that {p, q} is non-innocent with respect to p ∨ q. So, the set of IE-alternatives in A, given p ∨ q, is the result of subtracting the non-innocent set {p, q} from A: (20) EXCL (p ∨ q, A) = A − {p, q} = {p ∧ q} It follows that strengthening p ∨ q given the set of alternatives A will not be contradictory, and will generate the inference that the conjunctive p ∧ q is false. Consider now the case of (13), where disjunction is embedded under a universal modal. Here we may represent (13) itself as (p ∨ q), and its alternatives as p, q, and (p ∧ q): (21) A′ = {p, q, (p ∧ q)} It should be clear that negating all of the alternatives in A′ does not contradict (p ∨ q); the negation will merely require that not all accessible worlds be p-worlds, and not all accessible worlds be q-worlds. This is consistent with (p ∨ q), because the modal base may consist of a mix of worlds, some being p-worlds and others being q-worlds. There are therefore no non-innocent sets within A′ given (p ∨ q), (22) EXCL ((p ∨ q), A′ ) = A′ − {} = A′ and from this it follows that exhaustifying (13), given the set of alternatives in A′ , will generate the inference that each element in A′ is false: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 7 S. Alxatib & N. Ivlieva (23) Van Benthem’s problem, exhaustivity, and distributivity Exh(A′ , (p ∨ q)) = (p ∨ q) & ¬p & ¬q & ¬(p ∧ q) This concludes our introduction of Innocent Excludability. We now turn to the second of our two key ingredients, blindness. 2.3. Blindness We take ‘blindness’ to be a property of semantic operators or mechanisms. When we say that an operator O is blind to some informational content, we mean that O applies without any sensitivity to that content, that is, that O applies to representations (e.g. syntactic ones) where that information is absent. Though our discussion of blindness will remain somewhat vague in this paper, we see Gajewski (2002) as an important reference for how the notion may be made more precise (see specifically Gajewski’s definition of ‘logical skeleton’). We know of two proposals in the literature on implicatures that appeal to blindness. In one, Fox and Hackl (2006), it is argued that implicature calculation (and calculation of focus semantics) is blind to whether the predicates appearing in the given sentence utilize a discrete or dense scale of measurement. The claim is that implicatures are derived from representations where all measurement scales are assumed to be dense (we will explain the argument briefly below). If right, this means that implicature calculation (and calculation of focus semantics) is insensitive to content that on the surface appears to be lexical. As we will see later, our own proposal is similar to Fox and Hackl’s in this respect. In another proposal, Magri (2009), implicature calculation is argued to be blind to contextual/world knowledge. We will review Magri’s argument after we summarize Fox and Hackl’s, but we want to make it clear that we will not talk in detail about how either of these two accounts might interact with our own. Our intention is to use the two proposals as precedent for the hypothesis that exhaustification is blind.6 2.3.1. Fox and Hackl (2006) A central question in Fox and Hackl (F&H) is why sentences like (24) do not give rise to ‘exact’ implicatures. (24) John read more than 3 books ; ¬(John read more than 4 books) Assuming that (24) has an alternative where the numeral 3 is replaced with 4, we expect the latter to participate in exhaustifying the meaning of (24), since John read more than 4 books is stronger than (24). But then we expect (24) to imply that John read more than three but not more than four books, i.e. exactly four books.7 In their discussion of the problem, Fox and Hackl point out that this prediction is specific to cases where the relevant scale is discrete; if 6 Readers familiar with Fox and Hackl in particular will no doubt wonder how the density hypothesis interacts with our own exhaustification mechanism. This is by no means a trivial question, but we leave it for later work. 7 Note that this predictions hinges on the assumption that comparatives have other comparatives as alternatives. One could add constructions of the form exactly n . . . , and we would no longer predict comparatives to give rise to these exact inferences. This possibility was in fact proposed in Spector (2005), but argued against in Fox (2007b). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 8 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity the scale of degrees were dense, then there will be some alternative whose negation contradicts the utterance itself. Take (25) as an example. (25) John is taller than 6 ft. Let us assume that (25) requires that John reach a degree of height d above six feet. Unlike the integer scale, the scale of height is intuitively dense, meaning that for any two degrees of height d1 and d2 there is a degree of height d3 in between them. If (25) requires that John reach some height d above six feet, then by the density of the height scale there must exist some degree of height d ′ above six feet and below John’s actual height d. Consider now the alternative in (26). (26) John is taller than d ′ Since d ′ is above 6 feet, it follows that (26) is stronger than (25), which means that in strengthening (25) the algorithm should negate (26). But negating (26) means that John is at most d ′ -tall, which makes him shorter than d, i.e. shorter than his assumed actual height. The consequence is that, no matter how tall John is assumed to be, there is always a degree of height just below his own (and above six feet) that can form a stronger comparative sentence than (25), and whose negation will contradict the semantic content of (25).8 The broader consequence of this is that implicatures of comparatives are predicted to generate contradictions if the relevant scale of degrees is dense. Yet the absence of implicatures in comparatives appears to hold regardless of whether the scale is discrete, as in the case of (24), or dense, as in the case of (25). Given this, Fox and Hackl propose that the level of representation at which implicatures are calculated (as well as focus etc.) is one where all scales are dense. This is their Universal Density of Measurement hypothesis. The proposal we borrow from Fox and Hackl is that implicature calculation is in some sense blind to information provided by neighboring lexical material. That is, implicature calculation seems to proceed as if some abstract representations replaced the elements that make up the given sentence. By masking the properties of the elements they stand in for, e.g. the discreteness of the counting scale in (24), the abstraction renders implicature calculation insensitive to information that would otherwise change its outcome. 2.3.2. Magri (2009) Another empirical argument in favor of the blindness view was presented in Magri (2009).9 Magri claims that the notion of entailment relevant for implicature calculation is logical, rather than contextual. His argument is based on the oddness of sentences like (27): (27) Some Italians come from a warm country. The argument is this. (27) is odd because the use of some triggers a scalar implicature that the alternative with the universal quantifier, all Italians come from a warm country, is false. 8 See 9 See Gajewski (2009) for a discussion of how this interacts with innocent excludability. also Magri (2011); Schlenker (2012); and Magri (to appear) for discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 9 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity This leads to the strengthened proposition that some but not all Italians come from a warm country, which contradicts our knowledge that all Italians come from the same country. But as Magri points out, this explanation works only if we assume that this piece of world knowledge is unavailable to implicature calculation. While the alternative all Italians come from a warm country is logically stronger than (27), the two sentences are contextually equivalent; knowing that all Italians come from the same country, if some Italians come from a warm country, then it must be the case that all of them do (and vice versa). If this information is factored into the implicature-calculating mechanism, the all-alternative would not be negated, because it is equivalent to (27), and the oddness would no longer be predicted. If, on the other hand, the mechanism was blind to world-knowledge, and was sensitive only to logical information, then exhaustification would apply, and produce the detected oddness of (27).10 In what follows, we will attempt to exhaustify our E>few structure again, but with the blindness hypothesis and Innocent Excludability in mind. We will show that if the distributivity of the given predicate is hidden from the exhaustification mechanism—in parallel to how scale discreteness is hidden, in Fox and Hackl’s proposal—we predict that the upper bound be placed correctly, thus overcoming the challenge of van Benthem’s problem. 2.4. Exhaustification revisited Consider once again the E>few LF in (28), (28) [[ E fewer than 4 people] smiled] And consider the alternatives below: (29) a. b. c. d. {E fewer than 2 people smiled, E fewer than 3 people smiled, E fewer than 5 people smiled, E fewer than 6 people smiled, · · · E 2 people smiled, E 3 people smiled, E 4 people smiled, E 5 people smiled, E 6 people smiled, · · · } As we saw in Section 1.2, the distributivity of the verb smiled makes each of the alternatives in (29a–b) equivalent to (28), so negating any of them individually will contradict (28). This means that each alternative in (29a–b) makes its own singleton non-innocent set, since by definition, a set is non-innocent if its set-negation contradicts the utterance, and if it has no proper subset whose set-negation contradicts the utterance. The alternatives in (29a–b) are therefore not innocently excludable. 10 As Magri himself notes, the success of his analysis requires that (27) be obligatorily exhaustified, since the oddness of the sentence would otherwise not be predicted. The reader is referred to the original paper for details. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 10 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity What about the alternatives in (29c–d)? As we showed in Section 1.2, negating these together does not contradict the truth conditions of (28), so they are all predicted to be innocently excludable. It follows that exhaustifying (28) with respect to the alternatives in (29) will produce an excessively low upper bound: (30) Exh((29), (28))=1 iff ∃x(JpeopleK(x)=1 & |x|<4 & JsmiledK(x)=1) & ¬∃x(JpeopleK(x)=1 & |x|≥2 & JsmiledK(x)=1) & ¬∃x(JpeopleK(x)=1 & |x|≥3 & JsmiledK(x)=1) & · · · But recall also that the equivalence of (29a–b) and (28) does not hold when smiled is replaced with a collective predicate. In those cases, the alternatives with the lower numeral asymmetrically entail those with the higher numeral. If there exists a piano-lifting group of size less than four, then there exists a piano-lifting group of size less than five, namely the same one, but the reverse does not hold: if there is a lifting group of size less than five, it does not follow that there is one of size less than four. Now suppose that, by blindness, the exhaustification mechanism were insensitive to the lexical properties of the verb. Then the grouping of alternatives into non-innocent sets will change, and consequently change the contents of the (innocently) excludable set. Let us repeat (29) and (30), but abstract away from the NP/VP: (31) [[ E fewer than 4 NP] VP] (32) a. b. c. d. {E fewer than 2 NP VP, E fewer than 3 NP VP, E fewer than 5 NP VP, E fewer than 6 NP VP, · · · E 2 NP VP, E 3 NP VP, E 4 NP VP, E 5 NP VP, E 6 NP VP, · · · } We can immediately see that the alternatives in (32b) are non-innocent, because each of them is individually weaker than (31), and therefore comprises a singleton non-innocent set of its own. The alternatives in (32a) are stronger than (31), but they are not innocently excludable because they form non-innocent sets with alternatives in (32c). As an example, take the first alternative in (32a) and the first alternative in (32c). Negating the former amounts to saying that there are no groups (of NPs that VP) of size less than 2, which means that the size of VPing NP groups is 2 or greater. This contradicts the negation of the first alternative in (32c), which says that there are no groups of VPing NPs of size 2 or more. Note that, by themselves, each of these alternatives can be negated consistently with (31), so on their own, they do not form non-innocent sets with respect to (31). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 11 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity More generally, then, for any numeral (or degree) d lower than 4, there is a non-innocent set that contains the alternatives [ E fewer than d NP VP] together with the alternative [E d NP VP]. Any set containing just these two sentence is non-innocent, because its set negation is contradictory and therefore inconsistent with (31). What about the alternatives in (32d)? It may appear that each of these can be paired with an alternative from (32b) into a non-innocent set. But in fact, these sets have non-innocent proper subsets: remember that each alternative in (32b) individually forms a singleton non-innocent set, so pairing it with an alternative from (32d) will not produce a non-innocent set. It follows, then, that the excludable alternatives from (32) are the ones in (32d), and negating these produces the desired upper bound. (33) Exh((32), (31))=1 iff ∃x(JNPK(x)=1 & |x|<4 & JVPK(x)=1) & ¬∃x(JNPK(x)=1 & |x|≥4 & JVPK(x)=1) & ¬∃x(JNPK(x)=1 & |x|≥5 & JVPK(x)=1) & · · · 3. Discussion and consequences In a nutshell, our proposal derives the upper bound of E>few constructions not from their literal semantics, but from an exhaustification mechanism that negates whatever is excludable from the set of alternatives. In Section 2 we showed that, in order for the exhaustification mechanism to produce the correct upper bound, the entailment relations it ‘sees’ between the alternatives must be independent of whether the predicates in those alternatives are distributive or collective. We pointed to findings in the literature on implicatures, notably Fox and Hackl (2006) and Magri (2009), that suggest that exhaustification is blind to lexical/contextual information. But the proposal brings many questions with it. First, it is known that implicatures are often cancellable, so if an implicature-generating mechanism is responsible for the upper bound in the sentences that concern us, why is it that the upper bound is intuitively obligatory? Our answer to this is that, in the case of distributive predicates, lack of exhaustification produces underinformative truth conditions. We make this precise and borrow Buccola and Spector’s Pragmatic Economy Constraint: (34) Pragmatic economy constraint (Buccola and Spector, 2016): An LF φ containing a numeral n is infelicitous if, for some m distinct from n, φ is truth-conditionally equivalent to φ [n → m] (the result of substituting m for n in φ ). We will look more closely at Buccola and Spector’s proposal in the next section. At the moment we can simply point out that (34) is used by them to get around a similar problem to ours: why is exhaustification (or, on their account, maximality) obligatory? The effect of (34) is to require that numerals make a truth conditional difference. As we saw in Section 1.2, unexhaustified E>few constructions have the same truth conditions regardless of the numeral that appears in them, and because of this, they are ruled out by the economy constraint in (34). On the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 12 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity other hand, exhaustifying E>few constructions (blindly) retrieves the semantic import of the numeral, and thus satisfies (34). But now we face a second question. If exhaustification is made obligatory because of a filter against uninformative numerals, we predict that exhaustification be optional in non-distributive E>few sentences. The reason is simply that, as we saw in Section 1.2, changing the numeral in non-distributive E>few constructions does change the truth conditions, so there is no reason yet to favor either of the exhaustified or unexhaustified parses of (35): (35) Fewer than 4 people lifted the piano (together). Interestingly, sentences like (35) do not intuitively place an upper bound in the same way as distributive E>few examples. As Buccola and Spector point out, (35) requires only that some group of lifters reach a size below four; the sentence is still true if the piano was lifted by some other group of size five, six, etc. This reported judgment fits the prediction of the current proposal, which permits unexhaustified parses of (35) given that the numeral in it is non-trivial. But importantly, the proposal as it stands also allows exhaustified parses of non-distributive E>few structures. So we currently predict (35) to also have upper-bounded readings. We leave this issue to future work. Another important problem that we have set aside so far is the existence prediction of EC. The predicted truth conditions of E>few constructions, whether exhaustified or not, require that some existing plurality verify the predicates appearing in the sentence. We do not have a solution to this problem yet, but we will say more about it after we discuss Buccola and Spector’s account, to which we now turn. 4. Maximality: Buccola and Spector (2016) We must make it clear that our review of Buccola and Spector (B&S) is by no means representative of the many ideas they discuss. Our attention will be restricted to their syntactic maximality account (SMax) of modified numerals. Once we go over the basics of the account, we offer a brief comparison between it and our own proposal. As announced in the introduction, the comparison will be inconclusive, but it will highlight an advantage of B&S that has to do with the existence inference discussed earlier. 4.1. Syntactic Maximality (SMax) The ingredients of B&S’s SMax account are the following. First, expressions like fewer than 4 denote generalized quantifiers (GQs) over degrees (type hdt,ti) rather than predicates of individuals. Second, nodes that denote degrees (type d) can undergo two type-shifting operations, which we represent syntactically. One, I S C ARD, takes a degree d and returns a predicate of (plural) individuals. The predicate holds of individuals whose size equals d. The other, I S M AX, takes a degree d and returns a GQ over degrees. The GQ holds of a set of degrees provided that its maximal element is d. The definitions are shown below: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 13 S. Alxatib & N. Ivlieva (36) a. b. c. Van Benthem’s problem, exhaustivity, and distributivity Jfewer than 4K = [λ Dhd,ti . ∃d(d <4 & D(d)=1)] JI S C ARD K(d) = [λ xe . |x|=d] JI S M AX K(d) = [λ Dhd,ti . max(D)=d] On B&S’s account, a sentence like (37) can have two possible LFs. In one LF, the phrase fewer than 4 undergoes QR and binds a trace of type d in its base position. The trace is shifted by I S C ARD into a predicate of individuals, and the result is composed with other predicates ultimately closed by an EC operation. (37) Fewer than 4 people smiled (38) [fewer than 4] [λ d [[E [I S C ARD(d ) people]] smiled]] With the dislocated modified numeral scoping above EC, the resulting truth conditions require that some degree d below 4 exist, and that some smiling plurality be of size d. These are the same (uninformative) truth conditions as those predicted on our account (without exhaustification): (39) J(38)K=1 iff ∃d(d <4 & ∃x(|x|=d & JpeopleK(x)=1 & JsmiledK(x)=1)) =1 iff ∃x(|x|<4 & JpeopleK(x)=1 & JsmiledK(x)=1) In another LF of (37) the phrase fewer than 4 is moved further, and binds a trace that undergoes shifting by I S M AX. (40) [fewer than 4] [λ d ′ [I S M AX(d ′ )] λ d [[ E [I S C ARD(d) people]] smiled]] The truth conditions of this LF require that, for some degree d below 4, the maximal size of existing smiling groups equal d. This is the same as saying that the maximal size of existing smiling groups fall below 4, which matches the intuited upper-bounded reading of the sentence. (41) J(40)K=1 iff ∃d(d <4 & max{d ′ : ∃x(|x|=d ′ & JpplK(x)=1 & JsmiledK(x)=1)}=d) =1 iff max{d : ∃x(|x|=d & JpplK(x)=1 & JsmiledK(x)=1)}<4 The choice between LFs (38) and (40), for sentence (37), is based on the Pragmatic Economy Constraint (PEC) that we cited earlier. Recall that the constraint blocks LFs that contain uninformative numerals. In (38), the numeral is uninformative because of the distributivity of smiled (see discussion in Section 1.2), but in (40), changing the numeral clearly changes the truth conditions. By the PEC, then, only the latter LF can be associated with (37), which means that upper-bounded readings are obligatory when distributive predicates are used. In the case of non-distributive predicates, however, ‘non-maximal’ LFs incur no violation of the PEC, because their truth conditions depend crucially on the numeral. It follows that sentences like (42) can be interpreted without an upper bound—LF (43)—or with an upper bound—LF (45). (42) Fewer than 4 people lifted the piano (together) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 14 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity (43) [fewer than 4] [λ d [[E [I S C ARD(d ) people]] lifted the piano]] (44) J(43)K=1 iff ∃d(d <4 & ∃x(|x|=d & JpeopleK(x)=1 & JsmiledK(x)=1)) =1 iff ∃x(|x|<4 & JpeopleK(x)=1 & Jlifted. . . K(x)=1) (45) [fewer than 4] [λ d ′ [I S M AX(d ′ )] λ d [[ E [I S C ARD(d) people]] lifted. . . ]] (46) J(45)K=1 iff ∃d(d<4 & max{d ′ : ∃x(|x|=d ′ & JpplK(x)=1 & Jlifted. . . K(x)=1)}=d) =1 iff max{d : ∃x(|x|=d & JpplK(x)=1 & Jlifted. . . K(x)=1)}<4 4.2. A comparison: Exhaustification or maximality? As we said earlier, we cannot comprehensively compare our proposal to that of B&S. Nevertheless, we can take note of some features that the two accounts have in common, and other features that distinguish them. We leave a more detailed assessment to future investigation. One common ingredient to B&S and the current proposal is the reliance on the PEC, and the resulting prediction that, with non-distributive predicates, upper-bounded readings are permitted but not obligatory. In our account, this is because unexhaustified parses are not blocked by the PEC in non-distributive E>few LFs; in B&S, it is because the PEC permits both maximal as well as non-maximal LFs. Whether or not this prediction fits the facts remains to be seen, but it appears that in this respect the two accounts are similar.11 The proposals are also alike in deriving the upper bound from sources that are external to the modified numeral itself. In our account, the source of the upper bound is the (blind) exhaustification operator, while in B&S it is the I S M AX shift operation. But there are differences. Consider first the existence inference mentioned in Section 3. On our proposal the inference results from existentially closing the predicate fewer than 4, but importantly, the inference remains even when the LF is (blindly) exhaustified. We therefore predict that upper-bounded readings still require existence, and that sentences like (37) be false in situations where no one smiled. We see this as a disadvantage of our account, and an advantage of B&S’s, where applying I S M AX above I S C ARD effectively removes the requirement of existence.12 There is, however, a possible amendment to exhaustification that deserves further research, which involves adding null individuals to the domain of entities. At the moment we cannot present a concrete version of this idea, and leave it to future development (see Landman 2004, and also B&S’s maximal-informativity proposals in their Section 8). If such an analysis can be formulated, it may come with different predictions from B&S’s SMax proposal, which es11 B&S discuss cases where collective predicates take upper-bounded readings, citing personal communication with Philippe Schlenker. See their Section 7. 12 It must be noted that removing the existence inference in B&S depends on defining max so that it returns the degree 0 when its input is the empty set. In situations where no one smiled, there are no degrees in the set {d : ∃x(|x|=d & JpplK(x)=1 & JsmiledK(x)=1)}, and hence no maximal degree that can inform the semantics of I S M AX. To get around this, it must be explicitly stated that max{}=0. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 15 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity sentially correlates non-existence with upper-boundedness, since the two come together from applying I S M AX. 5. Conclusions We discussed a problem that arises with the interpretation of expressions few and fewer than 3 in certain environments. The problem can be described as follows. When combined with distributive predicates, those expressions intuitively impose an upper bound. However, assuming the adjectival semantics for few and deriving its quantificational meaning through EC, sentences with few are predicted to have uninformative truth conditions. We showed also that the needed upper bound cannot result from standard pragmatic strengthening mechanisms. We proposed a modified strengthening mechanism that can derive the correct upper bound. The key properties of the proposed mechanism are (i) its insensitivity to information about distributivity, and (ii) innocent exclusion (Fox, 2007a). Our proposal was compared to Buccola and Spector’s maximality-based account. As we pointed out, the comparison is incomplete and requires further investigation. References Alxatib, S. (2013). Only and Association with Negative Antonyms. Ph. D. thesis, MIT. van Benthem, J. (1986). Essays in Logical Semantics. Dordrecht: Reidel. Buccola, B. and B. Spector (2016). Modified numerals and maximality. Linguistics and Philosophy 39, 151–199. Fox, D. (2007a). Free choice and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and Implicature in Compositional Semantics. Houndmills: Palgrave Macmillan. Fox, D. (2007b). Too many alternatives: Density, symmetry, and other predicaments. In T. Friedman and M. Gibson (Eds.), SALT XVII, Ithaca, NY. CLC Publications. Fox, D. and M. Hackl (2006). The universal density of measurement. Linguistics and Philosophy 29, 537–586. Gajewski, J. (2002). On analyticity in natural language. Unpublished manuscript. Gajewski, J. (2009). Innocent Exclusion is not contradiction free. Unpublished manuscript. Groenendijk, J. and M. Stokhof (1984). Studies on the Semantics of Questions and the Pragmatics of Answers. Ph. D. thesis, University of Amsterdam. Krifka, M. (1995). The semantics and pragmatics of polarity items. Linguistic Analysis 25, 209–257. Landman, F. (1998). Plurals and maximalization. In S. Rothstein (Ed.), Events and Grammar. Dordrecht: Kluwer. Landman, F. (2004). Indefinites and the Type of Sets. London: Blackwell. Magri, G. (2009). A theory of individual-level predicates based on blind mandatory scalar implicatures. Natural Language Semantics 17, 245–297. Magri, G. (2011). Another argument for embedded scalar implicatures based on oddness in downward entailing environments. Semantics and Pragmatics 4, 1–51. Magri, G. (to appear). Blindness, short-sightedness, and Hirschberg’s contextually ordered Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 16 S. Alxatib & N. Ivlieva Van Benthem’s problem, exhaustivity, and distributivity alternatives: A reply to Schlenker (2012). In S. Pistoia-Reda and F. Domaneschi (Eds.), Linguistic and Psycholinguistic Approaches on Implicatures and Presuppositions. Palgrave Macmillan. van Rooy, R. (2002). Relevance implicatures. Unpublished manuscript. Available at http://semanticsarchive.net/Archive/WIyOWUyO/Implicfinal.pdf. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy 27, 367–391. Schlenker, P. (2012). “Maximize Presupposition” and Gricean reasoning. Natural Language Semantics 20, 391–429. Spector, B. (2005). Aspects de la pragmatique des opérateurs logiques. Ph. D. thesis, Université Paris 7. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 17 18 Unifying the canonical, historical, and play-by-play present1 Pranav ANAND — University of California, Santa Cruz Maziar TOOSARVANDANI — University of California, Santa Cruz Abstract. While the present tense is typically taken to index the reference time to the time of utterance, such a restriction cannot capture noncanonical uses of the present in English, such as the historical present or play-by-play present. We adopt a bicontextual semantics for present tense, in which the two time coordinates are mediated by pragmatics, allowing us to bring canonical, narrative, and play-by-play uses under a single denotation. Moreover, we show that such a treatment can also capture the novel observation that the historical use of the present tense can “anchor” the past perfect, while its other two uses cannot. Keywords: tense, aspect, discourse structure, contextualism The present tense in English has, in its canonical use, two properties that seem reasonably clear. First, it exhibits Utterance Indexicality: the present tense is used to describe eventualities that are simultaneous with the time of utterance. Second, it exhibits — unlike, say, German — what we might call Stativity: the present tense is only compatible with stative predicates, including derived ones (e.g., habituals). (1) a. b. c. Susan owns the farm. # Mary reads the newspaper. Intended: ‘Mary is reading the newspaper now.’ # James plays the violin. Intended: ‘James is playing the violin now.’ stative accomplishment activity (Smith, 1997: 111) There are, however, two uses of the present tense, often conflated (e.g., Smith 1997: 111), which run counter to this orthodoxy: the play-by-play present and the historical present.2 (2) Play-by-play present (USA vs. New Zealand, 2015 Women’s Soccer Friendlies) Commentator: Wambach leads it back and now Krieger has it. Tobin Heath goes far. (http://www.youtube.com/watch?v=Kqe9n7zvnnw, 1:40:55) (3) Historical present I couldn’t believe it! Just as we arrived, up comes Ben and slaps me on the back as if we’re life-long friends. “Come on, old pal,” he says, “Let me buy you a drink!” I’m telling you, I nearly fainted on the spot. (Quirk et al., 1985: 181) Neither of these noncanonical uses exhibits Stativity: both are quite congenial with nonstative predicates. The historical use, in addition, does not exhibit Utterance Indexicality. 1 We are grateful to audiences at Sinn und Bedeutung and the University of Arizona for their helpful comments and questions. 2 In addition to these, there are headline, futurate, and performative uses of the present. These all violate Stativity, while the first two also violate Utterance Indexicality. We return to this issue in the conclusion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 19 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present We propose a unified semantics for the present tense in English that accounts for the properties of these two uses and the canonical present. There have been some previous attempts to derive one or the other of the noncanonical uses with customized solutions (Smith 1997: 185; Schlenker 2004; Eckardt 2015). We aim for a general theory that takes advantage of two pieces of off-the-shelf technology: i) a bicontextual semantics for tense (Sharvit, 2004, 2008), and ii) a version of Kamp and Reyle’s (1993) semantics for the past perfect. Our invocation of the past perfect comes from an apparently hitherto unnoticed contrast between the play-by-play and historical uses. The play-by-play present cannot “anchor” the past pefect—that is, it cannot describe an event which the past perfect locates another event anterior to, as shown in (4a). But the historical present can, as shown in (5a). (4) Play-by-play present Commentator: Federer serves. It’s long. He looks at the line. He yells in protest. a. # The judge had called a fault. b. The judge has called a fault. c. The judge called a fault. (5) Historical present Rumors of Berlusconi’s crimes swirl. His advisors confront him. He scoffs. a. He had paid off the prostitute for her silence already. b. He has paid off the prostitute for her silence already. c. He paid off the prostitute for her silence already. In either of these uses, the present tense can, by contrast, be used to anchor the present perfect (4b, 5b) or simple past (4c, 5c). Specifically, we propose that the present tense is indexical to the time of a context of assessment (Sharvit, 2004, 2008), which can be pragmatically distinct from the speech time, a coordinate of the context of utterance (cf. Schlenker 2004). When the present tense is unmoored from the speech time, Utterance Indexicality and Stativity are simultaneously lifted. In turn, we argue that the contrast in (4) and (5) reflects an additional restriction of the past perfect, namely that it is indexical to both the context of assessment and the context of utterance, cf. Kamp and Reyle (1993: 598). Together, these two ingredients correctly predict that, under the pragmatic norms governing the play-by-play present, the past perfect is inadmissable. 1. The canonical present Both properties of the canonical present follow from standard treatments, where the present tense is sensitive to the time of the utterance context (u). A familar encoding of this is given in (6) within a referential theory of tense. (6) A standard treatment of the present tense J PRESi Ku,g is defined iff g(i) ⊆ TIME(u). When defined, J PRESi Ku,g = g(i) Utterance Indexicality follows straightforwardly. Stativity also follows with three assumptions: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 20 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present ◦ The utterance time, TIME(u), contains the reference time, g(i), as opposed to being contained in it (Kratzer, 1998: 101) or simply overlapping it (von Stechow, 1995: 365). ◦ Without progressive morphology, the present tense in English conveys perfective aspect (the eventuality is contained in the reference time) (Smith 1997: 110, Giorgi and Pianesi 1997: 163). ◦ Utterances are conceived of as instantaneous (Kamp and Reyle 1993: 536–537, Giorgi and Pianesi 1997: 160, Smith 1997: 110–112, 2003: 103–104, a.o.), a constraint we formulate concretely as follows: (7) Utterance Time Width (UTW) |TIME(u)| < ε, where ε is the minimum size for an event With Utterance Time Width, TIME(u) — and hence g(i) contained inside it — is too narrow to contain the event described by an activity or accomplishment. Only statives, which have the subinterval property (Dowty, 1979), describe an eventuality that is small enough. There is always some subpart of a state, satisfying the eventuality description, which can fit inside TIME(u). state minimal event reference time (g(i)) (8) u Even achievements and semelfactives are incompatible with the canonical present, unless they have an habitual interpretation. (9) a. b. # Bill wins the race. Intended: ‘Bill is winning/wins the race now.’ # Sue coughs. Intended: ‘Sue is coughing/coughs (once) now.’ achievement semelfactive (Smith, 1997: 111) We take this to mean that the utterance time must, in fact, be so narrow that punctual events cannot be contained within it. 1.1. Extension to the play-by-play use The play-by-play present, by our definition, is used in the direct reporting of circumstances as they unfold. It can be found in sportscasting (10a) and in demonstrations (10b) (Palmer 1965: 58, Leech 1971: 2–3). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 21 P. Anand & M. Toosarvandani (10) a. b. Unifying the canonical, historical, and play-by-play present (USA vs. New Zealand, 2015 Women’s Soccer Friendlies) Commentator: Wambach leads it back and now Krieger has it. Tobin Heath goes far. (https://www.youtube.com/watch?v=Kqe9n7zvnnw, 1:40:55) Demonstrator: Look, I take this card from the pack and place it under the handkerchief so. (Leech, 1971: 2) Such play-by-play discourses do not require the perfective (a.k.a. simple present). There is a choice of aspect, depending on the nature of the events being described (Ferguson, 1983: 164). The perfective is used to describe a sequence of rapid, completed actions, as in a soccer game (10a), while the progressive is used to report longer, more continuous events, like those in a boat race (11). (11) (Men’s 8 Rowing Final, 2008 Olympics) Commentator: Now the job for the Canadian crew is to hang on to the lead they had at the halfway mark. They are breathing hard. They really are gulping in the air there. But they know that they’ve got a good lead there. They know they can finish, but Great Britain are moving very well[. . . ] (http://www.youtube.com/watch?v=KkP3P5ucR4U, 5:37) The play-by-play present always describes events that occur roughly at the time of utterance, so it exhibits Utterance Indexicality. Smith (1997: 111) offers one intuitive solution for why playby-play sentences do not exhibit Stativity: they “telescope time. We understand them punctually, suspending our knowledge of their normal duration.” In other words, durative predicates are coerced into describing an event small enough to fit inside the utterance time. Presumably, since the play-by-play present describes a completed interpretation in the perfective, this would include at least its end point. coerced event reference time (g(i)) (12) u There are several arguments that coercion cannot be what allows the play-by-play use to avoid Stativity. First, even punctual events are too large to be contained within the utterance time, as shown in (9) above, since achievements and semelfactives do not have a nonhabitual interpretation in the canonical present. The coercion operation that Smith implicates in the play-by-play present might, in principle, output an event small enough to fit within the utterance time. But this runs counter to conventional wisdom, which takes coercion to operate within a certain fixed inventory of eventuality predicates (Moens and Steedman, 1988; de Swart, 1998). Second, if the play-by-play present involved coercion, then accomplishments should not exhibit the same ambiguity with almost that they do elsewhere (Dowty, 1979: 58). (13) John almost painted a picture. ‘John didn’t start painting a picture.’ ‘John started to paint a picture, but did not finish it.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde (Dowty, 1979: 58) 22 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present But in fact, accomplishment predicates do exhibit this ambiguity in the play-by-play present. (14) Commentator: Federer almost crosses the entire court. ‘Federer doesn’t start to cross the court.’ ‘Federer starts to cross the court, but does not get to finish.’ Finally, coercion cannot offer an explanation for why a play-by-play sentence cannot anchor the past perfect. In (4a) above, by the time the past perfect sentence describing the calling event is uttered, the yelling event is already in the past and should be able to anchor it. serving (15) calling looking yelling u That is, to account for the play-by-play use, it is not enough simply to manipulate the event structure of the predicate. Something must be said about how the eventuality described relates to other times in the context. 1.2. Extension to the historical use What we call the historical present is used to describe situations that have already taken place or are simply imagined. It makes them more “dramatic” as if “someone actually witness[es] the events as they are described” (Palmer 1965: 39, Leech 1971: 6–7, Close 1981: 106). This historical use is frequently found in ordinary narratives (16a) and stage directions (16b). (16) a. b. I couldn’t believe it! Just as we arrived, up comes Ben and slaps me on the back as if we’re life-long friends. “Come on, old pal,” he says, “Let me buy you a drink!” I’m telling you, I nearly fainted on the spot. (Quirk et al., 1985: 181) From the right, Willy Loman, the Salesman, enters, carrying two large sample cases. The flute plays on. He hears, but is not aware of it. He is past sixty years of age, dressed quietly. Even as he crosses the stage to the doorway of the house, his exhuastion is apparent. He unlocks the door, comes into the kitchen, and thankfully lets his burden down. . . (Miller, Death of a Salesman) Assuming a typical utterance context, it is clear that a standard treatment of the present tense is incompatible with the historical use, since it does not exhibit Utterance Indexicality. However, the historical present could arise when the utterance context is improper, when one or more coordinates (e.g., speaker and addressee) does not coincide with the time coordinate (Predelli, 2005). For instance, in an answering machine message — I am not here now, so please leave a message — the time coordinate of the context might pick out the time of listening (decoding), even though the speaker does not utter (encode) the message at that time. Eckardt (2015: 221–223) proposes that the historical present makes use of an improper context Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 23 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present (see also Bary 2016). At the risk of oversimplying, we might represent this as an operator that shifts just the time coordinate of the context. (17) J HP(φ) KhTIME(u),SPEAKER(u),... i,g = J φ Khti ,SPEAKER(u),... i,g In these discourses, then, the time coordinate of the context identifies a past time t i . A standard semantics for present tense will consequently locate the reference time at this time, rather than the actual time of utterance. This correctly predicts that the speaker coordinate can pick out an individual who does not even exist at the shifted time, as in (18). (18) Fifty eight years ago to this day, on January 22, 1944, just as the Americans are about to invade Europe, the Germans attack Vercors. My grandfather tries to escape. . . (Schlenker, 2004: 298) Under this account, however, it is mysterious why the historical present can anchor the past perfect, as in (5a) above. The past perfect describes a paying-off event that precedes the time of the scoffing event. With a standard semantics for the past perfect (e.g., Reichenbach 1947), this time must itself be located anterior to the time of the context. But the time of the context still overlaps the time of the scoffing event when the past perfect sentence is uttered. (19) paying off confronting scoffing u It is not enough simply to shift the time of the context to account for the historical present. Other tense-aspect categories, like the past perfect, are also sensitive to it. 1.3. The historical present in free indirect discourse Before moving on, we should address a potential worry. One might think that the historical present is simply an instance of free indirect discourse, a literary style used to directly represent the perspective of a character (Banfield 1982; Doron 1991; a.o.). Indeed, many cases of the historical use feel as if they are filtered through the lens of a protagonist. (20) a. b. Creeping Christ? he thinks. What does he mean? His head turns sideways, his hair rests in his own vomit, the dog barks, Walter roars, and bells peal out across the water. He feels a sensation of movement, as if the filthy ground has become the Thames. It gives and sways beneath him; he lets out his breath, one great final gasp. You’ve done it this time, a voice tells Walter. But he closes his ears, or God closes them for him. He is pulled downstream, on a deep black tide. (Mantel, Wolf Hall) She rejected one brush; she chose another. When would those children come? When would they all be off? she fidgeted. That man, she thought, her anger rising in her, never gave; that man took. She, on the other hand, would be forced to give. (Woolf, To the Lighthouse) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 24 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present It is not possible to reduce the historical present to free indirect discourse. The latter necessarily reports the perspective of a character (Banfield, 1982; Doron, 1991). (21) Context: Figaro sees Coutess Almaviva, who is wearing his wife’s clothes. Figaro froze in place. He couldn’t believe his eyes. His wife had swooned into the Count’s arms and was now kissing him passionately. (Doron, 1991: 54) By contrast, there are uses of the historical present that do not force reporting of a character’s perspective (i.e., definite descriptions that are not valid with respect to the protagonist). (22) Oedipus is very happy. He is going to see his mother again tomorrow. While the historical present can occur in free indirect discourse, they cannot simply be equated. As it will turn out, we will adopt the semantics for the present tense that Sharvit (2004, 2008) proposes to account for free indirect discourse, and so we return briefly to this interaction later. 2. A proposal We take natural language expressions to be interpreted relative to two contexts: a context of utterance (u) and a context of assessment (a). Such bicontextualism has been deployed in several empirical domains, including for free indirect discourse (Doron, 1991; Schlenker, 2004; Sharvit, 2004, 2008; Eckardt, 2015) and future tense (MacFarlane, 2003), as well as predicates of personal taste and epistemic modals (MacFarlane, 2014). Individual expression can be sensitive to one, the other, or both of these contexts. Adopting the division that Sharvit (2004, 2008) proposes, local pronouns are sensitive to the utterance context, while tense is sensitive to the assessment context. (23) a. b. (24) a. b. J I Ku,a,g = SPEAKER(u) J you Ku,a,g = ADDRESSEE(u) J PRESi Ku,a,g is defined iff g(i) ⊆ TIME(a). When defined, J PRESi Ku,a,g = g(i) J PASTi Ku,a,g is defined iff g(i) < TIME(a). When defined, J PASTi Ku,a,g = g(i) Sharvit takes temporal and locatival adverbials, such as tonight (25a) and here (25b), to be sensitive to the context of assessment. (25) a. b. J tonight Ku,a,g = the night of the day surrounding TIME(a) J here Ku,a,g = LOCATION(a) But we do not think that this is true of all temporal adverbials. In particular, those with ago seem sensitive to the context of utterance. The discourse below describes a series of past events. The continuation in (26a) is infelicitous because two years ago cannot receive a back-shifted interpretation: it picks out a time interval two years before the actual time of utterance. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 25 P. Anand & M. Toosarvandani (26) Unifying the canonical, historical, and play-by-play present I couldn’t believe it! Just as we arrived, up comes Ben and slaps me on the back as if we’re life-long friends. a. # Two years ago he stole twenty dollars from me. . . b. Two years before he stole twenty dollars from me. . . While Sharvit assumes that the two contexts are always identical in root contexts, we propose that the assessment context can be freely chosen, subject to pragmatic considerations. In this, we are adapting an idea of Schlenker (2004), who also makes use of two contexts in his account of the historical present. For him, there is a context of thought, where “a thought originates,” and a context of utterance, where “a thought is expressed.” In spite of a superficial similiarity, these do not line up with the two contexts we appeal to, as Schlenker divides up context-sensitive expressions differently. Simplifying somewhat, local pronouns and tenses are sensitive to the context of utterance, while temporal and locatival adverbials are sensitive to the context of thought. In the historical present, Schlenker proposes that the context of thought is set to the actual context, while the context of utterance is located elsewhere (in the past, in the thinker’s imagination, etc.) This leads to several complications. First, temporal adverbials — such as, tonight in (27) — can shift in historical present discourses, and hence must be fixed by his context of utterance. (27) Forty years ago today John Lennon is about to take to the stage at the Cavern. Tonight his life will change forever. (Schlenker, 2004: 296) Second, the context of utterance must be improper, since the speaker need not exist at the time of the events described in the historical present, as shown in (18) above. Consequently, Schlenker’s account cannot explain its ability to anchor the past perfect (§1.2). Most importantly, Schlenker does not offer a unified account of canonical and noncanonical uses of the present, which is our goal. While we adopt a different version of bicontextualism — in particular, a different division of context-sensitive expressions — we will crucially allow the context of assessment to diverge pragmatically from the context of utterance. 3. Deriving the noncanonical uses In the canonical present, the assessment time does not diverge from the utterance time. Stativity and Utterance Indexicality thus arise for the same reasons that we described earlier. (28) Canonical present TIME(a) = TIME(u) The noncanonical uses of the present tense arise when the assessment context stands in a different relation to the utterance context. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 26 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present 3.1. The historical present Intuitively, the historical present can make something in the past “the present.” For us, this involves pragmatically setting the time of assessment to some time before the utterance time. (For imagined events, the assessment time may not precede the utterance time, but it is similarly unmoored.) (29) Historical present TIME(a) < TIME(u) Stativity for the canonical use arises from linking the assessment time to the utterance time, which must be very small. But if the assessment time is anterior, it can be wide enough for the reference time to contain a non-state. event reference time (g(i)) (30) a u The historical present thus does not exhibit Stativity.3 3 Free indirect discourse can occur quite freely inside a narrative in the historical present. (i) Louise places the parcel on the kitchen table. She can’t wait to open it. Who could have sent it? What does it contain? How shiny the wrapping paper is! The sender certainly must be rich. Today seems to be her lucky day. (Eckardt, 2015: 221) This is easy to derive under Sharvit’s (2004, 2008) account of free indirect discourse (pace Eckardt 2015: 221–224 and Bary 2016). For the simplified version of this discourse in (ii), a FID operator in the present tense quantifies over contexts that are compatible with what Louise believes at the time of the assessment context, yielding the truth conditions in (iii). (ii) Louise places the parcel on the kitchen table. Today is her lucky day. (iii) When defined, J FID-Louise-PRES2 -w0 Today PRES3 be her lucky day Ku,a,g = 1 iff for every contextassignment pair ha0 , g0 i such that a0 is compatible with what Louise believes at g(2) (where g(2) ⊆ TIME(a)) in WORLD (a), the day surrounding TIME (a0 ) is her lucky day at g0 (3) (where g0 (3) ⊆ TIME(a0 )) in WORLD (a0 ) Is it possible to shift into the historical present inside an FID context? This is not easy to show, but perhaps not. (iv) Mary ran, stumbling, down the steps of the station. She was going to miss her train, she thought. How had she gotten here? She had been responsible and thought of everything. a. # That morning, she wakes up bright and early, heading straight out the door. She rushes to the DMV and gets in line right when they open. b. That morning, she woke up bright and early, heading straight out the door. She rushed to the DMV and got in line right when they opened. Under Sharvit’s account, a (non-double-access) present tense should in principle be possible when the FID operator is past, yielding a simultaneous reading like that available for a bound past tense. She argues that in such cases a preference for the bound past (based on a preference for de se pronouns) trumps the present tense (Sharvit, 2008: 388). The same should apply to the historical present as well. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 27 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present It remains an open question how the assessment time is chosen in the historical present, if TIME(a) must simply precede TIME (u). We do not yet completely understand when or how this happens. On the one hand, speakers seem able to move the context of assessment at will, as shown by their ability to alternate freely between the past and the historical use of the present. (31) Then all of a sudden everybody gets involved and they made a mess. So uh. . . this lady says. . . uh this uh Bert, “Oh, my son’ll make them. He’s an electrician.” So he makes them, and he charges all the neighbors twenty dollars a set, and there I paid three dollars. So I called her a crook. And I called her son a crook. So, they were really mad at me. (Schiffrin, 1981: 46) But on the other hand, there do seem to be constraints on what the context of assessment can be: it is hard to push it backwards. (32) He looks at the ceiling. a. # Yesterday, a spider is climbing there. b. Yesterday, a spider was climbing there. Perhaps, these two cases might be unified by a principle that only allows the assessment context to move forward in time. We leave this issue for the future. 3.2. The play-by-play present Intuitively, the play-by-play use describes an event that ends “at” the utterance time. There is some evidence that speakers wait until an event has terminated to report it (Mathon and Boulaki, 2011). This can arise if the assessment time is pragmatically set so that it properly contains the utterance time. (33) Play-by-play present TIME(a) ) TIME(u) The play-by-play use does not exhibit Stativity, then, because enough for the reference time to contain a non-state. TIME(a) can again be wide event reference time (g(i)) (34) a u A caveat: The relation in (33) allows, in principle, for the assessment time to continue after the utterance time. This would permit an event to be ongoing during the utterance time. But this is not how people use the play-by-play present. As we showed in (10–11) above, there is a contrast between the simple present (for culminated events) and the present progressive (for ongoing ones). This suggests that there is an additional constraint at work: the Upper Limit Constraint (Abusch, 1997), which bans reference to times after the local “now.” In our formulation, this amounts to a condition on the times of the two contexts: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 28 P. Anand & M. Toosarvandani (35) Unifying the canonical, historical, and play-by-play present Bicontextual Upper Limit Constraint (ULC) max({t : t ∈ TIME(a)}) = max({t : t ∈ TIME(u)}) If no part of the assessment time can follow the utterance time, then events will always have terminated by the utterance time in the play-by-play use of the present. 3.3. What other relations are possible? One salient question is what other temporal relations between the utterance and assessment contexts are possible. There are eight relations one might imagine: <, >, =, ⊆, (, ⊇, ), ◦. However, as the following shows, our constraints on the width of the utterance interval and upper limits on TIME(a) collapse several of these together. (36) a. b. c. d. historical present TIME (a) > TIME (u): forbidden by the Bicontextual ULC (35) TIME(a) = TIME (u): canonical present TIME(a) ( TIME(u): difficult to distinguish from TIME(a) = TIME(u), given UTW (7) TIME(a) ⊆ TIME(u): difficult to distinguish from TIME(a) = TIME(u), given UTW (7) TIME(a) ) TIME(u): play-by-play TIME(a) ⊇ TIME(u): difficult to distinguish from TIME(a) ) TIME(u) TIME(a) ◦ TIME(u): identical to TIME(a) ) TIME(u), given the bicontextual ULC (35) TIME (a) < TIME (u): In the end, all possible relations between the utterance and assessment times reduce to just the three that are attested. 4. Accounting for the past perfect contrast The ingredients are now in place to return to our initial empirical question: Why is the past perfect fine with the historical present, but not the play-by-play present? (37) Historical present Rumors of Berlusconi’s crimes swirl. His advisors confront him. He scoffs. a. He had paid off the prostitute for her silence already. b. He has paid off the prostitute for her silence already. c. He paid off the prostitute for her silence already. (38) Play-by-play present Commentator: Federer serves. It’s long. He looks at the line. He yells in protest. a. # The judge had called a fault. b. The judge has called a fault. c. The judge called a fault. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 29 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present It should be noted that the play-by-play use is not alone. The past perfect is also incompatible with the canonical use of the present. (39) Canonical present Trump isn’t listening to his new campaign manager. a. # She had let him down. b. She has let him down. c. She let him down. We suggest that this commonality is not accidental: both the canonical and play-by-play uses involve an assessment time that overlaps the utterance time. In the following we exploit this. We show how a perspectival treatment of the past perfect, like that of Kamp and Reyle (1993), can lead to temporal inconsistences in these uses, though not in the historical present, where the assessment time is unmoored from the utterance time. 4.1. Perspective in the past perfect Kamp and Reyle (1993) propose that the past perfect can encode a Reichenbachian pluperfect, locating the reference time anterior to a salient past “perspective point.”4 (40) Fred arrived at 10. He had got up at 5; he had taken a long shower, had got dressed and had eaten a leisurely breakfast. He had left the house at 6:30. (Kamp and Reyle, 1993: 594) In narrative flashbacks, a sequence of past perfect sentences is interpreted as forward moving. Each sentence’s reference time advances, though they are all anterior to the same perspective point. getting up showering dressing eating leaving (41) arriving p u For Kamp and Reyle, past perfect morphology is compatible with a combination of two semantic features, which require the reference time to precede a perspective point that precedes the utterance time. (42) a. b. +PAST: p < TIME(u) past: g(i) < p (Kamp and Reyle, 1993: 601) 4.2. Incorporating the perspective point We translate Kamp and Reyle’s framework into our own by equating p and TIME(a): 4 For Reichenbach (1947), the perspective point is the reference time. He does not aim to account for narrative flashbacks. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 30 P. Anand & M. Toosarvandani (43) Unifying the canonical, historical, and play-by-play present Past perfect in a bicontextual framework a. TIME (a) < TIME(u) b. g(i) < TIME(a) It is clear, then, why the past perfect is not compatible with the canonical and play-by-play presents. Its requirement that the assessment time precede the utterance time contradicts their pragmatic setting of the assessment time to (at least) contain the utterance time. (44) Canonical present TIME(a) = TIME(u) (45) Play-by-play present TIME(a) ) TIME(u) Thus, only the historical present, which locates fect. TIME(a) before TIME(u), allows the past per- 4.3. Equivalence with the simple past and present perfect After a sentence in the historical present, the simple past and present perfect are able, intuitively, to describe the same event as the past perfect, as in (46), repeated from above. (46) Rumors of Berlusconi’s crimes swirl. His advisors confront him. He scoffs. a. He had paid off the prostitute for her silence already. b. He has paid off the prostitute for her silence already. c. He paid off the prostitute for her silence already. The paying off event is anterior to the assessment time, satisfying the requirements of the past perfect. Those of the past tense are also met, which similarly requires that the reference time precede the assessment time. J PASTi Ku,a,g is defined iff g(i) < TIME(a). When defined, J PASTi Ku,a,g = g(i) (47) The present perfect, too, locates the paying off event before the assessment time. We assume that it encodes the combination of present tense and a (roughly Parsonian) perfect aspect, which describes the poststate of some eventuality. (48) a. b. J PRESi Ku,a,g is defined iff g(i) ⊆ TIME(a). When defined, J PRESi Ku,a,g = g(i) J PERF VP Ku,a,g (t) = 1 iff ∃e1 ∃e2 (J VP Ku,a,g (e1 ) = 1 ∧ POST- STATE(e2 , e1 ) ∧t ⊆ τ(e2 )) The conditions in (48a–b) together ensure that there is a poststate of Berlusconi’s paying off that overlaps the assessment time (e.g., the time of the scoffing in (46)). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 31 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present The temporal differences between the past perfect, present perfect, and simple past are leveled, then, when the assessment time and utterance time are decoupled, as in discourses with the historical present. 5. Conclusion and future directions We have combined three existing ideas in the literature: i) a bicontextual semantics for tense, proposed originally for free indirect discourse (Sharvit, 2004, 2008); ii) a bicontextual treatment of the past perfect, cf. Kamp and Reyle (1993); and, iii) pragmatic setting of the assessment context, cf. Schlenker (2004). Combining these approaches allows us to directly predict: the felicity of the present tense in its canonical, play-by-play, and historical uses; why the playby-play and historical present do not exhibit Stativity, but the canonical present does; and, why the historical use is compatible with past perfect, but the other two uses are not. Importantly, we do not have to appeal to any special mechanisms beyond the idea that pragmatics controls when the time of assessment diverges from the time of utterance. More generally, we have proposed that three diverse cases of temporal perspectival shift — free indirect discourse, past perfect anchoring, and the historical present — can be given a unified account as a shift in the same indexical coordinate, TIME(a). In closing, we would like to consider the prospects of extending this theory to other noncanonical uses of the present tense. In most cases, we believe, scrutiny will fall on our ancillary assumptions, not the bicontextual semantics itself. For performative uses, the question ultimately is how Stativity is obviated — is the assessment time unmoored, as in the play-by-play and historical present, or do such uses speak against the restriction on utterance width? For the futurate and future-like uses in (49a–b), the issues concern the ULC, which we appealed to for preventing the assessment time from following the utterance time. (49) a. b. The Yankees play the Red Sox tomorrow. Es bezieht sich. Wir kriegen Regen. it cover.PRES .3 SG self. we get.PRES .1 PL rain ‘It’s getting cloudy. We’ll get some rain.’ (Lakoff, 1971: 339) (Hilpert, 2008: 170) While the English case is a futurate (with a scheduled interpretation), the German just expresses probability. It thus may be that the present tense can impose different restrictions on TIME(a) and TIME(u) across languages. In addition, a broader theory of the present tense should account for how its various uses are deployed in the construction of larger discourses. One concrete case is narrative progression, which the historical present licenses in the same way that the simple past does. (50) a. b. John gets up, goes to the window, and raises the blind. It is light out. He pulls the blind down and goes back to bed. John got up, went to the window, and raised the blind. It was light out. He pulled the blind down and went back to bed. (Partee, 1984: 253) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 32 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present Early accounts of narrative progression linked it to specific properties of temporal and aspectual morphemes (Kamp and Rohrer, 1983; Partee, 1984; Hinrichs, 1986; Kamp and Reyle, 1993). The fact that the historical present also exhibits narrative progression suggests that it may, in fact, be more about the pragmatics of descriptions of event sequences (Kehler, 2002; Smith, 2003; Asher and Lascarides, 2003; Klein, 2009; Altshuler, 2010). What these pragmatic principles are, and how they should be integrated with tense, is a subject for future research. References Abusch, D. (1997). Sequence of tense and temporal de re. Linguistics and Philosophy 20, 1–50. Altshuler, D. (2010). Temporal Interpretation in Narrative Discourse and Event Internal Reference. Ph. D. thesis, Rutgers University. Asher, N. and A. Lascarides (2003). Logics of Conversation. Cambridge: Cambridge University Press. Banfield, A. (1982). Unspeakable Sentences: Narration and Representation in the Language of Fiction. Boston: Routledge and Kegan Paul. Bary, C. (2016). Why the historical present is not the mirror image of free indirect discourse. Paper presented at Generative Linguistics in the Old World (GLOW) 36. Close, R. A. (1981). English as a Foreign Language (3rd ed.). London: George Allen and Unwin. de Swart, H. (1998). Aspect shift and coercion. Natural Language and Linguistic Theory 16(2), 347–385. Doron, E. (1991). Point of view as a factor of content. Semantics and Linguistic Theory (SALT) 1, 51–64. Dowty, D. (1979). Word Meaning and Montague Grammar. Dordrecht: Kluwer. Eckardt, R. (2015). The Semantics of Free Indirect Discourse: How Texts Allow Us to MindRead and Eavesdrop. Leiden: Brill. Ferguson, C. A. (1983). Sports announcer talk: Syntactic aspects of register variation. Language in Society 12(2), 153–172. Giorgi, A. and F. Pianesi (1997). Tense and Aspect: From Semantics to Morphosyntax. Oxford: Oxford University Press. Hilpert, M. (2008). Germanic Future Constructions: A Usage-Based Approach to Language Change. Amsterdam: John Benjamins. Hinrichs, E. (1986). Temporal anaphora in discourses of English. Linguistics and Philosophy 9, 63–82. Kamp, H. and U. Reyle (1993). From Discourse to Logic: Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic, and Discourse Representation Theory. Dordrecht: Kluwer Academic Publishers. Kamp, H. and C. Rohrer (1983). Tense in texts. In R. Bäuerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use, and Interpretation of Language, pp. 250–269. Berlin: Mouton de Gruyter. Kehler, A. (2002). Coherence, Reference, and the Theory of Grammar. Stanford, CA: CSLI. Klein, W. (2009). How time is encoded. In W. Klein and P. Li (Eds.), The Expression of Time, pp. 39–82. Berlin: Mouton de Gruyter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 33 P. Anand & M. Toosarvandani Unifying the canonical, historical, and play-by-play present Kratzer, A. (1998). More structural analogies between pronouns and tense. Semantics and Linguistic Theory (SALT) 8, 92–110. Lakoff, G. (1971). Presupposition and relative well-formedness. In D. D. Steinberg and L. A. Jakobovits (Eds.), Semantics: An Interdisciplinary Reader in Philosophy, Linguistics, and Psychology, pp. 329–340. Cambridge: Cambridge University Press. Leech, G. N. (1971). Meaning and the English Verb. London: Longman. MacFarlane, J. (2003). Future contingents and relative truth. The Philosophical Quarterly 53(212), 321–336. MacFarlane, J. (2014). Assessment Sensitivity: Relative Truth and its Applications. Oxford University Press. Mathon, C. and G. Boulaki (2011). Le commentaire sportif en direct: Une combinatoire de différentes fonctions de la prosodie. In H.-Y. Yoo and E. Delais-Roussarie (Eds.), Actes de la conférence Interface, Discours, et Prosodie (IDP) 2009. Moens, M. and M. Steedman (1988). Temporal ontology and temporal reference. Computational Linguistics 14(2), 15–28. Palmer, F. R. (1965). The English Verb (2nd ed.). London: Longman. Partee, B. H. (1984). Nominal and temporal anaphora. Linguistics and Philosophy 7, 243–286. Predelli, S. (2005). Contexts: Meaning, Truth, and the Use of Language. Oxford: Oxford University Press. Quirk, R., S. Greenbaum, G. Leech, and J. Svartvik (1985). A Comprehensive Grammar of the English Language. London: Longman. Reichenbach, H. (1947). Elements of Symbolic Logic. Berkeley, CA: University of California Press. Schiffrin, D. (1981). Tense variation in narrative. Language 57(1), 45–62. Schlenker, P. (2004). Context of thought and context of utterance (a note on free indirect discourse and the historical present). Mind and Language 19(3), 279–304. Sharvit, Y. (2004). Free indirect discourse and ‘de re’ pronouns. Semantics and Linguistic Theory (SALT) 14, 305–322. Sharvit, Y. (2008). The puzzle of free indirect discourse. Linguistics and Philosophy 31, 353– 395. Smith, C. S. (1997). The Parameter of Aspect (2nd ed.). Dordrecht: Kluwer Academic Publishers. Smith, C. S. (2003). Mode of Discourse: The Logical Structure of Texts. Cambridge: Cambridge University Press. von Stechow, A. (1995). On the proper treatment of tense. Semantics and Linguistic Theory (SALT) 5, 362–386. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 34 Kinds, epistemic indefinites, and some-exclamatives1 Curt ANDERSON — Heinrich-Heine-Universität Düsseldorf Abstract. Although exclamative sentences have garnered much attention over the years, most work has focused on understanding what have been called wh-exclamatives and nominal exclamatives, to the exclusion of other types of exclamative constructions. I focus on what I call some-exclamatives, clausal exclamatives where the predicate uses the determiner some. I provide an analysis of these exclamatives, showing how their existence is motivated by independent properties of exclamative constructions and some. Keywords: exclamatives, exclamation, genericity, kinds, indefinites 1. Introduction In discussion of exclamatives in English, the vast majority of attention has been focused on analyzing and explaining the properties of wh-exclamatives (such as those in (1)), nominal exclamatives (as in (2)), and what Taniguchi (this volume) calls negative inversion exclamatives (like in (3)). These tend to form the canonical cases of exclamative sentences discussed in English. (1) a. b. What a large watermelon! How beautiful the birds sing! (2) The peppers he eats! (3) Aren’t you happy! However, other exclamative and exclamative-like structures exist in English that have received much less attention compared to the aforementioned ones. One example of such an exclamative (and the topic of this paper) is a construction making use of a DP headed by the determiner some, what I call some-exclamatives. Although some-exclamatives have been discussed before (Israel, 1996, 2011), they remain relatively understudied compared to the better-understood wh-exclamatives and nominal exclamatives. Some examples of these exclamatives are given in (4) through (7), with a paraphrase underneath each example. These exclamatives express a belief on the part of the speaker that the subject of the exclamative is of the type denoted by the noun phrase complement to some (such as dancer in (4)), but that their instantiation of this property is unexpected in some way. 1I thank Marcin Morzycki, Cristina Schmitt, Alan Munn, Sebastian Löbner, Willi Geuder, Kyle Rawlins, Ezra Keshet, Stephanie Solt, Ai Taniguchi, Ekaterina (Katja) Gabrovska, the semantics group at Michigan State University, and the audience at SuB 21 in Edinburgh for their comments and suggestions. This paper represents work done in part at Collaborative Research Center 991 at Heinrich-Heine-Universität, funded by the German Science Foundation. All errors are my own, of course. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 35 C. Anderson Kinds, epistemic indefinites, and some-exclamatives (4) Boy, was she (ever) some dancer! “She was a dancer and she was an exceptional dancer.” (5) That was some wine she brought to the party! “She brought wine to the party and it was very good wine.” (6) Some friend she turned out to be! “She was a friend and she was a particularly poor friend.” (7) It’s going to be some party! “We’re having a party and it’s going to be a great party.” Israel suggests that the exclamative meaning in these is likely to be related to the hedging (epistemic indefinite) use of some. I will argue that the exclamative use arises from an interaction of two components. First, like Israel, I suppose that the epistemic indefinite use of some plays a role by creating a set of alternatives, and furthermore propose the existence of an exclamative operator that structures this set of alternatives and asserts an attitude towards a particular alternative from the set. In looking at this particular type of exclamative structure, several questions arise. First, how does this type of exclamative structure relate to other types of exclamatives in English? Namely, what do some-exclamatives have in common with other exclamatives in English, such as whexclamatives, nominal exclamatives, and negative inversion exclamatives? To answer this question, it’s necessary to ask a second question: what are the properties of some that allow for it to be involved in generating this exclamative meaning? This paper concentrates on this second question, in particular looking at the lexical semantics of some and how its indefinite meaning allows for an exclamative meaning to arise. Additionally, this paper looks at not only how the exclamative meaning arises, but also what is exclaimed about. I claim that some-exclamatives exclaim about a kind, in the sense of Carlson (1977). This paper is structured as follows. Section 2 provides additional discussion of some-exclamatives; I distinguish some from the singular indefinite a, motivate some-exclamatives as exclamatives, and suggest that certain types of theories of exclamatives are not a very good fit for analyzing some-exclamatives. Then, in section 3, I argue that some-exclamatives are sensitive to kinds. In sections 4 and 5 I provide my analysis, with section 6 discussing additional data outside the purview of this paper. I wrap up my discussion in section 7. 2. Background 2.1. The data Some-exclamatives come in two variants, what I call the in-situ variant and the preposed variation. In the in-situ variant, as in (8), the DP headed by some appears after the copula. In the preposed variant, illustrated with (9), the DP appears before the subject. In this paper, I focus on the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 36 C. Anderson Kinds, epistemic indefinites, and some-exclamatives in-situ variant, with the assumption that it’s the underlying variant, while the preposed version is derived through movement of the some-headed DP. (8) a. b. John is some lawyer! This is going to be some party! (in-situ) (in-situ) (9) a. b. Some lawyer John is! Some party this is going to be! (preposed) (preposed) Some generally doesn’t give rise to exclamatives. One condition that must be met in order for the exclamative interpretation to be available is that there must be a particular intonational contour on the some indefinite. When this intonational contour is removed (marked with I in the examples below), the exclamative meaning is unavailable, and the ordinary indefinite meaning arises. (10) a. That was someI wine she brought to the party! b. #That was some wine she brought to the party. (11) a. It’s going to be someI party! b. #It’s going to be some party. I propose that the intonation plays a role in creating the exclamative, in marking the presence of a morpheme carrying an exclamative operator. This operator, as I develop later, structures the set of alternatives denoted by the sentential core of the exclamative, and assert an attitude towards one of the alternatives. Although some-exclamatives make use of some, which is used in constructing indefinite DPs in English, it is not simply being an indefinite that allows for some to have an exclamative use; English lacks a corresponding a-exclamative (as would be intended with the examples in (12)). (12) a. #John is a lawyer! b. #It’s going to be a party! This lack of an a-exclamative suggests that there are additional properties of some that make it well-suited for being used in an exclamative. The next section briefly discusses how some and a differ. 2.2. Some is an epistemic indefinite How does some differ from the singular indefinite a? The primary way that they differ is that some is an epistemic indefinite. Epistemic indefinites are indefinites that impose restrictions on the speaker regarding their knowledge of who the indefinite refers to. Unreduced some is the canonical case of this type of indefinite in English, although epistemic indefinites are well-attested cross-linguistically as well (Haspelmath, 1997). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 37 C. Anderson Kinds, epistemic indefinites, and some-exclamatives In English, some contrasts with a in committing the speaker to uncertainty regarding the referent of the indefinite. The speaker may know some description of the individual, but the particular individual who satisfies the description cannot be known.2 The short exchange in (13) illustrates this, where A’s use of some commits A to not being able to identify the individual who was shot. B’s question regarding the identity of the individual is odd because of speaker A’s commitments due to using some. (13) A: Some cabinet minister has been shot! B: #Who? In contrast, although a is compatible with a lack of knowledge, it doesn’t require it in the way that some does. The exchange in (14) is acceptable, since although the use of the indefinite may signal that the speaker does not know who was shot, it doesn’t commit the speaker to ignorance. (14) A: A cabinet minister has been shot! B: Who? This contrast shows that there must be additional constraints on the use of some in order to capture a difference between some and the singular indefinite a. In my analysis, I will make a proposal for this difference that builds on work by Kratzer and Shimoyama (2002). 2.3. Is this really an exclamative? Michaelis and Lambrecht (1996) note a collection of properties that exclamative constructions prototypically have. These are listed in (15). I argue that some-exclamatives should be considered as a type of exclamative based on the observation that some-exclamatives exhibit many of these properties. (15) Semantico-pragmatic properties of exclamatives (Michaelis and Lambrecht, 1996) a. presupposed open proposition b. scalar extent c. assertion of affective stance: expectation contravention d. identifiability of described referent e. deixis First, some-exclamatives exhibit the (a) property in the above list. What Michaelis and Lambrecht mean by presupposed open proposition is that exclamatives are factive. Some-exclamatives are also factive, as can be shown by using the ‘Hey, wait a minute!’ test for presuppositions (Shanon, 1976; von Fintel, 2004). 2 With some caveats, of course. Some can also express indifference with respect to the identity of the individual as well, which is plausibly related to its ignorance use. Some is also sensitive to different types of knowledge regarding an individual, such as naming them versus pointing them out in a crowd. See Maher 2013 for some discussion of this latter point. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 38 C. Anderson (16) Kinds, epistemic indefinites, and some-exclamatives A: John is some lawyer! He always loses his cases! B: Hey, wait a minute! I didn’t know John was a lawyer. As already noted, some-exclamatives seem to exclaim about some high scalar property as well, exhibiting the (b) property above. That exclamatives also express an attitude can be considered similar to the (c) property in the list. Finally, by deixis (property (e)) Michaelis and Lambrecht mean that the attitude in an exclamative is generally anchored both personally (with respect to an individual—the speaker) and temporally (to the speech time). This seems to hold in part for some-exclamatives as well, where the attitude is anchored to the speaker by default. These properties also match in some ways with Zanuttini and Portner (2003)’s claim that exclamative constructions are factive, express a sense of noteworthiness, and cannot function in question/answer pairs. Given the similarities between some-exclamatives and other exclamatives in terms of their meanings, then, I will consider some-exclamatives to be a type of exclamative construction. 2.4. Theories of exclamatives As exclamative constructions have been an important area for research for some time, there have been many different proposals for exclamatives in general as well as for constructions in particular languages. Although I cannot hope to do a thorough review of all of them, I’ll note (following Castroviejo Miró (2008)) that the field has in some ways coalesced around three main types of theories regarding exclamatives: theories that assimilate root exclamatives to embedded exclamatives, theories that treat exclamatives as degree constructions, and theories that derive exclamatives from question semantics. One style of theory of exclamatives attempts to understand exclamatives by assimilating root wh-exclamatives, such as those in (17), to embedded exclamatives like those in (18) (D’Avis, 2002; Abels, 2005). (17) a. b. How tall John is! What a success the party was! (18) a. b. It’s amazing how tall John is! I’m surprised what a success the party was! (root exclamative) (root exclamative) (embedded exclamative) (embedded exclamative) Embedded exclamatives clearly inherit much of their semantic force from the predicate they are embedded under (such as amazing). The hope for this style of theory is that root exclamatives can be represented by assuming that they too are embedded under an amazing-predicate, at some level of representation. The difficulty with extending this approach to some-exclamatives is that some-exclamatives do not embed under amazing, disappointing, or other predicates we might have reasonably expected Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 39 C. Anderson Kinds, epistemic indefinites, and some-exclamatives would be candidate predicates for this type of theory. This is shown in (19). It would seem then that, whatever the merits of this analysis, it is difficult to naively extend it to some-exclamatives. (19) *It’s amazing/disappointing/unexpected (that) John is some friend! I turn now to a different type of analysis of exclamative constructions. In contrast with question theories of exclamatives, which treat exclamatives as being underlyingly questions, degree theories of exclamatives treat exclamative constructions as being on par with other degree constructions, such as measure phrase modification or comparatives. In other words, rather than accounting for the semantics of exclamatives by saying that they are sets of propositions, the semantics of exclamatives is accounted for by assuming that exclamatives make use of sets of degrees. Some accounts in this type of theory are those of Castroviejo Miró (2006) and Rett (2008, 2011). Castroviejo Miró argues for a degree analysis of wh-exclamatives in Catalan based on the observation that the degree word tan in Catalan occurs in both exclamative environments and in canonical degree constructions. What makes exclamatives different from other sentence types is how they update the common ground. Assertions update the common ground to exclude worlds incompatible with the assertion, while exclamatives in this analysis background the information contributed by the degree construction, and implicate a speaker-oriented attitude towards a degree. Rett (2011) also argues that exclamatives are degree constructions. She observes that exclamatives often make use of overt gradable expressions, such as in (20). When no gradable predicate is overt, however, a covert gradable predicate M-O P is used, where M-O P measures over a contextually salient dimension (in the cases in (21) below, the dimensions corresponding to delicious and exotic might be licit in context). (20) a. b. What delicious desserts John baked! The exotic places John visited! (21) a. b. What M-O P desserts John baked! The M-O P places John visited! The core of the exclamative, for Rett, is a set of degrees (rather than a set of propositions). A process of default existential closure over degrees converts this into a proposition. A covert illocutionary operator expresses surprise towards that degree. But, it’s not obvious that this is the correct path to go down in order to analyze some-exclamatives as well. The reason for this is the nature of M-O P; M-O P is used to coerce gradability where none existed before, using some contextual salient scale. The difficult lies in the fact that some seems to already be involved with scalar meaning, namely quantity. For instance, the question-answer pair in (22) shows that some can be used to provide an answer expressing a quantity. Moreover, some is well-known to be part of a scale with the quantifier all. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 40 C. Anderson (22) Kinds, epistemic indefinites, and some-exclamatives A: Was any of the wine spilled? B: Some (of it). Since some participates in a scale denoting quantity already, it seems reasonable to think that some-exclamatives should have an interpretation where they express surprise at a quantity. This type of reading is available with nominal exclamatives as in (23), showing that in principle an exclamative could have this type of reading. However, some-exclamatives do not seem to be compatible with a quantity reading, as (23) demonstrates. (23) (24) The wine we drank! It would’ve filled buckets! *That was some wine we drank! It would’ve filled buckets! Finally, it’s not clear that some is involved with degree constructions in general. For instance, generally expressions of the style in (25) aren’t allowed in many varieties of English, including mine, further weakening a case for some having a degree component to it. (25) a. *some tall! b. *some sweet! With these facts in mind, I set aside the possibility that some-exclamatives should be analyzed as degree constructions (but this of course doesn’t rule out other exclamative constructions as being degree constructions). Moving on, another sort of theory of exclamatives treats exclamatives as being semantically related to questions. Specifically, the propositional content of an exclamative is equivalent to that of a question, but the difference between a question and an exclamative lies in their sentential force. These kinds of theories adopt a semantics for questions in the style of Hamblin (1973), Karttunen (1977), and Groenendijk and Stokhof (1984). Hamblin (1973) proposed that the denotations of questions were sets of propositions corresponding to answers to that question. A question of the form Who came to the party? could be considered as having the set of alternatives in (26), for instance, with who signaling the syntactic position where the alternative propositions should have their content varied. This set raises an issue as to which particular proposition is true. (26)  Mary came to the party,    Bill came to the party, JWho came to the party?K = Bob came to the party,    ...        This view of questions has come to be quite influential, and, with modifications later by Karttunen (1977) and Groenendijk and Stokhof (1984), the view that questions denote sets of propositions has become a dominant view in their analysis. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 41 C. Anderson Kinds, epistemic indefinites, and some-exclamatives Under normal assumptions, declarative sentences denote propositions, functions from worlds to truth values, type hs,ti. However, if this is so, what do sentences that aren’t declarative denote? Hamblin proposes that questions are sets of propositions, a view further developed by Karttunen (1977) and Groenendijk and Stokhof (1984). The question Who is coming? might be represented as in (27). (27) JWho is coming?K = λ p∃x [p(w) ∧ p = λ w0 [come(w0 )(x)]] Gutiérrez-Rexach (1996) adopts this view of questions and proposes that both questions and exclamatives have, at their core, essentially the same denotations. What sets exclamatives apart from questions is the use of an illocutionary operator EXC which operates on a variable indexed to the speaker, the world, and a set of propositions. Gutiérrez-Rexach’s definition for this is as in (28), where EMOT is a set of emotive properties that speakers can have towards propositions, such as surprise and amazement. (28) Let a be the speaker, w a world (typically the actual world), p a proposition, and P ∈ EMOT (the set of emotive properties). Then, def EXC = λ aλ wλ phs,ti ∃Phs,hst,etii [P(w)(p)(a)] A somewhat different theory of exclamatives is that of Zanuttini and Portner (2003). In their analysis, Zanuttini and Portner follow Gutiérrez-Rexach in analyzing the core of a wh-exclamative sentence as being a question. Where Zanuttini and Portner’s analysis differs is in the source of the exclamative reading itself. They argue that exclamatives have at their core a notion of domain widening. The concept of domain widening here is related to the analysis of any in Kadmon and Landman (1993), where any is a simple indefinite determiner, but shifts the domain of quantification to a stronger domain when embedded under negation. In Zanuttini and Portner, domain widening applies at the level of propositions. Domain widening applies to the set of propositions denoted by the sentential core of the exclamative, and widens this set to include propositions not previously under consideration. Their definition of widening is provided in (29). (29) Widening (Zanuttini and Portner, 2003) For any clause S containing Rwidening , widen the initial domain of quantification for Rwidening , D1, to a new domain, D2, such that i. JSKw,D2 − JSKw,D1 6= 0 and ii. ∀x∀y[(x ∈ D1 & y ∈ (D2 − D1)) → x < y] To illustrate how this works, let’s consider the exclamative in (30). Zanuttini and Portner follow Karttunen (1977) in treating questions as denoting sets of true answers, so the set of alternatives for this exclamative is as in (31). (30) What peppers he eats! Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 42 C. Anderson (31) Kinds, epistemic indefinites, and some-exclamatives JWhat peppers he eats!K = {p : p is true in w and ∃a such that p = [‘he eats a’]} = {‘he eats poblanos’, ‘he eats serranos’, ‘he eats jalapeños’} To build the exclamative interpretation, the domain of this set of alternatives is expanded to include propositions that weren’t under consideration before. In the set in (32), which has undergone widening, the proposition he eats habaneros is now included. In essence, what the widening operation does is build the interpretation that this person eats a variety of peppers, and he even eats these extremely spicy peppers, habaneros. If there are any other peppers he eats, they’re not worth our consideration, since they’ve fallen outside of the widened domain. (32) {‘he eats poblanos’, ‘he eats serranos’, ‘he eats jalapeños’, ‘he eats habaneros’} The difficulty in extending a question theory of exclamatives to some-exclamatives, however, is that some-exclamatives share little with questions in their surface structure. However, under some recent analyses (such as Kratzer and Shimoyama (2002)) indefinites do share semantic and pragmatic properties with questions, in that both interrogative sentences and declarative sentences with indefinites can be modeled as denoting sets of propositional alternatives. In the next sections, I develop a theory of some-exclamatives that builds on this kind of representation. 3. Kinds and some-exclamatives I argue that, at their core, some-exclamatives are ultimately kind-related. That is to say, someexclamatives make assertions involving kinds, as opposed to (say) degrees. There are two important pieces of evidence that kinds are involved in some-exclamatives. First, NPs that do not have clear, well-established kinds are odd in some-exclamatives. Going back to Carlson (1977), it’s been argued that reference to kinds depends on the accessibility of an established kind. Since green bottles (in (33a)) are not an established kind, they also do not allow for subkinds, and hence are illicit in some-exclamatives. A similar line of reasoning holds for (33b), as people that are in the next room do not form a kind. (33) a. ??This is some green bottle! b. #John is some person from the next room! As noted by Constantinescu (2011), some nouns do not have readily accessible stereotypical properties associated with them, such as building or room. Since kinds correspond to general properties that characterize groups of individuals, we might suppose that the lack of stereotypical properties for building and room would make subkinds for them difficult to construe in many contexts. This predicts that building and room would be difficult to use in some-exclamatives, which seems to be the case (34). Other nouns that lack stereotypical properties, such as nonMethodist, are also difficult to use. The difficulty in using these nouns that do not denote kinds is another piece of evidence that some-exclamatives are kind-related. (34) a. ??This is some building! b. ??This is some room! Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 43 C. Anderson Kinds, epistemic indefinites, and some-exclamatives (35) ??He is some non-Methodist! Finally, an additional piece of evidence suggesting that there is reference to kinds in someexclamatives can be found by looking at post-nominal adjectives like navigable and visible. As noted by Bolinger (1967), these adjectives obligatorily get temporary, episodic interpretations when used post-nominally, as in (36). However, when these adjectives are used in the canonical pre-nominal position, like in (37), these adjectives either get the episodic interpretation, or an interpretation where they are commenting on inherent, stable properties. Larson and Marušič (2004) go a step further and claim that this is a reflection of a stagelevel/individual-level distinction, in the sense of Carlson (1977), where stage-level properties are temporary properties applying to spatio-temporally located stages of individuals, while individual-level properties are permanent properties applying to the whole individuals theirselves. This idea is closely related to kinds, in that instantiations of kinds (but not kinds themselves) are the sorts of objects that stage-level predications can be made of. (36) a. b. the stars visible the rivers navigable (stage-level only) (stage-level only) (37) a. b. the visible stars the navigable rivers (stage-level or individual-level) (stage-level or individual-level) In some-exclamatives, pre-nominal adjectives are allowed, as shown in (38), while the same adjective is barred post-nominally. If Larson and Marušič (2004) are correct in identifying the post-nominal position as being related to stage-level interpretation, then this is further support for a kind-level interpretation being used in some-exclamatives. As episodic stage-level interpretations must be predicated of individuals, the fact that these post-nominal adjectives are allergic to the noun phrase in some-exclamatives suggests that the NP is also not a predicate of individuals. (38) a. b. This is some navigable river! (We barely made it to the river mouth alive!) These are some visible stars! (I can barely see them, and I know where to look!) Finally, it should also be noted that Weir (2012) has proposed that, in certain cases, the determiner some (in its more familiar use) is sensitive to kinds. He notices examples such as (39), where what the speaker is expressing ignorance about is which kind of object is being referred to. These examples cannot be paraphrased with the form ‘I saw a contraption in the copy room and I don’t know which contraption it was,’ but must be paraphrased with something more like ‘I saw a contraption in the copy room and I don’t know what kind of contraption it was.’ (39) a. b. c. I saw some contraption in the copy room this morning. I came home to find some plant growing through a hole in my wall. Doctor, some growth appeared on my arm. Should I be worried? Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 44 C. Anderson Kinds, epistemic indefinites, and some-exclamatives To conclude this, I will assume that kinds play a role in the interpretation of some-exclamatives. In particular, I’ll suggest that some-exclamatives make reference to subkinds of the kind denoted by the NP that the determiner some combines with. 4. Kinds within the DP In the previous section, I argue that some-exclamatives involve reference to kinds, at some level. The locus for reference to kinds in some-exclamatives, I’ll assume, is within the DP. I mention a few proposals that form the background to my analysis in this section, where I will ultimately assume a model that is similar in spirit to that of Zamparelli (1995)’s idea of a layered DP. There are many proposals that put reference to kinds with the DP. One proposal is Zamparelli (1995). Zamparelli suggests that the DP be expanded into a number of functional projections (as in (40)). This creates a division of labor between the various projects in the structure; different types of semantic information are available at different levels in the DP structure, creating a close connection between the semantic derivation and the syntactic derivation. Gehrke and McNally (2013) argue for a system similar to that of Zamparelli (1995), with kinds represented low within the DP. However, rather than treating the noun as directly denoting a kind, as Zamparelli does, they suggest that common nouns denote properties of kinds (see also McNally and Boleda 2004). (40) JcarK = λ xk [car(x)] In order to make this property something that can be predicated of ordinary objects, it must be transformed into a property of token entities and not kinds. They suggest, following related proposals by Déprez (2005) and Müller-Reichau (2011), that NumP is the locus for this operation. This is illustrated in (41), where R is a variant of Carlson (1977)’s realization relation, which relates kinds to individuals that instantiate them. (41) DP D NumP Num NP N ... (42) J[NumP [NP car]]K = λ y∃xk [car(xk ) ∧ R(y, xk )] This has the benefit of providing a transparent mapping between syntax and semantics. I will assume a version of this in my analysis, where some plays the role of a Num head and realizes kinds. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 45 C. Anderson Kinds, epistemic indefinites, and some-exclamatives 5. Analysis 5.1. Structure of the exclamative The basic core of a some-exclamative such as John is some lawyer! would be represented as in (43). I assume that these exclamatives are built essentially from a standard sentential core, with the crucial difference being the use of an exclamative operator E X -O P merged in C. The intonational contour of some-exclamatives is assumed to mark the presence of this otherwise covert operator. (43) CP TP C E X -O P T0 DP John T PredP DP Pred is NumP D Num some NP N doctor 5.2. The representation of some sentences As discussed earlier, some is an epistemic indefinite, requiring that the speaker not have precise knowledge as to the identity of some individual. Although the particular way that this gets cashed out in different theoretical analyses varies, there are several that are especially worth attention here. The first that of Farkas (2002). Farkas analyzes some as requiring that the variable it contributes be unidentified—that is, that the value that variable is assigned not necessarily be the same across all possibilities. In essence, this is a way of ensuring that the speaker can never commit to a particular valuation for that variable. A second is that of Alonso-Ovalle and Menéndez-Benito (2010). They propose that the ignorance implicature of Spanish algún, which is similar to some in some respects, can be modeled through competition with un. They analyze algún as in (44), where algún combines first with a subset selection function f , a function from sets to sets. The use of the subset selection function models contextual domain restriction. f in this analysis is restricted via the presupposition anti-singleton( f ) so that its range must be a non-singleton set. When f combines with the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 46 C. Anderson Kinds, epistemic indefinites, and some-exclamatives restrictor of algún, the NP, the effect is to make it so that there must be at least two individuals that could possibly satisfy the existential claim. Un is analyzed as not having the anti-singleton presupposition, and the ignorance component of algún surfaces as an implicature through competition with un. (44) JalgúnK = λ f λ Pλ Q : anti-singleton( f ).∃x [ f (P)(x) ∧ Q(x)] Finally, there is von Fintel (2000). This analysis is not about some per se, but about whatever, which also includes a sense of uncertainty about it.3 Von Fintel builds on Dayal (1997)’s analysis of whatever in assuming that whatever includes a presupposition of ignorance. The presupposition is most relevant for my purposes here, in that it forces the speaker to not be able to identify which particular individual across worlds satisfies the predicate P, just that there are at least two. (45) whatever(w)(F)(P)(Q) a. Presupposes: ∃w0 , w00 ∈ F : ιx.P(w0 )(x) 6= ιx.P(w00 )(x) b. Asserts: ∀w0 ∈ F : Q(w0 )(ιx.P(w0 )(x)) What these proposals have in common is a general analytical intuition that epistemic indefinites and other morphemes that express ignorance impose a requirement that the speaker cannot commit to a particular individual. Rather, what these must do is leave as an open possibility that there are multiple individuals who could satisfy the descriptive claim that is being made. I borrow this intuition for my analysis of some. For my purposes here, I adopt Kratzer and Shimoyama (2002)’s practice of analyzing all sentences—not only question sentences—as denoting sets of propositional alternatives. In particular, sentences making use of indefinites will have as their denotation a set of propositions that vary with respect to an individual (this will be developed in the next section). However, this formalization in and of itself does not build in a difference between the singular indefinite and some. To cash out the difference between the singular indefinite a and some in this sort of system, I give the principle in (46), the anti-singleton condition, which can be thought of as a use-condition associated with some but not a. What this principle serves to do is ensure that the speaker cannot narrow the set of alternatives to make an assertion about a single particular individual across worlds. This condition will be active in both normal sentences using some, and also exclamative sentences using some. (46) Anti-singleton condition on some: A sentence containing some must denote a set containing at least two alternatives. In the following sections, I show how the alternatives at the core of the exclamative vary with respect to a kind, and how an exclamative operator applies to this set. 3 In class notes, von Fintel has an analysis of some that is similar, according to Alonso-Ovalle and MenéndezBenito (2010). See von Fintel (1999). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 47 C. Anderson Kinds, epistemic indefinites, and some-exclamatives 5.3. The sentential core of some-exclamatives Following the discussion the previously, I’ll assume that NPs denote properties of kinds. The denotation for the NP lawyer will be the property corresponding to the lawyer-kind. This predicate will be true of any sub-kinds of the lawyer kind (or the kind LAWYER itself). (47) JlawyerK = λ k.lawyer(k) Based on proposals from Müller-Reichau (2011), Gehrke and McNally (2013) and others, Num will be the locus for shifting properties of kinds to properties of individuals. What shifts kinds to individuals in my analysis is some. Accordingly, some will be merged low, as a Num head, taking the NP as an argument, and yielding a property of individuals, as other indefinites do by assumption. The sentential core for a some-exclamative would be represented as in (48), where R is a realization relation. R(x, yk ) is true just in case x is a realization of kind yk . (48) JJohn is some lawyerK = {p0 : ∃xk s.t. p0 = [R(j, xk ) ∧ lawyer(xk )]} This representation of the sentence, though, still does not adequately model an exclamative meaning. In the next section, I propose an exclamative operator that is the final step in transforming the sentence into an exclamative. 5.4. The exclamative operator A set of propositions isn’t the right kind of semantic object to add to the discourse, as it is not a single truth value. In a non-exclamative sentence, a covert assertoric operator maps the set of alternatives corresponding to the sentence to a truth value (see Alonso-Ovalle and Menéndez-Benito 2010 and Kratzer and Shimoyama 2002 for discussion on what this kind of operator would look like). In the case of an exclamative sentence, a different operator applies. This operator, E X -O P, differs from an assertion operator in that it expresses a speaker-oriented attitude towards a proposition, rather than asserting a proposition itself. This attitude towards a proposition is what is added to the discourse. The special exclamative intonation that is attached to the some-exclamative marks the presence of this covert exclamative operator. The exclamative operator E X -O P I define as in (49). This operator applies to a set of propositions P, asserts that there is an ordering to P (e.g., an ordering based on a property such as unexpectedness or surprisal), and then asserts an attitude towards the maximal proposition on this scale of propositions (MAX(P)). This attitude is indexed to the speaker. (49) JEx-OpK = λ P  there is a salient ordering for P and ATTITUDE (speaker)( MAX (P))  This building of a scale goes some way towards explaining why some and not a can be involved in generating an exclamative; as E X -O P imposes an ordering over the set of propositions, it will require a set for which there can be a non-trivial ordering. By entailing that there are at least two members, some will be suitable for this, while a will not be. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 48 C. Anderson Kinds, epistemic indefinites, and some-exclamatives Applying E X -O P to the set of alternatives denoted by the sentence (e.g., a logical form such as in (48)) will yield a proposition such as in (50). (50) JEx-Op(John is some lawyer)K  there is a salient ordering for p0 : ∃xk s.t. p0 = [R(j, xk ) ∧ lawyer(xk )] and = ATTITUDE (speaker)( MAX ({p0 : ∃xk s.t. p0 = [R(j, xk ) ∧ lawyer(xk )]})) To summarize, some generates a set of alternatives that vary by subkinds instantiated by the subject. This set of alternatives is further constrained by a presupposition that says that this set must contain at least two alternatives in it. This constraint is what models the epistemic indefinite nature of some in other contexts. In the next section, I use this fact about some in conjunction with an exclamative operator to build the full meaning of some-exclamatives. 6. Addendum: Pejorativity and genericity in some-exclamatives The majority of this paper has concentrated on what I’ve called the in-situ variant of the someexclamative, where the DP containing some is in the position after the copula. In this section, I turn very briefly to the preposed variant. The preposed variant is similar to the in-situ variant, in that both exclaim about some extreme property and the speaker asserts an attitude towards this. However, the preposed variant differs from the in-situ variant in that it requires a negative or pejorative evaluation on the part of the speaker; although the in-situ variant is compatible with this attitude, it does not require it. In other words, the preposed some-exclamative rules out any positive or neutral evaluation on the part of the speaker. To illustrate this, consider the sentence in (51) with the (a) and (b) follow-ups. Both the (a) and (b) follow-ups are licit here, showing that the exclamative doesn’t necessarily commit the speaker to either a positive or a negative evaluation of the subject; the speaker can use the exclamative to exclaim about John being both a good lawyer, and also a not very good lawyer. (51) John is some lawyer! a. He always wins his cases and does lots of pro bono work. b. He loses every case and still charges a lot. However, the preposed variant is different, as shown in (52), in that the (a) follow-up is incompatible with the exclamative while the (b) follow-up is still compatible. This shows that the exclamative in this case commits the speaker to a negative evaluation of John’s abilities as a lawyer. This commitment to a negative evaluation rules out the follow-up in (a) that implicates a positive evaluation. (52) Some lawyer John is! a. #He always wins his cases and does lots of pro bono work. b. He loses every case and still charges a lot. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 49 C. Anderson Kinds, epistemic indefinites, and some-exclamatives One possibility is that the raising of the some-DP signals the presence of a syntactic projection encoding a pejorative attitude at the left edge of the clause. Similar proposals have been made for other phenomena, such as shm-reduplication in English (Grohmann and Nevins, 2004). But, a full analysis of the syntactic and semantic consequences of positing such a projection is beyond this paper. Turning back to the role of genericity in some-exclamatives, one rub in the analysis in this paper is that perhaps some-exclamatives don’t track the standard notion of kind very well, in that expressing surprise with respect to the subkind instantiated is marked. For instance, in (53), although knives with wooden handles and ceramic knives are subkinds of knives, the follow-ups in the (b) and (c) sentences suggest that the exclamative doesn’t allow one to exclaim about these properties. Rather, the licitness of the (a) follow-up in (53) suggests that what the some-exclamative is exclaiming about is how the knife relates to the commonly associated event with knives, cutting. Similarly, the (b) follow-up in (54) is illicit, even though foot specialists are a kind of doctor. The (a) follow-up, which is licit, relates to the doctor’s performance in doing his or her duties. (53) Some knife this is! a. It couldn’t even cut this banana! b. #It has a wooden handle! c. #It’s made of ceramic! (54) Some doctor he is! a. He couldn’t diagnose my athlete’s foot! b. #He’s a foot specialist! Although these examples do not (necessarily) weaken the claim I make that some-exclamatives involve kinds and genericity in some sense, it does raise questions about how to further define these notions with respect to some-exclamatives. 7. Conclusion In this paper I’ve laid out an analysis of some-exclamatives, which have remained understudied in the broader literature on exclamatives. Some-exclamatives are interesting in that they show another example of an exclamative construction where the exclamative is not derived from morphology related to the formation of questions. The analysis I propose suggests a refinement of our understanding of exclamative sentences. Proposals such as those of Gutiérrez-Rexach (1996) and Zanuttini and Portner (2003) analyze exclamatives as having a question semantics. Recent work in the semantics of indefinites has argued that indefinites also have an alternative semantics associated with them, making them quite closely related semantically to questions. This connection allows us to very easily make sense of some-exclamatives and exclamatives as a whole; exclamative constructions are not about questionhood, as proposed by Gutiérrez-Rexach (1996) and Zanuttini and Portner (2003), but are rather about manipulating sets of alternatives. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 50 C. Anderson Kinds, epistemic indefinites, and some-exclamatives References Abels, K. (2005). Remarks on Grimshaw’s clausal typology. Sinn und Bedeutung 9. 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Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 52 Games in linguistics1 Nicholas ASHER — CNRS-IRIT, Toulouse Julie HUNTER — Universitat Pompeu Fabra, Barcelona and Université Paul Sabatier, Toulouse Soumya PAUL — Université Paul Sabatier, Toulouse Abstract. In this paper we set out three consequences of a game-theoretic model for conversation, Message Exchange (ME) Games (Asher et al., 2016), which we think are of linguistic interest. We develop a notion of conversational success, explain subjectivity and bias in interpretation using concepts from epistemic game theory, and characterize the strategic usefulness of using so called expressions of “not at issue” content using ME games. Keywords: epistemic games, conversation, discourse, conversational success, at-issue content, subjectivity 1. Introduction The philosopher Grice long ago popularized the idea that conversation is a rational activity (Grice, 1975), yet curiously, efforts to apply philosophical and economic analyses of rationality and rational strategizing to linguistic phenomena have been sporadic and very restricted in their aims. Much of this work, including van Rooij (2004); Franke et al. (2012); Franke (2008) and Asher and Lascarides (2013), has been directed to the justification of Gricean maxims of conversation, often with the further aim of computing scalar implicatures. As argued in Asher and Lascarides (2013), the focus on Gricean maxims is largely misplaced: they are not in and of themselves an interesting linguistic phenomenon; they are an informal, and somewhat inchoate, description of what more formal models of rational interaction predict. Such formal models, when coupled with a well-developed theory of discourse structure and interpretation, have a much broader range of application to linguistic phenomena. In this paper, we argue that they play a crucial role in the analysis of three particular phenomena: evaluations of conversational success, not-at-issue/at-issue notions of content, and the subjectivity of interpretation. As we will make clear in our analysis of the subjectivity of interpretation, our formal model of rational strategizing affects how we structure and interpret a conversation. As some of us have argued at length that discourse structure affects many dynamic semantic phenomena (temporal structure, the interpretation of anaphora and ellipsis) as well as discourse content as a whole, these models thus have a general importance for understanding content in all its manifestations. Mathematics, theoretical computer science and economics have produced a rich and pertinent body of work on which to draw in building a model of rational behavior. Conversations, for example, have a natural analysis as games. They typically involve at least two agents, each with their own interests and goals. These goals may be compatible or they may be in conflict, but in either case, one agent’s successfully achieving her conversational goals will typically depend upon her taking her interlocutors’ goals and interests into account. In cooperative conversations, in which agents’ goals are completely aligned, conversational partners typically still need to coordinate actions, even linguistic actions. In strategic or non-cooperative conversations, in 1 We thank ERC grant 269427 for research support. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 53 N. Asher, J. Hunter, & S. Paul Games in linguistics which participants have opposing interests concerning the outcome of the conversation, the necessity to consider the opponents’ aims and actions is almost always even more important. A debate between two political candidates is an instance: each candidate has a certain number of points to convey to the audience, and each wants to promote her own position and damage her opponent’s or opponents’. To achieve these goals, each participant typically needs to plan for anticipated responses from the other. Our paper is organized into three main parts. First, we look at an application of a game theoretic model to the notion of conversational success and provide an abbreviated description of the technical details of the model, which we call epistemic message exchange games. We then show how the model sheds insight on the subjectivity of interpretation. In the third section, we apply the game theoretic model to an analysis of different types of content, in particular the distinction between what linguists call “at-issue” and “not-at-issue” content. 2. Conversational success While linguists are accustomed to semantic evaluations in terms of truth and satisfaction alone, ordinary people evaluate their conversational contributions and those of others more generally in terms of what we call success. Did the agent achieve her conversational goals with her contributions or not? Conversational success thus has to do with the goals a conversationalist has. What, then, are conversational goals? One possibility is to identify a conversational goal extensionally as the set of conversations that are successful from the point of view of the speaker. Conversational goals are then defined as subsets of the set of all possible conversations that exclude those conversations that do not go well. Sometimes a conversation will count as successful in virtue of containing a particular verbal string, as illustrated in (1). (1) a. b. c. d. EPA administrator : May I look inside the containment structure? Ghostbuster (Bill Murray): You didn’t say the magic word. EPA administrator: Please, may I look inside the containment structure? Ghostbuster (Murray): No. (from Ghostbusters) At least one of the goals of Murray’s character is simply to have the EPA administrator prefix his request with the word please. If we define this goal extensionally, we end up with the set of all conversations in which that string follows (1a) and (1b). Most conversational goals, however, are not defined by particular strings. What matters are the commitments to conversational contents that the interlocutors ultimately adopt. An evaluation of conversational success therefore typically has ties to a conversation’s content or its ordinary semantic evaluation. Importantly, this does not mean that the content of a conversation must be true or accurate; a conversational contribution may be successful in persuading an interlocutor to do something, for example, even if the contribution is inaccurate or false. Certain 2016 US Presidential campaigns provide ample evidence of this possibility. Content related goals can be tied to particular discourse moves. Following Asher and Lascarides (2003), asking a non-rhetorical question, for instance, indicates that the speaker has the conversational goal of obtaining an answer from her interlocutor or interlocutors. A simple Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 54 N. Asher, J. Hunter, & S. Paul Games in linguistics conversational goal for an assertion is typically to have one’s interlocutors agree or at least not openly object to it. Asher and Lascarides (2003) call such goals speech act related goals. Conversational goals, however, can also global, general properties of a conversation that guide a large stretch of discourse or even the conversation as a whole. Consider, for instance, a prosecutor who either wants a witness to commit to some issue or wants to demonstrate before a jury that the interlocutor is evading or refuses to answer the question. Success may require several discourse moves (and may never be achieved at all). As a real life example, consider the following exchange between CNN’s Jake Tapper and Mike Pence, who was the US Vice-President elect at the time.2 Tapper asks Pence if he was aware that the transition team for Trump’s presidency had put in for a security clearance for Michael Flynn Jr., the highly controversial son of Trump’s choice for National Security Advisor. Pence repeatedly dodges the direct yes or no question, forcing Tapper to point out why all of Pence’s attempts to deflect the question were not answers. While Tapper never succeeds in getting a direct answer from Pence, his eventual success in extracting at least a strong implicature that Pence was aware of the demand for clearance required a series of arguments pointing out why each attempt at diversion by Pence was just that. More often than not, the goal of a particular conversation such as an interview or a debate will be a combination of simpler conversational goals in some temporal logic like Linear Temporal Logic (LTL) (Lamport, 1980), which includes the temporal operators ♦ for eventually and  for always, as well as operators for the temporal relations since and until. A reporter, for example, might have the complex goal of eventually getting a satisfactory answer to each of her individual questions to her interlocutor, and the goal of getting an answer to a question Q, as we have seen, typically has the general form: until an answer to Q is produced, show that no answer to Q has been given and then repeat Q. A more complex goal, which might be adopted by a participant in a political debate, is to reply to every attack on her and to land more attacks on her opponent than he lands on her. This goal is not expressible in LTL, but is in the framework we develop below.3 Asher et al. (2016) provide many examples of such goals and show how these goals may differ in complexity. They also show how to link goals to strategies for achieving them. Games provide natural structures within which to investigate the success of sequences of linguistic actions. Game theory evaluates actions in terms of utility, and the simple Boolean case of winning conditions we have alluded to above is an instance of a utility function. Signalling games (Lewis, 1969; Spence, 1973), which have been very popular in linguistics, are not appropriate for the task, however. Signalling games are designed to tackle a different aspect of language, namely, the coordination on linguistic content in reflective equilibrium (see Lewis’s account of the emergence of linguistic conventions). By contrast, we are interested in evaluations of conversational success, even—and especially—in cases where interests of the conversationalists are opposed. In such cases the meanings of messages in the context of sig2 ‘Pence pressed on clearance for Flynn’s son,’ The Lead. The full exchange can be viewed here: http://edition.cnn.com/videos/politics/2016/12/06/mike-pence-trump-flynn-jr-transition-lead-bts.cnn 3 See Asher et al. (2016) for details. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 55 N. Asher, J. Hunter, & S. Paul Games in linguistics nalling games is problematic to say the least; Crawford and Sobel (1982) show that in cases of opposing interests messages cease to have content in reflective equilibrium. Our game theoretic model is different from signalling games in several respects. For one, we will take messages to have an exogenously given meaning that determines how one conversationalist responds to the messages of another. This allows us to avoid the problems of message interpretation in signaling games where the interests of the players are opposed. Another way in which our model differs from signaling games is that while signaling games are typically “one shot”, a good model of conversational goals, as suggested in the examples above and argued in detail in Asher et al. (2016), should require agents to strategize about conversations as open-ended sequences of moves with no set end. In the exchange between Jake Tapper and Mike Pence, described above, Tapper had the goal of eventually getting an answer to his question about Michael Flynn Jr., and he didn’t stop his line of questioning until he got at least an implied answer; he had to be prepared for an open-ended set of moves by Pence designed to avoid the question. In general, conversational agents must plan for any number of moves by their opponents to try to frustrate or to prevent them from achieving their goals. In fact, we can put no a priori upper bound on the number of moves that accomplishing this goal might require, and thus a game theoretic framework for conversation must countenance a potentially infinite sequence of exchanges of messages between conversational participants. To model these aspects of strategic conversations, Asher et al. (2016) developed a game theoretic framework of Message Exchange or ME games. The intuitive idea behind an ME game is that a conversation is a sequence, either finite or infinite, of turns. In each turn, one of the players ‘speaks’ or plays a sequence of moves, and each sequence of moves itself describes a discourse structure in the sense of SDRT (Segmented Discourse Representation Theory; Asher and Lascarides, 2003) that extends the discourse structure built up from previous turns. More precisely, the vocabulary V of an ME game contains a set of discourse unit labels DU = {π, π0 , π1 , . . .}, a set of formulas from a language for dynamic semantics that serve to describe the contents of the basic units (where ‘π : φ ’ means that the formula φ describes the contents of the discourse unit π), and a set of discourse relation symbols R relating discourse constituents from the different moves made so far in the game. Turns in ME games are relativized to players. In the case of conversations, it is essential to keep track of “who says what”; Tapper saying that Pence had knowledge of Flynn Jr.’s past is not the same as Pence himself admitting to having had this knowledge. To model this, each player i is assigned a copy Vi of the vocabulary V of SDRT moves, which is simply given as Vi = V × {i}. Thus when Player i plays u ∈ V , it is noted as (u, i). Conversations correspond to plays of ME games which are finite or infinite sequences over (V0 ∪V1 ), noted as (V0 ∪V1 )∞ , for a game with two players, 0 and 1 (for details see Asher et al., 2016; Asher and Paul, 2017). Given that we have defined a conversation as a sequence or element of (V0 ∪ V1 )∞ , a conversational goal will be a subset of (V0 ∪ V1 )∞ . But who determines what the goals are in a given conversation? That is, who determines which subsets of (V0 ∪ V1 )∞ represent success? Speakers presumably have their internal goals, but it is not necessarily those that determine Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 56 N. Asher, J. Hunter, & S. Paul Games in linguistics conversational success. Each person who is involved in or who witnesses a conversation has her own ideas about what the winning conditions of the participants are or should be. To this end, Asher et al. (2016) introduced a crucial component for analyzing conversations that they called the Jury. The Jury determines the conversational goals of the participants. The Jury is itself an abstract decision rule determining winning conditions, but it can be instantiated with the conversationalists themselves, or with a third party that evaluates the conversation. In strategic settings, taking conversational partners as evaluators can lead to trouble, as each will be tempted to declare him- or herself the winner. In many settings such as political debates, the natural Jury to consider is the actual audience, some segment of the population who witnessed the debate or the whole set of participants, or yet some other body like the editorial board of a newspaper. Asher et al. (2016) consider only an impartial Jury, who also enforces constraints like the consistency of a player’s contributions or the constraint that a player respond to questions or other moves of the other players. For most conversations, however, there will be many Juries. These Juries may disagree with each other about winning conditions, and some may have a very biased take on a conversation. Nevertheless, given what we have said so far, we will need to evaluate conversational success relative to a particular Jury. Accordingly, ME games pair the space of possible conversations (V0 ∪V1 )∞ with a Jury J . Evaluating conversational success is to a certain extent a subjective or relative matter, since it depends on the conversational goals assigned to players by the Jury. Different juries may disagree as to what the conversational goals should be, and a group of people or even a single person may be undecided as to what sort of Jury she is. Still, once a goal is set as a subset of (V0 ∪ V1 )∞ , it is an objective matter as to whether the conversation meets this goal or does not; either the conversational play is an element of the subset designating a conversationalist’s winning condition or it is not. A final point concerns the evaluation of conversational success. When does a Jury decide a conversationalist has met the winning condition assigned to her? While for Asher et al. (2016) a Jury must survey an entire conversational string and all its continuations, which may be infinite, Asher and Paul (2016) argue that this misses the fact that an actual Jury evaluates in a dynamic fashion, after each turn by one of the conversational participants. The idea is to represent a winning condition by a scoring function over players’ conversational turns. A turn can be rated more or less good with respect to the winning conditions the Jury has in mind, or more or less disastrous. If the Jury has a scoring function with a discounting parameter that lowers the score for turns later in the conversation, it will always being able to confidently pick a winner in a 0 sum game within a finite amount of time. Asher and Paul (2016) illustrate how such a scoring function works on a snippet from one of the debates between candidates for the Republican Presidential candidate of 2016. So what is the import of ME games for linguistics? The field of pragmatics has always been concerned with the use of language, and ME games yield a formal pragmatic framework that provides principled reasons for why and how we use language to attain conversational goals. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 57 N. Asher, J. Hunter, & S. Paul Games in linguistics Hearkening back to the concerns of traditional rhetoricians, our account answers the question: what is a reasonable scoring function and how should a conversationalist attempt to maximize her score? To answer this question, the framework of ME games replaces semantic evaluation in terms of truth at a world with pragmatic evaluation in terms of conversational success relative to a Jury. The underlying structure of game theory also generates a notion of logical consequence for conversational success, a very rough approximation of which would be LTL’s notion of consequence, which works for simple goals, though the nature of the full consequence relation is as far we know unexplored. Finally, the framework predicts whether there is a winning conversational strategy for a given goal and what it would look like in linguistic terms. 3. The subjectivity of interpretation In this section, we explore the nature of a Jury’s scoring functions, and in particular how subjectivity and bias naturally influence them. One of the astounding facts about conversations is that people who participate in or merely observe them can come away with dramatically different interpretations of what was said, even though not everything goes. Different Juries can disagree about what was said, what was implied, and about who was successful. Consider, for instance, the one-line retort by Presidential candidate Trump to Presidential candidate Clinton during the third US Presidential debate in 2016: (2) Such a nasty woman. The literal meaning and the conventional implicatures of this remark in context are clear; with (2), Trump committed himself to a negative assessment of Clinton. However, people perceived the role of (2) in achieving an agent’s conversational goals very differently. One Jury, an appreciable segment of the American population, found this remark totally out of place in a Presidential debate. Another one, Trump’s base, found the comment appropriate and would have assigned it a high score. Each of these interpretations depends on how the Jury assigns winning conditions to the players, which includes constraints under which, the Jury judges, conversations should be conducted. Bias and subjective beliefs will also influence the way that a Jury interprets the very structure of a discourse. Consider the following excerpt, discussed at length in Asher et al. (2016), from a press conference by Senator Coleman’s spokesman Sheehan. Senator Coleman was running for re-election as a US senator from Minnesota in the 2008 election. (3) a. b. c. d. e. f. Reporter: On a different subject is there a reason that the Senator won’t say whether or not someone else bought some suits for him? Sheehan: Rachel, the Senator has reported every gift he has ever received. Reporter: That wasn’t my question, Cullen. Sheehan: (i) The Senator has reported every gift he has ever received. (ii) We are not going to respond to unnamed sources on a blog. Reporter: (i) So Senator Coleman’s friend has not bought these suits for him? (ii) Is that correct? Sheehan: The Senator has reported every gift he has ever received. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 58 N. Asher, J. Hunter, & S. Paul Games in linguistics Sheehan continues to repeat, The Senator has reported every gift he has ever received seven more times in two minutes to every follow up question by the reporter corps.4 While many of the contributions by Sheehan and the reporter corps have a clear and uncontroversial meaning and discourse function, some contributions are open to interpretation. For instance, how are we to interpret the response α by Sheehan in (3b), (3d.i), and (3f)? ME games provide an insightful answer. To formulate the above exchange as an ME game, we first fix the players and the Jury. We can assume that there are two active players: the reporter corps (R) and spokesman Sheehan (S). We will also consider two Juries, each of which interprets the exchange differently. The first, Jury 1, starts out with a presumption of full disclosure and honesty from S; Jury 2 is a biased Jury that is disposed to believe whatever the spokesman says, because, for example, Jury 2 and S are from the same political party. We’ll see below that Juries 1 and 2 will arrive at different interpretations of the structure and content of (3), and in particular, of S’s repeated response. To model the subjectivity of conversational interpretation, we must clarify what elements of a discourse structure are influenced by subjective interpretation. Asher et al. (2016) and Asher and Paul (2016) assume no ambiguity in the discourse moves made by players in an ME game (though for a look at a prior treatment of ambiguity in the ME setting, see Venant and Asher, 2015). However, at least at a first pass and assuming a perfect communication channel, it is the ambiguous moves that are up for interpretation, so we will need to countenance some ambiguity. At the same time, not everything is up for interpretation—an emphatic no to a polar question doesn’t mean yes. We will assume that the grammar, including syntax and lexical and compositional semantics, delivers an unambiguous core or, following Asher and Lascarides (2003), an underspecified logical form (ULF) for a discourse. We will also distinguish between plays, the objective components of discourse moves that are uncontroversially part of the speakers’ public commitments, and histories. A play in our ME games is a ULF, and given our assumption about exogenously given meaning, we will assume this ULF and its interpretation are common knowledge of the players and the Jury. Of course, a ULF typically involves underspecified elements (whose semantics we can specify via existential quantifications over variables standing for the elements that require specification) that are specified via reasoning that depends on a variety of subjective sources. For (3), the observed play, call it play ρ, is a representation for (a-f), in which each contribution has its normal compositional semantics and some of the uncontroversial discourse connections, like the fact that (c) corrects the discourse connection between (a) and (b), are made explicit. Other relations are left underspecified, including the relation between (a) and (b), (c) and (d.i), and (e) and (f). (4) provides the ULF for (3), where each πn labels an SDRT formula, SelR is a selection function over discourse relations that signals the presence of underspecified relations, and SelΠ is a selection function over discourse units that marks the presence of underspecified arguments. 4 See http://www.youtube.com/watch?v=VySnpLoaUrI. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 59 N. Asher, J. Hunter, & S. Paul (4) Games in linguistics π2 : (π0 : 3a ∧ π1 : 3b ∧ SelR (π0 , π1 )) ∧ π3 : 3c ∧ Correction(π2 , π3 )∧ π7 : (π6 : (π4 : 3d.i ∧ π5 : 3d.ii ∧ Explanation(π4 , π5 )) ∧ SelR (SelΠ , π6 ))∧ π10 : (π8 : 3e.i ∧ π9 : 3e.ii ∧ Confirm-Question(π8 , π9 )) ∧ Result(SelΠ , π10 )∧ π11 : 3 f ∧ SelR (SelΠ , π11 ) Here is a gloss of the ULF (4). π1 is a complex discourse unit (CDU) that groups together π0 and π1 , which are related via some underspecified relation, R1 , which is the target of the correction in π3 . In SDRT, when a correction targets a relation instance, the Correction must take scope over a CDU containing that relation instance. It is also uncontroversial that Explanation holds between π4 and π5 and that a Confirmation-Question relation holds between π8 and π9 . On the other hand it is unclear how to connect the CDU π6 or the unit π11 to the preceding context.5 The explicit discourse connector So signals a result between π6 , π10 or some other discourse unit and the CDU π10 . However, the left argument of this relation and those of the two underspecified relations are themselves underspecified which we note using the function SelΠ . But (4) only represents one possible play in an ME game tree. There could be many more branches. Figure 1 below depicts how (4) and alternative plays branching out from it would form an ME game tree. The relation instances with underspecified arguments are drawn in red. π12 :yes qap π6 π0 :3a π1 : 3b SelR π2 corr ack qap ack π12 π53 :OK π32 :yes π22 :OK π3 :3c π10 π4 :3d.i exp SelR π5 :3d.ii π13 π8 :3e.i res π7 conf-Q π9 :3e.ii π13 :no qap qap qap qap selR π33 :no π11 : 3 f π71 :yes π72 :no Figure 1: A game tree of plays for (3) A history is a completed SDRS that fills in the underspecified elements of a ULF and thereby serves as an interpretation of a given play. (5) and (6) fill out two histories, h1 and h2 , for the observed play ρ and ULF of (4). IQAP stands for Indirect Question-Answer-Pair. (5) π12 : (π2 : (π0 : 3a ∧ π1 : 3b ∧ Background(π0 , π1 )) ∧ π3 : 3c ∧ Correction(π2 , π3 ))∧ π13 : (π7 : (π6 : (π4 : 3d.i ∧ π5 : 3d.ii ∧ Explanation(π4 , π5 )) ∧ Correction(π12 , π6 ))∧ π10 : (π8 : 3e.i∧π9 : 3e.ii∧Conf-Q(π8 , π9 ))∧Res(π7 , π10 ))∧π11 : 3 f ∧Backgr(π13 , π11 ) 5 In fact, it is unclear whether the CDU π6 even exists or whether π4 alone will relate to the preceding context. We have assumed a CDU for simplicity. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 60 N. Asher, J. Hunter, & S. Paul (6) Games in linguistics π12 : (π2 : (π0 : 3a ∧ π1 : 3b ∧ IQAP(π0 , π1 )) ∧ π3 : 3c ∧ Correction(π2 , π3 ))∧ π13 : (π7 : (π6 : (π4 : 3d.i ∧ π5 : 3d.ii ∧ Explanation(π4 , π5 )) ∧ Correction(π12 , π6 ))∧ π10 : (π8 : 3e.i∧π9 : 3e.ii∧Conf-Q(π8 , π9 ))∧Res(π7 , π10 ))∧π11 : 3 f ∧Correct(π13 , π11 ) To analyze how histories develop from plays, we use the tools of epistemic game theory. We present a detailed, formal development in Asher and Paul (2017), but sketch the essentials and the linguistic consequences here. In moving from ME games to epistemic ME games, we exploit the notion of a type, a fundamental tool in epistemic game theory that Harsanyi (1967) used to represent information that players have about each other. In particular, we add to an ME game G = ((V0 ∪V1 )∞ , J ), a set of types for the players 0 and 1 and for the Jury J . To model the beliefs of an individual i, which may be a player or the Jury, we also add a function β from a pair of a play ρ, where ρ ∈ (V0 ∪V1 )∞ , and type t for i to a probability distribution over types for the other players, types for the Jury, and possible histories (complete SDRSs) given ρ. As the conversation evolves, players will update their beliefs about the history of the conversation and the type of the other players using Bayesian conditionalization over new conversational events they observe (Stalnaker, 2009). Returning to Example (3), there are two types relevant for interpreting S: the dishonest type, tD , according to which S is trying to cover up the fact that Coleman received the suits but did not declare them, and the honest type, tH , according to which S truly implicates that the Senator did not receive the suits and simply does not want to respond to this charge based on an uncertain source (see (d.ii)). To illustrate how types affect interpretation, we will take the Jury to assign victory conditions in terms of two types: R wins if S’s conversational contributions confirm he is of type tD ; S wins if his contributions confirm he is of type tH . The Jury updates its beliefs about the types of the players as the players make new moves. We now break down the two cases, tD and tH , in more detail. Case 1: Before the start of the press-conference, in the absence of other information, Jury 1’s type t is indifferent with respect to S’s honesty. That is, the Jury starts with a prior assigning equal probability to tH and tD . Let α be the ULF for (3b). When the Jury updates with the unexpected α as a response to (3a), they are genuinely puzzled by the response. While it’s natural to assume that an honest senator has reported every gift he has received, the inference from α to an answer to (3a) (why won’t the Senator say who bought the suits?) is complicated and indirect. A Jury must consider the interpretation of (3a) and (3b) conditional on both tD and tH . Conditionalizing on α and the assumption that S is of type tD , the Jury, like R, assigns a high probability to the interpretation illustrated in h1 , that (3b) does not answer (3a) and is rather related to it via Background. Conditionalizing on α and the assumption tH confers only a slightly higher probability to an IQAP relation than a Background relation between (3a) and (3b). When we combine the probabilities over tD and tH —because Jury 1 is considering both—we therefore get a higher probability for ¬IQAP than for IQAP, leading to higher probability of h1 . Conditionalizing in turn on these relative values, the Jury naturally interprets R’s response in (3c) as a Correction of S’s move in (3b) under the interpretation of (3b) as implicating an answer and therefore satisfying R’s request for a direct answer in (3a). In (3d.i), however, S corrects R’s Correction, reiterating Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 61 N. Asher, J. Hunter, & S. Paul Games in linguistics his original response, and explains why he does so in (3d.ii): the Senator and his staff do not want to comment on unnamed sources on some blog. This would seem to follow whether we conditionalize on tH or tD . The upshot of Sheehan’s correction should be that (3b) is in fact related to (3a) via IQAP. R then picks up on this conclusion and asks a Confirmation Question to confirm that this is indeed the case. We show this by linking (3e) to the graph built up from (3a)-(3d) with Result in both h1 and h2 . At this point we could imagine that for our Jury J , probJ (tH ) is once again equal to probJ (tD ) and h1 and h2 are equally likely. But now things go downhill for Sheehan in the eyes of Jury 1. Sheehan in effect refuses to engage with R or confirm the implied result in (3e) by repeating α to every follow up question, Q, on the topic. Call the exchange in (3a) and (3b) ‘round 1’ and that in (3c) and (3d) ‘round 2’. We now examine how S’s responses after round 2 affect the Jury’s estimate of his type and its interpretation of what he says. Although S repeats α 10 more times in the press conference from which our excerpt (3) is drawn, for simplicity of this analysis, we shall consider only rounds 3 through 5, for which S has three possible responses to each Q: yes, which is short for Yes, the Senator has received gifts from his friend; no which is short for No, the Senator has never received gifts from his friend; and α. The possible continuations for Sheehan that are relevant for the three rounds where R repeatedly poses different forms of Q are presented below in tabular form: σ1 σ2 σ3 σ4 σ5 σ6 σ7 round 3 round 4 round 5 yes – – no – – α yes – α no – α α yes α α no α α α Let S = {σ1 , σ2 , . . . , σ7 }. S represents the relevant possible set of plays, over which the Jury has a probability distribution. σ7 is the actual case in which S responds with α to all instances of Q. An honest senator would have his spokesperson Sheehan respond with a no to the reporter’s question eventually. To give a precise model for what happens following Asher and Paul (2017), we need some numbers. The belief function for Jury 1 assigns the following probabilities to the sequences of moves σn relative to the types tH and tD . tH tD σ1 σ2 0 0.167 0.125 0 σ3 σ4 σ5 0 0.167 0 0.125 0 0.125 σ6 σ7 0.166 0 0 0.125 Notice that at the outset, the Jury accords an equal probability to tH and tD ; the values on the rows above each sum up to .5. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 62 N. Asher, J. Hunter, & S. Paul Games in linguistics We can now calculate how conversational moves can affect the Jury’s assessment of S’s type. In particular, we want to look at two “events”, EH and ED , representing an honest senator vs. a dishonest senator and defined as follows: EH = {tH } × S, ED = {tD } × S Now let’s take a belief function β over the empty play or ULF ε as our starting point to model the beliefs of the Jury 1, which is of some type t1 , at the start of the press-conference. β [ε](t1 )(EH ) = β [ε](t1 )(ED ) = 0.5 The Jury is thus equally unsure as to whether S is honest or dishonest. Recall that the Jury reverts to this distribution after round 2. Let ρ1 = hQihαi be the play after round 2, i.e., after (3d). The strategies that are compatible with ρ1 are S1 = {σ3 , σ4 , σ5 , σ6 , σ7 }. Hence, we can define the events EH (ρ1 ) = {tH } × S1 , Now, ED (ρ1 ) = {tD } × S1 , E(ρ1 ) = EH (ρ1 ) ∪ ED (ρ1 ) β [ε](t1 )(E(ρ1 )) = 0.708 Let j ∈ {4, 6}. Then we have, conditionalizing on the new event E(ρ1 ): β [ρ1 ](t1 )(htH , σ j i) = β [ε](t1 )(htH , σ j i | E(ρ1 )) = 0.167/0.708 = 0.238 and for k ∈ {3, 5, 7} β [ρ1 ](t1 )(htD , σk i) = β [ε](t1 )(htD , σk i | E(ρ1 )) = 0.125/0.708 = 0.175 Thus after round 3, the belief function of the Jury in Case 1, after Bayesian updates, can be represented in the following tabular form. tH tD σ3 0 0.175 σ4 σ5 σ6 0.238 0 0.238 0 0.175 0 σ7 0 0.175 and we have β [ρ1 ](t1 )(EH (ρ1 )) = 0.476 and β [ρ1 ](t1 )(ED (ρ1 )) = 0.525 Next, let ρ2 = hQihαihQihαi be the play after round 3, i.e., after (3f). The strategies that are compatible with ρ2 are S2 = {σ5 , σ6 , σ7 }. As before, we can define the events EH (ρ2 ) = {tH } × S2 , and hence ED (ρ2 ) = {tD } × S2 , E(ρ2 ) = EH (ρ2 ) ∪ ED (ρ2 ) β [ε](t1 )(E(ρ2 )) = 0.587 We have, as before β [ρ2 ](t1 )(htH , σ6 i) = β [ε](t1 )(htH , σ6 i | E(ρ2 )) = 0.238/0.587 = 0.404 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 63 N. Asher, J. Hunter, & S. Paul Games in linguistics and for j ∈ {5, 7} β [ρ2 ](t1 )(htD , σk i) = β [ε](t1 )(htD , σ j i | E(ρ2 )) = 0.175/0.587 = 0.298 Thus, β [ρ2 ](t1 )(EH (ρ2 )) = 0.404 and β [ρ2 ](t1 )(ED (ρ2 )) = 0.596. So after round 2, after Bayesian updates, the Jury believes even more that S has type tD The beliefs of the Jury about the type of S (and of the Senator) after each round of the conversation can be represented pictorially as follows. Belief probability 1 0.8 dishonest 0.6 0.4 0.2 0 honest 0 1 2 3 4 Number of rounds 5 Figure 3 Given these calculations, we can imagine that such a Jury might then stop the conversation once the probability of tD becomes high enough. For such a Jury, Sheehan’s repetitions doom his play to be losing. A key feature of our analysis is that the Jury’s estimation of S’s type also affects its interpretation of the conversation. The Jury’s beliefs about the interpretation of what S says evolve as the Jury conditionalizes on events that are a combination of a new element of play as given in S and an assignment of types. The yes and no responses in the continuations to (3) would have an unambiguous interpretation as answers to the preceding occurrence of Q. The response α, however, is more problematic; what exactly is the role of α as a response to (3a)? And while α has a natural interpretation in (3d.i) as a Correction, subsequent repetitions of α are even less clear than its use in (3b). Consider, for instance, S’s assertion of α as a response to R’s question (3e), an affirmative answer to which should be a consequence, were α an indirect answer to (3a). While this and further instances of α could be attached with Background or Correction or with no specified relation at all, the probabilities of these histories given a play are vastly different depending on the type assignments. To make things more concrete, let’s focus just on the two histories we’ve considered in (5) and (6). Given Jury 1’s belief function, repeating α to each variant of Q lowers the probability of tH . But what does conditionalization do to the probabilities of h1 and h2 ? One plausible hypothesis is that the probability of h1 covaries with the probability of tH . Conditionalizing on events of the form ED (ρi ) and EH (ρi ) thus lowers the probability that repetitions of α after Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 64 N. Asher, J. Hunter, & S. Paul Games in linguistics (3d.i) are Correction moves that provide answers to Q and raises the possibility that they are uncooperative moves unconnected with R’s questions. An honest Sheehan for this Jury would not have continued to make the α move as a Correction without further explanation. Once S continues to play α, the probability mass shifts more and more to the interpretation of α as a non-cooperative move. In turn, conditionalization on the event of the interpretation h1 entrenches the Jury’s belief that Sheehan is of type tD . Thus, histories and types have an important co-dependence. A person’s interpretation of a conversation can reinforce or change her beliefs about the players and or the Jury, which in turn may confirm or change how she shapes the history of the conversation. Case 2: An alternative Jury, which is strongly predisposed to assign Sheehan tH would have seen matters differently. Consider the following belief function for this Jury, in which the Jury already has a prior probability of .7 in tH . tH tD σ1 0 0.10 σ2 0 0 σ3 0 0.10 σ4 0.05 0 σ5 σ6 0 0.15 0.10 0 σ7 0.5 0 Such a Jury would have already accepted α as a perfectly acceptable indirect answer to (3a) and so opted for the history h2 for (3). It would also have constructed a different history for the rest of the conversation after (e). It would see each repetition of α as another correction of R’s attempts to reopen a topic that Sheehan has already settled. Since S is of type tH , he need not continue the discussion of a matter that has already been labelled as one that Sheehan will not comment on. Given this interpretation of the repetitions of α, the probability of tH on the belief function for this Jury would remain high when the Jury conditionalizes upon that interpretation, and S has a winning strategy. See Figure 4 below. Belief probability 1 honest 0.8 0.6 0.4 0.2 0 0 dishonest 1 2 3 4 Number of rounds 5 Figure 4 Given the continued high probability of tH , conditionalizing on events of the form {tH } × S in turn assigns a high probability and confirms the continuation of history h2 in which S continues to correct R. Jury 2 conditionalizes on events like those defined in our analysis of Jury 1 but Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 65 N. Asher, J. Hunter, & S. Paul Games in linguistics arrives at a very different conclusion; α is not interpreted as a non-cooperative move but as a Correction, and the updating of probabilities on types and on histories confirm each other. The co-dependence between an interpreter’s assessment of a speaker’s type and his interpretation of what she says has several interesting consequences. The first is that a priori biases are easy in general to strengthen through interpretation. Furthermore, we have seen that bias is dependent on context. Hence, the model predicts that the more biased talk to which the Jury is exposed, the more it will carry this bias into the interpretation of future conversations. The moral is that interpretation is subject to manipulation. Although we have assumed that few components of discourse moves are ambiguous, our example illustrates that discourse connections, which are often ambiguous, can lead different Juries to very different conclusions. This subjectivity goes even beyond language to the interpretation of “facts.” Hunter et al. (2017) argue that interpreting non-linguistic events has significant parallels to interpreting conversation and that the two interact to produce a complete picture of a situation. If we couple this view with what we have developed here, our model implies that the interpretation of facts also naturally gives rise to a subjective bias. Figuring out the truth from a collection of facts described to suit someone’s purposes is difficult. The counterpart to this is that being a fair or impartial Jury, being open to other interpretations is not a natural outcome of conversational interaction. The model predicts that constraints exogenous to the natural way speakers interpret conversation and interpretation are needed to lead to an impartial assessment of conversational moves. So how do we ensure fair or unbiased interpretation for the Jury, or anyone else for that matter? This question links our question of assessment of conversational success with the present concern about the subjectivity of interpretation. One important parameter to fix are the types evoked to drive interpretation, as well as the probability distribution over them. In the model of Asher and Paul (2017), the types are simply abstract objects, devices for encoding probabilities about discourse histories and, indirectly, strategies. As such, the set of types is vast and uncountable. Yet typically, only certain types are relevant to interpretation. How do we determine an appropriate restricted set? Doing this also involves bias. To take an extreme case, if we only picked one type in our interpretation of (3), all the probability mass would align on that one type; conditionalization on new evidence would yield nothing new. A Jury considering just the one type would perforce be biased in the extreme and its views impervious to change. A balanced or fair interpretation would thus need at least two types that are in an intuitive sense contraries of each other, as we have done in our treatment of (3). Moreover, one would need to start out with a balanced distribution over these types or at least be aware of the problems of bias coming from prior interactions. Nevertheless, we strongly suspect that having only two types is in general far from sufficient to arrive at the correct interpretations of conversational moves, and indeed, of the world around us. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 66 N. Asher, J. Hunter, & S. Paul Games in linguistics 4. Analyzing different types of content A final illustration of the relevance of epistemic games to linguistics comes from the way speakers use not at-issue (NAI) information (Potts, 2005). Consider the following dialogue excerpt from the movie The Princess Bride, in which Wesley (W) has kidnapped Buttercup (B) and is questioning her about her fiancée Prince Humperdink (H). Buttercup and Wesley were once in love, but Wesley has disguised himself as a pirate, so Buttercup does not recognize him. They have just noticed their pursuers: Humperdink and his men. (7) a. b. c. d. e. B: He (Humperdink) can find a falcon on a cloudy day, he can find you! W: So you think your dearest love will save you? B: I never said he was my dearest love and yes, he will save me. That I know. W: You admit to me that you do not love your financé? B: He knows I do not love him. As a background to (7), it is clear from the context that Wesley’s goal is to determine Buttercup’s feelings for Humperdink while concealing his identity. Concealing his identity is important because Buttercup would have good reason to hide her love for Humperdink from Wesley. Wesley uses a presupposition in (7b), a form that conveys NAI content, to try to discern whether Buttercup loves Humperdink. As many linguists have noted, NAI constructions do not admit of simple rejoinders; Buttercup cannot take issue with the presupposition that Humperdink is her dearest love with a simple ‘no’, ‘I disagree’, or ‘that’s not true’. Getting Buttercup to reveal her type in this situation involves a more complicated strategy than simply asking directly if she loves Humperdink. Why does Wesley choose such a strategy? Why does he pretend to play along with Buttercup’s apparent conversational goal—to convince Wesley that he should let her go because he is going to be caught—when he isn’t actually interested in it? We believe epistemic ME games can help clarify matters, but first, we need some background assumptions. We follow Hunter and Asher (2016)’s discursive, SDRT analysis of NAI content according to which NAI content results from the way that an utterance contributes to a hierarchical discourse structure. At any given point in a discourse, certain discourse moves will be more salient and easier to build off of than others. The set of salient discourse units, referred to as The Right Frontier in various discourse theories, will evolve as a discourse proceeds in a way that is subject to general discursive principles. Hunter and Asher’s central claim is that utterances that involve multiple discourse units, which they argue must be the case when an utterance contains both NAI and AI content, have their own internal discursive structure, and the same general discursive principles that determine whether other discourse units are on the Right Frontier or not also determine which parts of a multi-part utterance are on the Right Frontier and therefore salient. Speakers exploit these principles to make certain parts of their utterances easier to build off of than others. Those parts that are on the Right Frontier will be at-issue (so long as they are on the RF); those that are not will be NAI. In SDRT, presupposed content is attached to a position off the Right Frontier (Asher and Lascarides, 1998); the presupposition of (7b) is therefore NAI, as desired. With Buttercup’s correction in (7c) and Wesley’s subsequent Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 67 N. Asher, J. Hunter, & S. Paul Games in linguistics follow-up in (7d), however, the discourse shifts seamlessly to one in which the presupposed content is placed back on the Right Frontier and thereby made at-issue. With this background in place, let’s look more closely at the discourse structure of (7) and its interaction with conversational goals. Suppose that Buttercup is of one of two types: either she loves H and is of type tl , or she does not and is of type tn . We will suppose that in either case, she is not interested in dissembling her type. Wesley’s conversational goal can be formulated as getting Buttercup to reveal whether she is of type tn or type tl while concealing his type. We assume further that after (7a), Wesley has the option of using (7b) with the NAI device or asking the direct question DQ: Do you love Humperdink?. In the context of (7a) and the more general pursuit by Humperdink and his men, DQ would blatantly shift the topic and naturally arouse suspicions: why would an unknown pirate care about Buttercup’s affections for Humperdink? There is a high probability that Buttercup would fashion a conversational continuation—e.g., why should YOU care about that?—that would endanger Wesley’s goal of concealing his identity. By opting for an NAI construction, Wesley makes Buttercup responsible for the shift in discourse topic, which is less likely to arouse suspicion. The expected utility of DQ is thus lower than that of (7b) when it comes to achieving Wesley’s goal of concealing his identity. This goal in turn serves the larger goal of determining Buttercup’s type. Buttercup would have no obvious reason to hide her love for Humperdink from a total stranger, especially a stranger who knows that she is engaged to Humperdink. On the other hand, her old feelings for Wesley, whom she believes at this point to be dead, might give her reason to be less than forthcoming with him. Buttercup’s rejection of the NAI content in (7b) is more significant, and therefore more useful for determining Buttercup’s type, if she does not realize she is talking to Wesley. Thus the NAI device in (7b) has a higher expected utility for Wesley’s primary goal as well. Now suppose that Buttercup had been of type tl and had not questioned the NAI content, responding only to the AI content with something like, Yes, he will save me (Sv). By conditionalizing on Sv, which entails Buttercup’s acceptance and public commitment to the NAI content6 , the probability that Buttercup is of type tl is plausibly high. The NAI construction would be helpful in this case as well, because it would allow Wesley to cut his losses and infer that Buttercup’s romantic allegiances had shifted, another way of obtaining his winning condition. We have illustrated one example of a strategic use of NAI content, but there are many others (see Hunter and Asher, 2016). In each of these cases, NAI constructions are strategically useful when a speaker s0 has a conversational goal that he wishes to conceal. Our model predicts this strategic use of NAI devices if we make the reasonable assumption that a move by s0 to place a bit of content φ on the Right Frontier as a topic for discussion raises the probability that s0 has a conversational goal of getting a commitment from his interlocutor, s1 , to φ or ¬φ . Someone wanting to conceal his desire to extract such a commitment will be better off placing φ in an NAI position. In this case, he can still get the commitment he seeks: if s1 continues 6 Wesley’s use of a presupposition should not entail that Buttercup commits to its content, but once she opts to build on Wesley’s structured discourse contribution, she commits herself to the whole of both its content and its structure. See Hunter and Asher (2016) for more details. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 68 N. Asher, J. Hunter, & S. Paul Games in linguistics the conversation without disputing φ , s1 commits to the content of φ . Conversely, if s1 does dispute φ ,7 then she may reveal information to s0 without s0 making φ discourse salient. We formalize the strategic use of NAI content in Proposition 1. Recall that ♦φ is true on a conversational string just in case φ is true at some stage in the conversation; let C1 φ stand for ‘s1 commits to φ ,’ and let ‘|=’ stand for the satisfaction relation defined over the basic exogenous semantics for plays in (V0 ∪ V1 )∞ (for details, see Asher et al., 2016). Let ρn for ρ ∈ (V0 ∪V1 )∞ be a prefix of length n of ρ and let β1 be the belief function for a fixed type of s1 . Let tφ be a type of s0 whose winning condition includes a move that commits s1 to φ . Let ε be the empty play in (V0 ∪V1 )∞ . Proposition 1. Let G be an ME game with Win0 ⊆ {ρ ∈ (V0 ∪V1 )∞ : ρ |= ♦C1 φ } ∩ {ρ ∈ (V0 ∪ V1 )∞ : ¬∃nβ1 [ρn ](tφ ) > β1 [ε](tφ )}. Then if 0 has a winning strategy σ in G, σ will include a use of an NAI device for conveying a question about φ instead of an AI device for conveying φ . Hunter and Asher (2016) argued that the NAI status of a bit of content φ cannot be attributed to syntactic and semantic features of φ alone; its status is ultimately determined by how φ attaches to a larger discourse structure. Our discussion here makes a similar point about conversational goals: the nature of a goal cannot be recovered directly by considering the at-issue status of content in the discourse; its nature is ultimately determined by the larger discourse structure or history. In particular, we cannot assume that the difference between AI and NAI content is that AI content directly addresses a conversational goal while NAI content plays some secondary, supporting role relative to conversational goals, contra claims made in by Roberts (2012) and Simons et al. (2010) inter alia. If we consider only (7a)-(7c), then it is true that Wesley’s apparent conversational goal aligns with the AI content of his utterance in (7b); that is, it seems that he shares Buttercup’s goal to determine whether Humperdink will catch him. However, once we consider the longer string including not only (7d) and (7e), but also Wesley’s subsequent questioning of Buttercup, then we understand that his actual goal is more accurately reflected by his NAI moves. Even if Buttercup is not immediately aware of this actual conversational goal, the audience of the film, acting as a Jury, can see this clearly. 5. Conclusions and future work We have elaborated some consequences of using ME games for linguistic analysis, consequences that we think touch on important issues in pragmatics and semantics. We have shown how a notion of conversational success and a precise definition of conversational goals can affect the discourse structure of a dialogue. We have also shown how to add epistemic considerations to discourse interpretation, which has allowed us to formulate an analysis of the power and the limits of subjectivity in interpretation. We have further shown how the framework of epistemic ME games yields an analysis of bias, its ubiquity and its effects on interpretation. At the same time, we have argued that there are limits to bias; one cannot arbitrarily reinterpret unambiguous messages to mean something different from what they normally mean. Another very important issue that we leave for future work concerns the notion of a fair or “unbiased” interpretation, something of interest not only to linguists but the general public at 7 For an account of corrections, see Asher and Lascarides (2003). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 69 N. Asher, J. Hunter, & S. Paul Games in linguistics large. While such a notion has an intuitive meaning, working out a precise analysis within a framework like epistemic ME games requires an analysis of the types relevant to such an interpretation. We also feel that fair interpretations are hard. Given that a fair interpretation is a conversational goal, our framework can actually tell us precisely how hard it is, but we do not know at present the complexity of such a goal nor even how to formulate it precisely. Another application of epistemic ME games that we find linguistically interesting is their use in analyzing the strategic uses of vehicles of content that affect discourse salience or that introduce content without affecting salience. To this end, we have given a preliminary analysis of the strategic usefulness of not at-issue expressions of content. Future work will aim to improve this analysis with more case studies and a more careful taxonomy of expressions that affect discourse salience. References Asher, N. and A. Lascarides (1998). The semantics and pragmatics of presupposition. Journal of Semantics 15(2), 239–299. Asher, N. and A. Lascarides (2003). Logics of Conversation. Cambridge University Press. Asher, N. and A. Lascarides (2013). Strategic conversation. Semantics and Pragmatics 6(2), 1–62. Asher, N. and S. Paul (2016, July). Evaluating conversational success: Weighted message exchange games. In J. Hunter, M. Simons, and M. Stone (Eds.), 20th workshop on the semantics and pragmatics of dialogue (SEMDIAL), New Jersey, USA. Asher, N. and S. Paul (2017). Epistemic message exchange games. In progress. Asher, N., S. Paul, and A. Venant (2016). Message exchange games in strategic conversations. Journal of Philosophical Logic. doi.org/10.1007/s10992-016-9402-1. Crawford, V. and J. Sobel (1982). Strategic information transmission. Econometrica 50(6), 1431–1451. Franke, M. (2008). Meaning and inference in case of conflict. In K. Balogh (Ed.), Proceedings of the 13th ESSLLI Student Session, pp. 65–74. Franke, M., T. De Jager, and R. Van Rooij (2012). Relevance in cooperation and conflict. Journal of Logic and Computation 22(1), 23–54. Grice, H. P. (1975). Logic and conversation. In P. Cole and J. L. Morgan (Eds.), Syntax and Semantics Volume 3: Speech Acts, pp. 41–58. Academic Press. Harsanyi, J. C. (1967). Games with incomplete information played by “Bayesian” players, parts I–III. Management Science 14, 159–182. Hunter, J. and N. Asher (2016). Shapes of conversation and at issue content. In Semantics and Linguistic Theory 26, pp. 1022–1042. Hunter, J., N. Asher, and A. Lascarides (2017). A formal semantics for situated conversation. unpublished manuscript. Lamport, L. (1980). Sometime is sometimes not never: On the temporal logic of programs. In Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 174–185. ACM. Lewis, D. (1969). Convention: A Philosophical Study. Harvard University Press. Potts, C. (2005). The Logic of Conventional Implicatures. Oxford University Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 70 N. Asher, J. Hunter, & S. Paul Games in linguistics Roberts, C. (2012). Information structure in discourse: Towards an integrated formal theory of pragmatics. Semantics and Pragmatics 5(6), 1–69. Simons, M., J. Tonhauser, D. Beaver, and C. Roberts (2010). What projects and why? In N. Li and D. Lutz (Eds.), Semantics and Linguistics Theory (SALT) 20, pp. 309–327. Spence, A. M. (1973). Job market signaling. Journal of Economics 87(3), 355–374. Stalnaker, R. (2009). Iterated belief revision. Erkenntnis 70(2), 189–209. van Rooij, R. (2004). Signalling games select Horn strategies. Linguistics and Philosophy 27, 493–527. Venant, A. and N. Asher (2015). Ok or not ok? In Semantics and Linguistic Theory 25. Cornell University Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 71 72 Obligatory Additives in the Antecedent of Conditionals Nadine BADE — University of Tübingen Abstract. The paper investigates the obligatory insertion of additive particles in the antecedent of conditionals. Two theories are compared with regard to their different predictions regarding this insertion. One theory works with the principle Maximize Presupposition (Heim, 1991), the other postulates a relation between mandatory exhaustivity inferences and insertion of additive particles (Bade, 2016). The first theory predicts additives to be obligatory under downward entailing (DE) operators which are holes for presuppositions. The second theory predicts the insertion of additives to not be obligatory under DE-operators due to the fact that exhaustivity inferences are usually blocked in these environments for independent reasons (Chierchia et al., 2012). Previous studies already suggest that additives (and iteratives) are not obligatory under negation, contrary to the predictions of Maximize Presupposition (Bade and Tiemann, 2016). In the present paper, an experimental study on the insertion of German “auch” in antecedent of conditionals is reported which tests the predictions of both theories and further confirms an account of obligatory additivity working with Obligatory Implicatures. Keywords: presuppositions, conditionals, implicatures. 1. Introduction The paper investigates the obligatory insertion of additive particles in the antecedent of conditionals. Previous studies on obligatory presupposition triggers suggest that additive particles do not fall in the class of triggers whose obligatory insertion follows from the principle Maximize Presupposition (Bade, 2016). Rather, the data suggest that additives are inserted to block or cancel exhaustivity implicatures. One important prediction of Maximize Presupposition is that presupposition triggers are obligatory in contexts which are holes for presuppositions, such as under negation and in the antecedent of conditionals. It has been shown that additives are not obligatory under negation (Bade and Tiemann, 2016). This is straightforwardly explained under an account working with Obligatory Implicatures. Since exhaustification is blocked under negation for independent reasons, insertion of the trigger is unnecessary. The study presented here tested the predictions of Maximize Presupposition and the competing theory Obligatory Implicatures for the insertion of additives in antecedents of conditionals. The results show that additives are generally not obligatory in this environment. Moreover, the data suggest that the insertion of additives interacts with the interpretation of the conditional as a whole. The study is thus also revealing with regard to the ongoing question under which circumstances exhaustivity implicatures occur locally. Section 1 gives the theoretical background, specifically it discusses the two theories Obligatory Implicatures and Maximize Presupposition. In section 2 an acceptability rating study on German “auch” in antecedent of conditionals is presented which tested the predictions of the two theories. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 73 N. Bade Obligatory additives in the antecedent of conditionals 2. Theoretical Background Presupposition triggers are obligatory when their presupposition is fulfilled in the context, see examples in (1) (Heim, 1991; Sauerland, 2008; Percus, 2006; Chemla, 2008). (1) a. b. c. d. The / # A father of the victim arrived. Bob came to the store. Bill came, #(too). Peter went to Norway this year. He went to Norway #(again) last year. John # believes / knows Paris is in France. There are two approaches to the phenomenon of obligatory presuppositions, one is working with the principle Maximize Presupposition, the other makes use of Obligatory Implicatures. Previous experimental findings suggest that presupposition triggers fall into two classes with regard to their obligatory insertion. The insertion of one set of triggers is better captured using Maximize Presupposition, the insertion of the other group seems to follow from Obligatory Implicatures. Both theories predict the insertion of the triggers in (1) to be obligatory. Theories working with Maximize Presupposition assume that there is lexical competition between the trigger and its non-presuppositional counterpart, which are ordered on a scale, see examples in (2). (2) Scales: {the, a}, {both, every}, {believe, know}, {again, ∅ }, {SG, PL}, {too, ∅ }, {PRES, PAST} Using the weaker item on this scale of presuppositional strength will lead to an “anti-presupposition” or “implicated presupposition”, i.e. the inference saying that the presupposition of the stronger competitor is false. The inference arising from using (3a) instead of (3b), for example, is that it is not certain that there is a unique 6ft long catfish, see (3c). (3) a. b. c. Robert caught a 6ft long catfish. Robert caught the 6ft long catfish. ¬∃x.∀y.6ft-catfish(y) ↔ x =y Parallelly, (4a) has an inference that it is not certain that the victim has one unique father, which contradicts common knowledge. As a result, the definite determiner is obligatorily inserted. “Antipresuppositions” (Percus, 2006) are argued to have a special status. First, these inferences are said to be projective content, a property they share with presuppositions. Since the negated (4a) has the presuppositional stronger competitor in (4b) the same undesired inference arises that the presupposition of (4b) is false, see (4c). As a result the definite must be inserted under negation. (4) a. #A father of the victim did not arrive. b. The father of the victim did not arrive. c. ¬∃x.∀y.father-of-victim(y) ↔ x =y Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 74 N. Bade Obligatory additives in the antecedent of conditionals Another property is that these inferences usually resist strengthening. That is, the inference in (3a) cannot be strengthened to “It is certain that there is more than one 6ft long catfish”, as would be expected if they were implicatures. However, it has been observed that not all presupposition triggers behave alike when it comes to their obligatory insertion. Specifically, it has been shown that the inferences from not using presupposition triggers other than the definite determiner do not necessarily come with the features just discussed. First, it has been argued that some of the “antipresuppositions” can be strengthened in the same way as implicatures (Chemla, 2008). The sentence with “believe” in (5), for example, has a strong inference that it is certain that the speaker does not have a brother. This is because speakers are usually opinionated when it comes to them having siblings or not. (5) Jane believes I have a brother. Second, the presupposition triggers “too” and “again” (German “auch” and “wieder”) are not obligatory under negation, which shows that their “antipresuppositions” do not project, see examples in (6) below (Bade and Tiemann, 2016). (6) a. b. Yesterday Jenna went ice-skating. Today she did not go (again). Bob came to the party. It is not true that John came, (too). Moreover, the circumstances under which the trigger “too” is inserted seems to align with the circumstances under which exhaustivity implicatures arise. The more pressure to derive an exhaustivity implicature, the more pressure to insert the trigger (Bade, 2014, 2016). These facts are more compatible with a theory that assumes that obligatory insertion of the presupposition trigger follows from Obligatory Implicatures. The theory assumes that the (b) sentences in (7)-(9) have implicatures, given in (c) respectively, which are contradictory to the contexts in (a). (7) a. b. c. Paris is in France. Mary believesF that Paris is in France. It is not certain that Paris is in France. (8) a. b. c. John has visited Rome. PeterF has visited Rome. Peter is the only one who has visited Rome. (9) a. b. c. Mary came to John’s party last year. She came to John’s party this yearF . This year is the only time Mary came to John’s party. These implicatures are derived by a covert exhaustivity operator, see definition in (10) (Fox, 2007), which evaluates the focus, for example on “Peter” in (8b). One further assumption is that, in the absence of other overt alternatives, the Question Under Discussion (QUD, Roberts Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 75 N. Bade Obligatory additives in the antecedent of conditionals (1996)) which matches the focus provides the set of alternatives (Bade, 2016). The derivation of the exhaustivity implicature is given in (11). (10) a. b. [[ EXH ]](A<<s,t>,t> )(p<s,t> )(w) ⇔ p(w) & ∀q ∈ NW(p, A): ¬q(w) NW(p,A) = {q ∈ A: p does not entail q} (11) J [ [ EXH Q ] [ PeterF has visited Rome ] ]K = Peter was in Rome in w & ∀q[q ∈ [λp.∃x. p= λw. x was in Rome in w ] & p ; q → q(w) = 0 ] This theory does not predict triggers to be obligatory under negation since exhaustivity is blocked here for independent reasons (Bade and Tiemann, 2016). Moreover, the inferences arising from not using the trigger are supposed to be implicatures, which explains that they are dependent on context and can be strengthened (Sauerland, 2004). The empirical picture arising so far is that presupposition triggers fall into two classes with regard to obligatory insertion (Bade, 2016). One set of triggers, including the definite, is better captured by Maximize Presupposition since inserting it is obligatory below DE-operators and its insertion does not depend on the context, especially the QUD. Another set of triggers, including “know”, “again” and “too”, follow from Obligatory Implicatures. Leaving them out creates implicatures which can be contradictory to the context and do not arise under DE-operators. 3. Experimental Study 3.1. Idea: presupposition triggers in antecedents of conditionals Maximize Presupposition predicts presupposition triggers to be obligatory in antecedents of conditionals since they are holes for presuppositions. That is, the presupposition of “again” in (12a) that Peter was in Norway before projects out of the if-clause in (12b). (12) a. b. Peter was in Norway again this year. If Peter was in Norway again this year, he was fishing. As a result, if (13a) is used instead of (12b), which is the presuppositionally stronger competitor, the “anti-presupposition” in (13b) arises that the presupposition of the competitor is false. (13) C: Peter was in Norway last year. a. If Peter was in Norway this year, he was fishing. b. It is not true that Peter was in Norway before. Due to this inference, (13a) is predicted to be degraded in the context given in (13) which establishes that Peter was in Norway before by Maximize Presupposition. According to Obligatory Implicatures the insertion of the presupposition trigger should only be forced if an exhaustivity implicature arises which is contradictory to the context. The question thus is: what exactly are the exhaustivity implicatures that arise with if-clauses? There is Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 76 N. Bade Obligatory additives in the antecedent of conditionals evidence from scalar implicatures that exhaustivity implicatures arise below the if-clause. The sentence in (14) is ambiguous between the reading in (14a) and the one in (14b). (14) If you have salad or dessert, you pay $20. a. If EXH you have salad or dessert, you pay $20. ‘If you have salad or dessert but not both you pay $20.’ b. If you have salad or dessert, you pay $20. ‘If you have salad or dessert or both, you pay $20.’ Since the scale ordering the items {or, and} (Horn, 1984) is reversed under downward-entailing operators the sentence in (14b) is already the strongest competitor. Adding an exhaustivity operator below “if” usually would not lead to strengthening and thus is ruled out on the basis of the economy condition (Chierchia et al., 2012). Readings such as the one in (14a) are available, but are argued to require special circumstances and usually pitch accent on the scalar item (Fox and Spector, to appear). For sentences with particularized conversational implicatures yielded by focus, such as the one in (15), the picture looks very similar. There are two exhaustification strategies, given in (15a) and (15b) and both seem available. (15) If PeterF came, there were discussions. a. If EXH Peter came, there were discussions. b. EXH If Peter came, there were discussions. The LF for (15a) is given below in (16), the one for (15b) is given in (17). (16) MUST <s,t> IF EXH C <s,t> there were discussions PeterF came Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 77 N. Bade Obligatory additives in the antecedent of conditionals (17) EXH C MUST IF <s,t> <s,t> PeterF came there were discussions Let us assume that the context in which (16) is uttered is the one in (18). (18) Mary came. a. If EXH PeterF came, there were discussions. b. EXH If PeterF came, there were discussions. The relevant alternatives for (18a) are propositions of the form given in (19). (19) Alt = {Peter came, Mary came, Peter and Mary came, ...} If the exhaustification strategy in (18a) is chosen, both alternatives “Mary came” and “Mary and Peter came” are excluded since they are non-weaker and the reading in (20) is yielded. Assuming that a epistemic (realistic) modal base is chosen for the covert modal which is restricted by the if-clause this reading yields a contradiction (Kratzer, 1991). (20) ∀w ∈ {w’: w’ is compatible with the evidence available in the utterance situation in w@ } & Peter came in w & Mary did not come in w → there were discussions in w ‘If Peter and not Mary came, there were discussions.’ Since it is already established in the context that Mary came the indicative conditional with a low EXH operator must be perceived as contradictory. There is no possible world in accordance with the facts of w@ , the actual world, where Mary did not come. With the exhaustification strategy in (18b) the relevant alternatives are the one in (21). (21) Alt = {If Peter came, there were discussions; If Mary came, there were discussions; If Peter and Mary came, there were discussions ...} The sentence in (18b) entails that if Peter and Mary came there were discussions. The only alternative which is non-weaker and thus excluded is that if Mary came there discussions, see the interpretation of (18b) in (22). (22) ∀w ∈ {w’: w’ is compatible with evidence available in the utterance situation in w@ } & Peter came in w → there were discussions in w & ¬ ∀w ∈ {w’: w’ is compatible Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 78 N. Bade Obligatory additives in the antecedent of conditionals with the evidence available in the utterance situation in w@ } & Mary came in w → there were discussions in w ‘If Peter came there were discussions and not if Mary came there were discussions.’ This reading says that Peter’s coming is the condition for there being discussions and not Mary’s coming. This is not contradictory to the fact that Mary came. There is, of course, a third option where no exhaustivity operator is inserted into the structure. This reading is also predicted to not yield any inferences which could be contradictory to the the discourse. Only if the first option with EXH < If is chosen, the trigger should be obligatory according Obligatory Implicatures. Since this reading is predicted to be marginally available, leaving out the trigger should be fine in most cases. To sum up, the theories make different predictions with regard to the insertion of presupposition triggers in antecedents of conditionals. For Maximize Presupposition the trigger should be obligatory as long as its presupposition is fulfilled. According to Obligatory Implicatures, the trigger is only obligatory if exhaustification leads to a contradiction with the context. This can only happen when an exhaustivity operator is inserted below “if”. A correlation between interpretation and pressure to insert the trigger is thus predicted. The purpose of the study presented was to test these predictions. 3.2. Material and Design The idea behind the study was to test the predictions of the two theories Maximize Presupposition and Obligatory Implicatures regarding the obligatory insertion of the German additive particle “auch” in the antecedent of conditionals. The design of the study was simple. There was a context establishing that the presupposition of the additive was fulfilled, see the example in (23). (23) Teresa, Sabrina und Isa gehen in die selbe Klasse und haben gerade eine Klausur zurück bekommen. Sabrina sagt zu Teresa: Ich bin durch die Klausur gefallen. Theresa antwortet: Teresa, Sabrina and Ida are students in the same class and just got back an exam. Sabrina says to Theresa: I failed the test. Theresa replies: The target sentence was following the context and appeared in two conditions with and without the additive (+ ADD /- ADD). (24) a. b. Wenn Ida auch durchgefallen ist, muss der Test schwer gewesen sein. If Ida also failed the test, the test must have been hard. + ADD Wenn Ida durchgefallen ist, muss der Test schwer gewesen sein. If Ida failed the test, the test must have been hard. - ADD Participants were asked to read context and target sentences carefully and then judge the acceptability of the target in a given context on a scale from 1 to 5 (where 5 stands for totally Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 79 N. Bade Obligatory additives in the antecedent of conditionals acceptable). To test the prediction of Obligatory Implicatures that the insertion of the trigger is only obligatory under a certain interpretation participants were moreover asked two comprehension questions. The first question addressed the interpretation of the antecedent, an example is given in (25). Participants could choose between three answer options given in (25a-c). (25) Q1: a. b. c. According to Teresa, under which conditions must the test have been hard? Sabrina failing (IF A) Ida failing (IF B) Both Ida and Sabrina failing (IF A and B) The second question people were asked aimed at finding out whether there are inferences resulting from using the conditional which could yield contradictions, an example is given in (26). They had three options for answering, given in (26a-c). (26) Q2: Does Theresa believe that Sabrina failed? a. Yes (Y) b. Unclear (U) c. No (N) The answers to these two questions together were supposed to tell which interpretation people had in mind when judging the acceptability of the sentences. Especially interpretation question number two was supposed to give insights into whether the sentence without the additive was perceived as contradictory to the previous discourse, i.e. whether there was an inference (antipresupposition or implicature) that created a contradiction. With the additive, the sentence should make clear that the speaker (Teresa in the example given) believes that Sabrina failed, the answer to Q2 should thus clearly be “Yes”. However, it is not clear from the sentence with the additive that the speaker considers both Sabrina’s and Ida’s failing conditions for the test being hard, i.e. the sentence with “auch” is ambiguous between the two readings in (27). (27) If Ida failed too, the test must have been hard. a. ∀w ∈ {w’: w’ is compatible with the evidence available in the utterance situation in w@ } & Ida failed in w & Sabrina failed in w → the test was hard in w If both Ida and Sabrina failed, the test must have been hard. b. ∀w ∈ {w’: w’ is compatible with the evidence available in the utterance situation in w@ } & Ida failed in w → the test was hard in w If Ida failed, the test must have been hard. The reading in (27b) is considered to be less prominent but available. It said that only Ida’s failing is a necessary condition for the test being hard (but presupposes that Sabrina failed). The contexts were set-up in a way that principally allowed for both readings. No matter which one of the two was chosen, however, the acceptability of the sentence should not be affected by since they both do not lead to a contradiction. The more interesting question was which readings arose for the sentence without the trigger. If a reading was yielded which was contradictory to the previous discourse the difference in acceptability between the sentence with and without the trigger was assumed to be significant according to Obligatory Implicatures. Compared to Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 80 N. Bade Obligatory additives in the antecedent of conditionals that, the differences between acceptability of the sentence with and without the trigger should not reach significance if the sentence without the trigger was not considered being contradictory. The reading which yields a contradiction is one where the exhaustivity is inserted below “if” (IF > EXH). This reading requires the participants to answer that only Ida’s failing is a condition for the test being hard (Q1= If B). In addition, the sentence should imply that Teresa is unsure that Sabrina passed (Q2= No). One reading which is not contradictory to the previous sentence is one where the exhaustivity operator is inserted above “if” (EXH > IF). This reading is supposed to be reflected by participants saying that only Ida’s failing is a condition for the test being hard (Q1 = IF B), but in addition the speaker has no doubt that Sabrina failed too (Q2 = Yes). This reading is thus the same as the one in (27b) and available with and without “too”. The last reading does not involve any exhaustivity operator and is also not contradictory to the discourse; it is one where both Ida’s and Sabrina’s failing are considered conditions for the test being hard (Q1= If A and B) and the sentence is not perceived as a contradiction to the fact that Sabrina passed (Q2 = Yes). This reading is the one in (27a) and should hardly be available without the additive. The interpretations corresponding to the combination of answers given to Q1 and Q2 are summarized in figure 1 below. Figure 1: Interpretations corresponding to answers 3.3. Predictions Maximize Presupposition predicts sentences with the additive to overall be judged more acceptable than sentences without the additive in contexts which verify its presuppositions. This is because the sentence in (28a) in the context of (28) has the competitor in (28b). Not using this competitor should, through pragmatic reasoning, lead to hearer to calculate the “antipresupposition” in (28c), saying that the presupposition of (28b) is false. (28) Sabrina failed. a. If Ida failed the test was hard. b. If Ida failed too, the test was hard. c. ¬∃p ∈ C & p 6= Ida failed & p(w) =1 The inference in (28c) is contradictory to the fact that Sabrina failed. The sentence without the additive should thus be unacceptable in the context. Calculating this inference is supposed to be the default interpretation in the given context since the competition with “too” is made prominent by the overt alternative “Sabrina failed”. The prediction would thus be that sentences Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 81 N. Bade Obligatory additives in the antecedent of conditionals without the additive are most often interpreted as denying the truth of (28), which would result in a high percentage of “no” answers to Q2. If, however, no such inference (“antipresuppositions”) arises the sentence should be judged acceptable without the trigger. According to Obligatory Implicatures the sentence without the trigger should be less acceptable than the sentence with the trigger only if an exhaustification strategy is chosen which yields a contradiction. This is only the case if the exhaustivity operator is inserted below “if” (IF > EXH). The question under which circumstances exhaustification is mandatory versus optional is still open. However, some preferences for which exhaustivity implicatures arise in conditionals can be determined based on the research on scalar implicatures (Chierchia et al., 2012; Fox and Spector, to appear). Under the assumption that exhaustification below downward-entailing operators usually requires contextual pressure and pitch accent on the relevant alternative trigger, the exhaustification strategy which yields the contradiction (IF > EXH) should be the least likely interpretation. If one adopts the view that inserting EXH is the default if it leads to strengthening, the interpretation with EXH above “if” should be the most frequent one (EXH > IF). As a result, the insertion of the trigger in antecedents of conditional is considered not obligatory since the interpretation which triggers the insertion is a very marginal one (at least in the contexts used in the experiment). As Maximize Presupposition, Obligatory Implicatures predicts no decrease of acceptability for sentences without the trigger which do not yield a contradictory inference. The predictions of both theories are summarized in figure 2 below. Figure 2: Interpretations corresponding to answers 3.4. Analysis and Results One factor was manipulated for the study creating two conditions: the target items were conditionals which either were presented with or without the German additive “auch” in a context which satisfied its presupposition (+/- ADD). There were three dependent variables: the acceptability of the sentence on a Likert scale (1-5), and the answers to two comprehension questions. Six experimental items were created per condition, which made for 12 experimental items in total. 24 filler items were used. 24 German native speakers, students or former students of the university of Tübingen participated in the experiment, they received 5 Euros for their participation. Results were analyzed with linear mixed effect models using the lmer function in R (Bates, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 82 N. Bade Obligatory additives in the antecedent of conditionals 2005). The fixed factor was ADDITIVE, random factors were subject and items. The analysis revealed a significant effect of ADDITIVITY on acceptability. The insertion of the additive decreased acceptability of the conditional, see figure 3. Figure 3: Acceptability of sentences with and without additive Moreover, the additive had a marginally significant influence on which interpretation was chosen in response to Q1 (“What are the conditions for the event described by the consequent? IF A, IF B, IF A and B?) (p<.08): with “auch” more “both” (IF A and B) responses were chosen. “Auch” also had a significant influence on choice of interpretation for Q2 (Does the speaker believe the previously mentioned fact that A occurred? YES, NO, UNSURE) (p<.01), more “no” answers were given with the presence of the additive. Since the analysis revealed that pooling “yes” answers with “unsure” answers or pooling “no” answers with “unsure” answer did not affect the analysis, the interpretations “yes”/“uncertain” were pooled together as suggesting no contrast to previous discourse, whereas “no” responses were considered as suggesting a contrast/contradiction to previous discourse. Overall, using the additive increased percentage of interpretations without any exhaustivity operator (#EXH, no contrast + IF A and B response), it decreased percentage of interpretations with high EXH (EXH>IF, no contrast + If B response) and increased interpretations with low EXH (IF>EXH, contrast and IF B response) see figures 4 and 5. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 83 N. Bade Obligatory additives in the antecedent of conditionals Figure 4: Proportion of interpretations chosen with and without additive Figure 5: Proportions of interpretations chosen with and without additive The responses to Q1 and Q2 both have a significant influence on acceptability (Q1 p<.05, Q2 p<.01). Comparing different models using a chi-square test revealed that the best model for predicting acceptability included both the factor ADDITIVITY as well as responses to Q1 and Q2. A causal mediation analysis furthermore showed that both responses had an influence on acceptability which was not influenced by the presence of the additive. The interpretation without any exhaustivity operator (#EXH) is significantly more acceptable overall (M= 4,15) than the interpretation involving high or low exhaustivity operators (IF>EXH, M= 3,25; EXH>IF, M= 2,8). The interpretation with no EXH got even more acceptable with the presence of the additive, however the difference was not significant. The interpretations where there was either a low or high EXH got less acceptable with the presence of the additive, see proportions of interpretations in figures 6 and 7. This difference was only significant for the interpretation with EXH > IF. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 84 N. Bade Obligatory additives in the antecedent of conditionals Figure 6: Acceptability by interpretation chosen with and without additive Figure 7: Acceptability by interpretation chosen with and without additive 3.5. Discussion As predicted by Obligatory Implicatures the percentage of interpretations which were perceived as contradictory to the discourse was low (<5%). This is in line with the assumption that the inference arising when the trigger is not inserted is an exhaustivity implicature, which only occurs below DE-entailing operators under special circumstances. This is because under normal circumstances it yields to weakening of the statement. The inference resulting from the LF in (29) leads to the weaker statement in (29a) which is entailed by the stronger LF without EXH, see (29b). (29) If EXH Peter came, there were discussions. Alt = {Peter came, Mary came, Peter & Mary came} a. If Peter and not Mary came, there were discussions. b. If Peter came there were discussions. ⇒ If Peter and Mary came, there were discussions. ⇒ If Peter and not Mary came, there were discussions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 85 N. Bade Obligatory additives in the antecedent of conditionals Usually these circumstances where EXH is inserted below DE-operators involve pitch accent on the scalar item and are analyzed using stacked exhaustivity operators (Fox and Spector, to appear). Since the implicatures discussed in this paper are particularized conversational implicatures, not generalized ones, their occurrence might be even more restricted under DE operators. Since the sentences were only read by participants and there were no contextual cues for strong pitch accent, the low availability of these interpretations is expected from the viewpoint of a grammatical approach to implicatures. More research is needed on this issue to specify the circumstances under which local particularized conversational implicatures can occur at all. The results presented suggest that obligatorily inserting additives might be a good indicator. Theories working with Maximize Presupposition would have to explain why competition with the stronger version with the additive is not activated and the resulting anti-presupposition did not arise, since otherwise the sentence without “too” should have been perceived as contradictory to the previous discourse more often. Of course making Maximize Presupposition sensitive to discourse is not impossible. However, there seems to be a clear contrast to the anti-presupposition resulting from using the indefinite. This inference, sometimes referred to as an anti-uniqueness inference (Heim, 1991), seems to arise as a default and seems to be insensitive to DE-operators and the broader discourse, see the (obligatory) oddness of (30) (cf. Bade, 2016). (30) A man entered the bar. # If a man is thirsty, he will order a beer. The results thus speak in favor of an analyses which distinguishes these cases from one another and postulates two groups of presupposition triggers when it comes to obligatory insertion: one, including additives, is inserted to avoid an implicature. The other, involving definites, follows from Maximize Presupposition (Bade, 2016; Bade and Tiemann, 2016). The results further show that insertion of “auch” decreases acceptability of conditionals when its presupposition is fulfilled in the context. As predicted by Obligatory Implicatures the trigger is not obligatory per se but must be inserted only if an exhaustivity implicature must be blocked. The results suggest that the interpretation without any exhaustivity operators is the most acceptable one (M = 4,25). Its acceptability is not significantly affected by the presence of the trigger. However, it is significantly more available with the presence of the additive (35% versus 44%). That is, the additive must be considered optional for the acceptability of sentences with this interpretation (#EXH). For the rare cases in which the conditional was interpreted as contradicting the context, the additive did not affect the overall low acceptability either (M=3,15). What is puzzling is that the availability of these interpretations seemed to increase with the presence of the additive. One possible explanation is that the presence of an overt focus sensitive particle increased the pressure to put focus on the noun it associated with. This focus was then understood as contrastive to the previous discourse. However, that means that, to make the presupposition of “auch” true, participants must have accommodated another antecedent/true proposition in the discourse. More research is needed to understand why this option was available at all Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 86 N. Bade Obligatory additives in the antecedent of conditionals since additives are usually considered very hard to accommodate (Heim, 1992). Since the interpretation was rarely chosen and only by few participants individual differences might be at play here as well. The interpretation which was most often chosen (55% on average) and received the overall lowest acceptability is one which is in line with an analysis where an exhaustivity operator is present in the structure, but above the “if”-clause, see (31). (31) EXH If Peter came (too), there were discussions. ’Only if Peter came (too), there were discussions.’ a. ∀w ∈ {w’: w’ is compatible with the evidence available in the utterance situation in w@ } & Peter came in w → there were discussions in w This interpretation is available with and without the additive. However, its availability significantly decreased with the presence of “too” (62,3% versus 47,4%) and so did its acceptability (M=3 versus M=2,6). This interpretation must thus be considered the crucial one for explaining the overall decrease in acceptability with the presence of the additive. Whereas additional stipulations have to be made to explain this using Maximize Presupposition the results can straightforwardly be explained using Obligatory Implicatures. The relevant QUD (Question Under Discussion, Roberts (1996)) at play for this reading seems to be the one in (32), providing the set of alternatives in (32a). EXH above “if” excludes one alternative, see (32b). (32) If who came, there were discussions? a. {If Peter came,...; If Mary came...; If Peter and Mary came ... } b. ¬∀w ∈ {w’: w’ is compatible with the evidence available in the utterance situation in w@ } & Mary came in w → there were discussion in w What “too” marks in this case is not that the question in (32) has been previously answered but rather that the “local” question “Who came?” has already been answered (by the previously asserted “Mary came”). As was mentioned before, exhaustifying (31) with respect to the QUD in (32) will not be contradictory to the fact that Mary came. As a result, the additive is not considered obligatory. The fact that it is even perceived as disturbing in this case can be explained by assuming that making reference to an already answered QUD which is not relevant to the current QUD anymore is a dispreferred pragmatic move. The answer to the question whether additives are obligatory in antecedents of conditionals thus seems to depend on what interpretation is chosen for the conditional. If the context allows for an interpretation without any exhaustivity operators, the additive is optional. It does not change acceptability but can make this interpretation clearer. With an interpretation where an exhaustivity operator is inserted high, above the “if”-clause, the insertion of the additive is perceived as the dispreferred option. The results further supports Obligatory Implicatures and the view that additive particles can function as a window into local exhaustivity implicatures. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 87 N. Bade Obligatory additives in the antecedent of conditionals References Bade, N. (2014). Obligatory implicatures and the presupposition of “too”. In U. Etxeberria, A. Falaus, A. Irurtzun, and B. Leferman (Eds.), Proceedings of Sinn und Bedeutung 18, pp. 42–59. Bade, N. (2016). Obligatory Presupposition Triggers in Discourse - Empirical Foundations of the Theories Maximize Presupposition and Obligatory Implicatures. Ph. D. thesis, University of Tübingen. Bade, N. and S. Tiemann (2016). Obligatory triggers under negation. In N. Bade, A. Schoeller, and P. Berezovskaya (Eds.), Proceedings of Sinn und Bedeutung 20. Bates, D. M. (2005). Fitting linear mixed models in R. R News 5, 27–30. Chemla, E. (2008). An epistemic step for antipresuppositions. Journal of Semantics 25(2), 141–173. Chierchia, G., D. Fox, and B. Spector (2012). Scalar implicature as a grammatical phenomenon. In K. von Heusinger, C. Maienborn, and P. Portner (Eds.), Semantics: An International Handbook of Natural Language Meaning, Volume 3, pp. 2297–2331. Berlin: Mouton de Gruyter. Fox, D. (2007). Free choice and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and Implicature in Compositional Semantics, pp. 71–120. London: Palgrave Macmillan. Fox, D. and B. Spector (to appear). Economy and embedded exhaustification. Natural Language Semantics. Heim, I. (1991). Artikel und Definitheit. In A. von Stechow and D. Wunderlich (Eds.), Semantics: An International Handbook of Contemporary Research, pp. 487–535. Berlin: De Gruyter. Heim, I. (1992). Presupposition projection and the semantics of attitude verbs. Journal of Semantics 9(3), 183–221. Horn, L. R. (1984). Towards a taxonomy of pragmatic inference: Q-based and R-based implicature. In D. Schiffrin (Ed.), Meaning, Form, and Use of Context: Linguistic Applications, pp. 11–42. Washington: Georgetown University Press. Kratzer, A. (1991). Modality. In A. von Stechow and D. Wunderlich (Eds.), Semantics: An International Handbook of Contemporary Research, pp. 639–650. Berlin: De Gruyter. Percus, O. (2006). Antipresuppositions. In U. Ueyama (Ed.), Theoretical and Empirical Studies of Reference and Anaphora: Toward the Establishment of Generative Grammar as Empirical Science. Japan Society for the Promotion of Science. Roberts, C. (1996). Information structure in discourse: Towards an integrated formal theory of pragmatics. In H.-J. Yoon and A. Kathol (Eds.), OSU Working Papers in Linguistics: Papers in Semantics, Volume 49, pp. 91–136. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy 27(3), 367–391. Sauerland, U. (2008). Implicated presuppositions. In A. Steube (Ed.), The Discourse Potential of Underspecified Structures, pp. 581–600. Berlin: Mouton de Gruyter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 88 Two indefinite pronouns in Catalan Sign Language (LSC)1 Gemma BARBERÀ — Universitat Pompeu Fabra Patricia CABREDO HOFHERR — UMR 7023, CNRS / Paris 8 Abstract. This paper analyses two pronouns in Catalan Sign Language (LSC) that refer to unidentified human referents: WHOˆSOME up and ONE up . We first show that in contexts that discriminate between indefinite pronouns and existential readings of human impersonal pronouns, both pronouns pattern with indefinite pronouns. We then examine the semantic properties of the two pronouns. WHOˆSOME up and ONE up contrast with respect to their number, compatibility with collective predicates, scope with respect to event iteration and domain restriction requirements. In terms of specificity, both pronouns are epistemically non-specific, but ONE up is interpreted as scopally and partitively specific while WHOˆSOME up is neutral with respect to scopal and partitive specificity. Keywords: Catalan Sign Language (LSC), semantics, indefinite pronouns, specificity distinctions 1. Introduction This paper examines two expressions that refer to unidentified human referents in Catalan Sign Language (LSC, llengua de signes catalana): the pronouns WHOˆSOME up and ONE up .2 (1) ONE up HOUSE ENTER STEAL. ‘Someone broke into the house.’ (2) WHOˆSOME up GO INDIA VACCINATE MUST. ‘When one goes to India one must get vaccinated/ When someone goes to India he must get vaccinated.’ The goals of this paper are two-fold. First, we will show that these expressions correspond to indefinite pronouns comparable to (3), rather than existential uses of impersonal pronouns as exemplified by German man or French on in (4). 1 The research reported in this paper is part of the Franco-German ANR-DFG project Towards a typology of human impersonal pronouns (ANR-11-FRAL-0011, 2012–15). The work of G. Barberà was partly supported by the project GramRefLSC, Ministerio de Economı́a y Competitividad, FFI2015-68594-P. For their useful comments and interesting discussions on previous versions of this work, we would like to thank the audiences at the Workshop on the Semantic Contribution of Det and Num (UAB, May 2016), Formal and Experimental Advances in Sign Language Theory (FEAST) (Venice, September 2016), Sinn und Bedeutung 21 (Edinburgh, September 2016), and New Ideas in Semantics and Modelling (Paris, September 2016). We are grateful to Delfina Aliaga and Santiago Frigola for the eliciation sessions and for the discussions on LSC. Thank you to Rob Truswell and the editors for their careful comments and suggestions on this paper. All remaining mistakes are our responsibility. 2 This article follows the usual glossing conventions in the sign language literature. Manual signs are represented by the capitalized word corresponding to the translation of the sign. The abbreviations used in the glosses are the following (# is a placeholder for the loci in signing space corresponding to 1st, 2nd and 3rd person referents): IX# (index pointing sign); #-VERB-# (verb agreeing with subject and object). Sub-indices mark localizations in signing space: lo (low), up (up); lower indexed letters (a, b) mark lateral loci and coreference relations. Reduplication of signs is indicated by +++. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 89 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) (3) Someone stole my bike. (4) On a volé mon vélo. (Fr) Man hat mein Fahrrad gestohlen. (Ge) ON / MAN has (stolen) my bike (stolen) ‘They stole my bike.’ Secondly, we examine the profile of the two pronouns regarding epistemic, scopal and partitive specificity (see Farkas, 2002; von Heusinger, 2002). We will show that both pronouns are epistemically non-specific. WHOˆSOME up is neutral with respect to scopal and partitive specificity, while ONE up is interpreted as scopally and partitively specific. We proceed as follows. Section 2 provides some background on the referential use of space in sign languages in general and in LSC more specifically. In Section 3 we discuss the morphological composition of WHOˆSOME up and ONE up . In Section 4 we examine the two pronouns in contexts that are characteristic for human impersonal pronouns and we show that both expressions pattern with indefinite pronouns, not with existential readings of impersonal pronouns. In Section 5 we present an array of semantic contrasts between the two pronouns. Section 6 concludes. 2. Background: The use of space in sign languages In sign languages, space is used for grammatical purposes (see Perniss, 2012, for a detailed overview). In Western sign languages, signing space is considered to be constrained to the space in front of the signer’s torso. The signing space can be divided into the horizontal plane and the frontal plane. The horizontal plane is perpendicular to the body of the signer and is the default plane where the majority of signs are localized (Figure 1). The frontal plane runs parallel to the body of the signer from the waist up (Figure 2). Figure 1: Sign localized on the horizontal plane Figure 2: Sign localized high on the frontal plane Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 90 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) The figures above illustrate signs associated with a lateral area in the horizontal plane (Figure 1) and in the high part of the frontal plane (Figure 2). The spatial area associated with a Noun Phrase (NP) in sign language is called R- LOCUS (Klima and Bellugi, 1979). Canonically, NPs are associated with a locus on the horizontal plane of signing space, for example by a pointing index sign glossed IX3 (as in Figure 3) or by signing the lexical sign in the area of the locus (as in Figure 4 below). Figure 3: Sign IX3 a pointing to R-locus a In a sentence like (5) below, the two arguments are associated with two distinctive R-loci, indicated in the glosses by the subscripts a and b and shown in the pictures in Figure 4. The R-loci play a role for agreement and for anaphoric reference. As illustrated in Figure 5, the agreeing verb GIVE moves from the R-locus of the subject MARTÍ to the R-locus of the object JOANA. As shown by the continuation (6), R-loci may be used in coreferential contexts to refer to a previously introduced argument, for example by using a pronominal index sign IX3 a as in Figure 3. (5) MARTÍa IX3a JOANAb IX3b BOOK 3a-GIVE-3b. ‘Martı́ gave Joana a book.’ Figure 4: Sign MARTÍ at R-locus a Sign JOANA at R-locus b Figure 5: Verb GIVE articulated from R-locus a to R-locus b Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 91 G. Barberà & P. Cabredo Hofherr (6) Two indefinite pronouns in Catalan Sign Language (LSC) IX3a BOOK INTEREST. ‘He (Martı́) found the book interesting.’ In example (5) the R-loci for the NPs are on the horizontal plane in front of the torso, as illustrated by Figure 4. It has been shown that the height of localization in the frontal plane is also relevant for the expression of reference. In American Sign Language (ASL) high Rloci trigger an indefinite interpretation (Bahan, 1996; MacLaughlin, 1997). In LSC, the frontal plane is used to express specificity distinctions (Barberà, 2012): NPs localized at a low Rlocus are interpreted as epistemically specific (they are identifiable by the signer and belong to a restricted set), whereas NPs localized at a high R-locus are interpreted as epistemically non-specific (they are unidentifiable by the signer and do not belong to a restricted set). The following examples provide a minimal pair for the interpretation of high vs. low R-locus for an NP in LSC.3 In (7a) the determiner SOME is localized at a low R-locus (indicated in the glosses with lo, Figure 6) and corresponds to a reading where the signer is talking about a specific group of students, which he can identify. In (7b), in contrast, the determiner SOME is localized at a high R-locus (indicated in the glosses with up, Figure 7) and a non-specific reading arises: the signer cannot identify the set of students. (7) a. b. STUDENT SOME lo DEMONSTRATION GO. ‘Some students (that I can identify) went to the demonstration.’ STUDENT SOME up DEMONSTRATION GO. ‘Some students (that I cannot identify) went to the demonstration.’ Figure 6: Sign SOME at a low R-locus (LSC) Figure 7: Sign SOME at a high R-locus The two pronouns analysed in this paper are articulated in a high R-locus and trigger an epistemically non-specific interpretation, resembling the behaviour of NPs in this respect. However, in some contexts, pronominal elements in LSC articulated in high R-loci may have a scopally and partitively specific interpretation, unlike lexical NPs (see Section 5 below). 3 In sign languages, signing space may be also used topographically. In topographical uses of space the spatial location of the sign provides information about the actual locations of entities, for example when referring to a book located on a high shelf (see Perniss, 2012, for discussion of different uses of signing space). In this article we leave the topographical use aside. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 92 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) 3. Morphological properties of the two pronouns The pronoun WHOˆSOME up is the concatenation of the sign for the interrogative pronoun WHO with the sign for the determiner SOME. The manual component of both uses of WHO is an arc-shaped movement of the wrist with the thumb pointing upwards, localized on the chin of the signer and with final contact. The interrogative use of WHO (8) and the WHO forming part of the indefinite pronoun (9) differ in their non-manual components. While the interrogative particle co-occurs with furrowed eyebrows (Figure 8), the indefinite pronoun co-occurs with particular non-manuals that include sucking the cheeks in and pulling the mouth ends down, sometimes combined with a shrug (Figure 9). (8) COME WHO? ‘Who came?’ (9) IX3 WHOˆSOME up SEE. ‘She saw someone.’ Figure 8: The sign for the interrogative WHO Figure 9: Sign for the pronoun WHOˆSOME up The indefinite pronoun ONE up is signed in a high locus (see Figure 10) with the handshape of the numeral ONE (see Figure 11). The non-manuals for the indefinite pronoun ONE up resemble those for the indefinite pronoun WHOˆSOME up (Figure 9): they also consist in sucking the cheeks in and pulling the mouth ends down (Figure 10). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 93 G. Barberà & P. Cabredo Hofherr (10) ONE up HOUSE ENTER STEAL. ‘Someone broke into the house.’ (= (1)) (11) ONE GIRL HOUSE ENTER. ‘A/one girl broke into the house.’ Figure 10: The pronoun ONE up at a high locus, ex. (10) Two indefinite pronouns in Catalan Sign Language (LSC) Figure 11: The numeral ONE at a low locus, ex. (11) Both pronouns are articulated in a high location of signing space (as indicated by the subscript up in the glosses), rather than in the default lower area. Both receive an epistemically nonspecific interpretation, as is generally the case for elements associated with R-loci in the higher plane in LSC (see Barberà, 2012, and discussion of the example (7) above). 4. Indefinite or Impersonal Pronouns? In LSC non-specific human pronouns are a common strategy to encode an unspecified human referent (Barberà and Quer, 2013). Reference to an unspecified human referent is also part of the semantic domain of dedicated human impersonal pronouns that allow existential readings such as German man or French on. We have shown above that morphologically WHOˆSOME up looks like a wh-indefinite. The pronoun ONE up , however, could potentially be an impersonal pronoun derived from the numeral one, as English one or Spanish uno. To establish that WHOˆSOME up and ONE up are indeed indefinite pronouns, we examined their behaviour in contexts that distinguish indefinites from existential uses of impersonal pronouns cross-linguistically (see Cabredo Hofherr, 2008, and references cited there). Indefinite pronouns (i) are incompatible with a generalizing reading in simplex sentences, (ii) are incompatible with corporate readings, (iii) trigger disjoint reference when the pronoun is repeated in anaphoric chains, and (iv) have narrow and wide scope interpretations with respect to adverbs like twice. Impersonal pronouns, in contrast, (i) are compatible with a generalizing reading, (ii) are compatible with corporate readings, (iii) typically allow joint and disjoint reference when the pronoun is repeated in anaphoric chains, and (iv) have a narrowest scope interpretation in their existential uses. We consider each of the four contexts in turn. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 94 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) 4.1. Generalizing vs. episodic readings Episodic contexts are contexts in which an individual or an event is anchored to a particular spatio-temporal context (Yesterday John had breakfast at 10am). In contrast, in generalizing contexts either the individuals or the events are not anchored to a spatio-temporal context and express either recurring properties of an individual (John has breakfast at 7am) or general properties not tied to particular individuals (Pandas are big/eat bamboo). The French pronoun on has generalizing and episodic readings. The generalizing reading of on is exemplified in (12a). This reading is comparable to the English people or to non-anaphoric they, as in the translation of (12a). As (12b) shows, indefinite pronouns like someone do not allow generalizing readings over people in general. (12) a. b. Au Mexique, on mange des grillons. in Mexico ON eats indef.pl grasshoppers ‘In Mexico, they / people eat grasshoppers.’ (generalizing over people associated with Mexico) In Mexico, someone eats/ate grasshoppers. (not generalizing over people associated with Mexico, 6= (12a)) (Fr) The two LSC pronouns typically appear in episodic contexts (13). When inserted in generalizing contexts, the pronouns are interpreted on a par with (12b): (14) is understood as a habitual reading for an unspecified individual, but not as a generalization over individuals in Lleida in general. (13) a. YESTERDAY ONE up BIKE STEAL-3 up . b. YESTERDAY WHOˆSOME up BIKE STEAL-3 up . ‘Yesterday someone stole a/the bike.’ (14) a. LLEIDA ONE up SNAIL EAT. b. LLEIDA WHOˆSOME up SNAIL EAT. ‘In Lleida, there is someone who eats snails.’ (not generalizing over people associated with Lleida) In locative universal contexts as in (15) the null subject triggers a generic reading in LSC, meaning something paraphrasable with people associated with location X in general. When WHOˆSOME up is used in this context the episodic reading arises (16). The insertion of ONE up in the context triggers either an episodic reading (17a) or a habitual reading of the predicate, with an existential interpretation of the individual (17b). (15) CHINA AREA EAT CAT. (null subject) ‘In China they eat cats.’ (16) CHINA AREA WHOˆSOME up EAT CAT. ‘In China someone ate a cat/some cats.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 95 G. Barberà & P. Cabredo Hofherr (17) Two indefinite pronouns in Catalan Sign Language (LSC) CHINA AREA ONE up EAT CAT. a. ‘In China someone ate a cat/cats.’ b. ‘In China, there is someone who eats cats.’ 4.2. Corporate readings: predicates with designated subjects Corporate readings arise with predicates that have a designated subject such as deliver the mail, raise taxes (Kärde, 1943; Pesetsky, 1995). In French, the corporate reading is compatible with an existential reading of the impersonal human pronoun on. The impersonal on/they in (18) is interpreted as referring to the people charged with raising taxes. Indefinite pronouns like quelqu’un / someone, in contrast, do not receive an interpretation corresponding to the group prototypically associated with the predicate in (19). (18) On a augmenté les impôts. ‘ON raised the taxes.’ >‘They raised taxes.’ (corporate reading: the people in charge of raising taxes) (19) Quelqu’un a augmenté les impôts. ‘Someone raised the taxes.’ (no corporate reading: agent not part of the designated subject of the predicate). In LSC, neither WHOˆSOME up nor ONE up trigger the corporate interpretation in the parallel examples. Like (19), the examples in (20) are interpreted as saying that there was an unknown individual who raised the taxes but the examples do not imply that this individual belongs to a designated group of people in charge of raising taxes. (20) a. WHOˆSOME up RAISE TAXES. b. ONE up RAISE TAXES. ‘Someone raised the taxes.’ (∼ (19)) 4.3. Scope with respect to adverbials Existential uses of impersonal pronouns, like French on and German man, have obligatory narrow scope with respect to frequency adverbs like twice or always (Zifonun, 2000 for German; Cabredo Hofherr, 2008 for French). (21) On a volé mon vélo deux fois. ON has stolen my bike two times ‘ON stole my bike twice.’ (2 times >someone) (Fr) Neither of the two LSC pronouns takes obligatory narrow scope. WHOˆSOME up allows wide and narrow scope readings with respect to the adverb, with wide scope for the pronoun preferred in examples like (22a). ONE up differs from WHOˆSOME up with respect to scope: the use of ONE up only allows a wide scope reading (23). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 96 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) (22) WHOˆSOME up IX1 BIKE 1-STEAL-3 up ++ TWO TIMES. ‘Someone stole my bike two times. / Two times, someone stole my bike.’ a. someone > 2 times (preferred) b. 2 times > someone (23) ONE up BICYCLE 1-STEAL-3 up ++ TWO TIMES. ‘Someone stole my bicycle two times.’ (someone > 2 times) However, the use of signing space introduces a complicating factor: The localization of the R-loci in signing space can disambiguate in favour of a reading with co-varying subjects for the different events. In LSC the establishment of two different R-loci for the subject explicitly marks distribution over the subject, resulting in a reading where the indefinite subject co-varies with the stealing event (narrow scope reading). In example (22), the iterated movement of the verb STEAL is twice to an unspecified R-locus, marked ++ in the gloss. In example (24) below, in contrast, the agreeing verb STEAL is inflected with two distinct lateral R-loci (R-locus a and R-locus b) and this yields an interpretation according to which on two occasions my bike was stolen, by two different individuals. (24) WHOˆSOME up IX1 POSS BIKE 1-STEAL-3 up.a 1-STEAL-3 up.b TWO TIMES. ‘They stole my bike two times.’ (2 times > someone) The availability of this explicitly distributing inflection for the verb may contribute to the preference for example (22) to be interpreted as not distributed. We further tested the effect of adverb placement on interpretation. In order to avoid explicit distribution over different R-loci, we used the adverb ALWAYS in these examples. With the pronoun ONE up , the interpretation of the subject is a constant individual (∼ specific indefinite) independently of the position of the adverb ALWAYS (see (25a)/(26a)/(27a)). For WHOˆSOME up the position of the adverb ALWAYS makes a difference to interpretation. With an initial or final position of ALWAYS, the pronoun WHOˆSOME up is interpreted as (potentially) co-varying with the iterated events (25b)/(26b). A reading as a constant individual is forced when ALWAYS appears between WHOˆSOME up and the verb as in (27b). We analyse the contrast with respect to WHOˆSOME up as indicating that WHOˆSOME up is interpreted inside the VP by default and only takes wide scope if it is overtly separated from the VP by the adverb ALWAYS. (25) a. b. IX NEIGHBOURHOOD ONE up BIKE STEAL-3 up ALWAYS. ‘In this neighbourhood there is someone who always steals bikes.’ (constant agent of the stealing events) IX NEIGHBOURHOOD WHOˆSOME up BIKE STEAL-3 up ALWAYS. ‘In this neighbourhood they always steal bikes.’ (agent of stealing events need not be identical, can co-vary with the events) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 97 G. Barberà & P. Cabredo Hofherr (26) a. b. (27) a. b. Two indefinite pronouns in Catalan Sign Language (LSC) ALWAYS IX NEIGHBOURHOOD ONE up BIKE STEAL-3 up . ‘In this neighbourhood there is someone who always steals bikes.’ (constant agent of the stealing events) ALWAYS IX NEIGHBOURHOOD WHOˆSOME up BIKE STEAL-3 up . ‘In this neighbourhood they always steal bikes.’ (agent of stealing events need not be identical, can co-vary with the events) IX NEIGHBOURHOOD ONE up ALWAYS BIKE STEAL-3 up . IX NEIGHBOURHOOD WHOˆSOME up ALWAYS BIKE STEAL-3 up . ‘In this neighbourhood there is someone who always steals bikes.’ The data show that neither WHOˆSOME up nor ONE up has the scope behaviour with respect to adverbs observed for existential readings of impersonal pronouns. We will come back to this contrast in scope behaviour between the two pronouns in Section 5 below. 4.4. Anaphora In coreferential chains, impersonal pronouns (such as English man, French on, German man) allow co-referent interpretation of repeated pronouns as in (28), while indefinite pronouns do not (29). (28) a. b. When one i goes to hospital, one i / he *i/k always fears the worst. One i goes to hospital, and one i / he *i/k worries. (29) a. b. When someone i goes to hospital, someone *i/j / he i/*k always fears the worst. Someone i goes to hospital, and someone *i/k / he i/k worries. With respect to this diagnostic, the two LSC pronouns again pattern with indefinite pronouns: the repetition of ONE up and WHOˆSOME up triggers disjoint interpretation in (30)/(31). In LSC the equivalent of when-clauses is marked by the sign MOMENT as in example (30). Without MOMENT, the example corresponds to a paratactic coordination of two main clauses. (30) ONE up MOMENT HOSPITAL GO, ONE up ALWAYS THINK RESULT WORST. ‘When one k is admitted to the hospital, one j always fears the worst results.’ (= different people in hospital and worrying) (31) WHOˆSOME up HOSPITAL GO, WHOˆSOME up ALWAYS THINK RESULT WORST. ‘Someone i is admitted to the hospital; and someone k always fears the worst results.’ (= different people in hospital and worrying) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 98 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) 4.5. Summary The diagnostics examined here show that neither WHOˆSOME up nor ONE up behave like episodic readings of impersonal human pronouns available for French on or German man. Furthermore, there is evidence that WHOˆSOME up is not a relative pronoun introducing free relatives either. In LSC, relative clauses are marked with squinted eyes and, optionally, with the particle MATEIX (Mosella, 2012). The examples with WHOˆSOME up do not show either of these markings. The comparison of WHOˆSOME up with free relatives with a wh-pronoun as in (33) shows that the free relative is articulated with brow-raise with scope over the relative clause. (32) WHOˆSOME up EXAM DONE LEAVE CAN. ‘When someone finishes the exam he can leave. (33) [EXAM DONE WHO] brow raise LEAVE CAN. ‘Whoever has finished the exam may leave.’ We therefore conclude that both WHOˆSOME up and ONE up are indefinite pronouns in LSC that pattern with pronouns like someone in English. As we have seen in Section 4.3 above, however, the two indefinite pronouns differ in their interpretation with respect to frequency adverbs. In the next section we examine the semantic contrasts between the two pronouns in more detail. 5. Contrasts between WHOˆSOME up and ONE up In what follows, we show that WHOˆSOME up and ONE up differ with respect to a number of semantic properties: number specification, compatibility with collective predicates, co-variation of the referent with event pluralities and a requirement for domain restriction for the referent. 5.1. Plural vs. singular interpretation WHOˆSOME up and ONE up differ with respect to their number specification. When WHOˆSOME up is used, the subject need not be singular (34a). With ONE up the subject has to be singular (34b). (34) a. b. CHINA AREA WHOˆSOME up EAT CAT. In China someone/some people ate a cat/cats.’ (can be more than one person) CHINA AREA ONE up EAT CAT. ‘In China there is someone who eats cats.’ (one person only) The contrast between the pronouns with respect to number interpretation is further confirmed in contexts in which the plurality of the unknown agent is explicitly denied. In the context we Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 99 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) tested, an office has been broken into and after the event, the footprints belonging to a single person were found outside the office. The singular interpretation of ONE up coincides with the information about the number of the unknown agent from the context, and our informant added a confirmation headnod corresponding to an expression like as expected to the example in (35). In contrast, as WHOˆSOME up is interpreted as ‘more than one’ by default, a context in which the footprints belong to the same person cancels the implicature that there is more than one agent of the event, leading to an expression of surprise by the informant (How weird!?) in (36). (35) YESTERDAY HERE OFFICE ONE up c-STEAL-3 up . AFTERWARDS CHECK FOOTPRINT UNIQUE SINGLE SAME IX3 up headnod ‘Yesterday someone broke into the office. We checked the footprints afterwards and they belong to the same person, as expected.’ (36) YESTERDAY HERE OFFICE WHOˆSOME up c-STEAL-3 up . AFTERWARDS CHECK FOOTPRINT UNIQUE SINGLE SAME IX3 up . WEIRD. ‘Yesterday some people broke into the office. We checked the footprints afterwards and they belong to the same person. How weird!?’ 5.2. Collective and distributive readings The analysis proposed of between WHOˆSOME up as preferentially plural and ONE up as singular is further confirmed by the fact that WHOˆSOME up is compatible with collective predicates (37), while ONE up is not (38). (37) WAR CITY WHOˆSOME up SURROUND. ‘They surrounded the city during the war.’ (38) *WAR CITY ONE up SURROUND. ONE up has a plural distributive form, consisting of a reduplication of the pronoun, which is grammatical with collective and distributive predicates. When this reduplicated form of the pronoun is used, reduplication of the verb is also obligatory; otherwise the sentence is ungrammatical. The reduplicated verb further triggers a distributive reading of the object. (39) WAR CITY ONE up +++ SURROUND+++. ‘They each surrounded a different city during the war.’ (40) NEIGHBOURHOOD ONE up +++ BIKE STEAL-3 up +++. ‘In this neighbourhood, there is a number of (unidentified) people that each stole a bike/bikes.’ However, an exception is found with body-anchored verbs (like EAT), that do not admit reduplication. Because of this phonological restriction, the verb is not reduplicated when combined Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 100 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) with the plural distributive form of ONE up but the sentence is still grammatical and we get the distributive reading. (41) CAKE ONE up +++ EAT. ‘Some people had a piece of cake each.’ 5.3. Co-variation with the event As we have already seen in Section 4.3 above, the two pronouns differ in their scoping properties with respect to adverbs. WHOˆSOME up triggers undetermined reference of subject and allows subjects to co-vary with the events. In contrast, ONE up does not co-vary with respect to the events, yielding a scopally specific interpretation. The referent of WHOˆSOME up can co-vary with quantification over the event (here with the adverb ALWAYS): a scenario with a plurality of stealing events with different subjects for each event is possible. In contrast, with the pronoun ONE up there is not covariation of the subject with respect to the events. Therefore the iterated thefts are perpetrated by the same unknown person. (42) a. BUILDING IX POSS OFFICE DANGER. ALWAYS WHOˆSOME up STEAL-3up MONEY ‘The building of my office is very dangerous. They always steal money.’ b. BUILDING IX DANGER. IX1 POSS OFFICE ALWAYS ONE up STEAL-3 up MONEY ‘The building (of my office) is very dangerous. There is someone who always steals money in/from my office.’ 5.4. Domain restriction A restricted domain is compatible with both pronouns. However, while ONE up strongly favours a reading in which there is a salient set that the referent belongs to, such a set is not required with WHOˆSOME up . In the examples (43a) and (44a) with WHOˆSOME up , the unidentified human referent can but need not belong to a contextually salient set. With ONE up , however, the referent is interpreted as belonging to a particular set, as shown in examples (43b) and (44b). (43) a. BUILDING IX FIRE FIREMEN ARRIVED. WHOˆSOME up CL:GO-UP-ROOF ‘The building was on fire and the firemen arrived. One (fireman or normal person) went up to the roof.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 101 G. Barberà & P. Cabredo Hofherr (44) Two indefinite pronouns in Catalan Sign Language (LSC) b. BUILDING IX FIRE FIREMEN ARRIVED. ONE up CL:GO-UP-ROOF ‘The building was on fire and the firemen arrived. One (of the firemen) went up to the roof.’ a. LIBRARY WOMAN PERSON RETIRE. WHOˆSOME up SUBSTITUTE ‘The librarian is getting retired. Someone (from a non-restricted set) will substitute her.’ LIBRARY WOMAN PERSON RETIRE. ONE up SUBSTITUTE ‘The librarian is getting retired. One (of her team) will substitute her.’ b. Further evidence that ONE up explicitly favours a reading with a salient set is provided by continuations with the sign DE (meaning ‘belong’). In this context a continuation with a typical group inferred is more felicitous (45a) than a continuation with unexpected information (45b). (45) ONE up DEAN INFORM ‘Someone informed the dean.’ a. PERSON up DE FACULTY. ‘He is someone from the faculty.’ b. # PERSON up DE GYMNASIUM. ‘He is someone from the gym.’ 5.5. Interpretation of object and telicity We found some evidence that the two pronouns seemed to correlate with a difference in telicity. With a telic predicate like EAT, WHOˆSOME up triggers a specific interpretation of the object, an episodic context and the event is interpreted as punctual (perfective) (46a). With ONE up as a subject, the interpretation of the object was non-specific, with either habitual interpretation (imperfective) or an episodic interpretation that did not have a salient individual as an object (46b). (46) a. b. WHOˆSOME up CAT EAT. ‘Someone ate a/the cat.’ Informants added: IX SEE DISAPPEAR ‘I see it disappeared.’ (the (relevant) cat is no longer there) ONE up CAT EAT. ‘There is one who eats cats.’ Informants intuition: a/the salient cat has not disappeared In future work we will explore the hypothesis that the effect of the pronoun on the object is indirect. According to our working hypothesis, WHOˆSOME up is not interpreted as a topic, and the interpretation of the object as specific is triggered by the fact that it is interpreted as the most plausible topic. ONE up , on the other hand, corresponds to a constant, if unindentified, individual and as such can be interpreted as a topic itself, favouring an interpretation in which the object is semantically incorporated comparable to eat cats. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 102 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) 5.6. Summary Using the specificity distinctions discussed by Farkas (2002); von Heusinger (2002), the properties discussed in this section can be summarized as follows. Both WHOˆSOME up and ONE up are epistemically non-specific: the referent of the pronoun is unknown to the signer and to the addressee. The two pronouns differ with respect to their scopal properties: WHOˆSOME up is preferentially interpreted as having a narrow scope reading and co-varies with iterated events, while ONE up is interpreted as having wide scope with respect to event iteration. ONE up is scopally specific while WHOˆSOME up allows both wide and narrow scope interpretations. Finally, the two pronouns differ with respect to partitivity. WHOˆSOME up can, but need not, be part of a salient group while ONE up is interpreted as belonging to a contextually salient group: ONE up is partitively specific while WHOˆSOME up is compatible with partitive or non-partitive interpretations. The following table summarizes the contrasts between the two indefinite pronouns: Types of specificity Epistemic unknown to signer Scopal wide scope with TWICE wide scope (sentence final/initial ALWAYS) wide scope (pre-verbal ALWAYS) scope over event plurality (co-variation with events) Partitive interpreted as part of a salient group Other properties Cardinality Telicity punctual event vs. habitual Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde WHOˆSOME up ONE up + (16) + (17) +/– (25a) & (26a) + (27a) + (42a) + + (25b) & (26b) + (27b) (42b) – + (45) 1 or more (34a) + (46a) punctual singular (34b) (46b) habitual 103 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) 6. Conclusions We have shown that the expressions WHOˆSOME up and ONE up pattern with indefinite pronouns like someone, not with existential readings of impersonal human pronouns like on in French. Both pronouns are epistemically non-specific since the referent of the pronoun has to be unknown to the speaker. Future work has to establish how WHOˆSOME up and ONE up fit into the typology of epistemic indefinites discussed in the recent literature (Aloni and Port, 2011; Alonso-Ovalle and Menéndez-Benito, 2013). The data presented further show that the two pronouns differ with respect to a range of semantic properties. First, while WHOˆSOME up is number neutral, ONE up is interpreted as referring to a singular referent. For reference to a multiplicity, the sign ONE up needs to be reduplicated yielding a form ONE up +++ that forces a distributive reading. Secondly, WHOˆSOME up is preferentially interpreted has having a narrow scope reading with respect to unbounded event iteration, i.e. a reading in which the agent co-varies with the event, while ONE up is interpreted as having wide scope. We found that WHOˆSOME up only gets a wide scope reading if it is overtly separated from the VP by the adverb ALWAYS. With respect to a bounded adverb like TWICE, WHOˆSOME up takes wide scope. Finally, WHOˆSOME up need not have a partitive interpretation, while ONE up has a partitive interpretation as belonging to a salient set. These observations suggest that ONE up is a strong indefinite, whereas WHOˆSOME up is a weak indefinite. In future work we will explore the hypothesis that WHOˆSOME up and ONE up contrast with respect to their information structure status. Unless it is moved out of the VP, WHOˆSOME up does not function as a topic making it similar to the implicit agent of passives: a sentence containing it will be interpreted as thetic unless an alternative topic is available. We will explore the hypothesis that ONE up on the other hand is scopally specific and interpreted as part of a group that is contextually salient. If this hypothesis is correct, the contrast between the two pronouns would resemble the contrast in English between the following two examples: (47) a. b. They repaired the lift. There is someone who repaired the lift. Finally, the data discussed here show that in LSC the role of high loci in signing space is different for pronouns and for lexical NPs, suggesting that the structured use of signing space can be modulated depending on the grammatical category of the NP. Lexical NPs associated with a high locus are associated with an epistemically and partitively non-specific interpretation. In contrast, the pronoun ONE up is partitively specific despite the fact that it is associated with a high locus. References Aloni, M. and A. Port (2011). Epistemic indefinites cross-linguistically. In Proceedings of NELS 41. Alonso-Ovalle, L. and P. Menéndez-Benito (2013). Epistemic indefinites: Are we ignorant Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 104 G. Barberà & P. Cabredo Hofherr Two indefinite pronouns in Catalan Sign Language (LSC) about ignorance? In Proceedings of the 19th Amsterdam Colloquium. Bahan, B. (1996). Non-manual Realization of Agreement in American Sign Language. Ph. D. thesis, Boston University. Barberà, G. (2012). The Meaning of Space in Catalan Sign Language (LSC). Reference, Specificity and Structure in Signed Discourse. Ph. D. thesis, Universitat Pompeu Fabra. Barberà, G. and J. Quer (2013). Impersonal reference in Catalan Sign Language (LSC). In L. Meurant, A. Sinte, M. van Herreweghe, and M. Vermeerbergen (Eds.), Sign Language Research Uses and Practices: Crossing Views on Theoretical and Applied Sign Language Linguistics, pp. 237–258. Berlin–Boston: De Gruyter Mouton and Ishara Press. Cabredo Hofherr, P. (2008). Les pronoms impersonnels humains — syntaxe et interprétation. Modèles linguistiques XXIX-1(57), 35–56. Farkas, D. F. (2002). Specificity distinctions. Journal of Semantics 19, 1–31. Kärde, S. (1943). Quelques manières d’exprimer l’idée d’un sujet indéterminé ou général en espagnol. Uppsala: Appelbergs Boktryckeriaktiebolag. Klima, E. and U. Bellugi (1979). The Signs of Language. Cambridge, MA: Harvard University Press. MacLaughlin, D. (1997). The Structure of Determiner Phrases: Evidence from American Sign Language. Ph. D. thesis, Boston University. Mosella, M. (2012). Les construccions relatives en llengua de signes catalana (LSC). Ph. D. thesis, Universitat de Barcelona. Perniss, P. (2012). Use of sign space. In R. Pfau, M. Steinbach, and B. Woll (Eds.), Sign Language: An International Handbook (HSK — Handbooks of Linguistics and Communication Sciences), pp. 412–431. Berlin–Boston: De Gruyter Mouton. Pesetsky, D. (1995). Zero Syntax. Cambridge, MA: MIT Press. von Heusinger, K. (2002). Specificity and definiteness in sentence and discourse structure. Journal of Semantics 19, 245–274. Zifonun, G. (2000). “Man lebt nur einmal”. Morphosyntax und Semantik des Pronomens man. Deutsche Sprache 28, 232–253. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 105 106 H AVE as a relation between individuals and properties1 Toni BASSAGANYAS-BARS — Universitat Pompeu Fabra - Barcelona Abstract. This paper argues that the role of HAVE-predicates is to introduce relations into the discourse, one of whose arguments is the individual denoted by the sentence subject. This is the only token-level argument in the relation: the other is modeled as a nominalized property (Chierchia, 1984; Chierchia and Turner, 1988). A number of peculiarities of HAVE are argued to follow from this account, including its connection with existential predicates (McNally, 1992, 2009). Keywords: have, possession, properties, kinds, nominalized functions. 1. Introduction Ever since Keenan (1987), a significant share of the semantic literature on HAVE2 has focused on the compositional challenges posed by relational nouns in object position of this verb, i.e. the phenomenon dubbed ‘existential-HAVE’. The goal is to account for the putative contrast between (1a) and (1b): (1) a. b. John has a/many/the/every/both car(s) John has a/many/#the/#every/#both sister(s) From this perspective, what needs to be explained is: (i) why relational nouns trigger a definiteness effect, largely parallel to that found in the pivot of existential sentences, while sortal nouns do not; (ii) how the subject ends up saturating/being identified with the internal argument of the object; (iii) how to factor in the contribution of the determiner within the object; and (iv) what exactly HAVE contributes to the meaning of the whole. Several analyses of existential-HAVE have been suggested, all of which account for (at least some of) the data but make HAVE –or a small subset of its uses– look like a very peculiar creature full of idiosyncrasies. One of the consequences of such views is that they cast no light on the persistent intuition in the literature on possession that there is a some connection between HAVE, existential predicates and copular sentences. This paper presents a compositional account of HAVE as a predicate that introduces a 2-place relation into the discourse by linking it to one of its participants, the sentence subject. As a result of introducing a HAVE-sentence into a context, the individual that the subject is in a relation to is also introduced. This result is achieved in an indirect way: HAVE relates its subject not with a token-level entity, but with a description of an individual; this description is modeled as a nominalized property (Chierchia, 1984; Chierchia and Turner, 1988). The nature of the 1 I would like to thank Louise McNally, Josep M. Fontana, Bert LeBruyn, Henriette de Swart, Kjell Johan Sæbø, Joost Zwarts, and the audience of Sinn und Bedeutung 21 for discussion, and to Obra Social la Caixa, MINECO (grants FFI2013-41301-P and FFI2016-76045-P) and AGAUR (grant 2014SGR698) for financial support. 2 HAVE refers to an abstract, language-independent predicate of which English have, French avoir or Catalan tenir are concrete manifestations. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 107 T. Bassaganyas-Bars H AVE as a relation between individuals and properties relation introduced into the discourse as a result of uttering an—affirmative—HAVE-sentence depends on the relationality of the noun heading the object-NP.3 The analysis builds on the account of English existentials in McNally (1992, 2009), which was designed to account for the similarities between existentials and some copular predicates. It thus intends to capture both the observation that existentials and HAVE-sentences share a number of traits and the fact that if a language has a HAVE-verb, it is going to be an obvious candidate for the role of existential predicate. The paper is organized as follows: section 2 goes over some of the existing semantic accounts of existential-HAVE; section 3 presents a range of data that challenge the existing views in one way or another; in section 4 I introduce the view of relational nouns that I will assume; section 5 lays out the assumptions I make about the notion of nominalized property and its relation to kinds and tokens; section 6 is devoted to the formal analysis; section 7 concludes. 2. The received view(s) Space precludes an exhaustive summary of the analyses that have been put forward for existential HAVE in the last decades. I will limit myself to reviewing the assumptions and main elements that some of the existing accounts are built on (see e.g. Myler (2014) and LeBruyn and Schoorlemmer (2016) for up-to-date introductions to possession and HAVE-verbs). Partee (1999) is the first compositional account of the observation (made in Keenan (1987)) that HAVE takes a 2-place predicate as its object, the internal argument of which seems to be saturated by the sentence subject. She assigns the determiner a relational type, which results in an NP denoting an ‘unsaturated generalized quantifier’. H AVE is assigned a denotation that takes this special type, contributes an ‘exist’ predicate à la Barwise and Cooper (1981) (which explains the definiteness restriction), and makes sure the subject falls into the right place—the internal argument of the relational noun. Landman (2004) offers a different view that is reminiscent both of Milsark’s (1974) account of the English existential predicate and of analyses relying on the notion of semantic incorporation (Van Geenhoven, 1998), whereby HAVE combines with relations and provides existential quantification of one of their arguments—thus explaining the definiteness effect. BassaganyasBars (2015) applies a similar view both to existential-HAVE and to the existential predicate in Old Catalan, a language in which the two constructions differ only in the oblique marking of one of the arguments in the latter. LeBruyn et al. (2016) is another analysis that relies on the notion of incorporation (formalized in Dynamic Montague Grammar). On their view, HAVE takes properties (with implicit arguments) and ‘relationalizes’ them. The range of interpretations available is contributed by the lexical item in the case of relational nouns, and by the noun’s Qualia Structure (Pustejovsky, 1995) in the case of sortal nouns. This analysis provides an insight I will make use of: it suggests that there is no difference in type between relational and sortal nouns; the distinction 3 For the purposes of this paper, I am not making use of the NP/DP distinction. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 108 T. Bassaganyas-Bars H AVE as a relation between individuals and properties between them, however, is crucial for determining the relation the HAVE-sentence eventually expresses. This implies that there is no difference between the two types of nouns regarding the definiteness restriction, a point I will also argue for. This family of accounts shares the assumption that the analysis of ‘John has a sister’ needs to get us to the denotation logically represented in (2): (2) ∃x.sister(j)(x) In different ways, they all succeed. However, they encounter problems when the full range of determiners (indefinite and definite) that are possible in existential-HAVE contexts is considered, as we will see below. Two of them (Landman and LeBruyn et al.), in fact, are designed for cases where the determiner is a, but they leave unclear how to treat other determiners. Sæbø (2009) tackles the problem from a different angle. His account scopes beyond existentialHAVE to cover all the uses of HAVE . He suggests that HAVE always embeds small clauses (the predicate of which can be overt or implicit) and turns them into predicates, and the lambdaabstracted variable (which can come from a relational noun, an anaphoric element or an implicit relation of possession) is co-indexed with the sentence subject. The role of HAVE is, as in the other analyses, to connect the subject with the material in object position, but the options for accomplishing this go well beyond the binding of the internal argument of the relational noun. As in Partee (1999), the definiteness effect is ultimately attributed to an ‘exist’ predicate associated with relational nouns. Myler (2014) proposes a related analysis in the Distributed Morphology framework. Sæbø’s analysis is technically complex and requires some non-standard assumptions, but it is able to subsume practically all uses of HAVE under an appealing single account. However, it relies heavily on covert material to yield the right interpretation for HAVE-sentences. In addition, by providing HAVE with a very special sort of semantics, it does not capture any similarities between HAVE and existential and copular contexts in an obvious way. Although there are important differences among these analyses, in the next section we will see that they all run into complications once we consider all the data we naturally find with HAVE and the kinds of interpretation for HAVE-sentences they give rise to. 3. Bringing more data into the picture The literature on existential constructions has converged on the idea that the definiteness effect requires a more fine-grained explanation than a simple opposition between ‘strong’ and ‘weak’ NPs. Most literature on HAVE, however, still relies on this type of account. There are essentially two kinds of cases where we find HAVE embedding a relational noun with a definite or obligatorily quantificational determiner. The first is not problematic for any of the accounts above. The second, however, is harder to accommodate. The first case comprises those examples where the DP is not discourse-new and saturation of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 109 T. Bassaganyas-Bars H AVE as a relation between individuals and properties the internal argument of the relational noun does not depend on the sentence subject. This class of cases requires heavy contextual support. An example of such a context is provided by LeBruyn et al. (2016: 58). While playing a card-game based on the Simpson family, a player could utter (3a) if she had the card corresponding to Abraham J. Simpson, or (3b) if she were holding Bart, Lisa and Maggie’s cards in her hands. (3) a. b. I have the grandfather. I have every child. Following Abbott (1993), I will call these readings contextualized. They contrast with the normal interpretation of sentences with relational nouns, where the relation expressed by the noun holds between the subject and the object; these are the non-contextualized readings. Partee (1999) and LeBruyn et al. (2016) associate contextualized interpretations with another version of HAVE, that works like a regular transitive verb. The more problematic set of cases are those with definite NPs that clearly correspond to a noncontextualized reading. In some of them we get a kind or amount reading, as these examples from the Corpus of Contemporary American English (Davies, 2008) illustrate: (4) a. b. c. The guy looks good for his age and has the body of an athlete (COCA) Stafford has the arm and the intelligence to be a good NFL QB (COCA) Pigs have the intelligence of a three year old child (COCA) These sentences express non-contextualized relations between a person/animal and their body, arm, or intelligence, not context-dependent ones. Similar cases have the object of HAVE extracted from a restrictive relative clause. A cursory corpus search suggests that the main verb in the restrictive clause tends to be intensional (5a), but examples with extensional verbs can also be found (5b): (5) a. b. I’d like to tell ten-year old Sarwat that at last he has the friends he was looking for (COCA) At twenty you have the face nature gave you (COCA) Finally, NPs with overt classifiers like ‘kind’ or ‘type’ get a non-contextualized interpretation with definite articles and even obligatorily quantificational determiners. In a context where three kinds of sisters are being discussed (e.g. nice sisters, indifferent sisters and bully sisters), (6a) is perfectly possible with a non-contextualized reading; in a context where we assume that sisters come in different, recognizable kinds, (6b) is perfectly felicitous as well. (6) a. b. Mary has the three kinds of sisters. Mary has every kind of sister. The picture that starts revealing itself looks similar to the one we get with existential constructions. Definite or obligatorily quantificational NPs which preserve a non-contextualized reading with relational nouns are parallel to those that preserve a non-contextualized reading in Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 110 T. Bassaganyas-Bars H AVE as a relation between individuals and properties English existentials (Lumsden, 1988; McNally, 1992; Abbott, 1993, 1997): (7) a. b. There was every *(kind of) biologist at that conference. John has been every *(kind of) biologist. The analyses we have gone over in the previous section do not account in an obvious way for this pattern of data. One can however envisage ways to accommodate the definites, e.g. by invoking type-shifting mechanisms or some operation akin to Chierchia’s Derived Kind Predication (Chierchia, 1998).4 In contrast, the behavior of quantificational NPs if they quantify over kinds is harder to fit into any of the analyses. Other data point to the fact that HAVE does not behave like a regular, extensional transitive verb that relates two token-level entities. One such case is the resistance of the object of HAVE to be pronominalized with wh-relative pronouns. This feature is also shared with existential constructions, and contrasts with a common transitive like ‘date’: (8) a. b. c. I like some of the friends/qualities *which/that/0/ John has. I talked to some of the people *which/that/0/ there are in this class. I know some of the people which/that/0/ you’ve been dating. More evidence comes from dialects of English which allow for that-less subject relative clauses. They are permitted in intensional contexts, some copular constructions, existentials and HAVEsentences (examples from McNally (2009)): (9) a. b. I have an idea might work. There’s a man here can’t speak English. Finally, there is the fact that the most natural interpretation of an anaphoric pronoun in the object position of HAVE is a kind-level one (Myler, 2014). In a context where someone expresses admiration for a car parked on the street (say it is a Porsche 911), it or one in (10a) can be interpreted as referring to the car in question, whereas in (10b) they refer naturally to the kind of car, not the specific car-token. (10) a. b. Did you know Mary owns it/that’s the one Mary owns? Did you know Mary has it/that’s the one Mary has? Data of this kind involving the English existential construction led McNally (1992) to analyze the pivot not as a token-level individual, but a higher-level one—a nominalized property. The introduction of an actual individual into the discourse (satisfying the descriptive content of the property) results from an entailment of the use of a HAVE-sentence. The behavior of HAVE-sentences illustrated in (8), (9) and (10) looks mysterious under any of the accounts reviewed in the previous section, which in all cases consider HAVE a relation 4 Derived Kind Predication is type-shifting operation that applies to predicates of objects so that they can combine with kind-denoting NPs. See Chierchia (1998: 364) for details. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 111 T. Bassaganyas-Bars H AVE as a relation between individuals and properties between token-level individuals. In contrast, it gets a natural account if we consider that the object of HAVE denotes precisely a nominalized property. Wh-relative pronouns can be argued to be restricted to token-level entities; that-less relative clauses seem to be possible when the antecedent of the omitted pronoun refers to a non-token-level entity, and the kind-level interpretation of the anaphora in the object of HAVE follows if kinds are understood as higher-order individuals as well (as most literature making use of both nominalized properties and kinds assumes—see e.g. Chierchia (1998) and McNally (2009)). If we consider in addition that, as mentioned above, HAVE is one of the main sources of existential predicates cross-linguistically (Creissels, 2014), which is expected if the object of HAVE and the pivot in existential predicates are ontologically similar, an account that treats HAVE as a relation between a token-level individual and a nominalized property starts looking like a serious candidate for explaining what is it that makes HAVE look like such a strange, slithery creature. Before turning to the formal analysis, I will lay out the assumptions I will make about relational nouns and nominalized properties. 4. A non-transitive view of relational nouns Most of the accounts of existential-HAVE reviewed above rest on the view of relational nouns which conceives of them as transitive nouns.5 Making logical representations like (11) fit into the composition of HAVE-sentences is the thread that unifies this line of research. (11) [[mother]] = λ xλ y.mother(x)(y) This view of relational nouns is not, however, without problems. One of them is that it groups together classes like body-parts, kinship terms, parts and wholes and deverbal and deadjectival nominalizations (Barker, 1995), which on the one hand are treated in disparate ways in different languages, and on the other tend to behave differently with respect to tests within each individual language (Heine, 1997). A second (related) problem is that tests that select for the class of relational nouns as a whole are scarce. The most used one is compatibility with of -PPs in possessive NPs in English. This test is not free of problems either, as the felicity of (12a) (from LeBruyn et al. 2016), and the existence of contrasts like the one in (12b) shows.6 (See LeBruyn et al. (2016) and references therein for more issues on the conception of relational nouns as transitive nouns.) (12) a. b. The blog of Doctor Watson The hammer of Thor/#my uncle 5 LeBruyn et al. (2016) treat them as being of type he,ti, but they ultimately rely on providing them with another argument to explain their interaction with HAVE. 6 This particular example may point to a contrast between necessary and contingent relations, which some languages mark overtly (Heine, 1997). The relation between Thor and a hammer can be conceived as a necessary one; having a hammer is one of the features that defines Thor. In contrast, it does not define normal people’s normal uncles. The fact that relational nouns normally sound felicitous in the of -PP construction could stem from the fact that they express necessary relations, but the class of necessary relations is bigger than the ones expressed by relational nouns. Whether this hypothesis is worth pursuing remains for future research. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 112 T. Bassaganyas-Bars H AVE as a relation between individuals and properties Although these arguments against treating relational nouns as having argument structure are not absolutely conclusive, there might be room for an alternative treatment that avoids these problems, simplifies composition, and makes additional correct predictions. I will therefore treat relational nouns as one-place predicates with an associated meaning postulate whereby they entail the existence of another entity they are in a particular relation to: (13) a. b. (14) a. b. (15) a. b. JmotherK = λ x.mother(x) ∀x∀w[motherw (x) → ∃y[motherhoodw (y)(x)]] J f riendK = λ x.friend(x) ∀x∀w[friendw (x) → ∃y[friendshipw (y)(x)]] JtopK = λ x.top(x) ∀x∀w[topw (x) → ∃y[part-wholew (y)(x)]] On this view, relational nouns are relation-entailing predicates of individuals. Let us hypothesize that their use in discourse is governed by the condition in (16): (16) The introduction of a token discourse referent for a relation-entailing individual x needs to be anchored to a discourse referent corresponding to the other argument in the relation they entail. To see how this works, let us consider the following example, which illustrates how the relational noun ‘girlfriend’ can be used in discourse: (17) After a woman found out via Facebook that a man who’d ‘poked’ her in real life had a long term girlfriend, she turned to digital manners advice givers Farhad Manjoo and Emily Yoffe of Slate to ask whether she should tell the girlfriend. (COCA) The entity corresponding to the description ‘girlfriend’ is first introduced into this piece of discourse by a HAVE-sentence. The condition above is respected: the HAVE-sentence anchors it to the other entity in the relation. Once this is done, an entity satisfying the description has entered the discourse and can be referred to freely, as in the last sentence of (17).7 (17) illustrates that the most straightforward way English offers to introduce a relational noun into the discourse is a HAVE-sentence.8 The relation between HAVE and relational nouns seems to be a symbiotic one. These (individual-denoting) nouns need a predicate to introduce them 7 This view explains another putative test for relational nouns, viz. incompatibility with predicatively used genitives (Partee, 1997): (i) a. That computer is John’s b. ??That girlfriend is John’s The infelicity of (ib) can be attributed to a violation of (16). Making the relational noun the sentence topic strongly implies that the individual it describes is already part of the discourse model. This entails that the entity it is in a relation to has also been introduced. The only possibility to interpret (ib) is to look for an alternative relation between this ‘girlfriend’ and John. Lacking any context, we cannot find one. 8 Another possibility is the use of a possessive NP (either with ’s or an of -PP), in which case the existence of the relation is presupposed and needs to be accommodated by the hearer. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 113 T. Bassaganyas-Bars H AVE as a relation between individuals and properties into the discourse by linking them to an individual, to which they are in the relationship they entail. The job of HAVE, in turn, is precisely to introduce into the discourse relations linked to an individual—and eventually resulting in the addition of an individual describable with the relational noun into the discourse model. H AVE cannot supply a value for the relation, but the meaning postulate associated with the relational noun is there to contribute one. The treatment of relational nouns presented here is parallel to the one for deverbal nouns in Grimm and McNally (2013), a class of nouns which is usually analyzed as relational (Barker, 1995: 60-62). Grimm and McNally treat them as one-place, relation-entailing nouns. They denote properties of events and are subject to a discourse condition very similar to (16): when they are introduced into the discourse, they need to be anchored to one of the participants they entail (see Grimm and McNally (2013) for details). The account presented so far explains the relations conveyed by HAVE-sentences with discoursenew relational nouns. Turning to discourse-new sortal nouns, I will argue that they are used to convey non-ambiguous relations as well. Their value does not come from entailments of the noun, but from a combination of the semantics of the object and the subject, and worldknowledge. This is illustrated by the following sentences: (18) a. b. c. My neighbor has many dogs Have you visited John’s pet shop? He has many dogs! If you want to buy a dog, go to the dog pound first: they have many dogs Sentence (18a), uttered in a context where no specific information about the neighbor in question is part of the conversational background, expresses the standard relation that holds between human beings and dogs, the one we could call a ‘person-dog relation’. This relation, provided by world knowledge, entails things like having the dog at home, feeding it, walking it, petting it, etc. This contrasts with the relations between dogs and pet-shop owners (18b) and dog-pounds (18c), for which different sets of entailments hold. The upshot of that is that, when we hear a HAVE sentence with a non-relational noun like dog in object position, in a certain context, and after we have identified what kind of entity the subject is, world knowledge gives us a default relation between the two entities; this is how the nature of the relation introduced by HAVE is determined with non-relational nouns.9 It follows from the present account (as it does from LeBruyn et al. 2016) that the contrast between (1a) and (2) is an illusory one, and that something much like the definiteness effect should also hold for sortal nouns. That is, the way the full interpretation of (19a) and (19b) is determined differs. 9 This view thus goes against accounts that rely entirely on free ‘pragmatic determination’ to settle the actual relation holding between the subject of the sentence and a noun like ‘dog’. In contrast, it could in principle be compatible with the most elaborate account of how the meaning of these sentences is determined (LeBruyn et al., 2016), although how to factor in the contribution of the subject in this account is not immediately obvious. It is also compatible with a ‘co-composition’ account along the lines of Spalek (2014). Further details concerning this aspect of the analysis must be left for future research. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 114 T. Bassaganyas-Bars (19) a. b. H AVE as a relation between individuals and properties John has a/two/many beautiful car(s) John has the/every/both beautiful car(s) Tham (2006) defends this view. She argues that (19a) is an instance of ‘presentational have’, which requires the NP to be discourse-new; the definiteness effect is given a pragmatic explanation à la Abbott (1993). (19b), in contrast, is a special use where HAVE can take definite NPs, which is only possible when previous context supplies a relation between the two entities (Tham, 2006: 143). LeBruyn et al. (2016) reach a similar conclusion. Tham argues that there are languages (e.g. Mandarin Chinese) with a HAVE-verb that forbids definite objects. In the same vein, Heine (1997) points out that ‘there exists a strong correlation between haveconstructions and the presence of indefinite possessees, to the effect that, in many languages, have-constructions assume meanings other than possessive ones unless associated with indefinite possessees’ (Heine, 1997: 35). Therefore, there seems to be some evidence for an account that teases apart how we determine the meaning in (19a) and (19b), so that (19b) is grouped with (20) instead. (20) John has the/every/both child(ren) This sentence is possible in a context where a child (or some children) are already part of the discourse model. According to (16), this requires that the entity they are in a parent-child relation to has been introduced into the discourse as well. Therefore, the relation between John and the child(ren) in question that (20) refers to has to be determined in some other way. Tham and LeBruyn et al. argue that in at least some of these cases it is up to discourse context to provide a salient interpretation. For instance, (20) could be uttered in a context where a group of paparazzi are following a celebrity family and they are assigned family members as specific targets. Partee (1999) and Sæbø (2009) seem to rely on vague interpretations of ‘possessive’ relations such as control, part-whole, etc. The issue cannot be settled here—although see Tham (2006) for some examples that do not imply ‘control’ in any intuitive way. Equipped with these assumptions about relational and sortal nouns and the way they interact with HAVE, we can now tackle the next piece of the analysis: nominalized properties. 5. Nominalized properties, kinds and tokens Nominalized properties, also called ‘nominalized functions’ and ‘entity correlates of properties’ in the literature, are a sort in the domain of entities corresponding to the reification of the description of a standard he,ti property. They were introduced by Gennaro Chierchia (Chierchia, 1984) as part of his Property Theoretic analysis of nominalization. Chierchia’s motivation was to give a compositional account for sentences like (21): (21) {Being nice/Goodness/That John is here/Red} is nice. The operators ∪∩ are used to type-shift back and forth from properties as predicates to properties as individuals. Entity correlates of properties (generally adapted to a model-theoretic Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 115 T. Bassaganyas-Bars H AVE as a relation between individuals and properties framework) have since been used for the analysis of existential sentences (McNally, 1992; McCloskey, 2014), kinds (Chierchia, 1998) and possessives (Koontz-Garboden and Francez, 2010), and have been argued to offer an alternative to semantic incorporation of he,ti-type objects (McNally, 2009) with different empirical consequences. Nominalized properties are similar to kinds (Carlson, 1977); both are higher-order entities in De that are reified by token-level (possibly plural), particular individuals. How to tease the two notions apart has not been definitely established in the literature. It is generally agreed that kinds are a subset of nominalized properties; differences that have been suggested are the requirement that kinds have some degree of well-establishedness and a domain structured as a taxonomic hierarchy, whereas this does not necessarily hold for nominalized properties (Krifka, 1995; Chierchia, 1998; McNally, 2009; Müller-Reichau, 2011). In this section I will make a concrete proposal regarding the structure of the domain of entities, the relation between the different sorts inside this domain, and about NP-semantics. Full justification of each step would be beyond the scope of this article; see Bassaganyas-Bars (forthcoming). I will assume a subdivision within De into token-level entities (eo ), kind-level entities (ek ) and nominalized properties (e p ). The latter two form the sub-domain of higher-order entities. Variants of the realization relation R (Carlson, 1977) connect higher-order individuals to tokenlevel individuals, but also nominalized properties to kinds. R po eo ep R pk Rko ek The relation Rko is the Carlsonian R, the one that holds between an entity xo and the kind yk that it is an instance of. Unlike kinds, entities of sort e p can include information on degree and number.10 R po is the relation that holds between e.g. a (complex) individual xo which is the sum of two object cars, and the (nominalized) property of being two cars (two cars p ). Introducing the role of R pk requires first outlining how the sub-domain of kinds is organized. This sub-domain is structured by a (transitive, asymmetric) taxonomic relation T (Krifka et al., 1995): T(x, y) holds if x is a subkind of y. Turning away from artificially constructed Linnaean taxonomies, what counts as a subkind of what is context-dependent. If we take the kind cark , either of these taxonomies –and many others– can be operative depending on context: cark Audik A1k A4k cark Fordk Fiestak Mondeok small cark family cark A1k A4 Fiestak Mondeok R pk (x, y) holds if x is an individual or a sum consisting of a number n of individuals of sort ek , which are in the T relation with a kind zk , and y is the property of being n sub-kinds of zk . 10 For the present purposes, I will focus on count nouns, so I will consider only information on number. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 116 T. Bassaganyas-Bars H AVE as a relation between individuals and properties In the taxonomies above, A1k or Fordk are in the R pk relation to one kind of car p . Likewise, L L R pk (A1k A4k , two kinds of Audi p ) and R pk (small cark family cark ,two kinds of car p ) also hold. I will not consider well-establishedness as a prerequisite for kind-level denotation.11 This implies that most instances of noun modification can be treated as kind-level modification. In addition, I will consider, following Müller-Reichau (2011: 51), that a set of sub-kinds (e.g. λ xk [dog(xk )]) and the corresponding kind-qua-entity (dogk ) are informationally equivalent. A variant of the ∩∪ operators allows us to type-shift between the two kinds of denotation. This view draws heavily from the NP-semantics posited in Krifka (1995) which he terms ‘concept-level’, and which I will consider analogous to the view of nominalized properties I am defending. Combining Krifka’s insights and the assumptions made so far, I will adopt the following logical representation of the denotation of ‘two cars’: [[two cars]] = λ y p ∀x[(Rko T(x, cark ) ∧ two(x)) ↔ R po/pk (x, y p )] (22) This representation means that, in a classifier-less language like English, ‘two cars’ denotes the set of higher-order entities y p such that either (i) any complex entity x which realizes the kind cark , and is the sum of two atoms, is in the R po relation to y p , or (ii) any complex entity x comprised by sub-kinds of the kind cark is in the R pk relation to y p .12 Whether (i) or (ii) is the right interpretation will depend on context. If a conversation is about a new neighbor, ‘two cars’ in ‘she only has two cars’ will most likely refer to the property of being two object cars; if it is about where to buy a new car, the same NP in ‘this dealer only has two cars’ can very plausibly refer to the property of being two sub-kinds of cark . 11 Well-establishedness might be a prerequisite for some constructions (e.g. kind-denoting definite singular NPs), but not for kind-level denotation in general. That is, ‘blue shoe with pink dots’ can be as much of a kind as ‘mountain shoe’. (i) Blue shoes with pink dots are rare/common/trendy this year. 12 What this amounts to is that ‘two cars’ in English can denote the set of individuals in the second row of either of these lattices (corresponding to the domain of kinds and the domain of objects): L Fk L A1k L Ck A1k A1k L A1k Fk Fiestak Ck F1 Fk L Ck F1 Cliok L F2 Fiesta1 L F2 L F1 L F3 Fiesta2 F3 F2 L F3 Fiesta3 The atomic individuals in the object domain are the members of the set of objects resulting from applying Rko to one of the individuals in the kind-domain (in that case, λ x.Rko (x, Fiestak )). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 117 T. Bassaganyas-Bars H AVE as a relation between individuals and properties How do we get to the logical representation in (22)? I will follow the literature on so-called ‘layered’ approaches to the semantics of noun phrases in considering that the innermost layer of the NP denotes in the kind-domain. Common nouns denote predicates of kinds, adjectives can be treated as predicates of kinds as well, and composition with modifiers can be treated as predicate modification. As already mentioned, I follow Müller-Reichau’s (2011) claim that a set of subkinds and its corresponding kind-qua-entity are informationally equivalent. A variant of Chierchia’s ∩ type-shifter applies to yield an output of type ek . beautiful dogk ∩ λ xk [dog(xk ) ∧ beautiful(xk )] λ xk [beautiful(xk )] λ xk [dog(xk )] Following Krifka (1995), and deviating somewhat from the usual layered-DP accounts, I suggest that the layer that contributes information on number does not involve turning the kindlevel denotation inherited from the innermost layer into the set of objects realizing it. Instead, at this point we create the nominalized property y p of being a number n of realizations or subkinds of a certain kind zk . I will call this layer ClassP (Borer, 2005). Its head is a—covert or overt—classifier taking two arguments, a kind-level entity and a cardinality word (with N being a variable over cardinality predicates).13 [[Class]] = λ zk λ Nλ y p ∀x[((Rko T(x, zk ) ∧ N(x)) ↔ R po/pk (x, y p )] (23) After combination with the two arguments, we reach (22), repeated here as (24). [[two cars]] = λ y p ∀x[(Rko T(x, cark ) ∧ two(x)) ↔ R po/pk (x, y p )] (24) (24) denotes a set. At this point, two things can happen: this set can either be the input to a definite or obligatorily quantificational determiner, or we can pragmatically bind the variable corresponding to the nominalized property with the iota-operator, reflecting the fact that the nominalized property introduced into the discourse is presupposed to be unique, thus yielding (25). As we will see in the next subsection, this is of the type HAVE looks for. [[two cars]] = ιy∀x[(Rko T (x, cark ) ∧ two(x)) ↔ R po/pk (x, y p )] (25) English has some overt classifiers; one of them is ‘kind/sort/type of’. This classifier restricts the interpretation of the NP to the property of being n sub-kinds of a certain kind. 13 By making the cardinality word obligatory, the fact that overt classifiers in English need some kind of determiner is captured. That is, it rules out bare plurals with classifiers like ‘kind’, which are ungrammatical. (i) a. b. *Kinds of whales are extinct. *John sells kinds of cars. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 118 T. Bassaganyas-Bars (26) H AVE as a relation between individuals and properties [[kind of]] = λ zk λ Nλ y∀x[(T(x, zk ) ∧ N(x)) ↔ R pk (x, y)] At this point I have finally introduced the necessary pieces to undertake the compositional analysis of HAVE-sentences. 6. Analysis This is the logical representation I propose for HAVE, where π is an unspecified relation: (27) [[HAVE]] = λ x p λ yλ s[π(s) ∧ PROTO - WHOLE(s)(y) ∧ PROTO - PART(s)(x p )] This denotation assumes the view on argument structure in Dowty (1991). However, the protoroles used here are the ones proposed in Barker and Dowty (1993) for possessive NPs. Although it is not crucial, this move has two welcome consequences. First, it captures the fact that the relations expressible with a HAVE-sentence overlap with those that can be conveyed by possessive NPs (for which the PROTO - WHOLE and PROTO - PART proto-roles were designed).14 Second, it naturally filters out odd sentences like (28a)–(28c): (28) a. b. c. #Three windows have a house. #A problem has John. #The tail has a cat. With all the assumptions in place, let us begin with HAVE-sentences with a discourse-new object-NP containing a relational noun, as in (29). Relational nouns are treated as are oneplace predicates with an associated meaning postulate, as (30) illustrates: (29) John has two smart sisters. (30) a. b. [[sister]] = λ x.sister(x) ∀x∀w[sisterw (x) ↔ ∃y[siblinghoodw (y)(x)]] Applying the NP-semantics outlined in the previous section, we start from ‘sister’ as a set of (sub-)kinds and combine it with ‘smart’ (modeled as a predicate of kinds as well) by predicate modification, yielding (31). Following the assumptions above, ∩ steps in, returning (32): (31) [[smart sister]] = λ xk .sister(xk ) ∧ smart(xk ) (32) [[smart sister]] = smart sisterk Class, defined in (23) above, takes (32) as an argument, and the result combines with the 14 Note that ‘John has two houses’ denotes different relations if we refer to John as a regular guy, a realtor, a kid with divorced parents, etc, and that all of these relations can be expressed by a possessive NP like ‘John’s two houses’. However, the opposite might not be true, as Heine (1997) points out, because the NP can also mean in context ‘the two houses that John likes’, but it is not clear whether this relation can be expressed by the HAVE sentence ‘John has two houses’. The relevant point is that the same roles hypothesized for nominal possession could be used for HAVE-sentences. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 119 T. Bassaganyas-Bars H AVE as a relation between individuals and properties cardinality predicate, eventually yielding (34): (33) λ zk λ Nλ y p ∀x[((Rko T(x, zk ) ∧ N(x)) ↔ R po/pk (x, y p )] (smart sisterk ) = λ Nλ y p ∀x[((Rko T(x, smart sisterk ) ∧ N(x)) ↔ R po/pk (x, y p )] (34) λ Nλ y p ∀x[((Rko T(x, smart sisterk ) ∧ N(x)) ↔ R po/pk (x, y p )] (λ z.two(z)) = λ y p ∀x[((Rko T(x, smart sisterk ) ∧ two(x)) → R po/pk (x, y p )] The contextually triggered iota-operator applies at this point, yielding (35): (35) ιy p ∀x[((Rko T (x, smart sisterk ) ∧ two(x)) → R po/pk (x, y p )] = two smart sister p This is the input that HAVE can take, giving us (37) after combination with the subject: (36) λ x p λ yλ s[π(s) ∧ PROTO - WHOLE(s)(y) ∧ PROTO PART(s)(x p )] (two smart sister p ) = λ yλ s[π(s) ∧ PROTO - WHOLE(s)(y) ∧ PROTO - PART(s)(two smart sister p )] (37) λ s[π(s) ∧ PROTO - WHOLE(s)(john) ∧ PROTO - PART(s)(two smart sister p )] After this set of states is existentially closed at some point further in the derivation, (37) introduces an entity of sort e p into the discourse and an unspecified relation π linking it to John. Following McNally (1992), I suggest that adding a HAVE-sentence into the discourse entails the introduction of a discourse referent satisfying the description. A token-level individual in the R po relation to two smart sisters p thus enters the discourse model. This is the point where the value of π is determined. ‘Sister’ is a relational noun. Condition (16) above established that entities describable by such predicates can only be introduced into the discourse by anchoring them to the other argument in the relation they entail. This is what the HAVE-sentence does. Therefore, as a result of updating the discourse with (37), a relation (π) between John and two token-level individuals satisfying the descriptive content of two smart sisters p is asserted. Then, by virtue of the entailments on the introduction of a relational noun into the discourse, this relation is set to ‘siblinghood’: π gets its value. We reach the desired interpretation in an indirect way which allows us to account for the fact that the object of HAVE does not behave as a token-level individual, as shown in section 3. The derivation of a sentence with a discourse-new sortal noun, like (38), is only minimally different. Following the same steps as for (29) above, we reach the representation in (39). (38) John has three bicycles. (39) λ s[π(s) ∧ PROTO - WHOLE(s)(john) ∧ PROTO - PART(s)(three bicycles p )] As a result, the nominalized property three bicycles p , and an unspecified relation π between this property and John, are added into the discourse model; by the entailments of the use of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 120 T. Bassaganyas-Bars H AVE as a relation between individuals and properties HAVE -sentences, three object bicycles are introduced as well. ‘Bicycle’ is a sortal noun, so there is no meaning postulate to fall back on to retrieve a value for π. The object is discoursenew, so no context-dependent relations involving bicycles are being discussed. In such cases, world-knowledge is resorted to. Assuming that John is an individual with no particular relation to bicycles (he is not a professional cyclist, bicycle repairer or seller, etc.), the value of π will be set to the ‘person-bicycle-relation’, the one most of us have with our bikes (entailing exclusive right of use, responsibility for taking care of it, etc.). If John had been a cyclist, π would have been set to ‘cyclist-bicycle-relation’, with different entailments, and so forth. So far we have considered the most straightforward cases among the ones discussed in section 3. It will be useful to consider how this analysis treats other cases where HAVE-sentences get a non-contextualized reading. One of them involves sentences like (40). (40) John has three kinds of brothers. Note that condition (16) does not apply to kind-level NPs with relational nouns. (41) relies on a discourse context containing individuals of sort ek corresponding to sub-kinds of brothers. Whether it contains token-level individuals realizing them is immaterial. ‘Kinds of brothers’ can be introduced without having to anchor them to any other individual. (41) Some kinds of brothers are harder to put up with than others. Still, the natural interpretation of (40) is the one where John is one of the arguments of a siblinghood relation. How does this come about? Adding (40) to a context introduces the nominalized property three kinds of brother p and a relation π linking it to John. By entailment, a token-level discourse referent has to be added. The only way to satisfy this is by adding a complex individual whose atoms are (an unspecified number of) realizations of three different sub-kinds of brothers, with at least one token-level individual per sub-kind (e.g. two nice brothers, one bully brother, and two nerdy brothers). This means that token-level entities that satisfy the description ‘brother’ enter the discourse, and at this point, by virtue of the meaning postulate associated with token-level relational nouns, π is interpreted as ‘siblinghood’ and John is interpreted as the other member of the relation for each of the token-level entities eventually introduced into the discourse model. Sentence (42) differs from (40) in the presence of the definite article, which nonetheless does not block a non-contextualized interpretation. (42) John has the three kinds of brothers. The interpretation is derived similarly: the definite article implies that previous context contains entities corresponding to three sub-kinds of brother, but not necessarily entities realizing them. The nominalized property the three kinds of brother p , which refers to the property of being the specific three kinds of brother being discussed, is made the object of a HAVE-sentence, and this entails the introduction of an unspecified number of object-level entities such that there is at least one for each of the three sub-kinds. Again by virtue of the meaning postulate associated Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 121 T. Bassaganyas-Bars H AVE as a relation between individuals and properties with relational nouns, the relation between the entities and the subject of the sentence will be ‘siblinghood’. What (42) illustrates is that, in its role of introducing relations into the discourse with a non-contextualized interpretation, HAVE cares more about the sort of its object-NP (it needs to be higher-order) than about its being discourse-new. Let us now consider HAVE-sentences with obligatorily quantificational determiners which nonetheless yield non-contextualized interpretations, such as (43). (43) John has every kind of brother. The result of combining the overt classifier ‘kind of’ to a kind-denoting NP, as defined in section 5, yields the following representation: (44) [[kind of brother]] = λ Nλ y p ∀x[(T(x, brotherk ) ∧ N(x)) → R pk (x, y p )] ‘Every’ requires arguments of type he,ti, so there will be a type-mismatch. I will assume that, in cases where phrases headed by overt classifiers combine with quantificational determiners, there is a covert cardinality predicate (At) predicating atomicity, which saturates the N in the derivation.15 As a result, we get the desired type: (45) [[kind of brother]] = λ y p ∀x[(T(x, brotherk ) ∧ At(x)) → R pk (x, y p )] Since (45) denotes a set of entity correlates of properties, ‘every’ will quantify over higherorder entities, as illustrated by the simplified representation in (46). Sentences like (43) are thus licensed. The non-contextualized interpretation comes about as in (40) and (42) above. (46) Every x p [λ y p ∀x[(T(x, brotherk )) ∧ At(x)) → R pk (x, y)]] (π(x p )(John)) Derivation of sentences like (47a)–(47c) rely on the existence of covert kind classifiers. With all the assumptions about the interpretation of HAVE-sentences with kind-denoting NPs discussed in this section, their interpretation should be straightforward. (47) a. b. c. John has the hair of a metal star from the 80’s. John has the hair of Joey Tempest/Joey Tempest’s hair. John has the hair he always dreamed of. Space only allows for a brief remark on contextualized readings, cases like (3a), (3b), (19b) or (20) above. It was mentioned in section 3 that only some languages have a version of HAVE that supports these readings. On this analysis, it will be a version of HAVE that preserves its function of introducing relations linked to an entity in the discourse, but in this case the other entity in the relation will be of sort eo instead of e p , as in (48). (48) [[HAVEcontext. ]] = λ xo λ yλ s[π(s) ∧ PROTO - WHOLE(s)(y) ∧ PROTO - PART(s)(xo )] 15 This covert atomicity predicate has an overt expression in ‘every single kind of’. Note as well that there are cases of ‘every’ taking NPs with overt cardinality predicates (e.g. ‘every two days’). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 122 T. Bassaganyas-Bars H AVE as a relation between individuals and properties The main difference lies in the value π can take: the strategies used above with discourse-new NPs are not available, so previous context, or an all-encompassing notion of ‘control’, has to be called on. There are languages that distinguish these two uses of HAVE overtly: Spanish, for instance, does it through the presence or absence of Differential Object Marking.16 7. Conclusions The syntactic and semantic peculiarities of HAVE can be explained by analyzing it as a relation between token-level individuals and nominalized properties, and by considering that the way this relation is specified depends on the noun being sortal or relational. I have focused on cases where HAVE embeds NPs. Whether this approach can be extended to other uses of HAVE remains for future research (see Bassaganyas-Bars (forthcoming)). References Abbott, B. (1993). A pragmatic account of the definiteness effect in existential sentences. Journal of Pragmatics 19(1), 39–55. Abbott, B. (1997). Definiteness and existentials. Language 73(1), 103–108. Barker, C. (1995). Possessive Descriptions. CSLI Publications. Barker, C. and D. Dowty (1993). Non-verbal thematic proto-roles. In A. Schafer (Ed.), Proceedings of NELS 23, pp. 49–62. GSLA. Barwise, J. and R. Cooper (1981). Generalized quantifiers and natural language. Linguistics and Philosophy 4(2), 159–219. Bassaganyas-Bars, T. (2015). ‘Have’ and the link between perfects and existentials in Old Catalan. In E. Csipak and H. Zeijlstra (Eds.), Proceedings of Sinn und Bedeutung 19. Bassaganyas-Bars, T. (for.). H AVE is not Possessive. Ph. D. thesis, Universitat Pompeu Fabra. Borer, H. (2005). Structuring Sense, vol. 1: In Name Only. Oxford: Oxford University Press. Carlson, G. N. (1977). Reference to Kinds in English. Ph. D. thesis, University of Massachusetts, Amherst. Chierchia, G. (1984). Topics in the Syntax and Semantics of Infinitives and Gerunds. Ph. D. thesis, University of Massachusetts, Amherst. Chierchia, G. (1998). Reference to kinds across languages. Natural Language Semantics 6(4), 339–405. Chierchia, G. and R. Turner (1988). Semantics and property theory. Linguistics and Philosophy 11(3), 261–302. Creissels, D. (2014). Existential predication in typological perspective. Ms. University of Lyon. Davies, M. (2008). The Corpus of Contemporary American English (COCA): 520 million 16 In Spanish, Differential Object Marking is forbidden in non-contextualized interpretations (i), but preferable in contextualized ones (ii). (i) (ii) Tengo (*a) tres profesores muy buenos. I-have (DOM) three teachers very good ‘I have three very good teachers.’ Para la fiesta, ya tengo ? (a) tres profesores. for the party, already I-have (DOM) three teachers ‘I already have three teachers for the party.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 123 T. Bassaganyas-Bars H AVE as a relation between individuals and properties words, 1990–present. Available at: http://corpus.byu.edu/coca/. Dowty, D. (1991). Thematic proto-roles and argument selection. Language 67(3), 547–619. Grimm, S. and L. McNally (2013). No ordered arguments needed for nouns. In M. Aloni, M. Franke, and F. Roelofsen (Eds.), Proceedings of the 19th Amsterdam Colloquium. Heine, B. (1997). Possession: Cognitive Sources, Forces and Grammaticalization. Cambridge University Press. Keenan, E. L. (1987). A semantic definition of ‘indefinite NP’. In E. Reuland and A. ter Meulen (Eds.), The Representation of (In)definiteness, pp. 286–317. The MIT Press. Koontz-Garboden, A. and I. Francez (2010). Possessed properties in Ulwa. Natural Language Semantics 18(2), 197–240. Krifka, M. (1995). Common nouns: A contrastive analysis of Chinese and English. In G. N. Carlson and F. J. Pelletier (Eds.), The Generic Book, pp. 398–411. University of Chicago Press. Krifka, M., F. J. Pelletier, G. N. Carlson, A. T. Meulen, G. Link, and G. Chierchia (1995). Genericity: An introduction. In G. N. Carlson and F. J. Pelletier (Eds.), The Generic Book. University of Chicago Press. Landman, F. (2004). Indefinites and the Type of Sets. Blackwell. LeBruyn, B., H. de Swart, and J. Zwarts (2016). From HAVE to HAVE verbs: Relations and incorporation. Lingua 182(3-4), 49–68. LeBruyn, B. and E. Schoorlemmer (2016). Possession: Puzzles in meaning and form. Lingua 182(3–4), 1–11. Lumsden, M. (1988). Existential Sentences: Their Structure and Meaning. Croom Helm. McCloskey, J. (2014). Irish existentials in context. Syntax 17(4), 343–384. McNally, L. (1992). A Semantics for the English Existential Construction. Ph. D. thesis, UCSC. McNally, L. (2009). Properties, entity correlates of properties, and existentials. In A. Giannakidou and M. Rathert (Eds.), Quantification, Definiteness, and Nominalization, pp. 163–187. Oxford University Press. Milsark, G. (1974). Existential Sentences in English. Ph. D. thesis, MIT, Cambridge. Müller-Reichau, O. (2011). Sorting the World. On the Relevance of the Kind/Object-Distinction to Referential Semantics. Boston, Berlin: De Gruyter. Myler, N. (2014). Building and Interpreting Possession Sentences. Ph. D. thesis, NYU. Partee, B. (1997). Genitives: A case study. In J. van Benthem and A. ter Meulen (Eds.), Handbook of Logic and Language. Elsevier and The MIT Press. Partee, B. (1999). Weak NP’s in HAVE sentences. In J. Gerbrandy, M. Marx, M. de Rijke, and Y. Venema (Eds.), JFAK, [a Liber Amicorum for Johan van Benthem on the occasion of his 50th Birthday], CD-ROM. University of Amsterdam. Pustejovsky, J. (1995). The Generative Lexicon. Cambridge, Massachusetts: MIT Press. Sæbø, K. J. (2009). Possession and pertinence: The meaning of have. Natural Language Semantics 17(4), 369–397. Spalek, A. (2014). Verb Meaning and Combinatory Semantics: A Corpus-Based Study of Spanish Change of State Verbs. Ph. D. thesis, Universitat Pompeu Fabra, Barcelona. Tham, S. W. (2006). The definiteness effect in English have sentences. In P. Denis, E. McCready, A. Palmer, and B. Reese (Eds.), TLS 8. Cascadilla Proceedings Project. Van Geenhoven, V. (1998). Semantic Incorporation and Indefinite Descriptions: Semantic and Syntactic Aspects of Noun Incorporation in West Greenlandic. CSLI Publications. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 124 A unified existential semantics for bare conditionals1 Itai BASSI — Massachusetts Institute of Technology Moshe E. BAR-LEV — Hebrew University of Jerusalem Abstract. Bare conditionals show an unexpected quantificational variability contingent on whether they are embedded in an Upward Entailing context (universal import) or a Downward Entailing context (existential import). Contra Herburger (2015a, b)’s ambiguity theory, we argue in favor of a unified semantics for bare conditionals based on their behavior in VP ellipsis constructions and in non-monotonic contexts. We show that a similar pattern exists with Free Choice phenomena, and consequently suggest a parallel analysis to Fox (2007)’s treatment of such phenomena. We propose that bare conditionals have a basic existential semantics which is obligatorily strengthened into a universal meaning in UE contexts, while being preserved in DE contexts. Our claim that bare conditionals are underlyingly existential is further supported by Conditional Perfection data with bare and non-bare conditionals. Keywords: conditionals, homogeneity, exhaustivity, alternatives, conditional perfection, quantification, free choice 1. Higginbotham’s puzzle and existing solutions A bare conditional as in (1a) involves universal (or universal-like) generalization over cases (or worlds).2 As first observed by Higginbotham (1986), this meaning is preserved when the conditional is embedded in the scope of every, as in (1b), but when embedded in the scope of no as in (1c) it seems as though the conditional contributes an existential force.3 Having a universal meaning for the conditional in (1c), as in (1cii), will result in a too-weak meaning which is compatible with someone having a case where they goof off and succeed. (1) a. b. c. If you work hard you succeed. ≈ In all cases where you work hard, you succeed. Everyone will succeed if they work hard. ≈ For every x, in all cases where x works hard, x succeeds. No one will succeed if they goof off. (i) ≈ There is no x s.t. there is a case where x goofs off and x succeeds. (ii) ≉ There is no x s.t. in all cases where x goofs off, x succeeds. Higginbotham (1986) presents the paradigm in (1) as a problem for compositionality, and this surprising behavior has troubled semanticists ever since (see Kratzer 2015; Leslie 2008; Herburger 2015a, b, a.o.). 1 We would like to thank Sam Alxatib, Luka Crnič, Kai von Fintel, Danny Fox, Andreas Haida, Elena Herburger, Roni Katzir, Angelika Kratzer, Daniel Margulis, and the audiences in Sinn und Bedeutung 21 and NELS 46. All mistakes and shortcomings are our own. 2 We limit ourselves here to conditionals that have some intensional import, and ignore quantified conditionals of the kind discussed in Kratzer (2015) which seem to only care about the actual world. 3 Higginbotham’s own description is in terms of material implication vs. conjunction, but the puzzle persists in a more standard framework where conditionals aren’t truth-functional but involve quantification over worlds. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 125 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals It has been argued by von Fintel and Iatridou (2002) (and more recently by Herburger 2015a) that the behavior of the embedded conditional in (1c) is not unique to conditionals in the scope of no, but extends to other Downward Entailing (DE) environments, for example when a bare conditional is embedded under doubt: (2) I doubt that Mary will come if John comes. a. ≈ I doubt that there is a case where John comes and Mary comes. b. ≉ I doubt that in all cases where John comes Mary comes. The generalization that emerges is that systematically, bare conditionals contribute universal quantification in UE environments and existential quantification in DE environments. To conclude, we are left with a puzzle, which we’ll call Higginbotham’s puzzle: (3) Higginbotham’s puzzle: How can bare conditionals contribute universal quantification in UE environments and existential quantification in DE environments compositionally? Two main lines of compositional analyses with a unified semantics for conditionals have been proposed: (i) Analyses in which conditionals obey Conditional Excluded Middle (CEM) (Stalnaker 1968, von Fintel 1997, von Fintel and Iatridou 2002, Klinedinst 2011); (ii) proposals along the lines of the restrictor analysis of conditionals, according to which the quantificational force in question is supplied by a surrounding quantifier, with the if -clause serving as a domain restrictor (Leslie 2008; Kratzer 2015). For reasons of space, we cannot discuss at length the advantages and shortcomings of those analyses.4 Instead, our discussion in this paper will mainly relate to an alternative analysis which was recently advanced by Herburger (2015a, b). Herburger’s solution to Higginbotham’s puzzle is that conditionals are simply ambiguous: (4) Herburger’s hypothesis: Bare conditionals are lexically ambiguous. a. In UE environments they contribute universal quantification. b. In DE environments they contribute existential quantification.5 In this paper we argue against Herburger’s ambiguity hypothesis and provide a novel unified semantics that deals with Higginbotham’s puzzle. Our empirical motivation for rejecting the ambiguity hypothesis comes from the observation that bare conditionals don’t behave like classical ambiguities in VP ellipsis constructions and in non-monotonic contexts (section 2). We adopt Herburger’s idea (which is already entertained in von Fintel 1997) that existential bare conditionals exist, and contend that only they exist: bare conditionals are existential across the board. We present an analogy between bare conditionals and Free Choice disjunction in different contexts as a motivation for this assumption (section 3). To derive the universal im4 See Leslie (2008); Herburger (2015a, b) for arguments against CEM analyses, and von Fintel and Iatridou (2002); Huitink (2010) for a problematization of the restrictor analysis. We hope to conduct a more thorough comparison between these approaches and ours in future work. 5 One might wonder about the principle that governs the distribution of the two possible meanings as characterized in (4). Even though Herburger herself doesn’t explicitly suggests this, it seems natural to think of the Strongest Meaning Hypothesis (Dalrymple et al., 1994)) as a relevant principle. See also footnote 13. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 126 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals port of bare conditionals in UE contexts from their basic existential meaning, we utilize the grammatical strengthening mechanism proposed by Fox (2007) for the analysis of Free Choice inferences, using exhaustification over sub-domain alternatives (as in Chierchia 2013) (section 4). We further show that Conditional Perfection data, which pose a difficulty for Herburger’s ambiguity approach (as well as for standard universal semantics approaches), are naturally explained by our proposal, and that comparing Conditional Perfection in bare and non-bare conditionals provides another evidence for the existentiality of bare conditionals (section 5). 2. Shortcomings of an ambiguity theory Herburger’s hypothesis in (4) straightforwardly accounts for Higginbotham’s puzzle. However, in this paper we argue that it cannot be maintained and that a unified analysis is called for. The basis on which we make this claim consists of the considerations in (5): (5) a. b. c. Bare conditionals do not behave like ambiguities in ellipsis constructions where the antecedent and the elided material are in environments of different monotonicity. When embedded in non-monotonic contexts, bare conditionals give rise to a universal interpretation in the UE component of the meaning and an existential interpretation in the DE component of the meaning, which is an unexpected behavior for ambiguities. To derive the phenomenon known as Conditional Perfection, an ambiguity approach is forced to assume that the meaning of a bare conditional is resolved universally in computing the assertion and existentially in computing its implicature. In this section we elaborate on (5a) and (5b), deferring the discussion of (5c) to section 5. The common core of all of these arguments is that in cases where one occurrence of a bare conditional is involved in some way in both UE and DE parts of the interpretation, the meaning it contributes splits: universality for the UE part, and existentiality for the DE part. This is not the way ambiguities usually behave, and an ambiguity analysis clearly misses a generalization here. This pattern is above all reminiscent of Higginbotham’s (1986) characterization of if ’s behavior as “chameleon-like”. Let us discuss (5a) first. A familiar test for ambiguity is ellipsis: when an ambiguous phrase is elided, the ambiguity is resolved uniformly in the antecedent VP and the elided VP (Sag 1976; Heim 1996). However, bare conditionals fail this test: when bare conditionals are elided and the antecedent VP and the elided VP are in contexts with different monotonicity (namely when one of them is in a UE context and the other in a DE context), as in (6), they give rise to different quantificational forces. The conditional in the antecedent VP, which is in a UE context, is interpreted universally (6a), while the elided one, which is in a DE context, is interpreted existentially (6b). (6) Every boy calls his mother if he gets an A, and no girl does. ≈ a. For every boy x, in all cases where x gets an A, x calls x’s mother, and b. there is no girl x s.t. there is a case where x gets an A and x calls x’s mother. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 127 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals An ambiguity analysis would predict either a universal meaning for both VPs, or an existential meaning for both. However, neither of these meanings is in fact attested, while the attested meaning is not predicted. Turning to (5b), when a bare conditional is embedded in a non-monotonic context as in (7), the salient reading is one where the conditional seems to contribute a universal meaning for the UE component of the meaning and an existential meaning for the DE component. (7) Exactly two students call their mother if they get an A. ≈ a. UE component: There are two students x, s.t. in all cases where x gets an A, x calls x’s mother. b. DE component: There are no more than two students x s.t. there is a case where x gets an A and x calls x’s mother. Here too, an ambiguity analysis would presumably predict either a universal meaning for both components or an existential meaning for both, but not the attested reading where each component draws a different quantificational force from the bare conditional. This is the puzzling situation in which we find ourselves now: In UE contexts bare conditionals behave like universal quantifiers, and in DE contexts they behave like existential quantifiers. An ambiguity analysis then seems appealing, but their behavior in VP ellipsis constructions and in non-monotonic contexts suggests that it is not on the right track.6 A more promising direction is to assume one basic meaning and derive the other one from it. But which one should we choose as the basic meaning, the universal or the existential one, and how to derive the one from the other? It might seem intuitive to choose the universal meaning as the starting point. However, we see no empirical or theoretical reason to assume that the basic semantics of bare conditionals surfaces in UE contexts rather than DE contexts. Our proposal will in fact follow the less intuitive strategy, and take the weak existential meaning to be the basic one. To prepare the ground, in the next section we provide a preliminary reason for this choice, based on the similar behavior of bare conditionals and Free Choice disjunction which is standardly assumed to involve a basic weak semantics. In section 5.4 we provide evidence supporting an existential semantics from comparing Conditional Perfection with bare and non-bare conditionals. 3. Towards a unified account: Analogy with Free Choice disjunction Embedding the disjunctive marker or under an existential modal gives a stronger-than-expected conjunctive inference. This phenomenon is known as Free Choice (FC) and is illustrated in (8a). Since at least Kratzer and Shimoyama (2002), it has been argued that the FC inference of 6 Note, however, that to account for (6) and (7) one can salvage the ambiguity analysis with a more involved story such as the supervaluationist one suggested in Spector (2013) for homogeneity in definite plurals. Very roughly, the idea would be that for a sentence containing a bare conditional to be super-true, it should be true under both possible meanings. Even though we have no argument to show against this kind of analysis, our proposal in section 4 avoids assuming an unwarranted ambiguity, and instead utilizes mechanisms that are independently argued for. We leave a thorough comparison between the two approaches to further research. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 128 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals (8a) has the status of a scalar implicature, since it tends to disappear under DE operators, (8c): (8) a. b. c. John is allowed to eat ice-cream or cake ◇(A ∨ B) ≈ John is both allowed to eat ice-cream and allowed to eat cake ◇A ∧ ◇B Everyone is allowed to eat ice-cream or cake ∀x[◇(A(x) ∨ B(x))] ≈ Everyone is both allowed ice-cream and allowed cake ∀x[◇A(x) ∧ ◇B(x)] No one is allowed to eat ice-cream or cake ¬∃x[◇(A(x) ∨ B(x))] ≉ No one is both allowed ice-cream and allowed cake ¬∃x[◇A(x) ∧ ◇B(x)] The pattern in (8) parallels the data from bare conditionals in (1). In both, a universal/conjunctive meaning appears in UE contexts and disappears in DE contexts. Moreover, consider the ellipsis example in (9) and the non-monotonic example in (10) in comparison to (6) and (7). (9) (10) Every boy is allowed to eat ice cream or cake, and no girl is. ≈ a. For every boy x, x is both allowed to eat ice cream and allowed to eat cake, and b. there is no girl x s.t. x is allowed to eat ice cream or cake. Exactly two children are allowed to eat ice cream or cake. ≈ a. UE component: There are two children x, s.t. x is both allowed to eat ice cream and allowed to eat cake. b. DE component: There are no more than two children x s.t. x is allowed to eat ice cream or cake. In both FC and bare conditionals, then, whenever one occurrence is involved in providing meaning to both UE and DE components of the meaning, we get a conjunctive/universal meaning for the UE component and a disjunctive/existential meaning for the DE component. This similarity points towards a unified treatment of both phenomena. We follow Fox (2007) and others in assuming that FC disjunction involves the regular weak semantics of disjunction, and consequently assume a weak existential semantics for bare conditionals in analogy to it (for a more direct motivation see section 5.4). In the next section we propose an account of the quantificational split in bare conditionals using the same mechanism that derives FC inferences in Fox (2007), namely grammatical strengthening via recursive exhaustification. For reasons of space, we cannot spell out a full derivation of FC, rather we refer the reader to Fox (2007) for details and move on to present our analysis of bare conditionals.7 4. Proposal 4.1. The plot We propose that bare conditionals not only can have existential semantics as Herburger (2015a) has it, but rather this is the only semantics they have. The universal interpretation of bare conditionals in UE contexts is arrived at by grammatical strengthening, via recursive exhaustification over alternatives. Our answer to Higginbotham’s puzzle is summarized in (11). 7 Embedded FC data as in (8b) (and also (9) and (10)) don’t follow from Fox’s analysis without additional assumptions (see, e.g., Chemla 2009). We will return to this issue later (see footnote 15). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 129 I. Bassi & M. E. Bar-Lev (11) A unified existential semantics for bare conditionals Proposal in a nutshell: a. Bare conditionals are underlyingly existential across the board. b. In UE contexts they undergo grammatical strengthening and become universal. c. In DE contexts their basic existential meaning is preserved. In section 4.2 we lay out the details of the proposal. We do so in steps: we first introduce our assumptions about the core existential meaning of a bare conditional and the alternatives it triggers. Then we proceed to show how, with the help of recursive exhaustification, we can get from the basic existential meaning to the stronger universal meaning in UE environments, while preserving the basic existential meaning in DE environments. In section 4.3 we show how the analysis deals with the challenges from section 2. In section 4.4 we discuss the structure of alternatives we’re assuming and its implications on the difference between bare and non-bare conditionals. 4.2. A unified existential semantics We assume a semantics in which bare conditionals quantify existentially over antecedent worlds, restricted by a domain of quantification Ds . As can be seen in (12), we assume that Ds is syntactically realized and serves to restrict the domain of quantification for if :8 (12) JIfDs p, qK = 1 iff ∃w ∈ JpK ∩ Ds [JqK(w) = 1] (12) straightforwardly accounts for the cases where existential quantification was needed, such as (2). To derive the universal meaning in UE contexts, we hypothesize that bare conditionals trigger Sub-Domain Alternatives (SDAs) of the conditional, in the spirit of Chierchia (2013)’s analysis of Polarity Sensitive Items (see also Bar-Lev and Margulis 2014). (13) Hypothesis: ifDs gives rise to Sub-Domain Alternatives (SDAs). The SDAs we assume are derived by replacing the original domain variable Ds with its subsets: (14) Sub-Domain Alternatives: Alt(ifDs p, q) ⊇ {ifD′s p, q ∣ D′s ⊆ Ds } By way of illustration, take (1a) (repeated in (15)) as an example and assume a toy model with a set {h1 ,h2 } of two working hard worlds, in (16a), and a set {nh1 ,nh2 } of two non-working hard worlds, in (16b). Then the basic meaning of (15) is in (17a), and its domain alternatives, generated by replacing the Ds with its subsets (as prescribed by (14)), are in (17b): (15) (16) If you work hard you succeed. [=(1a)] Ds = {h1 ,h2 ,nh1 ,nh2 } 8 We will have nothing to say here about how the domain of quantification Ds is determined. We also don’t commit to what exactly is quantified over: it could be worlds, situations, events, etc. For concreteness we stick to worlds throughout our discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 130 I. Bassi & M. E. Bar-Lev a. b. (17) a. b. A unified existential semantics for bare conditionals JYou work hardK = {h1 ,h2 } JYou don’t work hardK = {nh1 ,nh2 } Basic meaning of (15) ∃w ∈ JYou work hardK ∩ Ds [you succeed in w] = ∃w ∈ {h1 ,h2 }[you succeed in w] = You succeed in h1 ∨ You succeed in h2 Sub-Domain Alternatives of (15) {ifD′s you work hard you succeed ∣ D′s ⊆ {h1 ,h2 ,nh1 ,nh2 }} (in short: a ∨ b) Looking at the denotations of the elements in (17b), we can translate (17b) to (18).9 Note that the relationship between the basic meaning (17a) and the SDAs (18b-c) can be rendered in terms of the relationship between a disjunction and its disjuncts. For this reason, we shorten the former to a ∨ b and the latter to a and b. (18) Sub-Domain Alternatives of (15) a. ∃w ∈ {h1 ,h2 }[you succeed in w] (= (17a))10 b. ∃w ∈ {h1 }[you succeed in w] = You succeed in h1 c. ∃w ∈ {h2 }[you succeed in w] = You succeed in h2 a∨b a b The domain alternatives have to be used up by an alternative sensitive operator, i.e., they are obligatorily exhaustified (as in Chierchia 2013).11 Following Fox (2007), we assume a covert EXH operator as defined in (19). EXH takes the prejacent and a set of alternatives and returns the prejacent conjoined with the negation of all INNOCENTLY EXCLUDABLE (IE) alternatives. Informally, the restriction to IE alternatives amounts to the requirement that exclusion of alternatives does not contradict the prejacent and that the choice of alternatives to exclude is not arbitrary. (19) (20) JEXHK(Alt(p))(p)(w) ⇔ p(w) ∧ ∀q ∈ IE(p,Alt(p))[¬q(w)] (Where Alt(p) is the set of alternatives of the prejacent p) IE (p,Alt(p)) = ⋂{Alt(p)′ ⊆ Alt(p) ∶ Alt(p)′ is a maximal set in Alt(p), s.t. {¬q ∶ q ∈ Alt(p)′ } ∪ {p} is consistent} The parse we propose for bare conditionals that yields universal interpretation contains two EXH operators: Here and throughout we neglect SDAs in which the sub-domain D′s is such that JpK ∩ D′s = ∅. These alternatives are not represented because they are contradictory, and therefore don’t affect the alternative computation mechanism (to be discussed shortly). 10 This is technically a SDA because by definition, the prejacent is a SDA of itself. But when talking about SDAs, we will sometime mean only “proper” sub-DAs, i.e. excluding the prejacent. 11 It is crucial that exhaustification here would be obligatory and that the SDAs cannot be ignored (‘pruned’), since otherwise we would wrongly predict that the universality of bare conditionals could be cancelled: (i) #If you work hard you succeed, and if you work hard you might fail. We leave open the important issue of how to motivate and implement this obligatoriness, and refer the reader to the discussion in Chierchia (2013). See also footnote 23. 9 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 131 I. Bassi & M. E. Bar-Lev (21) EXHC′ [α EXHC A unified existential semantics for bare conditionals [ifDs you work hard you succeed ] ] (Where C in EXHC [φ ] is the set of alternatives of φ , namely Alt(φ )) The semantic computation of (21) is given in (22), using the toy model and the abbreviations introduced above. The final step of (22) reveals that the basic existential meaning of the conditional was strengthened via double exhaustification to a universal meaning. (22) a. b. c. d. e. f. JIfDs you work hard you succeedK = 1 iff ∃w ∈ {h1 ,h2 }[You succeed in w] = You succeed in h1 ∨ You succeed in h2 = a ∨ b (cf. (17a)) C = Alt(a ∨ b) = {a ∨ b,a,b} (cf. (18)) JαK = EXHC [a ∨ b] = a ∨ b (EXH is vacuous because the SDAs are not IE) C′ = Alt(EXHC [a ∨ b]) = {EXHC [a ∨ b], EXHC [a], EXHC [b]} = {a ∨ b, a ∧ ¬b, b ∧ ¬a} J(21)K = EXHC′ [EXHC [a ∨ b]] = (a ∨ b) ∧ ¬(a ∧ ¬b) ∧ ¬(b ∧ ¬a) (All the alternatives in C′ except a ∨ b are IE) = (a ∨ b) ∧ (a ↔ b) = a ∧ b = ∀w ∈ {h1 ,h2 }[you succeed in w]12 Let us go through the steps in (22). Applying EXH once with respect to the set of alternatives in (22b) is in (22c), which corresponds to the phrase we named “α” in (21). Since no alternative is Innocently Excludable (cf. (20)), the result equals to the input—the prejacent. However, the set of alternatives of α is different from the one in (22b); this set is provided in (22d). The set in (22d) turns out to contain the original sentence (a ∨ b), and in addition, ‘only a’ (a ∧ ¬b), and ‘only b’ (b ∧ ¬a). Finally, applying EXH for the second time, this time with respect to the set in (22d), yields (22e). The derived meaning is, roughly, a or b, and not only a, and not only b, which is equivalent to a ∧ b. We have started with a disjunctive assertion, equivalent to an existential one, and ended up with a conjunctive meaning, that is—a universal one, (22f). The derivation straightforwardly extends to models with more than two antecedent worlds. Importantly, the strengthening mechanism does not make the wrong predictions for the DE cases that initially motivated the existential semantics assumption, as in (1c) and (2). DE environments flip entailment relations, so that the prejacent entails (rather than entailed by) all the domain alternatives, see (23c). Therefore applying matrix EXH (any number of times) would not contribute anything to the semantics, cf. (23d). Thus, no strengthening from existential to universal applies when the bare conditional is embedded in a DE environment.13 In (22f) and throughout the paper, we omit the prejacent’s contribution, namely ∃w ∈ {h1 ,h2 }[you succeed in w], whenever we provide a strengthened meaning for it. This is harmless, since we assume as is standard that quantification triggers a non-vacuity presupposition. Furthermore, given this presupposition, the antecedent of a conditional becomes a Strawson-DE environment after the application of recursive EXH. This makes our analysis in line with the generalization that NPIs are licensed in the antecedent of a conditional, if the mechanism responsible for NPI licensing applies above the exhaustivity operators. 13 One might wonder what blocks recursive EXH to appear in an embedded position under the DE operator, which would give us the ¬∀ meaning we claim is absent. On our analysis, this question reduces to the issue of embedded implicatures in DE environments (Fox and Spector 2013, Chierchia 2013 a.o.), which are known to arise only in special, non-neutral contexts, and require a specific intonation. (i) a. He didn’t talk to Mary or Sue. # He talked to both 12 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 132 I. Bassi & M. E. Bar-Lev (23) a. b. c. d. A unified existential semantics for bare conditionals No one will succeed if they goof off [=(1c)] Jno one will succeed ifDs they goof offK ⇔ ¬∃x[∃w ∈ Jgoof offK(x) ∩ Ds [x succeeds in w]] (23b) ⇒ ∀D′s ⊆ Ds [¬∃x[∃w ∈ Jgoof offK(x) ∩ D′s [x succeeds in w]]] (All domain alternatives of (23b) are entailed by (23b)) Jno one will succeed ifDs they goof offK ⇔ J(EXH) EXH no one will succeed ifDs they goof offK ⇔ ¬∃x[∃w ∈ Jgoof offK(x) ∩ Ds [x succeeds in w]] (Any matrix EXH attached to (23b) is vacuous) What about cases where the bare conditional is in the scope of a universal quantifier, such as (24a)? To derive the right result for these, we must assume that the recursive EXH is embedded under the universal quantifier, (24b). The resulting semantics is in (24c), which is essentially just the embedding of (21) under everyone.14 (24) a. b. c. Everyone will succeed if they work hard Everyone λ x [EXH [ EXH [x will succeed ifDs x works hard] ] ]. J(24b)K ⇔ ∀x[∀w ∈ Jwork hardK(x) ∩ Ds [x succeeds in w]] [=(1b)] For now the assumption of local exhaustification under every is admittedly a stipulation.15 However, the same stipulation is needed to account for Free Choice disjunction embedded under universal quantification as in (8b), given Fox (2007)’s analysis (see Chemla 2009; Singh et al. 2016). 4.3. VP ellipsis resolution and non-monotonic contexts We saw in section 2 that a lexical ambiguity theory along the lines of Herburger (2015b) runs into problems in the face of the behavior of conditionals in VP ellipsis constructions and in non-monotonic contexts. Regarding the VP-ellipsis data, recall that the problem was how to predict that in a case like (25) the conditional in the antecedent contributes universal semantics, and the one in the elided VP existential semantics. On our proposal, the LF of (25) is in (26). b. He didn’t talk to Mary OR Sue. He talked to both. The general dispreference of embedded implicatures is taken by many to result from a violable (pragmatic) principle that prohibits implicatures from weakening the global meaning of the sentence. We thus take such a principle to be responsible for the general inavailabililty of ¬∀ intepretations of negated bare conditionals. Herburger (2015a) argues that universal bare conditionals in DE contexts do exist, based on examples such as (ii). (ii) a. It is not true that if a fair coin is flipped it will come up heads. b. If a fair coin is flipped it will NOT come up heads. We take the fact that such readings, if they exist, are only available with what is arguably “meta-linguistic negation” as in (iia) or special intonation as in (iib) to parallel the facts in (i) and thus to be in line with our approach. 14 And here too, just like in (21), we ignore the SDAs that yield contradictory propositions, see footnote 9. That is, for each individual x quantified over by everyone, the SDAs that end up being entailed by the recursive EXH in (24b) are only those for which D′s ∩ JpK(x) ≠ ∅. 15 This stipulation can be dispensed with if we use the exhaustification mechanism proposed by Bar-Lev and Fox (in prep.), who provide an analysis of the embedded Free Choice inference of (8b) that doesn’t rely on embedded exhaustification, and instead uses only matrix EXH. In this paper we preferred to use the more familiar mechanism of recursive exhaustification from Fox (2007) over Bar-Lev and Fox’s solely due to the unfamiliarity of the latter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 133 I. Bassi & M. E. Bar-Lev (25) (26) A unified existential semantics for bare conditionals Every boy calls his mother if he gets an A, and no girl does. ≈ [=(6)] a. For every boy x, in all cases where x gets an A, x calls x’s mother, and b. there is no girl x s.t. there is a case where x gets an A and x calls x’s mother. Every boy λ x EXH EXH [VP x calls x’s mother ifDs x gets A], and (EXH) no girl does λ x [VP x calls x’s mother ifDs x gets A]. (26) produces the desired quantificational split between the antecedent and the elided VP, and at the same time both are LF-identical.16 The crucial assumption is that the EXH operators can be outside the VPs, which allows the two VPs to be semantically identical even though we ultimately derive a different quantificational force for each bare conditional. This is similar to the way that generally EXH operates in VP ellipsis constructions. For example, in (27a) the antecedent VP contains some which is intuitively interpreted exhaustively as some but not all, while in the elided VP some is interpreted non-exhaustively under negation (see Fox 2004 for a similar data point, attributed to Tamina Stephenson, p.c.). This is explained if the representation of (27a) is (27b). (27) a. b. John solved some of the problems and Mary didn’t. EXH John [VP solved some of the problems], and (EXH) Mary didn’t [VP solve some of the problems]. The proper analysis of the non-monotonic example in (7) within our framework requires some elaboration which for space limitations we cannot provide here. However, given the close analogy between (7) and the FC disjunction example (10) discussed in section 3, and given that we proposed that FC disjunction and bare conditionals share an underlying mechanism, the facts in (7) will fall out from an exhaustification-based analysis of (10). Under an ambiguity theory, on the other hand, it is not clear how the facts in (7) can be explained, given the way ambiguities usually behave. 4.4. The structure of alternatives in bare vs. non-bare conditionals For the derivation of universality in (22) to be successful, it was crucial that the bare conditional didn’t have a universal alternative (which amounts to a ∧ b in our toy model above), as schematized in (28). Had it been present, EXH would have negated it, and we would have achieved the opposite of what our goal is. 16 We are aware that the representation in (26) is problematic in light of established constraints on binding in parallelism contexts. Specifically, (26) does not respect the standard requirement that the binder of any elided bound variable be inside the parallelism domain for ellipsis (e.g. Heim 1996; Hartman 2011. See Crnič 2015 for arguments showing that EXH enters into parallelism considerations). We aim to avoid this obstacle in future work by using a mechanism that can derive universal Free Choice globally and assuming the representation in (i) (see footnote 15). (i) [EXH Every boy [VP λ x x calls x’s mother ifDs x gets A], and (EXH) no girl does [VP λ x x calls x’s mother ifDs x gets A]] We thank Luka Crnič for bringing up this issue. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 134 I. Bassi & M. E. Bar-Lev (28) A unified existential semantics for bare conditionals X  Alt((1a)) = Alt(a ∨ b) = {a ∨ b,a,b  ,aX ∧ b }. X (cf. (22b)) We justify the assumption that bare conditionals don’t have the universal meaning as an alternative by the fact they don’t seem to have a lexical scalar alternative at all. In this we follow other analyses that make use of the lack of a strong alternative for strengthening a weak element. See a.o. Meyer (2016); Bar-Lev and Margulis (2014); Bowler (2014); Singh et al. (2016); Oikonomou (2016). Moreover, potential stronger alternatives like if p, must q would involve adding lexical material to the prejacent, an operation which is ruled out by structural (complexity-based) approaches to alternatives, see Katzir (2007); Fox and Katzir (2011). This perspective has interesting consequences when we consider non-bare conditionals (i.e., conditionals with an overt quantificational element, exemplified in (29)): it allows us to capture the semantic difference between bare and non-bare conditionals solely based on the kinds of alternatives they generate. We assume along with the Kratzerian tradition (Kratzer 1986) that the quantification in non-bare conditionals is contributed by the overt quantifier (and there is no additional layer of quantification). (29) a. b. If you work hard you sometimes succeed. If you work hard you always succeed. Of course, (29a) is not interpreted universally like (29b), and moreover it gives rise to the inference that (29b) is false. We capture this by the fact that crucially, and differently from bare conditionals, the overt quantifier in a non-bare conditional can be replaced with a stronger/weaker quantifier without making the structure more complex. Namely, (29a) has (29b) as an alternative. Given our toy model from above, this feature of non-bare conditionals amounts to admitting a ∧ b into the set of alternatives of (29a), in contrast to bare conditionals: (30) Alt((29a)) = Alt( a ∨ b ) = {a ∨ b,a,b, a ∧ b } ± ± (29a) (29b) Thus, only bare conditionals undergo strengthening into a universal meaning, due to the absence of a universal alternative; non-bare existential conditionals cannot undergo such strengthening, since they generate a universal alternative which blocks this derivation. We return to non-bare conditionals in the context of Conditional Perfection in section 5.4. 5. Only if and Conditional Perfection In section 2 we presented data from VP ellipsis (6) and non-monotonic contexts (7) showing that when one occurrence of a bare conditional is involved in some way in both UE and DE contexts, the meaning it contributes splits: universality for the UE context, and existentiality for the DE context. In this section we provide one more piece of evidence showing the same behavior, from Conditional Perfection. Furthermore, we argue that Conditional Perfection data provides additional support to the conjecture that bare conditionals are underlyingly existential. Before we get to that, however, we have to take a small detour and discuss the analysis of only if sentences. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 135 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals 5.1. Only if Only if sentences as in (31) have been argued to show another instance of a bare conditional interpreted existentially (see von Fintel 1997; Herburger 2015a). Since only is standardly assumed to presuppose its prejacent and assert the negation of its alternatives, the prejacent is in a Strawson-DE environment (von Fintel 1999). The existential interpretation is then expected given the generalization stated in section 1 upon which Higginbotham’s puzzle is based. (31) Only if you work hard you succeed. What are the compositional details of (31) that produce the correct result? Since only takes a prejacent and a set of alternatives, we have to decide what alternatives are in this set. For simplicity, let us follow von Fintel (1997)’s assumption, according to which the alternative that’s negated by only in a sentence of the form only if p, q is if not-p, q.17 In our case, the relevant alternative for the prejacent of only in (31) would be If you don’t work hard you succeed. The interpretation of (31) can then be paraphrased as in (32). The important observation here is that to get the right result for the assertive component, the alternative conditional that only negates cannot contribute a universal meaning, but must contribute an existential meaning; otherwise we would only derive the too-weak meaning in (32bii), which is compatible with there being cases where you don’t work hard and succeed. (32) Only if you work hard you succeed. [=(31)] a. Presupposition: If you work hard you succeed. (See fn. 18) b. Assertion: ¬ if you don’t work hard you succeed. (i) ≈ ¬ there is a case where you don’t work hard and you succeed. (ii) ≉ ¬ in all cases where you don’t work hard you succeed. Herburger shows that the case of only if is predicted by the ambiguity analysis: since only creates a Strawson-DE environment, the prejacent if p, q is interpreted existentially. According to her, this correctly captures the presupposition triggered by only if sentences.18 Crucially, 17 Instead of having if not p, q as the alternative, a more plausible assumption from the perspective of the theory of alternative formation (Katzir 2007) is that we have a set of alternatives of the form if r, q, where r is a relevant alternative to p. The two options ultimately boil down to the same thing (for reasons we can’t go over here), so for ease of exposition we work with the single alternative if not-p, q. We thank Andreas Haida for pointing this out. 18 Our main focus here is capturing the assertive component of only if, and we take no stance on whether the presupposed prejacent of only should indeed be existential. Herburger argues that it should be existential based on contrasts like (i). Famously, whereas (ia) is non-contradictory, (ib) is not (von Fintel 1997): (i) a. Only if you work hard do you succeed, and even if you work hard you might fail. b. #If you work hard you succeed, and even if you work hard you might fail. However, we do not know whether this is a strong argument in favor of the existentiality of the prejacent, since only independently gives rise to presuppositions that are weaker than its prejacent, as the felicity of (ii) shows: (ii) Only JohnF can speak French, and maybe not even he can. (Ippolito 2008: ex. 37) Furthermore, in some environments only does seem to presuppose its prejacent (for ill-understood reasons), e.g., under negation (as can be seen in (iiia)). And accordingly, when embedding only if p, q under negation, it is also much harder to cancel the universal inference that if p, q. Compare (ia) with (iiib): (iii) a. #Not only JohnF can speak French, and maybe he can’t. (Ippolito 2008: ex. 38) b. #Not only if you work hard do you succeed, and if you work hard you might fail. For these considerations, we do not rely on the presupposition of (31) to determine the quantificational force of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 136 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals since the prejacent if p, q is existential, the alternative if not-p, q which is derived from it is interpreted existentially as well. Note, however, that for Herburger the existentiality of the alternatives only follows from the assumption that the prejacent is existential. This point will be crucial in the following discussion of Conditional Perfection inferences, where the prejacent is unarguably interpreted universally, but the alternatives are still interpreted existentially. 5.2. Conditional Perfection (CoP) When an if p, q sentence is uttered, we often understand it as the ‘perfected’ conditional if and only if p, q. For example, utterance of if you work hard you succeed (=(1a)) “invites the inference” (as Geis and Zwicky 1971 put it) that only if you work hard you succeed (=(31)). The Conditional Perfection (CoP) inference is cancellable, (33a), and it disappears under negation, (33b). Therefore, it is widely accepted that CoP should be analyzed as an implicature (Geis and Zwicky 1971; von Fintel 2001, a.o.). (33) a. b. If you work hard you succeed, and you might succeed even if you don’t. No one will succeed if they goof off. [=(1c)] ≉ No one will succeed if and only if they goof off The existence of CoP raises a theoretical difficulty for previous analyses of conditionals, given standard theories of implicature calculation. The challenge, as can be seen by the descriptive characterization of CoP in (34), is to derive an existential meaning at the level of the implicature, while retaining universality for the assertion. One can already see that the issue here is very similar to what we have seen with ellipsis and non-monotonic contexts in section 2: in all three cases, from one occurrence of a bare conditional we want to derive different quantificational forces for different ingredients of the overall meaning. (34) If you work hard you succeed. [=(1a)] a. Assertion: In all cases where you work hard, you succeed. b. Implicature: ¬ there is a case where you don’t work hard and you succeed. To appreciate the problem, assume (i) that the prejacent if p, q triggers the alternative if not p, q, (ii) that this alternative is derived from if p, q by replacing p with not p, and (iii) that this alternative is (optionally) negated, supposedly giving us the inference only if p, q. Hence: If the prejacent if p, q has universal meaning, then if not p, q also has universal meaning. Namely, we should expect the implicature to be the negation of a universal meaning, contrary to fact. It is not straightforward to achieve the right results for CoP in analyses that posit a uniform universal semantics for bare conditionals.19 Even under an ambiguity analysis, it is not clear a bare conditional under only. The relation between this kind of data and FC disjunction embedded under only (see Alxatib 2014) calls for further investigation given our view. We thank Danny Fox and Sam Alxatib for very helpful discussions on this issue. 19 See for instance von Fintel (2001)’s analysis, in which CoP is derived when if p, q has alternatives of the form Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 137 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals why the alternative if not p, q is interpreted existentially: Unlike the case of only if sentences, in CoP the prejacent is definitely not interpreted existentially, but rather universally as can be seen in (34a). The alternative if not p, q, which is generated on the basis of the prejacent, is then also expected to be interpreted universally, contrary to fact.20 5.3. Deriving Conditional Perfection The assumption that bare conditionals are existential provides a simple account of CoP. We assume that if not p, q is an additional (and optional) alternative to if p, q (but see footnote 17). Namely, (34) has the alternative in (35). Being a bare conditional, its basic meaning is existential, (35a). Negating this meaning would then yield the desired CoP inference in (34b). (35) If you don’t work hard you succeed. a. JIfDs you don’t work hard you succeedK = 1 iff ∃w ∈ JYou don’t work hardK ∩ Ds [you succeed in w] Let us show the derivation in some more detail, illustrating with our toy model from (16) in which JYou work hardK = {h1 ,h2 } and JYou don’t work hardK = {nh1 ,nh2 }. The alternatives we generate for (34) when we add (35) are listed in (36). (36a) repeats from (18) the by-now familiar SDAs of (34). (36b) is the meaning of the new alternative (35) given our toy model. This alternative is logically independent from the prejacent in (36a-i) and the other SDAs in (36a-ii,iii), since its domain of quantification is disjoint from theirs, and we can thus name it c. The resulting set of alternatives, which we call C+ , is in (36c). (36) a. b. Sub-Domain Alternatives of (34) (see (18)) (i) ∃w ∈ {h1 ,h2 }[you succeed in w] (= (17a)) a∨b (ii) ∃w ∈ {h1 }[you succeed in w] = You succeed in h1 a (iii) ∃w ∈ {h2 }[you succeed in w] = You succeed in h2 b If not p, q alternative of (34) ∃w ∈ {nh1 ,nh2 }[you succeed in w] = You succeed in nh1 ∨ You succeed in nh2 c if r, q where r denotes any proposition, and importantly propositions that pick out a singleton set of worlds. This essentially reduces universal quantification to existential quantification. On the cost of such reduction see footnote 22. 20 Herburger (2015b) adopts a non-standard way of implicature calculation to get the right result within her ambiguity approach. For her, an implicature for a sentence S is derived by adjoining to S a covert and only S. Effectively, the result is that the prejacent and its alternatives are in environments of different monotonicity. Thus CoP is derived with the structure if p, q and only if p, q, where there are two occurrences of if p, q: the overt one is in a UE environment, hence we get a universal prejacent, and the covert one is in a DE environment, hence we get existential alternatives. This kind of analysis faces some problems. First, recall our argument against ambiguity from ellipsis (section 2), which was based on the fact that ambiguities cannot be interpreted differently in the antecedent material and the elided material. However, Herburger’s analysis of CoP essentially relies on an ellipsis construction, and on the idea that the overt if p, q can be interpreted universally while the elided if p, q is interpreted existentially. Thus our argument from ellipsis extends to her treatment of CoP. Second, it is not clear to us what motivation there is for such an analysis of implicatures other than the CoP data. Third, since the CoP data mirrors the chameleonic behavior of bare conditionals in ellipsis constructions and in non-monotonic contexts, for which such an analysis is not available, a principled analysis for all of these cases is called for. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 138 I. Bassi & M. E. Bar-Lev c. A unified existential semantics for bare conditionals Enriched set of alternatives of (34) C+ = {a ∨ b,a,b,c} Given C+ , the result of recursive EXH is in (37). The if not p, q alternative c is negated by the lower EXH without affecting the workings of the higher EXH. Namely, adding the if not p, q alternative to the set of alternatives of if p, q does not interfere with the generation of universality for the latter, essentially because their domains of quantification are disjoint. (37) JEXHC+ ′ ifDs you work hard you succeedK = 1 iff ∀w ∈ {h1 ,h2 }[you succeed in w] ∧ ¬∃w ∈ {nh1 ,nh2 }[you succeed in w] ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹¶ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ EXHC+ Universal strengthening (matrix EXH) (≈(34a)) CoP inference (embedded EXH) (≈(34b)) In sum, the fact that bare conditionals give rise to a universal meaning in their assertion and an existential meaning in their implicature is predicted under our analysis. 5.4. Conditional Perfection with non-bare conditionals as evidence for an existential semantics for bare conditionals In section 2 we have presented arguments against an ambiguity analysis of bare conditionals, and in section 3 we proposed a unified existential semantics based on the analogy with FC disjunction. In the previous section we have shown that the existential semantics assumption correctly predicts the CoP inferences of bare conditionals with no further complications. In what follows we present another motivation for the assumption that the basic semantics of bare conditionals is existential, coming from the behavior of CoP with non-bare conditionals. A fact that (to our knowledge) has been largely unnoticed is that the behavior of non-bare conditionals is different from that of bare conditionals with respect to CoP. As Herburger (2015b) observes, when the conditional contains an overt universal adverb that the if -clause restricts, as in (38), we get a weaker CoP implicature than with bare conditionals, namely (38a) rather than (38b).21 This difference between (38a) and the CoP inference of bare conditionals in (34b) is already surprising if we assume that bare conditionals are universals.22 (38) If you work hard, you always succeed. a. ↝ Weak CoP: if you don’t work hard, you don’t always succeed. b. ↝̸ Strong CoP: if you don’t work hard, you don’t succeed. Even more striking is the fact that existential non-bare conditionals like (39) give rise to strong 21 An issue that arises is why (38) doesn’t have (i) as an alternative, the negation of which would produce the unattested strong CoP in (38b). (i) If you don’t work hard, you sometimes succeed. A possible way to avoid it is to assume a non-weakening constraint on the generation of alternatives, as suggested in Fox (2007: fn. 35) (see also Romoli 2012; Trinh and Haida 2015), such that (i) would not be generated. 22 Under von Fintel (2001)’s analysis of CoP (see footnote 19), for instance, there is no apparent reason why non-bare universal conditionals should not generate alternatives where the antecedent picks out singleton sets of worlds, while this option would be available for bare conditionals. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 139 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals CoP, in (39a), just like bare conditionals do. (39) If you work hard, you sometimes succeed. a. ↝ Strong CoP: if you don’t work hard, you don’t succeed. We take this pattern as further evidence that the basic semantics of bare conditionals should be existential, in light of their resemblance to existential rather than universal non-bare conditionals in terms of the kind of implicatures they give rise to. Admittedly, this is indirect evidence. However, as we have seen the chameleonic behavior of bare conditionals leaves little room for direct evidence. 6. Concluding remarks Higginbotham’s puzzle casts doubts on views according to which bare conditionals are uniformly interpreted universally. We have shown however that a simple ambiguity theory such as Herburger’s is also questionable given the behavior of bare conditionals in VP ellipsis constructions and in non-monotonic contexts, as well as Conditional Perfection data. We argued for a unified existential semantics for bare conditionals, based on (i) the similarity in distribution between their quantificational force and the availability of Free Choice inferences for disjunction under an existential modal, and (ii) the fact that their Conditional Perfection inferences pattern with those of existential non-bare conditionals rather than universal ones. Following the analogy with FC disjunction, we proposed an analysis that derives the universality of bare conditionals in UE contexts using the same mechanism of grammatical strengthening utilized by Fox (2007) to derive FC inferences. The crucial assumptions for this derivation to go through are (i) that bare conditionals give rise to sub-domain alternatives which are obligatorily exhaustified (as in Chierchia 2013’s analysis of NPIs), and (ii) that bare conditionals don’t have a universal alternative. One might wonder about the seemingly stipulative nature of assuming obligatory sub-domain alternatives for bare conditionals. We have no direct evidence for this assumption, and it is currently justified only in so far as it (together with independently suggested mechanisms) predicts the correct pattern of behavior. However, an interesting line of research worth pursuing is that sub-domain alternatives are generated for the restrictor of every quantificational operator, but their effect is mainly noticeable when there is no scalar alternative (see section 4.4). If this is developed successfully, then the assumption that bare conditionals give rise to sub-domain alternatives would be just a special case of this hypothesis.23 The analysis presented here opens up a new line of investigation into the research of homogeneity phenomena in general, of which Higginbotham’s puzzle is arguably only one manifestation. A notable case in point is definite plurals: it has been suggested by Magri (2014), following 23 The assumption that these alternatives are obligatorily exhaustified requires further justification, which we are unable to provide yet. A promising direction, though, is to relate it to Singh et al. (2016)’s independently motivated proposal that applying EXH is highly preferred when it provides the complete answer to the Question Under Discussion. Note that the universal meaning we derive for (1a) by applying EXH provides the complete answer to the question under what circumstances do you succeed?, while the basic existential meaning doesn’t. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 140 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals Spector (2007), that definite plurals bear existential semantics which is strengthened in UE environments, on similar lines to what we propose. Independently, Schein (2003) and Schlenker (2004) have suggested an analysis of conditionals as definite plurals. Brought together, these approaches may lead to a new perspective on homogeneity phenomena. In future work we hope to compare this perspective with other approaches, most notably Križ (2015). References Alxatib, S. (2014). Free choice disjunctions under only. In Proceedings of NELS 44. Bar-Lev, M. E. and D. Fox (in prep.). Universal free choice and innocent inclusion. Bar-Lev, M. E. and D. Margulis (2014). Hebrew kol: A universal quantifier as an undercover existential. In U. Etxeberria, A. Fălăuş, A. Irurtzun, and B. Leferman (Eds.), Proceedings of Sinn und Bedeutung 18, pp. 60–76. Bowler, M. (2014). Conjunction and disjunction in a language without ‘and’. In Semantics and Linguistic Theory 24, pp. 137–155. Chemla, E. (2009). Universal implicatures and free choice effects: Experimental data. Semantics and Pragmatics 2(2), 1–33. Chierchia, G. (2013). Logic in Grammar: Polarity, Free Choice, and Intervention. OUP. Crnič, L. (2015). Ellipsis, parallelism, and polarity. In Semantics and Linguistic Theory 25, pp. 308–327. Dalrymple, M., M. Kanazawa, S. Mchombo, and S. Peters (1994). What do reciprocals mean? In Semantics and Linguistic Theory 4, pp. 61–78. von Fintel, K. (1997). Bare plurals, bare conditionals, and only. Journal of Semantics 14(1), 1–56. von Fintel, K. (1999). NPI licensing, Strawson entailment, and context dependency. Journal of Semantics 16(2), 97–148. von Fintel, K. (2001). Conditional strengthening: A study in implicature. MIT. von Fintel, K. and S. Iatridou (2002). If and when if clauses can restrict quantifiers. Unpublished MS, MIT. Fox, D. (2004). Implicature calculation, pragmatics or syntax, or both? Class notes on Implicatures and Exhaustivity, USC, November 2004. Fox, D. (2007). Free choice and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and Implicature in Compositional Semantics, pp. 71–120. London: Palgrave Macmillan. Fox, D. and R. Katzir (2011). On the characterization of alternatives. Natural Language Semantics 19(1), 87–107. Geis, M. and A. Zwicky (1971). On invited inferences. Linguistic Inquiry 2, 561–566. Hartman, J. (2011). The semantic uniformity of traces: Evidence from ellipsis parallelism. Linguistic Inquiry 42(3), 367–388. Heim, I. (1996). Lecture notes in ellipsis. Unpublished, MIT. Herburger, E. (2015a). Only if: If only we understood it. In E. Csipak and H. Zeijlstra (Eds.), Proceedings of Sinn und Bedeutung 19, pp. 284–301. Herburger, E. (2015b). Conditional perfection: The truth and the whole truth. In Semantics and Linguistic Theory 25. Higginbotham, J. (1986). Linguistic theory and Davidson’s program in linguistics. In E. LePore Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 141 I. Bassi & M. E. Bar-Lev A unified existential semantics for bare conditionals (Ed.), Truth and Interpretation: Perspectives on the Philosophy of Donald Davidson, pp. 29– 48. Oxford: Basil Blackwell. Huitink, J. (2010). Quantified conditionals and compositionality. Language and Linguistics Compass 4(1), 42–53. Ippolito, M. (2008). On the meaning of only. Journal of Semantics 25(1), 45–91. Katzir, R. (2007). Structurally-defined alternatives. Linguistics and Philosophy 30(6), 669– 690. Klinedinst, N. (2011). Quantified conditionals and conditional excluded middle. Journal of Semantics 28(1), 149–170. Kratzer, A. (1986). Conditionals. Chicago Linguistics Society 22(2), 1–15. Kratzer, A. (2015). Chasing hook: Quantified indicative conditionals. In L. Walters and J. Hawthorne (Eds.), Conditionals, Probability, and Paradox: Themes from the Philosophy of Dorothy Edgington. Oxford: OUP. Kratzer, A. and J. Shimoyama (2002). Indeterminate pronouns: The view from Japanese. In Y. Otsu (Ed.), 3rd Tokyo Conference on Psycholinguistics, pp. 1–25. Hituzi Syobo, Tokyo. Križ, M. (2015). Aspects of Homogeneity in the Semantics of Natural Language. Ph. D. thesis, University of Vienna. Leslie, S.-J. (2008). “if”, “unless”, and quantification. In R. J. Stainton and C. Viger (Eds.), Compositionality, Context and Semantic Values: Essays in Honour of Ernie Lepore. OUP. Magri, G. (2014). An account for the homogeneity effects triggered by plural definites and conjunction based on double strengthening. In Pragmatics, Semantics and the Case of Scalar Implicatures, pp. 99–145. London: Palgrave Macmillan. Meyer, M.-C. (2016). Generalized free choice and missing alternatives. Journal of Semantics 33(4), 703–754. Oikonomou, D. (2016). Imperatives are existential modals: Deriving the strong reading as an implicature. In Semantics and Linguistic Theory 26, pp. 1043–1062. Romoli, J. (2012). Soft but Strong. Neg-raising, Soft Triggers, and Exhaustification. Ph. D. thesis, Harvard University. Sag, I. (1976). Deletion and Logical Form. Ph. D. thesis, MIT. Schein, B. (2003). Adverbial, descriptive reciprocals. Philosophical Perspectives 17(1), 333– 367. Schlenker, P. (2004). Conditionals as definite descriptions. Research on Language and Computation 2(3), 417–462. Singh, R., K. Wexler, A. Astle-Rahim, D. Kamawar, and D. Fox (2016). Children interpret disjunction as conjunction: Consequences for theories of implicature and child development. Natural Language Semantics 24(4), 305–352. Spector, B. (2007). Aspects of the pragmatics of plural morphology: On higher-order implicatures. In Presupposition and Implicature in Compositional Semantics, pp. 243–281. Dordrecht: Springer. Spector, B. (2013). Homogeneity and plurals: From the strongest meaning hypothesis to supervaluations. Presented at Sinn und Bedeutung 18. Stalnaker, R. (1968). A theory of conditionals. In N. Rescher (Ed.), Studies in Logical Theory, pp. 98–112. Oxford: Basil Blackwell. Trinh, T. and A. Haida (2015). Constraining the derivation of alternatives. Natural Language Semantics 23(4), 249–270. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 142 Towards a model of incremental composition1 Sigrid BECK — Universität Tübingen Sonja TIEMANN — Universität Tübingen Abstract. This paper reviews some recent psycholinguistic results on semantic processing and explores their consequences for a cognitively plausible model of incremental composition. We argue that semantic composition is neither strictly incremental (in the sense that every incoming word is composed immediately) nor global (in the sense that composition only proceeds when the entire syntactic structure is available). We conjecture that incremental composition is type driven: elements in the same type domain (e.g. temporal <i>) are composed immediately; elements that concern different type domains (e.g. temporal <i> vs. event <v>) cause delayed processing. Keywords: Incrementality, composition, semantic processing. 1. Introduction The central question explored in this paper is how a theory of semantic composition can be combined with processing results arguing that interpretation has incremental properties. Semantic theory takes as its starting point the principle of compositionality: The interpretation of a complex expression is determined by the interpretations of its parts and the way they are combined. This is usually implemented in terms of assigning a compositional interpretation to the complete syntactic representation of the sentence to be interpreted (see standard introductions, e.g. Heim and Kratzer, 1998; Chierchia and McConnel-Ginet, 2000; Zimmermann and Sternefeld, 2014; Beck and Gergel, 2014). However, certain results from psycholinguistic research fairly clearly show that people begin to compose meanings before the end of the sentence has been perceived, so no complete tree is available. A suggestive data point is the familiar garden path effect (Bever, 1970), illustrated in (1) (Ferreira, Christianson and Hollingsworth, 2001). (1) While Anna dressed the baby spit up on the bed. So far, neither compositional semantics nor psycholinguistics has established a psycholinguistically plausible model of how compositional interpretation proceeds incrementally (cf. also e.g. Chater et al., 2001; Bott and Sternefeld, to appear). This is a problematic gap in linguistic theory because results on semantic processing don’t get integrated into a theory of the semantic parser or aligned with the theory of composition. This paper is a contribution towards closing this gap. Our plot is to use a standard semantic framework (concretely a Heim and Kratzer, 1998, type theory) as our starting point, and revise it according to a set of concrete processing results we take to be exemplary, as a step towards a model of incremental composition. 1 We are very grateful to Gerhard Jäger, Detmar Meurers, Lyn Frazier, Florian Schwarz, David Beaver, Mark Steedman, the members of the SFB 833 ‘Construction of Meaning’ and the audience at Sinn und Bedeutung 21, Edinburgh, for their helpful comments on this complex and daunting enterprise. We thank the DFG grant to the SFB 833 ‘Construction of Meaning’ for financial support. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 143 S. Beck & S. Tiemann Towards a model of incremental composition Section 2 defines our task and outlines some relevant existing work in semantics and in psycholinguistics. In section 3, we present the evidence for incremental composition from a set of processing studies and an incremental analysis of those data points. Section 4 combines the results of section 3 and generalizes towards a model of incremental interpretation. Our conclusions are presented in section 5. 2. Specifying the task 2.1. What is needed? Standard semantic theory defines an interpretation function [[.]] recursively. [[.]] maps LF trees to meanings (e.g. Heim and Kratzer, 1998). Compositional interpretation proceeds as sketched in (3) for a simple example. We call this global interpretation. (2) T -- [[]] --> ÈDt (3) a. John invited Bill. b. structure: [IP John [VP invited Bill]] c. [[ [IP John [VP invited Bill]] ]] = 1 iff [[invited]] ([[Bill]]) ([[John]]) = 1 iff John invited Bill. (t a semantic type) (2x Function Application FA) (Lexicon + l-conversion) What if we start interpreting on the basis of a partial structure (4a)? Plausibly we anticipate (4c). A theory that can predict (4c) requires the concepts defined in (5), (6) and (7). (4) a. partial structure: b. from the lexicon: c. projected meaning: [IP John [VP invited … {[[John]], [[invited]]} ly. [[invited]](y)([[John]]) = ly. John invited y (5) a. Let Q be the set of syntactic structures produced by the human parser. Each TiÎQ is a possibly partial syntax tree. b. Let S be the set of interpretations produced by the corresponding human interpretive processor. The elements of S are sets of meanings, i.e. each SiÎS is a set whose members are elements of ÈDt (t a semantic type). c. A pair <Ti, Si> is a stage reached in sentence processing. (6) Incremental processing is a series of mappings <Ti,Si> -> <Ti+1,Si+1> (1≤i≤n) such that (i) Tn is an LF tree; (ii) each mapping Ti -> Ti+1 is a matter of parsing (not our concern here); (iii) each Si is a set of meanings from ÈDt; (iv) card(Sn)=1 (i.e. everything is composed into one meaning in the end); (v) <Tn,Sn> Î[[.]]. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 144 S. Beck & S. Tiemann (7) Towards a model of incremental composition Incremental composition is the derivation of Si+1 from Si. Define a function [[.]]h (‘heuristic interpretation’): Suppose at stage i, the processor receives the structure σ as input, leading to Ti+1. [[.]]h defines a mapping <Ti+1, Si, [[σ]]h > -> Si+1. On the basis of the new tree, the available set of meanings plus the new meaning, a new semantic stage is reached. We can think of the function [[.]]h as an interpretive heuristic. It makes predictions about the meaning of partial trees, yielding a projected or anticipated meaning (which could be proven wrong by further input). A model of incremental composition is a recursive definition of the function [[.]]h. For each stage that the parser may reach, [[.]]h defines the accompanying stage of the interpreter. 2.2. What has been proposed in semantics? Several linguistic frameworks have made proposals towards incremental interpretation, prominently including the categorial grammar tradition. A representative is Combinatory Categorial Grammar CCG (e.g. Ades and Steedman, 1982; Steedman, 2000; Steedman and Baldridge, 2011) and a simple example is given below. The syntax of CCG allows the incremental parse in (8b) — we are still looking for an NP to complete the sentence — and the semantics corresponds to this, employing Function Composition (9) to compose the meaning of the subject and the meaning of the verb as in (8d). (8) a. John invited Bill. b. basic syntax: c. incremental parse: d. semantics: (9) John invited Bill S/(S\NP) (S\NP)/NP NP S\NP John invited S/(S\NP) (S\NP)/NP S/NP [[John]] = λP<e,t>.P(John) [[invited]] = λy.λz.z invited y [[John]]•[[invited]] = [λP<e,t>.P(John)]•[ λy.λz.z invited y] = λx. [λP<e,t>.P(John)]([λy.λz.z invited y](x)) = λx. John invited x Function composition: If g is a function: A->B and f is a function: B->C then f•g : A->C is the composition of f and g with f•g=λx.f(g(x)) The example illustrates what we call strict incrementality. Each new element that is parsed is added immediately to the tree and composed immediately with the semantics already available. At each stage i, card(Si)=1. In section 3, we will reject strict incrementality as a property of the semantic processor. There is a tendency in the CCG tradition towards strict incrementality (recently e.g. Kato and Matsubara, 2015), though details vary and Steedman’s Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 145 S. Beck & S. Tiemann Towards a model of incremental composition (2000) Strict Competence Hypothesis SCH does not lead one to always expect strict wordby-word incrementality (see e.g. Demberg, 2012; Ambati, 2016 for discussion). Outside CCG, our most immediate predecessor in the search of a model of incremental composition is Bott and Sternefeld (to appear). Bott and Sternefeld differ from us in two important respects: (i) they aim for strict incrementality, and (ii) they use a different framework (namely a dynamic Neo-Davidsonian continuation semantics with unconstrained λ-conversion), which we will not present here. But they point out the same gap in linguistic theory (cf. their paper also for further references), they consult an overlapping set of psycholinguistic results to inform their model of incremental composition, and they develop an incremental perspective on complex semantic analyses e.g. of tense and aspect. We return to their paper below. 2.3. What has been done in processing? First, a cautionary note: We want to know when composition of meanings in complex structures occurs; not all results to do with immediate semantic processing are therefore of relevance for us (e.g., a finding could be based on immediate lexical access but not immediate composition; see e.g. Altmann and Kamide, 1999; or Frazier, 1999 for an overview). In recent years, psycholinguistic research on semantics has produced a lot of results on how different phenomena are processed (e.g. quantifiers, presuppositions etc. - a recent overview is given in Pylkkänen and McElree, 2006). The findings indicate particular properties of semantic processing and define certain constraints on it. What has not been established is a semantic processing model in the sense of heuristic composition [[.]]h, i.e. there is no model that we know of (with the exception of Bott and Sternefeld) which describes how actual incremental composition works. There is of course more work on syntactic processing, and this is important as the input to compositional interpretation (see e.g. discussion in Crocker, 2010). Resnik (1992), building on earlier work, argues for an arc-eager left corner parser, i.e. a variant of a left corner parser in which nodes that are predicted bottom-up can be immediately composed with nodes that are predicted top-down. We assume that the syntactic processor continuously integrates new material in a roughly left corner parser fashion. At any point during processing, a partial tree structure like (10) is projected by the syntactic parser. In this paper we simplify in that only one parse tree will be entertained as a possible structure at a time. (Ideally, we would adopt whatever proposal about the parser is best motivated.) Importantly, the tree Ti is the LF structure (the input to compositional interpretation). The terminal nodes in Ti include the words heard so far (in their proper places in the structure). The tree is the projected syntax. (10) a. b. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 146 S. Beck & S. Tiemann Towards a model of incremental composition Another input to compositional interpretation is lexical meaning. There is evidence that the interpretation of lexical terminal nodes is available immediately from the lexicon (e.g. Frazier and Rayner, 1990). Hence we assume that these meanings are added to Si (the set of meanings made available by the parse so far). And finally, compositional interpretation depends on the values assigned to variables. Free variables get their value from the context via the salient variable assignment function gc. When all goes well, they are assigned their values immediately (e.g. Carreiras and Clifton, 1993). The resulting meanings are also added to Si. When there is no salient referent, binding of the variable is preferred; this may lead to a revision of the LF tree in such a way as to include a binder, or to optimize the chances of including a binder (that is, it can lead to delayed semantic interpretation, see section 3.2.; Bott and Schlotterbeck,2013). The anticipated lexical meaning and anticipated contextual reference are the recursion basis for the function [[.]]h: If α is a terminal element, [[α]]h=[[α]]. As an interim summary, we note that two interpretive strategies (11), (12) are made readily available by existing theories of interpretation. As a preview of what is to come, we argue that neither type of approach is the desired model of incremental composition. (Of course Global interpretation is not claimed to be a model of the semantic processor in the first place). (11) Global interpretation: Assume a syntactically complete parse tree T (i.e. no "…"). The meanings in S (here, the terminal nodes in T) are composed by [[.]] according to T and the standard composition principles. (12) Strictly incremental interpretation: Assume an incrementally generated partial tree T, and a set of available meanings S. Whenever card(S)>1, compose the meanings in S according to T and some combinatory heuristic [[.]]h. 3. Some psycholinguistic findings on incremental composition In section 3.1. we collect a set of experimental results that argue for immediate composition in certain sentence contexts, and offer an incremental analysis of these cases. In section 3.2. we consider several cases of delayed composition, i.e. experimental evidence that there is no strictly incremental composition. The section summary sets the scene for our generalizations in section 4. 3.1. Results supporting immediate composition Subject + Verb: There are early effects indicating that before the object is encountered, the meanings of the subject and the verb are already put together (e.g. Kuperberg et al., 2003; Kim and Osterhout, 2005; Kamide et al., 2003; Knoeferle et al., 2005). We take this to mean that subject and verb are interpreted incrementally, before the sentence is finished. (13) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 147 S. Beck & S. Tiemann Towards a model of incremental composition illustrates the relevant structure; # marks the point where studies have found an interpretive effect in processing. (13) The soup greeted … | # This invites the following interpretation: The parse tree contains (14a); this leads to a combination of the meanings of the verb and the subject as in (14b). (14b) can be derived by the heuristic rule in (15). If we suppose that the subject has the type <<e,t>,t> rather than <e>, the alternative formulation in (16) is applicable. (16) amounts to function composition (17). (14) a. projected parse tree contains: b. projected meaning: λy.[[greet]](y)([[the soup]]) = λy.the soup greet y (15) Subject-Verb-Heuristic (SVH): If α= [ βsubj [ γverb … then [[α]]h = λy.[[γ<e,et>]]h(y)([[ β<e>]]h) (16) Subject-Verb-Heuristic (<<e,t>,t> subject) (SVH'): If α= [ βsubj [ γverb … then [[α]]h = λy.[[ β<et,t>]]h([[ γ<e,et>]]h(y)) SVH' defines [[β]]h•[[γ]]h (17) Function composition: If g is a function: A->B and f is a function: B->C then f•g : A->C is the composition of f and g with f•g=λx.f(g(x)) Within DP: There is evidence that determiner and adjective are combined very early on (Sedivy et al., 1999). (18) illustrates this. Our interpretation is that the meaning of the determiner plus the meaning of the NP is incrementally interpreted as indicated in (19). (18) Touch the tall … | # Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 148 S. Beck & S. Tiemann (19) Towards a model of incremental composition a. projected parse tree contains: b. projected meaning: λP.[[the]]([[tall]]∩P) Part of predicting (19b) is the expectation that the meaning of the determiner is applied to a suitable argument, as modelled by the DP-Heuristic below. This heuristic defines predictive Function Application FA. (20) DP-Heuristic: If α= [DP βDet [NP γ … then [[α]]h = [[β]]h ([[NP]]h) Subject + Adverb: Under certain circumstances, people anticipate a complex meaning given the input of a subject plus an adverb, here wieder ‘again’ (Tiemann, 2014; Tiemann et al., 2011). We interpret this as our participants anticipating that the adverb will modify some property attributed to the subject. (21) a. context: Inge hat letzte Woche rote Handschuhe gekauft. Inge has last week red gloves bought b. Susanne hat wieder… Susanne has again | # (22) a. projected parse tree contains: b. projected meaning: λP<e,vt>. [[wieder]]( λe.P(e)(Susanne)) = λP<e,vt>.λe:∃e'[e'<e & P(e')(Susanne)].P(e)(Susanne) This projected meaning can be predicted by the heuristic rule in (23). Once more, if the subject is taken to be of type <<e,t>,t> rather than <e>, the heuristic is rephrased in such a way as to reveal it as function composition (24). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 149 S. Beck & S. Tiemann Towards a model of incremental composition (23) <v,t>-Adverb-Subject Heuristic (AdvSH): If α= [[ βsubj …] γadverb ] and γ is of type <vt,vt>, then [[α]]h = λP<e,vt>.[[γ]]h(P([[ β]]h)) (24) <v,t>-Adverb-Subject Heuristic (<<e,t>,t> subject) (AdvSH'): If α= [[ βsubj …] γadverb ] and γ is of type <vt,vt>, then [[α]]h = λP<e,vt>.[[γ]]h([[ β]]h(P)) AdvSH' defines [[γ]]h•[[β]]h Temporal Adverb + Tense: Bott (2010) found that participants respond immediately to a mismatch between verbal tense and the meaning of an adverb, as in (25). Our take on what happens in processing is (26). (25) Morgen tomorrow gewann… won | # (26) a. projected parse tree contains: b. projected meaning: λP<i,t>.[[PAST tnow]](λt'.t'⊆tomorrow & P(t')) = λP<i,t>.∃t'[t'< tnow & t'⊆ tomorrow & P(t')] The heuristic predicting this anticipated interpretation and the clash contained in it can be phrased as in (27) (assuming <i,t> type modifiers) or (28) (assuming <<i,t>,<i,t>> modifiers). (27) Temporal adverb – Tense Heuristic (intersective modifiers): If α= [βTense [ γadverb …]] and γ is of type <it>, then [[α]]h = λP<i,t>.[[β]]h(λt'[[γ]]h(t') & P(t')) (28) Temporal adverb – Tense Heuristic (functional modifiers): If α= [βTense [ γadverb …]] and γ is of type <it,it>, then [[α]]h = λP<i,t>.[[β]]h([[γ]]h(P)) The Temporal adverb–Tense Heuristic (shifted) defines [[β]]h•[[γ]]h Russian Aspect: Bott and Gattnar (to appear) found that in Russian a mismatch of aspect with an adverb (29) was detected immediately, suggesting incremental interpretation. This Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 150 S. Beck & S. Tiemann Towards a model of incremental composition finding is especially interesting when compared to the processing of German aspect, discussed in the next subsection. The Russian results indicate that the compositional step in (30) is taken immediately: (29) Celych tri casa Whole three hours vyigrala win.pfv.Past … | # (30) a. projected parse tree contains: b. projected meaning: λP<v,t>. ∃e[[[pfv]](e) & [[for three hours]](e) & P(e)] No detailed analysis or heuristic is offered because the details of the analysis for Russian are not sufficiently clear to us (see Bott and Gattnar, to appear; Bott and Sternefeld, to appear, for discussion). It is clear however that there is an immediately perceived clash between the aspect information and the adverbial. Those two expressions must be part of a local tree in the AspP. We conjecture that the example is (abstractly) parallel to the temporal adverb– tense case above. To sum up this subsection, we have identified five circumstances that showcase immediate composition of two semantic units that do not form a constituent in the LF. Note that in each case, the two units occur in the same LF domain (DP, VP, TP, AspP). Their combination may be understood as predicted function application or function composition. (See Bott and Sternefeld, to appear, for a different, but similarly incremental analysis of e.g. the tense and the aspect cases.) 3.2. Results supporting delayed composition Quantifiers: Hackl et al. (2012) (see also Varoutis and Hackl, 2006; Breakstone et al., 2011; but cf. Gibson et al., 2014) argue that there is evidence for quantifier raising (QR) and delayed interpretation of quantifiers in object position (31). We illustrate our interpretation of this finding in (32): encountering the quantified determiner leads to a revision of the parse tree. (31) John fed every dog. | no composition here. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 151 S. Beck & S. Tiemann (32) Towards a model of incremental composition a. 1st projected parse tree contains: b. revised parse tree contains: Note that consequently, it is not the case that the meaning calculated so far — presumably [λy. John fed y] — is combined with the meaning of every (yielding e.g. [λP<e,t>. for every y such that P(y), John fed y]). Hence this is a case that does not work according to strict incrementality. It seems extremely plausible that recovering from a garden path like (1) also involves such a revision (cf. e.g. Chater et al., 2001), i.e. in addition to throwing out the parse that turned out to be misguided, the corresponding interpretation is thrown out along with it. German Aspect: Bott (2013) and Bott and Gattnar (to appear) show that aspectual mismatch in German is only processed when the verb has received its full argument structure, suggesting that the meaning of an adverbial (‘for two hours’) is not immediately combined with the meaning of a verb (‘won’). Composition only happens later (in contrast to Russian). (33) Zwei Stunden lang two hours for gewann der Boxer won the boxer | no composition here. den Kampf. the fight It seems plausible that the meanings of the available items are added to the set of meanings made available by the processor, but not composed. So this is an instance of delayed composition. In very general terms, the so-called sentence wrap-up effect (Just and Carpenter, 1980) may also be an indication of late processes in semantic composition. Further candidates: We mention two further candidates that have been presented as indicators for late composition processes. The model in section 4 will not properly include them because they involve semantic issues we can’t yet address (variable binding and presupposition projection) but they provide general support of our position. First, Bott and Schlotterbeck (2013) present an eyetracking study investigating the processing of inverse scope as in (34a) vs. (34b) without scope inversion. Their results suggest that scope inversion is only computed at the end of the sentence (this is also the interpretation of this finding in Bott and Sternefeld). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 152 S. Beck & S. Tiemann (34) Towards a model of incremental composition a. Jeden seiner Schüler hat genau ein Lehrer voller Wohlwollen gelobt. Each of-his pupils has exactly one teacher full-of goodwill praised ‘A teacher praised each of his pupils full of goodwill.’ b. Jeden dieser Schüler hat genau ein Lehrer voller Wohlwollen gelobt. Each of-these pupils has exactly one teacher full-of goodwill praised ‘A teacher praised each of these students full of goodwill.’ Second, Schwarz and Tiemann (to appear) conducted experiments on the processing of sentences with unfulfilled embedded and unembedded presuppositions (35a,b). Whilst presupposition failure in the unembedded cases (35b) was immediately detected in online processing, there was no such effect in the embedded conditions. We take this to mean that the composition of embedded presuppositions does not happen strictly incrementally, otherwise presupposition failure should result in immediate processing effects as they do in the unembedded cases. (35) a. Heute war Tina nicht wieder schlittschuhlaufen. Today was Tina not again ice-skating ‘Today, Tina didn’t go ice skating again.’ b. Heute war Tina wieder nicht schlittschuhlaufen. Today was Tina again not ice-skating ‘Today, once more Tina didn’t go ice skating.’ In sum, we have evidence that semantic units are not always composed immediately. Predictive combinatory mechanisms do not seem to be explored to exhaustion to calculate a composed meaning under all circumstances. This is why we depart from strict incrementality (as developed e.g. in Bott and Sternefeld). Interim Conclusion: If the above view is correct, neither global interpretation nor strict incrementality seems to be the right model of semantic processing. Composition in semantic processing has incremental properties, but it also seems to require certain units to be built before composition proceeds. The required model needs to employ what we might call enlightened incrementality: sometimes composition is immediate, but under other circumstances it is delayed. What would be a useful hypothesis about when the processor applies which type of strategy? The next subsection addresses this question. 4. First steps towards a general framework This section generalizes from the concrete incremental compositional analyses in section 3. The desired outcome is (the beginnings of) a framework for theories of semantic parsing: a definition of a function [[.]]h (‘heuristic interpretation’) as anticipated in section 2. Naturally, we are far from being able to propose a complete model for this mapping. But we can distill some generalizations from the case studies in section 3. We propose that a realistic semantic processor sometimes composes ‘early’ and sometimes ‘late’, depending on the linguistic input. Our evidence indicates the general possibility of four cases: (i) wait and see, (ii) revision of LF, (iii) predictive Function Application (FA), (iv) predictive Function Composition (FC). These are generalizations over the interpretive strategies that section 3 provides evidence for. Subsection 4.1. examines the ‘late’ strategies, subsection 4.2. the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 153 S. Beck & S. Tiemann Towards a model of incremental composition ‘early’ composition strategies. In subsection 4.3. we develop a hypothesis as to when the semantic processor employs which type of strategy. 4.1. Delayed composition Beginning with ‘late’ composition strategies, section 3 provides evidence for (i) wait and see. The example indicative of this strategy is German aspect (and also (34), (35)). Stages of the processor are sketched in (37). (i) wait and see Given <T,S> and input σ, map to <T',S'>, where T' is the modification of T derived by the syntactic parser and S' is defined by: [[.]]h: <T',S,[[σ]]h> -> S∪{[[σ]]h} (36) Zwei Stunden lang two hours for (37) a. T=[CP [PP zwei Stunden lang] …]] S={[[for 2h]]} b. T'=[CP [PP zwei Stunden lang] _ [TP Past … ]]] S'={[[for 2h]], [[Past]]} gewann der Boxer won the boxer | no composition here. den Kampf. the fight The second case of non-incremental interpretation we have seen is (ii) revision of LF. The example for this strategy from section 3 is quantifiers in object position (and also (1)). (ii) revision of LF Given <T,S> and input σ, map to <T',S'>, where T' is the revision of T derived by the syntactic parser, and S' is defined by: [[.]]h: <T', S, [[σ]]h> ->{x: x is the meaning of an atom in T}∪[[σ]]h> (38) John fed every dog. | no composition here. At this point we digress a little in order to explain more fully our take on what happens in (38). Revision of the parse tree from T to T' would be compatible with keeping the meanings composed so far and adding the new meaning, according to the (i) wait and see strategy, as sketched in (39). We conjecture, however, that the processor also reconsiders the store of meanings. Our motivation comes from examples that have, in addition, a quantifier in subject position, (40). If the processor kept the meanings composed so far, we would get (41). Continuing processing on this basis would in our framework (i.e. without type shifting or further scope mechanisms) lead to the inverse scope reading (40b). It seems implausible that the processor smoothly generates the intuitively harder reading. It is more plausible that the processing of the doubly quantified example involves the steps in (42) — the composition of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 154 S. Beck & S. Tiemann Towards a model of incremental composition subject and verb is thrown out. This motivates our assumption that (ii) is operative in this case. (39) a. T= [VP John [V' fed … ]] S={[[John fed]]} = {λy. John fed y} b. T'=[VP [NP every …][1[VP John [V' fed t1 ]]] S'= {λy. John fed y, [[every]]} (40) Some guy fed every dog. a. ∃x[∀y[dog(y) -> x fed y]] b. ∀y[dog(y) -> ∃x[x fed y]] (surface scope) (inverse scope) (41) a. T= [VP [NP some guy] [V' fed … ]] S={[[some guy fed]]} = {λy. ∃x[x fed y]} b. T'=[VP [NP every …][1 [VP [NP some guy] [V' fed t1 ]]]] S'= { [[every]], λy. ∃x[x fed y]} (42) a. T=[IP _ [I' [VP [NP some guy] [V' fed … ]]]] S={[[some guy fed]]} = {λy. ∃x[x fed y]} b. T'=[IP [NP some guy] [2[I' [VP [NP every …][1[VP t2 [V' fed t1 ]]]] S'= {[[some guy]], [[every]], [[fed]]} In the (ii) revision of LF case, therefore, the processor performs a revision of the parse tree and throws out a predicted meaning in S as well, reconsidering composition. 4.2. Incremental composition. Let’s next turn to ‘early’ composition. Section 3 anticipates (iii) predictive Function Application. (iii) predictive Function Application (FA) Given <T,S> and input σ, map to <T',S'>, where T' is derived by the syntactic parser and if there is a δ∈S such that (a) [[σ]]h(δ) or (b) δ([[σ]]h) is defined, then, (a) S'=S\δ ∪ {[[σ]]h(δ)} or (b) S'=S\δ ∪ {δ([[σ]]h)} (whichever is defined). The example from section 3 is immediate compositional interpretation in the DP, (43). Predictive FA would similarly be involved in (44). This proposal could be further tested by data like (45), which we give as a suggestion for future research. (43) Touch the tall … (44) a. Every dog… b. S={[[every]]}, S'={[[every]]([[dog]])} Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 155 S. Beck & S. Tiemann (45) Towards a model of incremental composition a. Every dog that greeted its master was fed. b. Every dog was fed that greeted its master. The second ‘early’ composition mechanism from section 3 is (iv) predictive Function Composition (assuming the higher types for the heuristics). Examples from above were the data types in (46). (iv) predictive Function Composition (FC) Given <T,S> and input σ, map to <T',S'>, where T' is derived by the syntactic parser and if there is a δ∈S such that (a) δ•[[σ]]h or (b) [[σ]]h•δ is defined, then, (a) S'=S\δ ∪ {δ•[[σ]]h} or (b) S'=S\δ ∪ {[[σ]]h•δ} (whichever is defined). (46) a. The soup greeted… b. Morgen gewann… tomorrow won … c. Susanne hat wieder… Susanne has again … (subject–verb) (tense–adverb) (subject–adverb) 4.3. When is composition ‘early’ and when ‘delayed’ – a possible generalization A model of semantic processing in the sense of enlightened incrementality should be an optimal compromise regarding two conflicting demands: (a) a low load on working memory: it is unrealistic that we carry around a large number of separate meanings until the end of an utterance; (b) reliable predictions: it is undesirable to randomly compose word meanings when the confidence that this is the actual interpretation is low. We offer the conjecture below for what this compromise could look like. (47) Enlightened Incrementality Conjecture: Units in the same LF domain (DP, VP, TP, AspP). are composed incrementally. The idea is that there is incremental (‘early’) composition, but it is limited to a local LF domain. LF domains are defined by semantic type. E.g., we predictively combine the verb with its arguments within the VP <e,t> (‘the soup greeted…’). We predictively combine tense with temporal adverbials within the TP layer <i,t> (‘Morgen gewann…’) and eventlevel adverbials with expected event descriptions just above the core VP <v,t> (‘Susanne hat wieder…’). It appears that predictive composition occurs in layers. (This does not mean that you have to finish a layer before you start the next one, cf. ‘Morgen gewann…’.) The tree below illustrates the LF architecture this proposal is based on (e.g. von Stechow and Beck, 2015). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 156 S. Beck & S. Tiemann Towards a model of incremental composition The examples that we have seen for ‘delayed’ composition, e.g. German aspect/Aktionsart (‘Zwei Stunden lang gewann…’), concern material that in the LF is scattered over several layers (TP, AspP, VP). Quantifiers in object position also concern more than one layer: QR takes a quantifier above aspect as illustrated in (48) (e.g. von Stechow and Beck, 2015). (48) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 157 S. Beck & S. Tiemann Towards a model of incremental composition In sum, late composition facts mean that predictive FA and predictive FC cannot always apply. We conjecture that predictive composition happens in local LF domains, identifiable by semantic type, where the confidence that this is the correct composition is high. Next steps: There are a couple of issues that need to be addressed for a more complete proposal. The QR data draw our attention to movement and the question of how Predicate Abstraction in standard composition transfers to incremental composition. Analyses are available in CCG (see e.g. Steedman, 2000; Demberg, 2012 for relevant discussion). Similarly, the tense and aspect data show that for an incremental analysis of a complete fragment, we need to think about the interaction of the several LF layers. A proposal is made in Bott and Sternefeld (to appear). We must leave an investigation of these issues, consideration of the available processing evidence and its integration into our proposal for future research. 5. Conclusions We have seen that semantic processing has incremental properties (e.g. subject + verb seems to be composed immediately) but also ‘global’ properties, i.e. processing requires larger units (e.g. quantifiers). Standard theories of semantic composition do not model this because they require the whole LF tree and only assign meanings to constituents. Strictly incremental theories of semantic composition do not model this because every sentence prefix is assigned a meaning strictly incrementally. Hence the field is still in search of a model of incremental composition. We formulate first ideas towards a definition of a heuristic interpretation function [[.]]h which models incremental composition (keeping as much as possible from standard semantic theories). Our goal is to offer the beginnings of a framework for theories of semantic parsing. Naturally, the question when and to what extent the semantic parser composes incrementally needs to be addressed for further phenomena (variables, decomposition phenomena, presupposition etc.). Central to our proposal is the enlightened incrementality conjecture: incremental composition occurs within a local LF domain, when the confidence is high that the composition will prove correct. Our model for a semantic processor concentrates on grammatically determined aspects of incremental interpretation. This is not to deny that other factors may enter into (incremental) understanding. An important factor is what we might call expectations, coming from e.g. frequency, contextual fit or background knowledge. It is clear that these factors affect processing, for example of garden path sentences (e.g. MacDonald, Perlmutter and Seidenberg, 1994) and even scope (Raffray and Pickering, 2010; Chemla and Bott, 2015). We take them to be relevant for our model as well: for instance, the very early effect on again noted in section 3 is plausibly due to the kind of context used in the experiment. One way this can be thought about is in terms of when to apply which heuristic rule. Hale (2003) models syntactic expectations by adding the likelihood of the application of a rule of the parser as a probability. A similar path would be open to models of the semantic processor. At any rate, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 158 S. Beck & S. Tiemann Towards a model of incremental composition we assume that a component handling such factors can and should be added to what we propose about the processor. We find it important to model findings on processing in terms of a compositional semantic processor, even though our empirical knowledge in this area is still quite limited. We offer the heuristics in this paper as a framework for beginning this enterprise. If semanticists don’t worry about incremental interpretation, and psycholinguists don’t model the composition steps, there will be a regrettable gap in linguistic theory. Individual results on semantic processing remain isolated instead of contributing towards a theory of incremental interpretation. References Ades, A. E. and M. Steedman (1982). On the order of words. Linguistics and Philosophy 4, 517–558. Altmann, G.T. and Y. Kamide. (1999). Incremental interpretation at verbs: Restricting the domain of subsequent reference. Cognition 73, 247–264. Ambati, B. (2016). Transition Based Combinatory Categorial Grammar parsing for English and Hindi. Ph.D. thesis, University of Edinburgh. Beck, S. and R. Gergel. (2014). 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Lappin (Eds), Handbook of Computational Linguistics and Natural Language Processing. London: Blackwell. Demberg, V. (2012). Incremental derivations in CCG. In Proceedings of the 11th International Workshop on Tree Adjoining Grammars and Related Formalisms: TAG+11, pp.198–206. Ferreira, F., K. Christianson and A. Hollingsworth (2001). Misinterpretations of garden-path sentences: Implications for models of sentence processing and reanalysis. Journal of Psycholinguistic Research 30, 3–20. Frazier, L. (1999). On Sentence Interpretation. Dordrecht: Springer. Frazier, L. (1979). On Comprehending Sentences: Syntactic Parsing Strategies. Ph.D. thesis, University of Connecticut. Frazier, L. and K. Rayner (1990). Taking on semantic commitments: Processing multiple meanings vs. multiple senses. Journal of Memory and Language 29, 181–200. Gibson, E., P. Jacobson, P. Graff, K. Mahowald, E. Fedorenko and S. Piantadosi (2014). 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Carlson (1999). Achieving incremental semantic interpretation through contextual representation. Cognition 71, 109– 147. Shan, C-C. and C. Barker (2006). Explaining crossover and superiority as left-to-right evaluation. Linguistics and Philosophy 29, 91–134. Von Stechow, A. and S. Beck (2015). Events, times and worlds – An LF architecture. In C. Fortmann (Ed.), Situationsargumente im Nominalbereich, pp. 13–46. Berlin: de Gruyter. Steedman, M. J. (2000). The Syntactic Process. Cambridge, MA: MIT Press. Steedman, M.J. and J. Baldridge. (2011). Combinatory Categorial Grammar. In R. Borsley and K. Borjars (Eds.) Non-Transformational Syntax: Formal and Explicit Models of Grammar. Malden, MA: Wiley-Blackwell. Tiemann, S. (2014). The Processing of wieder (‘again’) and other Presupposition Triggers. Ph.D. thesis, University of Tuebingen. Tiemann, S., M. Schmid, N. Bade, B. Rolke, I. Hertrich, H. Ackermann, J. Knapp and S. Beck (2011). Psycholinguistic evidence for presuppositions: On-line and off-line data. In I. Reich, E. Horch and D. Pauly (Eds.), Proceedings of Sinn und Bedeutung 15, 581–597. Varvoutis, J. and M. Hackl (2006). Parsing quantifiers in object position. Presented at CUNY 2006. Zimmermann, E. and W. Sternefeld (2013). Introduction to Semantics – An Essential Guide to the Composition of Meaning. Berlin: de Gruyter Mouton. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 161 162 Embedded disjunctions and the best response paradigm1 Anton BENZ — Leibniz–Centre General Linguistics, ZAS, Berlin Nicole GOTZNER — Leibniz–Centre General Linguistics, ZAS, Berlin Abstract. The current study investigates implicature of embedded disjunctions. We employ a paradigm in which implicatures are inferred indirectly from action choices of test subjects. This avoids meta–linguistic judgements on which previous studies relied. The focus is on four different types of implicature that may be triggered by embedded disjunctions in a situation with a competent speaker. We distinguish between local and global scalar implicatures, exhaustive and existence implicatures. The results provide evidence that varieties all four types of implicature have been inferred by a majority of subjects. Keywords: experimental pragmatics, embedded implicature, disjunctions. 1. Introduction The connective ‘or’ is one of the core examples illustrating different types of quantity implicature. In (1), the disjunction gives rise to three quantity implicatures, the scalar implicature which says that the sentence with ‘or’ replaced by ‘and’ is false, the so–called ignorance or clausal implicatures which says that, for all that the speaker knows, it is possible that any of the disjuncts may be true or false, and the exhaustive implicature which says that Kate did not find, for example, the green marble, if she has a green marble: (1) Kate found her blue or her red marble. ; Scalar: Kate did not find her blue and her red marble. ; Ignorance: 3 /3¬ Kate did find her blue marble; 3 /3¬ Kate did find her red marble; ; Exhaustive: Kate did not find any other marble except the blue or the red one. In this example, the connector is not embedded. The ignorance implicature is inconsistent with a situation in which the speaker knows the actual state of the world. Hence, un-embedded disjunction is generally not licensed in such situations. This marks a difference to embedded ‘or’. For example, ‘All of the girls found their red or their blue marble’ can be uttered by a competent speaker. The current study investigates the complex sentences with embedded disjunctions in (2). (2) a. b. c. d. All of the girls found their red or their blue marble. Some of the girls found their red or their blue marble. All of the girls found their red, their blue, or their green marble. Some of the girls found their red, their blue, or their green marble. 1 This work was supported by the Bundesministerium für Bildung und Forschung (BMBF) (Grant Nr. 01UG1411), and the Deutsche Forschungsgemeinschaft (DFG) (Grant Nr. BE 4348/4-1). We are grateful to Felicitas Enders, Mady Thonicke, and Danny Belitz for preparing the experimental stimuli. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 163 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm In particular, we test the status of the following types of implicature: (3) (A) the embedded scalar implicature of the disjunction, e.g. for (2a) the implicature ‘all either r or b’ leading to an exclusive reading of ‘or’; (B1) the global implicature from (2b) to none r ∧b, and from (2d) to none r ∧b, none r ∧g, and none b ∧ g; (B2) the global implicature from (2b) to not all r ∨ b, and from (2d) to not all r ∨ b ∨ g; (C) the exhaustive implicature from (2a) and (2b) to none found their green marble; (D) the strong existence implicature of the embedded disjunctions, for example from (2a) all (r ∨ b) to some r ∧ some b. (D’) the weak existence implicature of the embedded disjunctions, for example from (2a) all (r ∨ b) to it is possible that some r and it is possible that some b. The weak existence implicature (D’) is implied by the strong existence implicature (D). We treat them as two variants of the same type of implicature. Likewise, (B1) and (B2) are treated here as two variants of the same type of implicature. The labels have to be understood descriptively. By using them, we do not mean to commit to any specific theoretical framework. Throughout, we only consider situations in which the speaker is commonly known to be competent, i.e. knowledgeable of the true state of the world. A further assumption is that the objects that can be connected by disjunction are also commonly known. For example, in a scenario in which (2a) is uttered, it will be assumed that each of the girls owns a commonly known finite set of marbles, each with a distinct colour, that could be found by the girl. Theories make different predictions concerning the implicatures in (3). For example, Chierchia ˙ and ¬all r ∨b) but does (2004) predicts (A) and a weaker version of (B1), e.g. (2b) ; (some r∨b not address (D). Franke (2009) predicts (A) and (B1), and Sauerland (2004) (B1) and for (2a) a weaker version of (A) (¬all r ∧ b). None of the theories predicts (C), and (D) is only explained by Sauerland (2004) and Crnič et al. (2015) for the sentences with universal quantifier. All theories predict (B2). This is only a sample of the theories about embedded implicature that could be considered (e.g. Asher, 2013; Chierchia et al., 2012; Benz, 2012; Potts et al., 2016). None of the theories addresses all types of implicature, and not all of them are specific enough to be testable. We present clear experimental evidence that the implicature of types (A), (B1), (C), and (D’) can be drawn reliably in a scenario that is based on a game theoretical design (best response paradigm, Gotzner and Benz, 2018). In contrast to previous experimental studies (e.g. Geurts and Pouscoulous, 2009; Chemla and Spector, 2011), our paradigm provides an organic setting that avoids meta-linguistic judgement. In the first section, we discuss the general methodological motivation for the best response paradigm. The second section presents the experiments and their results, and the third discusses their evidence for the different types of implicature listed in (3). For example, we will see that there is no evidence for the type (B2) implicature being inferred reliably, which is surprising as they are predicted by all theories. In the fourth section we compare our results to the more recent study of Crnič et al. (2015), who found evidence for strong existence implicatures (D) in absence of implicatures of type (A) and (C). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 164 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm 2. Embedded disjunctions: some theory and some experimental issues A large body of experimental research on implicatures has emerged over the past decade. The majority of experiments concentrate on questions of acquisition (Noveck, 2001; Papafragou and Musolino, 2003; Katsos and Bishop, 2011), the time course of implicature processing (Noveck and Posada, 2003; Huang and Snedeker, 2009; Grodner et al., 2010; Tomlinson et al., 2013), or the question whether they are generated by default or triggered in context (Breheny et al., 2006). There have been considerably fewer studies on embedded implicatures (Chemla 2009; Geurts and Pouscoulous 2009; Clifton Jr and Dube 2010; Chemla and Spector 2011; Potts et al. 2016; Crnič et al. 2015; Gotzner and Romoli 2017). These studies have employed various paradigms, picture verification tasks (e.g. Geurts and Pouscoulous, 2009), inferencing tasks (e.g. Chemla, 2009), graded acceptability tasks (e.g. Chemla and Spector, 2011), and picture selection tasks (Clifton Jr and Dube, 2010). In these studies, sentences as (2a) are considered ambiguous between a semantic and one or more pragmatic interpretations. The task is to determine whether there is a sub-population that interprets the test sentence in accordance with the critical pragmatic interpretation. There has been a sharp controversy about methodological issues. For example, on the one side it has been argued that inferencing tasks inflate the proportion of pragmatic interpretations (Geurts and Pouscoulous, 2009), and that graded acceptability judgements and picture selection tasks are susceptible to typicality effects (Geurts and van Tiel, 2013; van Tiel, 2014), so that the evidence for embedded implicatures provided by experiments based on these designs may be doubted. On the other side, it has been argued that picture verification tasks induce subjects to interpret semantically, and therefore to underestimate the real proportion of subjects adopting the critical pragmatic interpretation (Clifton Jr and Dube, 2010; Benz and Gotzner, 2014). With the exception of Crnič et al. (2015), the studies were only concerned with embedded scalar implicatures, and generally showed only low proportions of subjects choosing the critical interpretation. The low proportions may seem unproblematic if the goal is to show that subjects can arrive at certain interpretations. In the standard neo-Gricean theory of conversational implicature (Levinson, 1983), implicatures are not alternative readings of a sentence but supplements to semantic content and part of communicated meaning. To show that an interpretation is implicated in this stronger sense, it has to be shown that it is understood by all addressees on a par with semantic content. We are therefore interested in the question which potential implicatures are reliably inferred such that they can count as part of communicated meaning, and which are not. Experiments show a certain degree of random behaviour. We, therefore, can only try to determine, however, which propositions are inferred with high probability, where the term ‘high probability’ introduces a certain amount of vagueness. Pragmatics is about language in use. We, therefore, devised a scenario in which critical sentences are used for communicating facts that the addressee needs to know for subsequent decision making. Our initial hypothesis was that all four types of implicature (A) to (D) are drawn reliably. We will see that the observed response pattern indicates that implicatures of type (A), (B1), (C), and (D’) are drawn reliably. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 165 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm 3. The Best Response paradigm The following experiment takes advantage of the fact that interpretations can be indirectly inferred from action choices of interpreters. In this way, meta-linguistic judgements can be circumvented. As we have argued elsewhere, meta-linguistic judgements, in particular, picture verification tasks, bias subjects towards literal interpretation (Benz and Gotzner, 2014). The presence of a substantial group of literally interpreting subjects dooms any attempt at showing that certain implicatures are communicated reliably. We therefore developed a scenario in which utterance selection and interpretation are embedded in a cooperative action selection task. 3.1. Methods 3.1.1. Participants Participants with US IP addresses were recruited on Amazon’s Mturk platform and were screened for their native language. In total, 20 native English speakers (mean age: 32.7, 13 female, 7 male) took part in the experiment. 3.1.2. Scenario and task In Gotzner and Benz (2018), we presented the basic version of the best response paradigm. For the current experiment, we use the same basic scenario with minor modifications. Participants in our experiment were presented with a scenario involving four girls who each own a set of three special edition marbles, consisting of a blue, a green and a red marble (a scenario introduced by Degen and Goodman 2014, which we extended with an action-based task). While the girls are playing, the marbles get lost and they have to find them again. Participants in our experiment were told that the mother of the girls wants to reward them depending on how many marbles they find. In particular, participants were presented with the following reward system in the instructions. (4) Reward system: • chocolate: all 3 marbles • candy: 2 marbles • gummy bear: 1 marble – green gummy bear: green marble – red gummy bear: red marble – blue gummy bear: blue marble • pretzel stick: 0 marbles The participants’s task in the experiment is to buy sweets as rewards for the four girls depending on the statement the mother utters. After participants had read the instructions, they were asked control questions about the number of marbles each girl owns and which reward type a girl gets depending on how many marbles she found. Then, participants were given an example Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 166 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm item involving the statement ‘None of the girls found any of their marbles’, in which case they should buy pretzels and nothing else. 3.1.3. Experimental items In the main part of the experiment, participants were asked to give binary responses (YES/NO) for each of the six types of sweets: chocolate, candy, gummy bears (red, green or blue) and pretzel sticks. There were two types of critical test sentences: either simple or complex disjunction was embedded under all and some. The test sentences are shown in (5). Our four critical sentences were repeated twice in the experiment. (5) a. b. c. d. All of the girls found their red or their blue marble. Some of the girls found their red or their blue marble. All of the girls found their red, their blue, or their green marble. Some of the girls found their red, their blue, or their green marble. An example experimental trial with All (r ∨ b) and a possible response choice is presented in (6). Participants had to check one of two radio buttons (‘YES’ or ‘NO’) for each type of sweets. The mother says: chocolate candy (6) green gummy bear red gummy bear blue gummy bear pretzel stick ‘All of the girls found their red or blue marble’ # YES NO # YES NO # YES NO YES # NO YES # NO # YES NO In addition, participants saw 15 filler items such as the statement ‘Sue and Kate found some of their marbles’ as well as the original test sentences used in Gotzner and Benz (2018) involving the quantifier some embedded under all and some itself. Hence, each participant saw 23 items in total. 3.2. Results Figure 1 shows the mean percentage of YES responses across reward type for simple disjunctions and Figure 2 shows the data for complex disjunctions (Table 4 in the appendix details the percentages of each combination of action choices per condition). We computed two separate logit mixed models for simple and complex disjunctions. Our dependent variable was binary (choice of sweet: 1 or 0) and we included the fixed factors quantifier condition (All (r ∨ b) vs. Some (r ∨ b)), reward type (candy, chocolate, red, green, blue gummy bear, pretzel stick), their interaction as well as random factors for participants and items. As reference level we chose the condition (All (r ∨ b), candy) and (All (r ∨ b ∨ g), candy) respectively. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 167 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm All(rvb) Some(rvb) 100 % YES 75 reward choc candy red bear blue bear green bear pretzel 50 25 0 Figure 1: % YES responses for sentence All (r ∨ b) (left column) and Some (r ∨ b) (right column) across reward type. Error bars represent SEM. All(rvbvg) Some(rvbvg) 100 % YES 75 50 reward choc candy red bear blue bear green bear pretzel 25 0 Figure 2: % YES responses for sentence All (r ∨ b ∨ g) (left column) and Some (r ∨ b ∨ g) (right column) across reward type. Error bars represent SEM. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 168 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm Mixed model for simple disjunctions. The model showed a significant difference across reward type: Participants chose candy less often than red bears (p <.001) and blue bears (p <.001). There was no difference between the two quantifier conditions at the baseline level or between candy and the other two reward types. However, the model revealed an interaction between quantifier condition and reward type (pretzel : Some (r ∨ b): p <.0001). Table 5 in the appendix shows a summary of the mixed model. Mixed model for complex disjunctions. The model showed a significant difference across reward type: Participants chose candy less often than red bears, green and blue bears (all p’s <.0001). There was also a marginal difference compared to the condition with pretzels (p = .09) as well as an interaction across condition and reward type (pretzel : Some (r ∨ b ∨ g) p <.001). There were no further main effects nor any interactions. Table 6 in the appendix shows a summary of the mixed model. 4. Evaluation of results We tested the four sentences presented in (2). The task of the participants was to buy sweets for the four girls. They were asked to give binary responses (yes/no) for each of the six types of sweets: chocolate, candy, red, blue, and green gummy bears, and pretzel sticks. If subjects draw the implicatures (A)–(D), then their expected response pattern is that shown in (7). condition (2a) (7) (2b) (2c) (2d) All (r ∨ b) Some (r ∨ b) All (r ∨ b ∨ g) Some (r ∨ b ∨ g) choc. candy red b. blue b. green b. pretzel no no no no no no no no yes yes yes yes yes yes yes yes no no yes yes no yes no yes As we have seen, the observed choices conform to this prediction. The only exception are the choices with respect to pretzels in the some-conditions. We observe a larger proportion of subjects buying no pretzels (about 30%),2 which is inconsistent with there being a group of girls that found none of their marbles. This implicature follows from an utterance of (2b) by the following reasoning: First, with (B2) Some (r ∨ b) implicates ¬all (r ∨ b); second, (C) implies that none found the green marble. Together, this implies that some found none. If subjects would not adhere to (C), then they should have bought either chocolate, candy or green gummy bears in the ‘some (r ∨ b)’ condition (2b). As they did not buy them, the problem must be the implicature of type (B2). Hence, the experiments indicate that there is a significant proportion of subjects that do not draw the (B2) implicature, i.e. global scalar implicature from embedding ‘some’. However, we can conclude that the hypothesis that subjects draw implicatures (A), (B1), (C), and (D) is consistent with the experimental results. We next consider the more difficult question of how far the results shown in Table 4 in the appendix imply that subjects infer (A), (B1), (C), and (D). As the percentage values follow the 2A mixed model analysis with disjunction embedded under some and the reward type pretzels as reference level revealed that this condition differed significantly from all other reward types (all p’s < .001, both for simple and complex disjunctions). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 169 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm response pattern shown in (7), with the exception of the pretzel results for (2b) and (2d), we abstract from the precise numerical values and concentrate on the evidence provided by the categorical pattern in (7). What we have to show is that for all possible belief states that are consistent with the subjects’s choices of sweets, the implicatures generated by (A), (B1), (C), and (D) hold true. In our scenario, each observable world can be identified with a 4-tuple (m1 , m2 , m3 , m4 ) of sets of marbles mi ⊆ {b, g, r}. The set mi represents the set of marbles found by the ith girl. There are (23 )4 = 4096 different observable worlds. The reward system with different kinds of sweets 6
4 6 distinguishes 2 − 1 = 63 relevant states, of which ∑i=1 i = 56 can be instantiated by four girls. In the following, we mean by ‘possible world’ always one of the 63 possible worlds defined by the reward system, and not one of the observable worlds. We consider the four conditions (2a) to (2d) one after the other. First, let us consider (2a): (2a) All of the girls found their red or their blue marble. This sentence is semantically consistent with 24 possible worlds, 8 of which are shown in Table 1. The other 16 worlds can be found by making one copy of the table and replacing the 1s in the ‘blue’ column by 0s, and then by making another copy and replacing the 1s in the ‘red’ column by 0s. Of the 24 worlds only one world is consistent with the pragmatic choice as indicated by the X in the last column. Possible worlds (8 of 24) Information states consistent with choice pretzl blue green red candy choc cons inf. state pretzl blue green red candy choc 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 − − − − − − − X I 0 1 0 1 0 0 II 0 0 1 1 0 0 1 0 0 0 0 0 III 0 0 1 0 0 0 1 1 0 0 0 0 IV 0 0 1 0 0 0 0 1 0 0 0 0 Table 1: Target sentence (2a) All of the girls found their red or their blue marble. If the addressee infers an exact state of the world, then we can conclude that she believes to be in the world indicated by X. However, there are three other belief states that are consistent with the choice of only red and blue gummy bears. They are also shown in in Table 1. The experimental set up does not allow us to distinguish between the four states. We now have to check whether the implicatures predicted by (A), (B), (C), and (D) are supported by all four of them. (A) is the embedded implicature that none found both the red and the blue marble; if the addressee believes that this implicature might be false, then there must exist a belief world in which it is appropriate to buy hard candy; as in neither of the four belief states there exists such a world, we can conclude that the addressee does not believe it possible that the implicature is Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 170 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm false. Hence, the embedded implicature (A) is true. (B1) and (B2) only apply to the ‘some’ sentences. The exhaustive implicature (C) that none found the green marble is also true in all belief states. We can also immediately see that the weak existence implicature (D’) holds: each belief state contains a world with a 1 in the red column, and a world with a 1 in the blue column; hence, in each belief state it is possible that a girl found a red marble and it is possible that a girl found a blue marble. The stronger existence implicature (D) is violated in information states II, III, and IV: in each of these states there is a world in which either the red column contains a 0 or the blue column. We next consider condition (2b): (2b) Some of the girls found their red or their blue marble. This sentence is semantically consistent with 48 possible worlds, 9 of which are shown in Table 2. The 48 worlds consist of the 24 worlds consistent with (2a) together with a copy of these worlds where the 0s in the ‘pretzel’ column are replaced by 1s. Of the 48 worlds only two worlds are consistent with the experimental results: one world consistent with the choice of the subjects who bought pretzels, and one world consistent with the choice of the subjects who did not by them. The two worlds are indicated by X in the last column of Table 2. Possible worlds (9 of 48) Information state consistent with choice (1 of 57) pretzl blue green red candy choc cons pretzl blue green red candy choc 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 − − − − − − − X X 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Table 2: Target sentence (2b) Some of the girls found their red or their blue marble. For (2b), there are many more belief states than for condition (2a). One belief state is shown in Table 2. We can generate 57 belief states by taking all subsets of this state which contain a world with a 1 in the ‘blue’ column and a world with a 1 in the ‘red’ column. If the addressee believes to be in one of the worlds indicated by X, then she believes in the implicature generated by (A), (B1), (C), and (D). If it is the world with a 1 in the ‘pretzel’ column, then she also draws the global scalar implicature for embedding ‘some’ (B2). Our results showed that this is true only for about two-third of the subjects. If no belief state contains a world where candy or chocolate has to be bought, then the addressee must believe in the (A) implicature. As all belief states are subsets of the one shown in Table 2, this holds true. The global implicature of embedded ‘or’ (B1) says that none of the girls found the red and the blue marble. This follows from the fact that no belief state contains a world in which candy or chocolate has to be bought. The global implicature (B2) stating that not all girls found the red Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 171 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm A A A A A B B B B B C C C C C D D D D D E E E E E F F F F F Table 3: A critical item probing for existence implicature from Crnič et al. (2015: p. 15). or the blue marble is violated if a belief state contains a world with a 0 in the ‘pretzel’ column. We have seen that such belief states are not ruled out by our data. There is a larger proportion of subjects whose choice of sweets is consistent only if they are not drawing the (B2) implicature, as we have argued before. The exhaustive implicature (C) that none found the green marble is true in all belief states. We can again immediately see that the weak existence implicature (D’) holds. The stronger existence implicature (D) is violated in all but three belief states. For the remaining conditions (2c) and (2d), the claims follow by analogous arguments. (2c) All of the girls found their red, their blue, or their green marble. (2d) Some of the girls found their red, their blue, or their green marble. The motivation for testing these sentences in addition to (2a) and (2b) was that deriving the embedded scalar implicatures (A) for double disjunction in contrast to single disjunction is more difficult in localist frameworks (Chierchia et al., 2012). However, our results do not indicate any significant difference between them. 5. Comparison with Crnič et al. Our aim was to test whether the different types of implicature associated with embedded ‘or’ are part of communicated meaning. Within common error ranges, subjects followed the response pattern shown in (7), except for ‘some’ sentences, for which a substantial proportion of subjects failed to infer that some of the girls found none of the marbles. This pattern suggests that indeed implicatures from (A), (B1), (C), and (D’) are reliably drawn in our scenario. As mentioned earlier, the goal of our study contrasts with that of many other studies of embedded implicature. A relevant example is that of Crnič et al. (2015) who tested for strong existence implicature in a picture verification task. They only considered sentences of type (2a), i.e. no sentences with embedding ‘some’: (8) Every box contains an A or a C. A critical picture is shown in Table 3. For this picture, a significant proportion of subjects rejected sentence (8) while almost all accepted the following sentences: (9) a. Every box contains a B or a D. b. Every box contains an A or a B. c. Every box contains an A or an F. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 172 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm As the strong existence implicature (D) from sentence (8) is false in the given situation, it can be inferred that some subjects draw this implicature. As subjects accepted (9b) and (9c), they must have ignored the embedded scalar implicature (A), as well as the weaker global scalar implicature from ‘all p ∨ q’ to ‘¬all p ∧ q’. None of the sentences in (9) is consistent with the exhaustive implicature (C). Hence, the results differ significantly from our study. We assume that this difference is due to the different tasks the subjects had to perform. As mentioned before, picture verification tasks push subjects to purely semantic interpretations. In contrast, we provided them with an action selection task which does not directly involve reasoning about truth conditions. This does not necessarily entail that one design is deficient, and the other does it right. They simply test interpretation in different contexts. The question is what we want to find out about language use. Crnič et al. (2015) wanted to show that there exist a non-empty group of subjects that draw existence implicatures without drawing other implicatures. They are not concerned with showing that they are drawn by almost all subjects. The critical sentence was accepted in 78.4% of all occasions, in contrast to 97% and 93.1% for sentences (9b) and (9c). Hence, the existence implicature has been inferred in at most 22% of all cases in which a critical sentence was presented. In terms of individuals, they found that only 6 out of 51 subjects drew the existence implicature consistently. It is clear that these percentages could not count as evidence that they are drawn reliably. A drawback of the design we used is that it is not sensitive to the distinction between weak and strong existence implicature. We would have to rule out uncertainty about interpretations on the hearer side. If their belief states consist of only one world, for example of the worlds marked by X in Tables 1 and 2, it would be obvious that the strong existence implicature is inferred. In order to show that uncertainty can be ruled out, we have to develop our paradigm further.3 6. Conclusions The results of our study provide clear evidence that participants compute local scalar implicatures (A), global implicature for strengthened ‘or’ (B1), exhaustive implicaures (D), and weak existence implicature (D’). If uncertainty about interpretation on the hearer side can be ruled out, the strong existence implicature (D) can be assumed. We were concerned with implicature as part of communicated meaning. Hence, we had to show that a very high proportion of subjects draw these implicatures. As shown in the introduction, none of the existing theories can account for all these implicatures. In our previous discussions, we have not addressed the issue of how the observed implicature can be accounted for theoretically. The contrast between picture verification tasks, for example (Geurts and Pouscoulous, 2009; Crnič et al., 2015), and the best response paradigm (Gotzner and Benz, 2018) show that context specific parameters, as for example shared assumptions about the speaker’s knowledge about the exact state of the world, and general domain tasks that define relevant meaning differences, play a crucial role in implicature generation. 3 To simply add an answer option ‘I don’t know’ to the options ‘yes’ and ‘no’ would not be enough as this option introduces new uncertainties about its interpretation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 173 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm References Asher, N. (2013). Implicatures and discourse structure. Lingua 132, 13–28. Benz, A. (2012). Implicatures of complex sentences in error models. In A. Schalley (Ed.), Practical theories and empirical practice, pp. 273–306. Amsterdam: John Benjamins. Benz, A. and N. Gotzner (2014). Embedded implicatures revisited: Issues with the truth-value judgment paradigm. In J. Degen, M. Franke, and N. D. Goodman (Eds.), Proceedings of the Formal & Experimental Pragmatics Workshop, Tübingen, pp. 1–6. Breheny, R., N. Katsos, and J. Williams (2006). Are generalised scalar implicatures generated by default? An on-line investigation into the role of context in generating pragmatic inferences. Cognition 100, 434–463. Chemla, E. (2009, May). Universal implicatures and free choice effects: Experimental data. Semantics and Pragmatics 2(2), 1–33. Chemla, E. and B. Spector (2011). Experimental evidence for embedded scalar implicatures. Journal of Semantics 28(3), 359–400. Chierchia, G. (2004). Scalar implicatures, polarity phenomena, and the syntax / pragmatics interface. In A. Belletti (Ed.), Structures and Beyond, pp. 39–103. 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Pragmatic tolerance: implications for the acquisition of informativeness and implicature. Cognition 120(1), 67–81. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 174 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm Levinson, S. C. (1983). Pragmatics. Cambridge: Cambridge University Press. Noveck, I. (2001). When children are more logical than adults: Investigations of scalar implicature. Cognition 78/2, 165–188. Noveck, I. and A. Posada (2003). Characterizing the time course of an implicature: An evoked potentials study. Brain and Language 85, 203–210. Papafragou, A. and J. Musolino (2003). Scalar implicatures: experiments at the semanticspragmatics interface. Cognition 86, 253–282. Potts, C., D. Lassiter, R. Levy, and M. C. Frank (2016). Embedded implicatures as pragmatic inferences under compositional lexical uncertainty. Journal of Semantics 33, 755–802. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy 27, 367–391. Tomlinson, J., T. M. Bailey, and L. Bott (2013). Possibly all of that and then some: Scalar implicatures are understood in two steps. Journal of Memory and Language 69, 18–35. van Tiel, B. (2014). Quantity Matters: Implicatures, Typicality and Truth. Ph. D. thesis, Radboud Universiteit Nijmegen. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 175 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm 7. Appendix 7.1. Instructions Ann, Sue, Mary and Kate are sisters. They are really into collecting marbles. Each of the sisters has a set of 3 special edition marbles. One set consists of a green, a blue, and a red marble. Each set is special, so the girls know which marble belongs to whom. Their mother is playing a game with them. She hides their marbles in the house. Then the girls search for their sets. In the end, they receive a reward. • If a girl finds – call 3 of her marbles, she will win a chocolate – 2 of her marbles, she will win a candy – 1 of her marbles, she will win a red gummy bear, if she found her red marble a green gummy bear, if she found her green marble a blue gummy bear, if she found her blue marble – 0 of her marbles, she will win a pretzel stick as consolation prize. The mother is really good at hiding marbles. So, it is really difficult for the girls to find them. The girls never help each other, and if one of them spots the marble of another one, then she ignores it. In this experiment you will read sentences that were uttered by the mother after she checked the marble bags. Before you begin the experiment, please answer the following question: How many special edition marbles does each sister own? What reward will a girl get when she has found... all 3 of her marbles? only 2 of her marbles? only 1 of her marbles, if she found the red one? only 1 of her marbles, if she found the green one? only 1 of her marbles, if she found the blue one? none of her 3 marbles, if she found the red one? The Main Task: Please decide which sweets you would buy as a reward for the girls depending on the mother’s statement. 7.2. Detailed percentages of action choice across conditions Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 176 A. Benz & N. Gotzner Embedded disjunctions and the best response paradigm Reward/condition All (r ∨ b) candy 18% chocolate 8% green bear 8% red bear 93% blue bear 93% pretzel stick 11% Some (r ∨ b) 15% 10% 18% 95% 93% 69% All (r ∨ b ∨ g) Some (r ∨ b ∨ g) 20% 13% 15% 23% 95% 100% 98% 95% 95% 98% 5% 65% Table 4: Different reward choices for simple and complex disjunctions embedded under all and some (Intercept) choc red bear blue bear green bear pretzel Some (r ∨ b) choc : Some (r ∨ b) red bear : Some (r ∨ b) blue bear : Some (r ∨ b) green bear : Some (r ∨ b) pretzel : Some (r ∨ b) Estimate -1.7518 -1.2033 4.6708 4.6600 -1.2074 -0.8132 -0.2592 0.6246 0.7245 0.2909 1.4368 3.8622 SD 0.5292 0.8227 0.7963 0.7943 0.8235 0.7560 0.6805 1.1228 1.1758 1.1019 1.0685 0.9969 z-value -3.310 -1.463 5.866 5.867 -1.466 -1.076 -0.381 0.556 0.616 0.264 1.345 3.874 p-value 0.000932 0.143590 0.000 0.000 0.142592 0.282065 0.703291 0.577997 0.537774 0.791762 0.178716 0.000107 Table 5: Summary of logit mixed effects model for simple disjunction (n = 474, log-likelihood = -150.9) Estimate (Intercept) -2.44296 choc 0.52841 red bear 7.20754 blue bear 6.40951 green bear 6.41877 pretzel -1.71050 Some (r ∨ b ∨ g) 0.72414 choc : Some (r ∨ b ∨ g) -1.54500 red bear : Some (r ∨ b ∨ g) -1.53248 blue bear : Some (r ∨ b ∨ g) 0.04538 green bear : Some (r ∨ b ∨ g) 20.60431 pretzel : Some (r ∨ b ∨ g) 4.45654 SD 0.69573 0.73897 1.27769 1.04230 1.04435 1.01189 0.73288 1.07413 1.48651 1.47837 273.67643 1.23688 z-value -3.511 0.715 5.641 6.149 6.146 -1.690 0.988 -1.438 -1.031 0.031 0.075 3.603 p-value 0.000446 0.474567 0.000 0.000 0.000 0.090951 0.323119 0.150329 0.302576 0.975511 0.939986 0.000314 Table 6: Summary of logit mixed effects model for complex disjunction (n = 488, log-likelihood = -117.7) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 177 178 The pragmatic ingredients to get perfect biscuits1 María BIEZMA — University of Konstanz Arno GOEBEL — University of Konstanz Abstract. Building on previous work, we present a proposal for a pragmatic account of biscuit conditionals (BCs). We present a new phenomenon that we dub biscuit perfection to support our proposal and argue that differences between BCs and hypothetical conditionals can be explained once we consider the relation between if -constructions and discourse. Keywords: Biscuit conditionals, contrastive topic, inferences in conditionals, causality. 1. Introduction There is a contrast between the two if -constructions in (1): (1) a. b. If you are hungry, I’ll give you some biscuits. If you are hungry, there are biscuits on the sideboard. In its most prominent reading, an utterance of (1a) conveys that whether I give you biscuits or not depends on you being hungry. If -constructions with this reading are often called hypothetical conditionals, (HCs). In contrast, by uttering (1b) the speaker conveys that there are biscuits on the sideboard regardless of whether you are hungry or not, and in addition conveys a suggestion to eat the biscuits to still hunger. If -constructions with this reading are called biscuit conditionals after Austin’s (1956) original example or, e.g., relevance conditionals (although in these cases the consequent is not at all ‘conditional’ on the antecedent). This contrast has been characterized as a difference in information update within a Stalnakerian model of communication (Stalnaker, 2002, 2014): the consequents in HCs update only the temporary context created by the antecedent clause, while in BCs the consequents update the entire context set. Theories of biscuit conditionals have aimed to explain this contrast, which we dub the global update puzzle (GUP). A second issue is why a speaker would utter (1b) instead of the plain declarative there are biscuits on the sideboard. We dub this second question the conditional form puzzle (CFP). As a third point, we would also like to understand how the ‘extra meaning’ pertaining to a suggestion arises in examples like (1b). There are, roughly, two linguistic approaches to the study of BCs. Semantic theories (DeRose and Grandy 1999; Siegel 2006; Ebert et al. 2014 a.o.) claim that BCs and HCs have different logical forms that result in a different interpretation. Such accounts provide explanations for the GUP and the CFP and can also account for the fact that an utterance of (1b) conveys a suggestion. 1 We are grateful to Ana Arregui for comments. Thanks also to Anja Arnhold, Andrea Beltrama, Marc Brunelle, Nate Charlow, Eva Csipak, Felicitas Enders, Sven Lauer, Brian Leahy, Erlinde Meertens, Thomas Müller, Doris Penka, Eric Raidl, Eva Rafetseder, Kyle Rawlins, Maribel Romero, Antje Rumberg, Wolfgang Spohn, Andreas Walker, Mark-Matthias Zymla and the audience of the XPrag-Workshop Rationality, probability and pragmatics and of SuB 21 for their very useful comments. All remaining errors are our own. This research has been supported by the Deutsche Forschungsgemeinschaft (DFG, Project 1836/1-1) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 179 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits Pragmatic theories (Franke 2007, 2009; Sano and Hara 2014; Lauer 2015; Francez 2015 a.o.), in contrast, argue that the semantic meaning of if -constructions is the same and differences between HCs and BCs are derived pragmatically taking into account the independence between antecedent and consequent. While semantic theories are designed to explain all the points in our desiderata so far, pragmatic theories have focused on how to derive the GUP, with the other puzzles often only sketched. In this paper we defend a pragmatic view of BCs. We build on previous work to provide a fleshed-out account of the factors that result in if -constructions being interpreted as either HCs or BCs. We further argue that the pragmatic mechanisms underlying one or the other reading of if -constructions are independently motivated. This point will be made by exploring new data illustrating a phenomenon that we call biscuit perfection. An example is provided in (2) (with prosodic annotations resulting from a pilot study, see §4 for more details): (2) a. Oh, you are making pasta bolognese! If you need wine for the sauce . . . there is a bottle by the microwave. b. Oh, you are making pasta bolognese! If you need wine for the sauce . . . there is a bottle by the microwave. (L)-H* L+H* L-H% L+H* L-H% The two different prosodic patterns above lead to two different interpretations. In (2a), representing a “neutral” pattern, the speaker is not suggesting that the wine should not be used for other purposes, such as drinking (though such inferences could arise as a result of worldknowledge regarding the kinds of wine we cook with.). However, with the prosody in (2b) the speaker indicates that the recommendation to use the wine by the microwave extends only to the making of the sauce (i.e. the speaker wouldn’t recommend drinking the wine). In this case, the suggestion inference we had already noted is strengthened to be applied only in the circumstances described by the antecedent. We call this biscuit perfection. A theory of BCs should also explain how biscuit perfection is derived, which becomes now the fourth point in our desiderata. As we will show, accounting for biscuit perfection requires taking into account the mapping between BCs and discourse structure, providing independent support for a pragmatic account of BCs. The reminder of the paper is organized as follows: in §2 we briefly explain how pragmatic theories solve the GUP and introduce the notion of independence in BCs. In §3 we make a proposal regarding how BCs map into discourse. We argue that this mapping is what triggers the inferences in BCs. The case of perfect biscuits, §4, provides support for the idea that the mapping of BC s into discourse is crucial in the construction of meaning. Biscuit perfection is argued to be no more than C(ontrastive)T(opic)-marking in BCs. We conclude with a comparison between the resulting theory and semantic theories of BCs in §5. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 180 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits 2. Strengthening the consequent to a global update (GUP) 2.1. Independence Pragmatic theories claim that independence between antecedent and consequent is key to biscuithood (in HCs they are dependent). However, there are different takes on how to spell out what it means for propositions to be independent (Merin, 2007; Sano and Hara, 2014; Francez, 2015; Franke, 2009). Here, we will confine ourselves to an informal characterization of independence emphasizing the core insight shared by the different positions.2 Independence is regarded as an epistemic notion defined relative to an agent’s information state. (3) Epistemic independence of propositions Two propositions ϕ , ψ are independent relative to an information state Σ iff learning the truth of ϕ does not provide information regarding ψ and vice-versa. With this rough characterization of independence at hand let us turn now to the semantics of indicative if -constructions. We will then be prepared to tackle the GUP. 2.2. A dynamic semantics for the (indicative) if -constructions and the GUP in BCs We employ a dynamic semantics for (indicative) if -constructions operating on a Stalnakerian context set c, the global context.3 The meaning of an expression is its context change potential (CCP), i.e. a function from contexts to (updated) contexts. The CCP of a simple declarative proposes to eliminate from c all worlds in which the corresponding proposition is false. For conditionals, we adopt Heim’s (1983) CCP (see Biezma and Goebel 2017 for an analysis building on Isaacs and Rawlins’s 2008 proposal using a stack-based model): (4) Conditional declarative update: Where M\N = M ∩ (W − N) c + If α , β = c \ (c + α \ c + α + β ), where α and β are declarative clauses. To evaluate a conditional, the antecedent clause sets up a temporary context c + α containing only worlds where the antecedent is true. Given that indicative conditionals presuppose that the antecedent proposition is a live option in c, c + α is a subset of c. Furthermore, c + α is updated with the consequent β . Complementation in (c + α \ c + α + β ) gives us all α ∧ β -worlds, i.e. those worlds eliminated when c + α is updated by β . In the final step, all α ∧ β -worlds are eliminated from the global context c. However, for BCs this is not the end of the story. In pragmatic accounts of BCs following Franke (2009), the interplay with the contextual assumption of independence has the effect of eliminating all β -worlds from the global context c, not only α ∧ β -worlds. Why is this so? The proposal is that in the context prior to the utterance of the BC there is a shared contextual assumption of 2 The reader is referred to Biezma and Goebel (2017) for a full discussion and an improved alternative. we restrict ourselves to indicative BCs. In Biezma and Goebel (2017) we extend our account to also cover subjunctive BCs as observed by Swanson (2013) and further subjunctive cases. 3 Here Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 181 M. Biezma & A. Goebel (a) The pragmatic ingredients to get perfect biscuits (b) (c) (d) (e) Figure 1: Dynamic update and strengthening in BCs independence between antecedent and consequent (while in HC-interpretations we take them to be dependent). We follow Francez (2015) in postulating that this means that dependence is excluded by shared world-knowledge of “causal and epistemic relations”. Independence enforces that in c all possible truth-value distributions over antecedent and consequent are possible, as depicted in fig. (1a). This structure makes sure that learning that either the antecedent or the consequent is true doesn’t provide information regarding the other proposition. The utterance of the conditional proposes to update c by first creating a temporary context c + α formed by all the α -worlds (fig. (1b)), and then eliminating from them the β - worlds, leaving us only the α ∧ β -worlds (grey area in fig. (1c)). At this point we return to the global context where all α ∧ β -worlds are eliminated (fig. (1d)). However, the induced structure on c depicted in (fig. (1d)) clashes with the independence assumption. The latter requires that learning about the truth of one proposition does not imply learning anything about the other proposition. In contrast, the structure depicted in fig. (1d) is fit for modus ponens, i.e. if the truth of the antecedent is learned, the truth of the consequent is also learned in c since after an update with α there are only α ∧ β -worlds left. Hence, we arrive at a contradiction, since α and β are not independent here. The clash of the independence assumption and the semantically encoded update exerts pragmatic pressure on the addressee to modify her view of the context while preserving the assumptions of independence and that there are worlds in the context set in which the antecedent is true. With these constraints the only way to retrieve a coherent context set is to eliminate all β -worlds from the global context c (fig. (1e)). In the resulting context set, in which β is always true, learning whether the antecedent α is true or false does not allow us to learn anything about the status of β , preserving in this way the assumption of independence as well. Hence, it is the assumption of independence what accounts for the GUP. It is important to note that strengthening as described is a rational reconstruction and not an explicit reasoning process the interpreter goes through. Strengthening is a contextual entailment that is not cancellable, because it is an entailment of the context set given that certain presuppositions, i.e. independence and antecedent possibility, are met. 3. The discourse function of BCs Having explained the GUP, let us tackle now the CFP: why does a speaker utter a BC when the utterance of the main clause alone (the consequent) would apparently suffice? We believe that part of the answer, following Franke (2009) and going back to DeRose and Grandy (1999), is Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 182 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits that BCs help to establish relevance (and hence felicity) of the utterance. The following example (adapted from Franke 2009: 275) illustrates the point: (5) B has been helping A to pack for a trip by handing him stuff, and is obviously tired: A: There are biscuits on the sideboard. [B hands out the cookies to A who starts laughing. A explains that he was just suggesting that B eat them since he looks tired and sugar would do him good.] B’s interpretation of A’s utterance was perfectly coherent given the overall context, but that is not what A intended (hence the laughter). Uttering the BC ‘If you are hungry, there are biscuits on the sideboard’ would have avoided the confusion and would have unambiguously resulted in the intended interpretation, i.e. that the speaker is suggesting that B eat some biscuits. The BC would have informed the addressee about the presence of biscuits on the sideboard and also about the intended context for that information. In this way the BC is more informative (while relevant) than the utterance of the main clause alone.4 We now must face the question of how to capture the intuition that the participants’ overall interpretation is that the speaker is providing the relevant context for that information as well as suggesting that the addressee eat the biscuits. It is worth noting that classic BCs are not the only conditionals where antecedent and consequent are independent. Other examples have been discussed in the literature under the label of non-interference conditionals (see discussion in Bennett 2003: 122). In these cases, the intuition is also that our beliefs about the consequent proposition are unaffected by our beliefs about the antecedent. Bennett offers the following example: (6) I express fear that the refrigerator will explode if you open its door, and you assure me that if I open the door, it won’t explode. You base this on your belief that the dooropening and the non-explosion are irrelevant to one another, and put it in conditional form because I think they are connected. (p. 123) In pursuing a unified analysis, we would conclude that examples like this are of the same kind as traditional BCs, with differences that should follow from pragmatics. This is interesting because in the case of non-interference conditionals, the role of the conditional does not (always?) seem to be to establish relevance. Consider the following example: (7) A: Oh look at the weather! It’s probably going to rain. Poor Betsy is still out there. She will get completely soaked. B: Don’t worry. She has her umbrella. A: But the poor child! This is terrible! Dreadful! B: Stop exaggerating. If it rains, she has her umbrella. B’s utterance of the conditional is not meant to establish relevance (this was already clear!). B’s point is to emphasize that Mary has her umbrella. If the only discourse purpose of the ‘independent’ conditionals were to establish relevance, it would have been redundant, but it is 4 This can be formalized in a number of neo-Gricean approaches, see Potts (2006) and reference therein a.o. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 183 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits not. We will not be able to investigate all cases of if -constructions with independent antecedents and consequents. Our focus remains on ‘classic’ BCs. But the observation that there is a larger group, and that some members of that group do not appear to serve the discourse function of establishing relevance, is important in terms of deciding how it is that BCs come to establish relevance. A theory of BCs has to derive the old intuitions that BCs help to establish relevance, but also allow if -constructions with independent antecedents and consequents to serve other purposes, since they can also be used in scenarios like (7). In what follows we argue that the key is to be found in how conditionals map into discourse. 3.1. The mapping of if -constructions into discourse We adopt the Q(uestion) U(nder) D(iscussion) discourse model (Roberts 1996; Büring 2003 a.o.) in which conversation is taken to be a cooperative inquiry and is modeled as as a hierarchical order of moves. Discourse moves are understood as either answering a (implicit) question (pay-off moves) or setting up a question for participants to answer (set-up moves). The hierarchical nature of discourse can be represented by Büring’s (2003) D(iscourse)-trees: (8) Big question Question subq subq answer answer Question subq subq answer subq subq answer answer answer Each node in the tree represents a discourse move. Participants can adopt strategies to address a given question (a strategy is a set of subquestions to the dominating question). Well-formedness in discourse is constrained by several notions, amongst them entailment and relevance: (9) Entailment: One interrogative q1 entails another q2 iff every proposition that answers q1 answers q2 as well. Relevance: A move M is Relevant to a question q iff M either introduces an (at least) partial answer to q in context cM (M is an assertion) or is part of a strategy to answer q (M is a question). The question now is how if -constructions map into discourse. Haiman (1978) already claimed that the antecedent clause in if -constructions is understood as establishing the topic of the utterance. In the QUD model this translates into the antecedent establishing the question that is being addressed. The consequent, on the other hand, provides the answer. This mapping is also suggested for BCs in Starr (2014) (although not directly in the QUD model), and Ebert et al. (2014). However, these proposals either encode the mapping in the semantics of if constructions without allowing for other possibilities (which we will see is problematic), or fail to explain why this is the only possible mapping in BCs. A default mapping of if -constructions does not mean that other mappings are not possible. It has been argued, for example, that focus Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 184 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits particles associating with the entire antecedent proposition makes conditionals reverse this default mapping to one in which the consequent presents the QUD while the antecedent provides the answer (Biezma 2011a, b). This reverse mapping can also be forced contextually and has been claimed to be necessary in von Fintel (2009) to explain classic conditional perfection: (10) A: When would you give me $5? B: Well, if you mow the lawn, I’ll give you $5. ⇝ If you don’t mow the lawn, I won’t give you $5. [Conditional perfection] Conditional perfection arises when the antecedent is understood as an exhaustive answer to the on-going question presented by the consequent. The discussion above argues against encoding the mapping between if -constructions and discourse in the semantics. In what follows we first assume that in BCs the antecedent always indicates the QUD, while the consequent provides the answer. This mapping, we argue, explains how inferences arise in BCs (when they do) and allows us to explain why some BCs are infelicitous. We close the section by explaining why this is the only possible mapping for the cases we identify as BCs. 3.2. Inferences in if -constructions and discourse-relevance Under our unified perspective, an if -construction of the form if α , β will be true iff in all ‘relevant’ worlds in which α is true, β is also true (where ‘relevant’ depends on the particular theory of conditionals and how such theory restricts the domain of quantification). Assuming the default mapping of if -constructions, a BC (posits and) answers the following question: (11) ‘What do the ‘relevant’ worlds in which α is true look like?’ (≃ What if α ?)5 The consequent is interpreted as a (relevant) response to such question. This relevance assumption, we argue, is what gives rise to inferences in BCs: (12) QUD: What do the relevant worlds in which the addressee is hungry look like? (≃ What if the addressee is hungry?) Answer: There are biscuits on the sideboard. Given that the consequent is taken to be a relevant response to the established question the addressee reasons that the speaker is trying to provide a way to solve hunger.6 In paradigmatic cases of BCs like (1b), reasoning towards the relevance of the consequent as the answer to the question set by the antecedent leads the addressee to additionally infer, via pragmatic enrichment, that the speaker is suggesting that s/he eats the biscuits. 5 The paraphrase what if α ? is just a shortcut to illustrate the discourse inquiry and it may not be always suitable. We abstract away from additional meanings triggered by the utterance of these questions. 6 The question established by the antecedent is rather vague, but in providing the answer, the speaker provides enough for the addressee to make out what the goal of the question is. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 185 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits One prediction from this proposal is that the pragmatic inferences triggered in if -constructions are the same as the ones found in question-answer pairs. This prediction is borne out. (That the conditional form is congruent in giving rise to the same inferences as the distributed fragments had already been observed in Starr 2014: 18.7 ) (13) A: What if I get hungry? B: There are biscuits on the sideboard. ⇝ I suggest that you eat the biscuits. B’s utterance in (13) is interpreted as providing an answer to A’s question. Assuming that participants are cooperative, the response leads to the interpretation that A is allowed to eat the biscuits. Note also that unless it is done immediately the inference triggered via relevance in this case cannot be cancelled and becomes part of the common ground.8 In each of these cases, the inference is a result of a process of pragmatic enrichment derived by the same mechanisms that are at work in pragmatic enrichment generally. An example is given in (14) where the addressee A infers by pragmatic enrichment that B wants to bring across that it is very late. (14) A and B are attending a party together and have been there for a while. A: What time is it? B: Most people already left. ⇝ It’s very late We won’t get into the matter of how the mechanism of pragmatic enrichment works exactly (see e.g. Benz 2012 for a proposal). Rather, our point is to argue that an utterance of a BC leads to a triggering of such inferences in the same way as other discourse-relevance inferences are derived (where relevance is as defined in 2). The proposal can also explain Sano and Hara’s (2014) empirical observation that BCs like (15) are (almost always) judged infelicitous. As predicted in our theory, the same is found with the corresponding question-answer pair: (15) If France is hexagonal, there is beer in the fridge. (16) A: What if France is hexagonal? B: There is beer in the fridge. 7 There are several differences between Starr’s (2014) proposals and the one in this paper. Most importantly, Starr establishes in the semantics of the if -constructions that the antecedent signals the question being addressed. It is not clear to us whether his proposal can be modified to allow for the required flexibility in the mapping between if -constructions and discourse argued for above. 8 While we have no space to address all BC s, our proposal can also handle discourse hedging BC s such as if you want to hear a big fat lie, George W. and Condi Rice are secretly married. The QUD inquires ‘what do the worlds in which the speaker tells a big fat lie look like?’. The response is that these are worlds in which the addressee says that George and Condi are secretly married. More, certainly, needs to be said about these cases and their apparently special behavior (see Csipak 2015). The reader is referred to Biezma and Goebel (2017) for discussion within the framework presented in this paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 186 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits Our proposal allows us to predict that these BCs and the parallel question-answer pair will be bad unless the participants can come up with an explanation as to why the consequent is relevant to the QUD. There are in fact contexts in which (15) and (16) are good. Imagine a context in which a couple of friends are making a bet regarding the shape of France. While one thinks it’s hexagonal, the other thinks it’s a square. When clarifying what’s at stake, the speaker betting for the square shape can felicitously utter (15), or respond to the question as in (16), to establish what the addressee will win were the shape be hexagonal. Our proposal also applies to HCs and intuitions regarding ‘causality’. The mapping from if constructions to discourse we have been exploring for BCs is also possible for HCs (although HC s also can have the reverse one). The difference is that when interpreting the relation between question and answer in a HC via relevance, we can recover a dependence relation between the two propositions: (17) If you are hungry, I’ll make you some sandwiches. QUD: What if I’m hungry? Response: I’ll make you some sandwiches. In a scenario in which it is conceivable that sandwiches wouldn’t necessarily be made and that the making of the sandwiches can be dependent on someone’s hunger, we can draw the inference that the addressee being hungry is what ‘causes’ / ‘leads to’ the making of the sandwiches (the intuition being that if the addressee is not hungry, the sandwiches won’t be made). The intuition that there is a dependence between the antecedent and consequent proposition can be taken to respond to the mapping of if -constructions into discourse and the need to satisfy relevance. When there is no plausible dependence relation between antecedent and consequent, the inference of causality does not arise.9 9 Ippolito (2016) also considers the mapping of BCs into discourse and their differences in interpretation with in a short note on relevance conditionals, although her overall proposal is rather different. Ippolito (2016) proposes that conditionals (what we carefully term if -constructions) of the form if ϕ , ψ address a ‘conditional question’ of the form if ϕ , Q?, where ψ is a possible answer to Q. The BC in (1b), for example, is taken to address an ongoing QUD that can be paraphrased by ‘If you are hungry, is there anything to eat?’. The BC addresses this question by offering the ‘premise’ in the consequent that, indirectly, answers it. It is not clear to us how this question is identified in Ippolito’s system, i.e. what are the conventional cues in the information structure of the utterance identifying that such is the inquiry being addressed, which is essential within the QUD model. In addition, given the arbitrary choice of question, it is not clear to us how this system would account for cases of ‘classic’ conditional perfection like (10), or cases of ‘biscuit perfection’ (see §4), which are explained by assuming a mapping to discourse that does not involve conditional questions but a classic information-structural division of labor between antecedent and consequent like the one explained above and adopted in this paper. In addition, Ippolito (2016: 56) also aims to offer and explanation as to why some if -constructions have a ‘causal’ interpretations while others don’t: “The proposal that I would like to make is that the difference between causal and non causal counterfactuals lies in their relation to the [QUD]. A causal counterfactual answers the [QUD] directly, whereas a non-causal counterfactual answers de [QUD] indirectly by spelling out a premise assuming which the [QUD] is then answered.” In our system, causality is also an inference, but it does not result from the utterance providing a direct answer. In our account, that the HC is taken to provide a direct answer to a QUD is the byproduct of there being a dependence relation between antecedent and consequent. Overall, Ippolito (2016) is not devoted to BCs but aims to explain how context dependence allows us to identify the premises relevant in the interpretation of counterfactuals. We leave for future research the evaluation of her claims once we adopt a mapping between if -constructions and discourse that considers their information structure. HC s Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 187 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits In sum, BCs are merely if -constructions in which we understand that antecedent and consequent are independent. This is a possibility for if -constructions and can be reinforced through linguistic means. For example, many stereotypical examples of BCs involve stative predicates. This is not accidental. With stative predicates it can be easier (though not necessary) to interpret that the antecedent and consequent temporally overlap, without a causal dependency. On the other hand, linguistic means can block the independent interpretation. Following Biezma (2014), the presence of the discourse maker then prevents a BC-reading since it conventionally requires that two propositions (antecedent and consequent) enter into a ‘causal explanatory claim’-relation in which one (the antecedent) provides the ‘reasons’ for the other (the consequent) and causality is not cancellable anymore (but see discussion on then in §5).10 Let us finish this section with a discussion of why the reverse discourse-mapping for if - constructions, one in which the antecedent provides the answer to a question signaled by the consequent, is not available for BCs. According to the (rough) semantics of if -constructions adopted in this paper, the QUD for such a mapping would be what are the propositions such that for all ‘relevant’ worlds in which those propositions are true, the consequent is true? We can paraphrase this inquiry with the question When q?,11 and this is indeed what we take the question to be in the ‘regular’ perfect conditional in (10). We illustrate this mapping for BCs in (18): (18) QUD: When are there biscuits on the sideboard? Response: If you are hungry (there are biscuits on the sideboard). A BC is not a felicitous answer to this QUD and a mapping of the BC to this discourse structure is ruled out. Given the QUD in (18), it is relevant whether or not all circumstances are such that there are biscuits on the sideboard, and, if not all, in which. The BC leads to an answer (in all of them) but only indirectly as a result of the BC-strengthening process. It also provides extra information that is not requested (i.e. that, in particular, the worlds in which you are hungry are worlds in which there are biscuits on the sideboard). One way to explain the infelicity is using the economy principle in Romero and Han (2004).12 We have claimed that considering how BCs map into discourse can explain several properties of BC s. In the following section we argue that the proposed mapping is necessary independently to explain biscuit perfection. 4. Biscuit perfection We have seen above that some BCs can give rise to inferences such as suggestions. As we have noted in §1, however, there is a contrast between (19) and (20) (‘⇝’ signals any non10 Obviously this is derived from the original temporal meaning of then: when found coordinating two events it requires that the two take place sequentially. 11 The same caveat as above holds for this rough paraphrase, i.e. the topical question is not to be confused with proper utterance of this specific interrogative. This is merely a shortcut to illustrate the discourse inquiry. 12 The principle of economy prevents the use of meta-conversational moves unless they are necessary to resolve epistemic conflicts or to ensure Quality. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 188 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits conventional meaning):13 (19) Oh, you are making pasta bolognese! If you need wine for the sauce . . . there is a bottle by the microwave. (L)-H* L+H* L-H% ⇝ There is a bottle of wine by the microwave [BC strengthening] ⇝ I suggest that you use the wine by the microwave. [Discourse relevance] ̸⇝ I only suggest that you use the wine by the microwave if it is for the sauce. (20) Oh, you are making pasta bolognese! If you need wine for the sauce . . . there is a bottle by the microwave. L+H* L-H% ⇝ There is a bottle of wine by the microwave [BC strengthening] ⇝ I suggest that you use the wine by the microwave. [Discourse relevance] ⇝ I only suggest that you use the wine by the microwave if it is for the sauce. [?] We will now focus on (20). As we have noted earlier, a speaker uttering the BC in (20) provides information regarding what wine to use for the sauce while explicitly signalling that there are other circumstances in which wine may be needed that s/he is not addressing (contrary to what happens with (19)). In this sense, the BC in (20) is explicit about the fact that it offers only a partial resolution to a question regarding what wine is to be used when. This results in the inference that the use of the wine by the microwave is only a suggestion for the making of the sauce and nothing else, i.e. the suggestion-inference is strengthened. This is what we have called biscuit perfection. How can we derive this strengthened inference? In what follows we argue that it results from the specific details of the mapping of (20) into discourse. Our proposal is that the strengthened reading results from mapping the BC in (20) to the D-tree in (21): (21) What use has what wine? What wine do I use if I need it for the sauce? What wine do I use if I need to drink a glass? ... If you. . . there is a bottle by the microwave Given this D-tree, the QUD addressed by the BC is part of a larger strategy to answer a complex question. With this mapping, the speaker has clearly marked that s/he is addressing a specific (sub-)question and not others contextually salient that contrast with it. Given that the speaker was careful to signal that this answer was not provided with respect to any other salient question, the resulting inference is that the suggestion to use the wine by the microwave is only made if it is for the purpose of making the sauce. The question now is: why does (20) map into a D-tree like (21) while (19) doesn’t? 13 Notice that even though the shape of the complex accent is the same, the height of the pitch is different. In a pilot study the H* in sauce is much higher (≃ 290Hz) in the perfected version, (20), than in the non-perfected one in (19) (≃250Hz). Also, the high pitch on wine is ≃365Hz in (19) whereas it only receives a pre-nuclear accent at best in (20). We are very grateful to Anja Arnhold and Marc Brunelle for their help discussing the prosodic data. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 189 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits Our proposal is that the mapping of (20) into the D-tree in (21) depends on conventional linguistic devices that give rise to such a mapping. In this case, it is prosody that is (conventionally) responsible (but see below for additional mechanisms).14 In what follows we argue that the phenomenon of biscuit perfection is nothing more than contrastive topic (CT) marking in BCs. The discussion revolves mostly around BCs because this data is used in this paper as an argument in favor of a pragmatic account of BCs. However, notice that similar phenomena can be observed in HCs, with the only difference that the inference that is perfected in HCs concerns causality. At the end of the day, the claim is that ‘inference perfection’ via linguistic marking in if -constructions is nothing more than contrastive topic in if -constructions. In what follows we sketch Constant’s (2014) proposal for CT and examine a straight-forward application of this account to conditionals. We close the section with a discussion of the fact that CT-marking in if -constructions seems to be more complicated than it is taken to be in Constant (2014). The discussion serves the purpose of showing how if -constructions can serve as probes to broaden our understanding of CT-marking in English. 4.1. A theory of Contrastive Topic and BCs We adopt Constant’s (2014) theory of CT (see references therein for other accounts and discussion). In this section, we sketch Constant’s (2014) proposal and examine its application to BCs. As we will see, CTs provide the crucial insight to understand biscuit perfection. The phenomenon of CT in simple sentences is illustrated in (22) (adapted from Constant 2014): (22) I arrive late to a potluck party and I am not aware of who brought what. I have asked another guest to fill me in on the details. A few minutes into the conversation, the next exchange takes place: A: What about Persephone and Antonio? What did they bring? B: PERSEPHONE . . . brought the GAZPACHO. L+H* L-H% Antonio, I’m not sure about. H* L-L% As Constant puts it, by using these specific prosodic features B indicates that he has decided to break the asked question in two smaller pieces, one about Persephone and one about Antonio. In a way, Persephone and Antonio become “topics of smaller issues, and they contrast” (Persephone is the contrastive topic). In addition to indicating that the question is now split in two parts, the speaker provides an exhaustive answer regarding what Persephone brought, this is the constituent the gazpacho. (The constituent that provides the exhaustive answer is the exhaustive focus.) A paraphrase could be as follows: “As for the issue of Persephone, the answer to the question of what she brought is the gazpacho.” The claim in the literature is that there is a systematic relationship between the surface realization of B’s response and the discourse role of its constituents, so we can predict one from the other. In Constant (2014), contrastive topic is an information-structural category indicating the question that is being answered. Regarding 14 Notice that not all BCs trigger extra inferences such as suggestions and hence not all biscuits can perfect via conventional mechanisms such as the use of prosody. See discussion in §4.2 below. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 190 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits the interpretation, CT-marking is merely focus marking (it evokes alternatives à la Rooth as any other focus marking) with additional information of how the focus alternatives are used in the semantic computation. The instructions regarding how to manipulate the generated alternatives are cashed out in the CT-operator indicated in English by a special intonation, the complex contour L+H∗ L-H%. The CT constituent is “a F-marked phrase in a particular structural position, or bound by a particular focus-sensitive operator” (Constant, 2014: 85). This proposal can be seen as belonging to a family of configurational approaches, “[a theory that tries] to establish what configuration defines a focus as CT, and to model how this configuration is spelled out in surface syntax and phonology” (see Constant 2014 for discussion). The mapping between utterances and discourse is done via focus anaphora in the Roothian tradition: focus structure helps identify the question in discourse that the utterance is answering. This is done via the familiar ‘∼’ operator with a slight modification to relax the membership relation in (23ciii) (see Constant 2014 for discussion). The ‘∼’ introduces the presupposition that there is a discourse antecedent that is a question of a particular shape: (23) Constant’s (2014) ‘∼’ a. J∼ ϕ Ko = Jϕ Ko b. J∼ ϕ K f = { Jϕ Ko } c. . . . and presupposes that the context contain an antecedent C such that: (i) C ⊆ Jϕ K f (ii) |C| > 1 (iii) Jϕ Ko ∗ ∈ C “C contains Jϕ Ko somewhere within it.” The other addition to the system is the mechanism that combines the focus alternatives in utterances with CT-marking. This is done via the CT-operator, with CT-hood linked in English to the complex contour L+H* L-H% that we find in standard CT-constructions:15 (24) Topic abstraction a. b. JCT-λi ϕ Kog = λ x. Jϕ Kog[i→x] f (Ordinary semantic value) f JCT-λi ϕ Kg = {λ x. Jϕ Kg[i→x] } (Focus semantic value) The ordinary semantic value of CT-λ is merely predicate abstraction, but at the focus value provides us with the expected result. Following Constant, let us look at the structure of the CT-utterance in (22): (25) f J[Persephone]F brought [the beans]F Kg 3 [Persephone]F 2 CT-λ7 1 t7 15 Constant brought [the beans]F (2014) considers that the complex pitch accent could also adopt other forms, such as H* or L*+H. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 191 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits f J 1 Kg = {g(7) brought the beans, g(7) brought the pasta . . .} J 2 K f = {{λ x.{g(7) brought the beans, g(7) brought the pasta . . .}} } {Persephone brought the beans, Persephone brought the pasta, . . .}, f J 3 K = {Mary brought the beans, Mary brought the pasta, . . .} , ... a. b. c. CT here involves left-dislocation of the contrastive topic constituent, justifying predicate abstraction and the CT-operator. Topic-abstracting the subject helps to create a nested focus value containing a set of questions varying in the position of Persephone. The resulting focus value is a complex question sorted by the topic-abstracted argument (who brought what?).16 This focus value is the input of the squiggle operator enforcing the congruence that derives the interpretation of utterances with CT: (26) J∼ [[Persephone]F CT -λ7 t7 brought [the beans]F ]K f = {Persephone brought the beans} felicitous iff there is a question in discourse made up of multiple questions of the form “What did x bring?”, one of which is the question “What did Persephone bring?”. That is, the utterance of Persephone brought the beans with the CT-marking in (22) is felicitous in a discourse structure like (27): (27) Who brought what? What did Persephone bring? What did Mary bring? ... Persephone brought the beans The structure in (27) is exactly like the one we want to derive in (21). We propose that in both cases, CTs provide the key to understanding how the D-tress are generated. The question is whether we can merely adopt Constant’s (2014) proposal to explain biscuit perfection. The answer is yes, mostly. We turn to the straight-forward application of Constant’s (2014) proposal below and discuss some problems in §4.2. Following much of the literature (see Bhatt and Pancheva 2006 for discussion), we take it that if -clauses are correlative/free-relative adjuncts and assume the syntax in (28a). In if constructions we do not need to assume movement of the topic-constituent. We have binding of the restrictor to the modal in the matrix clause being interpreted via predicate abstraction. With CT-marking we get the CT-operator and not just mere predicate abstraction, (28b). (28) a. Conditionals as correlatives λi if-clause b. Conditionals as correlatives with CT-marking if-clauseF CT -λi modal ti consequent modal ti consequentF The interpretation of the utterance in (20), unlike the utterance in (19), is then as follows:17 16 This assumes that questions denote sets of propositions, specifically, their possible answers (Hamblin 1973). speaking, focus marking is on sauce (see (20)). This is what evokes alternatives to the antecedent. 17 Strictly Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 192 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits (29) [[If you need wine for the sauce]F CT-λ9 [ t9 there is a bottle by the microwave]F ] (30) J∼(29)K f = {If you need wine for the sauce there is a bottle by the microwave} felicitous iff there is a question in discourse made up of multiple questions of the form “What if the addressee needs wine for x?”, one of which is the question “What if the addressee needs wine for the sauce?”. At the core of CT is partial answerhood. In contrast with (20), in (19) we do not convey (linguistically) that there are contrasting alternatives that the speaker is not answering, hence do not mark conventionally that the utterance is embedded in a D-tree like (27). To summarize, we have seen above that ‘biscuit perfection’ and in general conventional strengthening of the inferences in if -constructions is just CT-marking in if -constructions and can be explained by using mechanisms argued for independently of conditionals. Crucially, these mechanisms result in a mapping of BCs to discourse that explains the inferences in BCs and the effect of biscuit perfection. No special BC-specific semantics needs to be invoked. 4.2. Shedding light on CT-marking in English Constant (2014) also discusses the case of conditionals and their mapping in discourse. The claim is that conditionals “generally make good CT” , but Constant explicitly excludes BCs and factual conditionals (without considering that there are biscuits that are factual) and, hence, only (non-factual) HCs are taken to be able to encode CT. The reason, he states, is that “the antecedent of a HC makes good contrastive topics, since considering one hypothetical possibility almost inevitably leads to questions about contrasting possibilities[. . .] Non-hypothetical conditionals, on the other hand, do not typically set-up contrasts with different antecedents” (Constant, 2014: 321).18 He provides the following prosodic characterization of a conditional with a CT-reading. (Constant 2014 does not provide prosodic annotation for BCs):19 (31) If it’s RAINING . . . L+H∗ L-H% we’ll have to cancel the PICNIC . H∗ L-L% (Constant, 2014: 285) According to Constant, it is the interpretation of factual conditionals and BCs what prevents them from being interpreted as conveying CT: to a non-factual HC like (31) one can respond with “And if it doesn’t rain?”, but that is not a possible response to the former merely because either other alternatives to the antecedent are already discarded (in factual conditionals the antecedent is taken to be true) or because the consequent is taken to be true across the board (in BC s). However, while it is true that questions about what is the case in circumstances other than the ones established in the antecedent are impossible in factual conditionals and BCs, one can ask about the inferences triggered by the utterance of a BC (if there are any). For example, given 18 Constant’s discussion of conditionals aims to explain the contrast between if -constructions and becauseclauses. In both cases we find the prosodic markings tied to CT-interpretations, i.e. L+H∗ L-H%, but becauseclauses do not have a CT-interpretation. His conclusion is that not all L-H% in English convesys CT: “while sentence final L-H% is robustly interpreted as CT, non-final L-H% is unreliable in this regard”. 19 We take it from the discussion that he assumes this to be the default intonation for HC s. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 193 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits an utterance of (2b), one could ask “And if I want to pour myself a glass? (does the suggestion still hold? shall I use the same wine?)” Notice that when a BC doesn’t trigger extra-inferences, such as in (7) (or at least these are harder to grasp), no question of this sort is possible and there, in fact, we do not (easily) get a CT interpretation. Several questions arise at this point pertaining to CT-marking in conditionals and CT-marking in general. Given that (2b) does have a CT-reading while (2a) doesn’t, and both have L+H∗ L-H% marking, it seems that it is not this specific complex contour what is responsible for the CT-reading in conditionals. The data suggests that what delivers the CT-reading is merely the marking of contrast in the constituent that is understood as establishing the QUD (the antecedent): this happens in (2b) by de-accenting everything else but one word, while in (2a) there are two words that receive H∗ or L+H∗ .20 In if -constructions, L-H% is merely a continuation tone. This is also true for non-factual HCs.21 The general claim is that the CT-reading appears in if -constructions when we understand that there are salient alternative questions to the one being addressed and that they won’t get necessarily the same answer. We can enforce this reading conventionally by using specific prosody, or by other means that indicate that the speaker is answering only a particular question amongst a contextually salient set (the others remain un-answered). An illustration is provided in (32). The presence of only/just in (32) ensures that the use of wine the speaker is talking about contrasts with others. (32) Well, if you only/just need the wine for the sauce, there is a bottle by the microwave. A CT-type interpretation can also arise in BCs without any linguistic marking as an inference from world-knowledge. In (33), it is world-knowledge what tells us that the suggestion/permission regarding killing people is tied to people turning into zombies. (33) A virus is transforming people into zombies. A farmer in an area suspected of infection tells his farm workers: Farmer: If the virus breaks out, the rifles are in the safe. It is understood that if the virus does not break out, shooting of people should not happen, i.e. we understand that there are contextually salient alternatives to the antecedent for which the answer wouldn’t be the same, leading to a CT-type interpretation without CT-marking. The conclusion is that CT-marking is not necessarily done prosodically via the complex L+H∗ L-H% contour. When the information structure of the sentence already establishes what is the 20 More work needs to be done regarding the prosody of BC s. Notice however that marking contrast in rained in (7), where no extra-inference can arise, doesn’t seem to be felicitous. The explanation would be that the enforced discourse structure doesn’t have a plausible interpretation. 21 As mentioned above, HC s often perfect. Constant (2014) argues that this is due to the prosodic marking L+H∗ L-H%, but just as in the case of BCs this specific prosodic marking does not convey CT in conditionals. We do not have space to provide a fair discussion on the matter, but we would like to argue that the CT-type interpretation that often arises in HCs is an inference resulting from there being a dependence relation between antecedent and consequent, together with the fact that the speaker has decided to make a claim about only a subset of c. This inference, hence, arises via world-knowledge and (Gricean-) reasoning about why the claim was only made about a subdomain. However, this interpretation can also be enforced with specific prosodic marking (as discussed in ftn. 13) or other means (see below), all CT-marking, and in this case the interpretation is not an inference anymore. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 194 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits QUD being addressed, marking that there are other contrasting questions that are not being addressed with other prosodic means (see ftn. 13), or lexically, is a type of CT-marking (i.e. it conventionally derives a CT-type reading). Research in this direction is left for the future. 5. Comparing theories One question that remains to be addressed is whether the resulting theory of BCs is superior to semantic theories of BCs. While we cannot draw here a full comparison, we will conclude this paper by pointing to some advantages that this theory has over semantic approaches. The first point is that in order to explain perfect biscuits, semantic theories would actually have to appeal to mechanisms similar to the ones proposed here in addition to stipulating that the semantics of BCs is different from that of HCs. For the remainder of this section, let us take Ebert et al.’s (2014) proposal (henceforth EEH) as a point of comparison, since this is a recent sophisticated semantic proposal and it covers the largest range of data. In EEH’s proposal, all if -constructions introduce two speech acts: the antecedent introduces a referential speech act (identifying a maximal plurality of possible worlds compatible with the world of evaluation, X), and the consequent introduces another speech act. HCs are if -constructions in which the consequent is evaluated in the worlds identified by the antecedent, (34a). In BCs the consequent is evaluated in the actual world and there is no interpretational link with the antecedent (34b): (34) EEH’s analysis of conditionals applied to the contrast between (1a) and (1b) above: a. HCs (aboutness topicality) If you are hungry, I’ll give you some biscuits: REF x (w0 .λ w′ .Mw′ (λ w.hungry(w)(listener))) & ASSERT (X, λ w.give_you_some_biscuits(w)) b. BC s (relevance topicality) If you are hungry, there are biscuits on the sideboard: REF x (w0 .λ w′ .Mw′ (λ w.hungry(w)(listener))) & ASSERT (w0 , λ w.biscuits_on_sideboard(w)) Where Mw′ (p) = σ (λ w.p(w) ∧ Rep (w′ )(w)) and Rep (w′ )(w) is the set of worlds epistemically def compatible with w′ ; ASSERT(w, p⟨s,t⟩ ) ≡ the speaker commits herself to the truth of p in w REFX (w, d⟨s,σ ⟩ ) ≡ the speaker draws the listener’s attention to d(w) EEH capitalize on the claim often repeated in the literature that then is not possible in BCs. Adopting a correlative account of conditionals, they take then to be a proform that when present at LF (if covertly) forces the consequent to be interpreted in the antecedent worlds delivering the HC-reading. The LF in BCs does not have then. Differences between HCs and BCs result from different LFs. We discuss this proposal below, pointing to problematic issues. 1. Then is possible in BCs! When naive speakers of English are asked about (35), they often accept it without hesitation: (35) If you are hungry, then there are biscuits on the sideboard. The paraphrase that is given is that “given the possibility that you are hungry, I’m telling you that there are biscuits on the sideboard”. The reading that biscuits will magically appear upon Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 195 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits your being hungry could also be conveyed by uttering (35), but given our knowledge of how the world works (the dependence relations), this reading is discarded because of its implausibility. It is possible if our assumptions about dependencies change (e.g. if the sentence is uttered in a movie involving a magical world). Another example is provided in (36), judged to be perfect: (36) If you want to know my opinion, then I think you are making a mistake marrying him. Again, (36) has two readings, one in which my thinking of you making a mistake is caused by your will to know my opinion, a HC-reading, and one in which my telling you what I think (which is that you are making a mistake) is the result of you wanting to know it. This last reading is still a BC in our account (since for an if -construction to be a BC it is the relation between the propositional content of antecedent and consequent what has to be independent). That then is possible in BCs is a problem for EEH’s account, since we now lack support for the proposal that there are two different LFs responsible for the two different readings. What then does can be explained in a theory along the lines of Biezma (2014) where then is a discourse marker that enforces a causal explanatory relation between an antecedent and a consequent. Crucially, in Biezma (2014) there is enough freedom to allow the fact that a particular move was made to be the content manipulated by then (see Biezma 2014). The different readings described above depend on the choice of content targeted by then. 2. If they ask you how old you are, you are four BC s like 2 are handled very easily with the theory proposed here: (37) In a bus, the father doesn’t want to pay his kid’s fare. Knowing that kids under five ride for free he says: Father: If they ask you how old you are, you are four. The interpretations of this BC is that the speaker is requesting the addressee to lie (which would be derived as a relevance inference in our proposal). Notice, however, that the speaker does not mean for the addressee to go right away to the ticket collector and tell him that he is four (which would, for example, be the interpretation derived in EEH, in which the consequent is headed by a command speech act regardless of the fact that the clause is a declarative).22 BCs providing a command always perfect, and this is so because commands are always tied to specific circumstances and hence, to the circumstances specified in the if -clause. Our knowledge of commands and their dependence on the circumstances allows us to understand that when the circumstances in the antecedent are not met, the command doesn’t apply. The consequent in 2 is a declarative, but this can be shown with an imperative too: ...tell them you are four.23 Obviously this anchoring to the circumstances does not arise when the imperative conveys dis22 Note that EEH end up needing to postulate a number of rather idiosyncratic speech acts that raise questions about the predictive power of the account, such as “not run of the mill assertions”, invoked in EEH(:361) to explain the interpretation of the consequent in if you want to hear a big fat lie, George W. and Condi Rice are secretly married (the consequent is understood here as being claimed to be false). 23 This wouldn’t be a BC in our account. The semantics of the imperative form can be taken to be either the content proposition or a deontic statement, and in this case it obviously depends here on the truth of the antecedent. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 196 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits interested wishes or when using equivalent modal statements: (38) If I don’t see you before you leave, have a good trip!! / I wish you a good trip. By uttering (38) I am not saying that I desire you to have a good trip only if I don’t see you before you leave. Crucially, it is due to our understanding of how disinterested wishes work that we understand that in any circumstances alternative to those expressed in the antecedent, you desire the addressee a good trip. 3. Encoding the mapping into discourse in the semantics is not a good idea Ebert et al. (2014) propose that we can understand the referential speech act in conditionals as identifying the QUD in discourse. However, this means encoding the mapping of conditionals to discourse in the semantics. As we have seen above, any theory that forces a unique mapping of conditionals to discourse runs into problems to explain cases in which the mapping has to be the opposite, as in classic conditional perfection illustrated in (10). 6. Conclusion Taking into account discourse congruence and relevance, BCs are revealed as examples of the flexible set of strategies we deploy in the construction of meaning, requiring no departure from the semantics of other conditionals. Furthermore, BCs and perfect-BCs show that the interplay between semantic meaning and considerations regarding discourse-structure, as well as information gained in discourse reasoning, are crucial in the construction of meaning. References Austin, J. (1956). Ifs and cans. Proceedings of the British Academy 42, 109–132. Benz, A. (2012). Errors in pragmatics. Journal of Logic, Language and Information 21(1), 97–116. Bhatt, R. and R. Pancheva (2006). Conditionals. In M. Everaert and H. van Riemsdijik (Eds.), The Blackwell Companion to Syntax, Volume 1, pp. 638–687. Oxford: Blackwell. Biezma, M. (2011a). Anchoring Pragmatics in Syntax and Semantics. Ph. D. thesis, University of Massachusetts Amherst. Biezma, M. (2011b). Optatives: Deriving desirability from scalar alternatives. In I. Reich, E. Horch, and D. Pauly (Eds.), Proceedings of Sinn und Bedeutung 15, pp. 117–132. Saarbrücken: Saarland University Press. Biezma, M. (2014). The grammar of discourse: The case of then. In T. Snider, S. D’Antonio, and M. Weigand (Eds.), Proceedings of SALT 24, pp. 373–394. LSA and CLC Publications. Biezma, M. and A. Goebel (2017). Being pragmatic about biscuits. Ms. University of Konstanz. Büring, D. (2003). On D-Trees, beans, and B-Accents. Linguistics and Philosophy 26, 511– 545. Constant, N. (2014). Contrastive Topic: Meanings and Realizations. Ph. D. thesis, UMass Amherst. Csipak, E. (2015). Free Factive Subjunctives in German. Ph. D. thesis, University of Göttingen. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 197 M. Biezma & A. Goebel The pragmatic ingredients to get perfect biscuits DeRose, K. and R. E. Grandy (1999). Conditional assertions and “biscuit” conditionals. Noûs 33(3), 405–420. Ebert, C., C. Ebert, and S. Hinterwimmer (2014). A unified analysis of conditionals as topics. Linguistics and Philosophy 37(5), 353–408. von Fintel, K. (2009). Conditional strengthening, again. Invited talk at XPRAG 2009; Lyon, France; April 24, 2009. Francez, I. (2015). Chimerical conditionals. Semantics and Pragmatics 2, 1–35. Franke, M. (2007). The pragmatics of biscuit conditionals. In M. Aloni, P. Dekker, and F. Roelofsen (Eds.), Proceedings of Amsterdam Colloquium 16, pp. 91–96. Franke, M. (2009). Signal to Act: Game Theory in Pragmatics. Ph. D. thesis, Universiteit van Amsterdam. Haiman, J. (1978). Conditionals are topics. Language 54(3), 564–589. Hamblin, C. L. (1973). Questions in Montague English. Foundations of Language 10, 41–53. Heim, I. (1983). On the projection problem for presuppositions. In M. Barlow, D. Flickinger, and M. Wescoat (Eds.), Proceedings of WCCFL 2, pp. 114–125. Stanford, CA: CSLI. Ippolito, M. (2016). How similar is similar enough? Semantics & Pragmatics 9(6), 1–60. Isaacs, J. and K. Rawlins (2008). Conditional questions. Journal of Semantics 25, 269–319. Lauer, S. (2015). Biscuits and provisos: Conveying unconditional information by conditional means. In E. Csipak and H. Zeijlstra (Eds.), Proceedings of Sinn und Bedeutung 19. Merin, A. (2007). Unconditionals. Forschungsberichte der DFG Forschergruppe ‘Logik in der Philosophie’, no. 129. Potts, C. (2006). How far can pragmatic mechanisms take us? Theoretical Linguistics 32(3), 307–320. Roberts, C. (1996). Information structure in discourse: Towards an integrated formal theory of pragmatics. In OSU Working Papers in Linguistics 49: Papers in Semantics, Volume 49, pp. 91–136. Reprinted in Roberts (2012). Romero, M. and C.-H. Han (2004). On negative yes–no questions. Linguistics and Philosophy 27, 609–658. Sano, K. and Y. Hara (2014). Conditional independence and biscuit conditional questions in dynamic semantics. In T. Snider, S. D’Antonio, and M. Weigand (Eds.), Proceedings of SALT 24, pp. 84–101. Siegel, M. (2006). Biscuit conditionals: Quantification over potential literal acts. Linguistics and Philosophy 29, 167–203. Stalnaker, R. (2002). Common Ground. Linguistics and Philosophy 25, 701–721. Stalnaker, R. (2014). Context. Oxford: OUP. Starr, W. B. (2014). What if? Philosophers’ Imprint 14(10). Swanson, E. (2013). Subjunctive biscuit and stand-off conditionals. Philosophical Studies 163(3), 637–648. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 198 Reportative deontic modality in English and German1 M. Ryan BOCHNAK — Leipzig University Eva CSIPAK — University of Konstanz Abstract. We discuss the dual uses of the English adjectival modal be supposed to and the German modal auxiliary sollen under their deontic and evidential readings. While deontic modality is a familiar category, we discuss novel data on the expression of reportative evidentiality in English. We argue for a truly unified analysis for both be supposed to and sollen, which are specified for a reportative informational conversational background. The apparent difference in “flavours” (reportative vs. deontic) is an illusion, caused by differences in the types of reports that feed the ordering source. Although we assign be supposed to and sollen an identical semantics, their distributions are not identical. We hypothesize that this is due to the fact that in German, sollen competes with the quotative modal wollen, which carries a stronger presupposition, triggering Maximize Presupposition effects which are absent in English. Keywords: modality, deontic, reportative, be supposed to, sollen, wollen 1. Introduction In this paper, we discuss the dual uses of the English adjectival modal construction be supposed to and the German modal auxiliary sollen. In both languages, these modal expressions display both deontic and evidential readings. Specifically, the evidential reading has a reportative flavour, whereby the source of evidence for a claim is a prior report. As shown in (1), sentences containing be supposed to and sollen are compatible with contexts favouring either a deontic or reportative interpretation. (1) Deontic context: A student asks the department administrator when Professor Plum will be in the office. The university’s rules state that professors must have office hours between 10-11am every day. The administrator says: Reportative context: A student asks the department administrator when Professor Plum will be in the office. Earlier that day, Professor Plum’s partner called the administrator and said that they are running late but will come in at 10am. The administrator says: a. Professor Plum is supposed to be here at 10. b. Professor Plum soll um 10 hier sein. Professor Plum SOLL at 10 here be While the reportative use of sollen has received some attention in the literature (Faller, 2006, 2012; Hinterwimmer, 2013; Kratzer, 1981, 2012; Schenner, 2008), we show here that reportative evidentiality is also lexicalized in English in be supposed to. This observation complements the work of von Fintel and Gillies (2010), who argue that the epistemic modal must in English 1 We would like to thank Martina Faller, Sven Lauer, Lisa Matthewson, Hubert Truckenbrodt, audiences at the University of Konstanz, the LSA Annual Meeting 2016 in Portland, Oregon, and Sinn und Bedeutung in Edinburgh, as well as participants at the SIAS Summer Institute 2016 in Durham, North Carolina for comments and discussion. All errors are our own. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 199 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German lexicalizes an indirect inferential evidential component. Furthermore, although deontic modality is a familiar category, we show that the deontic flavour of these modal expressions is narrower than the deontic uses of must or have to. Specifically, be supposed to and sollen cannot be used performatively, i.e., they can only describe obligations that already exist, and cannot be used to place new obligations. We make use of this fact to argue for a unified analysis of the reportative and deontic uses of these modals. Specifically, we reduce the deontic use to the reportative one, arguing that these apparently different “flavours” are both derived from a circumstantial modal base and a reportative informational ordering source within a Kratzerian framework. We furthermore argue that our account fares better than recent analyses for sollen invoking intentional acts (Hinterwimmer, 2013) or external bouletic ordering sources (Matthewson and Truckenbrodt, 2017). This paper proceeds as follows. We first discuss the deontic use of be supposed to and sollen in section 2. Section 3 discusses the reportative use. We present our unified analysis for both uses in section 4. Section 5 focuses on German sollen and its competitor, the reportative modal wollen, while section 6 discusses previous accounts. Section 7 concludes. 2. Non-performative deontic use We first discuss the deontic use of be supposed to and sollen in more detail, as already shown in (1). Like other deontic modals, these can be used in different contexts to convey different flavours of deontic necessities. For instance in (2) they can be used to talk about laws, while in (3) they are used to talk about rules. (2) Context: Your friend has just parked in front of a fire hydrant. You say: a. You’re not supposed to park there. b. Du sollst hier nicht parken. you SOLL here not park (reports a law) (3) Context: Your friend has just landed on a community chest in Monopoly. You say: a. You’re supposed to pick up a card. b. Du sollst eine Karte nehmen. you SOLL a card take (reports a rule) However, an important feature of be supposed to and sollen is that they cannot be used performatively. Rather, they can only be used to report on existing laws or rules. This can be shown in (4), where the context provides that the rules of the game Calvinball are not pre-determined, but made up on the spot. In such a context, be supposed to and sollen cannot be used, whereas other deontic modals such as must, have to or müssen ‘must’ can be. (4) Context: You are playing Calvinball, a game where the rules are made up on the spot, and no rule can be re-used. The players shout out the rules as they make them up. a. Now you {have to/must/#are supposed to} throw the ball across the field. b. Jetzt {musst/#sollst} du den Ball über das Feld werfen. now must/SOLL you the ball across the field throw Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 200 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German (Calvin and Hobbes, Bill Watterson, originally published 26.08.1990) Note that the problem with (4) is not that the speaker is the source of the rule. As shown in (5) and (6), the speaker can serve as the deontic authority. (5) Context: Parent to child: a. You’re supposed to go to bed by 9pm. b. Du sollst um 9 im Bett sein. you SOLL at 9 in.the bed be (6) Context: The speaker made a New Year’s resolution to smoke less this year. On January 2, she is offered a cigarette. a. I’m supposed to smoke less this year. b. Ich soll dieses Jahr weniger rauchen. I SOLL this year less smoke Lauer (2015) discusses “anti-performative” modals, and argues that the restrictions on performativitiy can be derived from the temporal profile of such expressions. Lauer argues that anti-performative modals are simple stative predicates. Like other statives, they are required to be true throughout the reference time interval. In the case of present-tense modals, this means the modal statement is required to be true throughout the speech time. We can schematize this restriction in the case of be supposed to and sollen as in (7). In prose: for all moments m contained within the speech time τ(u), it is necessary at m that p. (7) Jbe supposed to/sollen(p)Ku = 1 iff ∀m ∈ τ(u) : 2m (p) (sketch) Performativity clashes with these temporal requirements on stative modals. Intuitively, an event of imposing an obligation will result in a state of an obligation holding. Let us assume with Lauer that if a state s is the result of an event e, then s will not obtain before the final moment of τ(e). It follows then, that if an obligation is created as a result of uttering a modal sentence, then a present tense stative modal statement will never be true at speech time, since the condition in (7) that the requirement that p hold throughout the speech time would be violated. Following this chain of reasoning, for a sentence containing present tense be supposed to or sollen to be Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 201 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German true, it must be the case that the obligation already exists before the speech time. A performative use of these modals is thus ruled out.2 The upshot of this discussion is that although be supposed to and sollen can take on a deontic flavour, they behave differently from other deontic modals in being anti-performative. That is, they require a preceding event that brings the obligation into existence. We now turn to describe the reportative use in more detail, which also requires an antecedent event, namely a report. 3. Reportative use Cross-linguistic research in the last decade or so has shown that modals can encode a speaker’s evidence type, and in some languages, evidence type restrictions are grammaticalized in evidential modals (e.g., Faller 2012; Matthewson et al. 2007). Even for English, it has been argued by von Fintel and Gillies (2010) that epistemic must lexicalizes an inferential evidential component. Whereas the reportative use of sollen has been discussed in the literature already (e.g., Faller 2006, 2012; Hinterwimmer 2013; Kratzer 1981, 2012; Schenner 2008), we add here novel data from English that the modal construction be supposed to also has a reportative use, cf. (1). Adapting the diagnostics from von Fintel and Gillies (2010), we show that the indirect evidence component of be supposed to and sollen does not have an inferential flavour. While must and müssen are acceptable in the inferential context in (8), be supposed to and sollen are not. Meanwhile, like must and müssen, be supposed to and sollen are unacceptable when direct evidence for the prejacent proposition is available, as shown in (9). (8) Context: The ball is either under cup A, cup B, or cup C. It’s not under A, and it’s not under B. a. The ball must be under cup C. / Die Kugel muss unter Becher C sein. b. #It’s supposed to be under cup C. / #Sie soll unter Becher C sein. (9) Context: You look out the window and see that it is raining. a. It is raining. / Es regnet. b. #It must be raining. / #Es muss regnen. c. #It’s supposed to be raining. / #Es soll regnen. We wish to also highlight two additional properties of be supposed to and sollen in connection with the literature on modal evidentials (e.g., Faller 2012; Matthewson et al. 2007; Schenner 2008). First, note that be supposed to and sollen can be embedded.3 This is shown in (10), where be supposed to and sollen occur in the antecedent of a conditional. We note that the modals are interpreted within the antecedent, and do not take scope over the entire conditional. 2 On Lauer’s view, there are no truly performative uses of deontic modals – rather, these are actually bouletic modals tracking speaker preferences, uttered by a speaker who has deontic authority. There is a possibly interesting connection here to the proposal by Matthewson and Truckenbrodt (2017), which we discuss further in section 6.2. 3 See Schenner (2008) for discussion of the embedding possibilities for sollen based on corpus data. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 202 M. R. Bochnak & E. Csipak (10) Reportative deontic modality in English and German Context: You and a friend are planning to go sightseeing in Edinburgh. Your friend asks if you should bring umbrellas. You don’t know what the weather will be like, so you say: a. If it’s supposed to rain, we will bring umbrellas. = ‘If it is reported that it will rain, we will bring umbrellas.’ 6= ‘It is reported that if it will rain, we will bring umbrellas.’ b. Wenn es regnen soll, bringen wir Schirme mit. = ‘Wenn berichtet wird, dass es regnen wird, bringen wir Schirme mit.’ 6= ‘Es wird berichtet, dass wenn es regnet, wir Schirme mitbringen.’ Second, note that the reportative component projects out of negation. For instance in (11), the reportative component of be supposed to or sollen is not what is being denied. It appears then that the reportative component be supposed to and sollen is presuppositional, as has been claimed for evidential modals in other languages (e.g., Matthewson et al. 2007). (11) Context: You and a friend are planning to go sightseeing in Edinburgh. Your friend asks if you should bring umbrellas. You say: a. It’s not supposed to rain. = ‘It is reported that it won’t rain.’ 6= ‘There is no reportative evidence that it will rain.’ 6= ‘The evidence that it will rain is not reportative.’ b. Es soll nicht regnen. = ‘Es wird berichtet, dass es nicht regnen wird.’ 6= ‘Es gibt keine Berichte darüber, dass es regnen wird.’ 6= ‘Die Evidenz dafür, dass es regnen wird, ist nicht reportativ.’ In sum, the projection behaviour of be supposed to and sollen is similar to what has been described for other reportative evidential modals. We now turn to which sources for reports can serve to license be supposed to and sollen. As illustrated in (10) and (11), speakers can use information they got from a specific definite entity, such as a weather report website. The reportative context in (1) showed that a speaker’s utterance can also serve as a source for a report. Below we discuss some cases where identifying the source is more difficult. The source of a report may be indefinite or unknown. As illustrated in (12), the precise identity, and in turn the reliability of the report, may be unknown. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 203 M. R. Bochnak & E. Csipak (12) Reportative deontic modality in English and German Context: A and B are newspaper reporters working on a story about a corrupt politician. A receives an anonymous phone call from an individual claiming that the politician accepted a bribe from a construction company. B asks what the phone call was about, and A replies: a. The politician is supposed to have accepted a bribe from the construction company on August 15. b. Der Politiker soll am 15. August Schmiergeld von der the politician SOLL on 15 August bribe from the Baufirma angenommen haben. construction.company accepted have Here, the identity of the anonymous caller is unknown to A, but nevertheless serves as a source for a report made by be supposed to/sollen. When asked later, A is able to pick out the time of the report: namely when the call happened. However, A is not able to pick out the source of the report as A’s acquaintance relation to the source does not allow this. In some cases, speakers can use be supposed to and sollen reportatively even when they are not able to pick the individual who is the source of the report or even the exact time the report was made. Consider the following context in (13). (13) Context: A goes to dinner with a group of people. The conversation turns to ways to avoid sunburn. B says he has started to drink carrot juice. B: Carrot juice is supposed to protect the skin from sunburn. B: Möhrensaft soll vor Sonnenbrand schützen. carrot.juice SOLL before sunburn protect A: Oh, where did you hear that? B: I don’t remember. In this context, speaker B can use sollen to indicate that he has reportative evidence for his statement, even though he cannot remember the exact source of the information. In a context where the speaker is the source of the prejacent p and has complete control over p, this may be reported using be supposed to/sollen(p).4 As shown in (14), a modified version of (6), the speaker may not have even said anything aloud to anyone. (14) Context: The speaker spent New Year’s at home by herself, but made a resolution to smoke less this year. On January 2, she is offered a cigarette. a. I’m supposed to smoke less this year. b. Ich soll dieses Jahr weniger rauchen. I SOLL this year less smoke We also note that be supposed to/sollen(p) can be licensed even if a report was not literally of p, but where p is entailed or conversationally follows from a report in context. 4 In terms of a public commitment, which we will make reference to in our analysis in the next section, a commitment counts as public as soon as the speaker has formed a conscious thought about it. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 204 M. R. Bochnak & E. Csipak (15) Reportative deontic modality in English and German Context: A goes to dinner with a group of people who are discussing how to avoid sunburn. B says he has started drinking carrot juice. Then A comes home and reports what she learned. a. Carrot juice is supposed to help avoid sunburn. b. Möhrensaft soll vor Sonnenbrand schützen. carrot.juice SOLL against sunburn protect 4. Towards a unified analysis Given the similarities we have observed between the deontic and reportative uses of be supposed to and sollen, we wish to provide a unified analysis for these modal expressions. We will make use of a standard Kratzerian framework (Kratzer, 1981, 1991, 2012), whereby modals quantify over possible worlds. We propose that both be supposed to and sollen are necessity modal expressions, which lexically specify a circumstantial modal base and a reportative informational ordering source. We discuss each of these ingredients in turn. Given a circumstantial modal base, be supposed to and sollen quantify over worlds where salient facts in the evaluation world also hold (Kratzer, 2012; Portner, 2009). Crucially, one of the salient facts will be that a report of some kind has been made. This seems to be what we need for the reportative use, but for the deontic use it is possibly too strong. Specifically, what counts as a deontic report for be supposed to and sollen? It seems that someone need not have actually said anything at all. In (2), for instance, the parking prohibition may be indicated by a sign; in (3), it is likely the instruction booklet written by the creators of Monopoly that serves as the source of the rule. And even for true reportatives, the speaker may not be able to identify the individual or exact time of the relevant report, only that there was one. For these reasons, we leave fairly vague what counts as a relevant report in the circumstantial modal base, and state this “reportative” restriction on the circumstantial modal base as one where some agent α has some public commitment(s) from with the prejacent proposition p follows, as in (16): (16) “Reportative” restriction on circumstantial modal base: ∃α : p follows from α’s public commitments We assume that entities such as the city councillors responsible for parking laws or the creators of Monopoly count as relevant agents α for this purpose. Note that given cases like (15), it is too strong to say that α’s public commitments entail p; in at least some cases, such as (15) above, p follows conversationally from α’s public commitments. Nevertheless, in some cases entailment will turn out to follow, as in (17). (17) Context: The weather report predicts rain every day next week. a. It’s supposed to rain on Wednesday. b. Es soll am Mittwoch regnen. it SOLL on Wednesday rain Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 205 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German Note also that if it is already part of the circumstances that p follows from α’s existing public commitments, this means that the temporal condition in (7) holds. That is, 2p holds throughout the reference time t, since α’s commitment to p already holds at t. As for the ordering source, we adapt the notion of a reportative informational conversational background developed by Kratzer (2012) for evidential modals. Our proposed ordering source is stated as in (18); although we maintain the terminology “reportative”, this notion is here relativized to α’s public commitments, and not literally a report. (18) “Reportative” informational ordering source: a function gα,t such that for any w in the domain of gα,t , gα,t (w) represents the propositional content of α’s public commitments in w at a time t Putting this all together, be supposed to and sollen take as a modal base a set of worlds where a set of relevant circumstances are true, and in particular where there is some α from whose public commitments p follows. These worlds are then ordered by the ordering source. Worlds where the content of α’s public commitments are true are ranked higher than worlds where this content is not true. Both be supposed to and sollen then universally quantify over the best worlds of the modal base as ranked by the ordering source. We assume that the lexical specification of the modal base and ordering source is treated as a presupposition on available conversational backgrounds in the context (cf. Matthewson et al. 2007). This is summarized in (19). (19) Jbe supposed to/sollenKc,w,t T = λ Pλ x[∀m ∈ t[∀w0 ∈ maxgm (w) ( fm (w)) : P(x)(w0 ) = 1]] defined only if the context c provides a circumstantial modal base fm and reportative informational ordering source gα,m One last comment is in order regarding our semantics in (19). We follow Hinterwimmer (2013) in treating the subject as an external argument of sollen, and by extension be supposed to. In other words, we treat be supposed to and sollen as control predicates rather than raising predicates.5 There is some debate over the status of (non-epistemic) modals as raising or control predicates (see von Fintel and Iatridou 2009 for discussion). We have no new syntactic tests to bear on this issue, and applying the standard tests yields unclear results. Since the reportative reading of be supposed to and sollen is plausibly epistemic, while the deontic reading is root, and our analysis merges the two, it is not clear what behaviour we would predict. As we will see in the next section, we will need the semantics to make reference to the grammatical subject when we compare sollen with wollen, another German modal with a reportative flavour. We turn to this now. 5. Comparing German sollen and wollen It is quite well-known that sollen is dispreferred when the issuer of the report is identical with its grammatical subject (Hinterwimmer, 2013; Kratzer, 1981; Schenner, 2008). In such a case, 5 This means that technically we don’t have a prejacent proposition, but we will ignore this issue in this paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 206 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German the quotative modal wollen ‘want’ is typically used in order to convey that its subject is the source of a report of the prejacent proposition. This contrast is shown in (20)-(22). (20) Anna soll in Oslo sein. Anna SOLL in Oslo be ‘Anna is said to be in Oslo.’ b. Anna will in Oslo sein. Anna want in Oslo be ‘Anna claims to be in Oslo.’ (adapted from Schenner 2008) a. (someone other than Anna is the source) (Anna herself is the source) (21) Context: Julia has overheard Max saying that he climbed Mount Everest. Max will den Mount Everest bestiegen haben. Max want the. ACC Mount Everest climbed have ‘Max claims to have climbed Mount Everest.’ (adapted from Gärtner 2012) (22) Context: You’re at a party, and at 8pm someone asks when Maria will arrive. Earlier today, she told you she would arrive at 9pm. a. Maria is supposed to be here at 9pm. b. Maria {will/#soll} um 9 hier sein. Maria want/SOLL at 9 here be It would seem that our analysis as it stands now cannot account for these facts. Our analysis simply requires that the fact that some agent α has a public commitment to p be part of the circumstantial ordering source associated with sollen (and be supposed to). It is thus mysterious why sollen is infelicitous in (22). Our proposal to account for this data is the following. We maintain our semantics for sollen and be supposed to as in (19). However, we argue that sollen is infelicitous in (22) due to pragmatic competition with wollen. The main idea is that the quotative use of wollen has the same semantics as sollen, but with the extra presupposition that the source of the report is the same as the subject of the sentence (cf. Gärtner 2012; Schenner 2008). In such a setup, sollen and wollen compete via Maximize Presupposition (e.g., Percus 2006; Schlenker 2012; cf. Heim 1991), defined in (23). (23) Maximize Presupposition: If a sentence S is a presuppositional alternative of a sentence S0 , and the context C is such that a. the presuppositions of S and S0 are satisfied within C b. S and S0 have the same assertive component relative to C c. S carries a stronger presupposition than S0 then S should be preferred to S0 . (adapted from Schlenker 2012) Under our analysis, sollen and wollen have the same assertive component, but wollen carries a stronger presupposition. Namely, wollen is associated with the presupposition that its subject Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 207 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German has the public commitment to the prejacent, whereas sollen carries no presupposition about the identity of the agent who has a public commitment. Therefore, by (23) sentences containing sollen and wollen are presuppositional alternatives for a Maximize Presupposition competition, and wollen must be used whenever its presuppositions are supported in the context. In such contexts, the use of sollen is blocked, leading to the contrast in (22). An analysis along these lines makes the prediction that in cases where it is not known by the speaker whether the subject carries the relevant public commitment, sollen can be used. This prediction is borne out, as illustrated in (24). In the context provided, the source of the public commitment could very well be the subject, but could also be someone else. The judgment here is that A’s utterance with sollen is neutral with respect to whether A thinks that Chris or someone else is the source of the report, whereas the response in A0 strongly implies that A0 believes that Ben’s knowledge comes directly from Chris as the source of the report.6 (24) Context: Alex and Ben are planning a party. Their flaky friend Chris only sometimes RSVPs to parties, and one might only hear about Chris’s attendance through rumours. A: Soll Chris zur Party kommen? SOLL Chris to.the party come ‘Is Chris coming to the party?’ (A doesn’t know whether B heard from Chris or someone else) A0 : Will Chris zur Party kommen? want Chris to.the party come ‘Is Chris coming to the party?’ (only: A0 believes Chris is the source) In sum, we maintain an identical analysis for sollen and be supposed to. The apparent restriction of sollen to cases where the subject is not identical to the source of the report is due to a Maximize Presupposition competition with wollen. Since English be supposed to does not have a competitor akin to wollen, we observe differences in the distribution of be supposed to and sollen despite their identical semantics. 6. Comparison to other analyses We have claimed that the modal expressions be supposed to and sollen both have uses that place a restriction that there exists an agent α who has a public commitment towards the prejacent. We have also argued that apparently deontic uses of these modal expressions should be assimilated to reportative uses as well. In such a case, a pre-existing law or rule can count as a report to license be supposed to and sollen. In this section, we would like to defend our analysis by comparing it to two recent proposals for sollen, both of which deny that sollen is reportative per se: Hinterwimmer (2013), which invokes intentional acts rather than reports, and Matthewson and Truckenbrodt (2017), who argue for an external bouletic ordering source for sollen. 6 Note that this example involves so-called “interrogative flip,” whereby A expects B to base their answer on reportative evidence. This use of reportatives is quite common cross-linguistically (e.g., Davis et al. 2007; Faller 2002; Garrett 2001; Matthewson et al. 2007). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 208 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German 6.1. Hinterwimmer (2013) As we have already seen, it seems too strong to say that it is strictly antecedent reports that license be supposed to and sollen. We need to at least allow pre-existing laws and rules under the umbrella of licensors. Hinterwimmer (2013) also argues that reports are strictly speaking too narrow a category to account for the uses of German sollen. He argues that sollen requires an antecedent intentional act, which is not necessarily a speech act. He takes cases like (25) as evidence for this claim. (25) Context: Peter is singing Yesterday to his baby daughter. A: Why is he doing that? B: Das soll das Baby beruhigen. it SOLL the baby calm.down ‘It’s supposed to calm the baby down.’ (Hinterwimmer, 2013) The idea is that in this context, there is no prior report (or rule or law for that matter) that Peter should sing in order to calm the baby down; rather, Peter is just trying anything he can think of to calm the baby down. In such a context, what licenses B’s use of sollen is thus not a report of any kind, but rather the singing itself. That is, the singing itself serves as an antecedent intentional act for B’s use of sollen in (25) – Peter’s intentional act of singing is enough to license sollen. Thus, Hinterwimmer claims, sollen requires any sort of antecedent intentional act, even if it is not strictly speaking a speech act. We believe Hinterwimmer’s analysis is not on the right track for at least two reasons. First, native speakers we have consulted seem to agree that there is a prior report in (25) that is accommodated in contexts where it is not explicitly mentioned. This is what is predicted by our account. Under our analysis, that an agent α has p as a public commitment is part of the content of the circumstantial modal base, which under our analysis is a presupposition associated with be supposed to and sollen. This means that an antecedent report (or rule/law) must be retrievable to the interlocutors. In cases where this fails, we predict that a report must be accommodated by the hearer for the use of be supposed to or sollen to be felicitous. Second, even when the context is such that no prior report can be accommodated because the interlocutors have never met each other or Peter, there is a world knowledge rule ‘singing calms the baby down’ that could in principle serve as the ‘source of the report’ and thus as a possible confound. Consider (26) which avoids this confound. (26) Context: Peter is stirring ketchup into his coffee. A: Why is he doing that? B: Das soll gut schmecken. = ‘It’s supposed to taste good.’ A: Oh. Where did you hear that? B: I don’t remember, I think I read it in some magazine a while ago. B0 : #He’s doing it right now. We assume that there is no world knowledge rule stating that adding ketchup to coffee will make it taste better. A’s continuation of B’s use of sollen is very natural here. We take this to show Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 209 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German that while A interprets B’s utterance as referring to a prior report, but is unable to accommodate the existence of a source for such a report. It is important to note that the response of B0 that ‘He’s doing it right now’ is not a felicitous continuation of the exchange. This is unexpected if we assume the action of stirring ketchup to be an antecedent intentional act in the sense of Hinterwimmer. Sollen should be able to pick up Peter’s intentional act. 6.2. Matthewson and Truckenbrodt (2017) We next turn to a recent proposal by Matthewson and Truckenbrodt (2017), who distinguish between root and evidential sollen and argue that root sollen is ‘externally bouletic’, i.e., the modal flavour of root sollen is always bouletic, and the subject of the clause cannot be the holder of the desire. What they mean by this is illustrated in (27), their own example. (27) A: B: Why have you put on loud and unpleasant music in the basement? It is supposed to chase away the mice. Das soll die Mäuse verjagen. that SOLL the mice chase.away The context for this example is similar to, though slightly different7 from, the earlier example (25) from Hinterwimmer about calming down the baby. Similar to (25), we disagree with the judgment regarding B’s use of be supposed to/sollen in (27). In particular, we find the continuation in (270 ) to be the most natural follow-up to B’s utterance in (27). Like in (26), A’s response here seems to be a variety of a “Hey wait a minute” response (see von Fintel 2004) that challenges the presupposition of B’s utterance, namely the presupposition that there is some agent from whose public commitments the prejacent follows. (270 ) A: Where did you hear that? Wo hast du das gehört? Additionally, we believe that the restriction that the subject of the clause not be equal to the holder of a desire does not quite capture all the relevant facts. This condition is both too weak and too strong. First, it is too weak because it predicts that sollen should be licensed whenever there is an inanimate or expletive subject, so long as there is some holder of a desire in the context. Although Matthewson and Truckenbrodt’s (27) appears to show this prediction is upheld, we have already indicated that our judgments in this case do not match theirs. In (28) with an expletive subject, we see that sollen cannot take on the bouletic reading; only a reportative reading is available here. (28) 7 It Context: A and B hear that Peter, an author, has started writing another story. A: In seiner Geschichte soll es um Pferde gehen. in his story SOLL it about horses go ‘His story is supposed to be about horses.’ (reportative only) 6= ‘Peter (or someone) wants his story to be about horses.’ is different in that the speaker is the bouletic source in (27). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 210 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German Matthewson and Truckenbrodt predict that an externally bouletic interpretation should be available, either such that the speaker desires Peter to write his next story about horses, or that Peter has that desire himself, since Peter is not the subject of (28). Despite the availability of two plausible sources for the bouletic desire, such an interpretation of (28) is not available. The only available interpretation is a reportative one: A has heard a report that Peter’s new story will be about horses and is sharing this information with B by uttering (28). Second, the restriction that the subject be distinct from the holder of a desire also seems to be too strong in certain cases. We have already seen in (24) that in ignorance contexts, the use of sollen is compatible with the subject being the holder of a desire. That is, by uttering Soll Chris zur Party kommen? (‘Is Chris coming to the party?’), the speaker is not committed to Chris not being the source of a bouletic attitude towards coming to the party. We have also seen in (6) and (14) more cases where the speaker is source of the report.8 Matthewson and Truckenbrodt could perhaps not consider these as counterexamples if they treat them as purely reportative uses of sollen, which they treat as distinct from their root bouletic use. Under a Kratzerian framework, this amounts to leaving underspecified the types of modal bases and ordering sources that sollen can take, just like other modals that can take on several modal flavours. However, given the similarities we have observed between the deontic and reportative uses of be supposed to and sollen, we believe our unified analysis provides an explanation for the lexicalization of the reportative and non-performative deontic readings together in the same modal expressions: these two readings are in essence one and the same. Even allowing that in an example such as (1), Professor Plum’s presence is bouletically desired by the university rather than mandated, it is not clear how this extends to, e.g., the city parking laws as discussed in example (2), repeated here as (29). (29) Context: Your friend has just parked in front of a fire hydrant. You say: a. You’re not supposed to park there. b. Du sollst hier nicht parken. you SOLL here not park Here it seems like a stretch to argue that the city is an agent with desires, so assuming a bouletic flavour seems impossible. On Matthewson and Truckenbrodt’s account, (29) would have a purely reportative reading with no deontic flavour. On our account, both are present. There are some cases where Matthewson and Truckenbrodt’s analysis makes different predictions than ours. First, they observe a case where the judgments come apart for be supposed to and sollen in a deontic context, namely (30). Matthewson and Truckenbrodt take this as evidence that sollen can not take on a deontic flavour, although be supposed to can. 8 Note that wollen is also acceptable in these cases. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 211 M. R. Bochnak & E. Csipak (30) Reportative deontic modality in English and German Context: Nobody said anything to A about locking the building. However, there is a rule that you lock the building when you are the last to leave. a. A to B: I’m supposed to lock the door. b. A to B: #Ich soll noch das Gebäude abschließen. I SOLL still the building lock (Matthewson and Truckenbrodt, 2017) We agree with the judgment here and have no explanation for this. We would, however, like to point out two additional factors that may influence the judgments here. The German particle noch ‘still’ seems to play a crucial role in making (30) unacceptable. Without noch, the utterance with sollen is fine. Additionally, we also observe that adding auch ‘also’ improves acceptability. (300 ) Ich soll (auch noch) das Gebäude abschließen. I SOLL also still the bulding lock ‘I’m also supposed to still lock the building.’ While Matthewson and Truckenbrodt’s account does not predict the acceptability of (300 ), ours does not predict why (30) is unacceptable. Another possible factor causing the inacceptability of (30) is competition with müssen. A version of this sentence with müssen as in (3000 ) can convey both deontic necessity and inferential reasoning and thus captures both the fact that A is following a rule, and that A had to deduce that the rule applies to him. (3000 ) Ich muss noch das Gebäude abschließen. I must still the building lock ‘I still have to lock the building.’ A case that Matthewson and Truckenbrodt can deal with easily, but which causes problems for our account, are examples like (31). In this bouletic context, be supposed to is unacceptable, as we predict. However, sollen is (marginally) acceptable here. (Note that our English translation for (31b) is not intended as an analysis of the German sentence; we simply offer this as a paraphrase that is colloquially appropriate in the given context.) (31) Context: I haven’t yet looked at what the cafeteria is offering for lunch, but I really hope they are serving pasta. a. #They are supposed to have pasta today! b. Sie sollen heute Nudeln haben! they SOLL today noodles have ≈ ‘I hope they have pasta today!’ This stands in contrast to (32), where both be supposed to and sollen are unacceptable. Here, there is a report in the context that the prejacent of be supposed to and sollen is in fact false. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 212 M. R. Bochnak & E. Csipak (32) Reportative deontic modality in English and German Context: I just checked the cafeteria’s lunch offers for the day and saw that they are not offering pasta, my first choice. a. #They are supposed to have pasta today! b. #Sie sollen aber heute Nudeln haben! they SOLL but today noodles have It seems to us that the speaker of the German sentence in (31) appears to be childish or irrational. We take this to be an effect caused by using an expression expressing deontic modality where bouletic modality would be appropriate. It is our intuition that the speaker is attempting to make the desire more ‘objectively necessary’ by using an expression that is only compatible with deontic modality – the speaker is exploiting the fact that only deontic modality, but not bouletic modality, is available for sollen. We would like to make one final comment here about the relation between bouletic and deontic modality. Lauer (2015) suggests that performative deontic modals actually convey speaker preferences. When the speaker is a deontic authority, a statement about speaker preferences can take on the force of placing an obligation on the hearer via pragmatics. Thus, there may be an important connection between deontic and bouletic modality that could go some way towards unifying our account with that of Matthewson and Truckenbrodt. However, note that Lauer’s idea is about performative uses of deontic modals, and we have argued in this paper that the deontic uses of be supposed to and sollen are crucially anti-performative. 7. Conclusion We have proposed a unified analysis for the deontic and reportative readings of be supposed to and sollen: both readings are derived from a circumstantial modal base and a reportative informational ordering source. This accounts for the fact that even the deontic use of these modals still have a reportative flavour in that they cannot be used performatively to issue an obligation on the hearer. Despite the open questions that remain, we hope to have made a contribution to the enterprise of making more precise the properties of the modal flavours associated with be supposed to and sollen. References Davis, C., C. Potts, and M. Speas (2007). The pragmatic values of evidential sentences. In M. Gibson and T. Friedman (Eds.), Proceedings of Semantics and Linguistic Theory (SALT) 17. Ithaca, NY: CLC Publications. Faller, M. (2002). Semantics and Pragmatics of Evidentials in Cuzco Quechua. Ph. D. thesis, Stanford University. Faller, M. (2006). Evidentiality above and below speech acts. Ms. University of Manchester. Faller, M. (2012). Evidential scalar implicatures. Linguistics and Philosophy 35, 285–312. von Fintel, K. (2004). Would you believe it? The king of France is back! Presuppositions and truth-value intuitions. In M. Reimer and A. Bezuidenhout (Eds.), Descriptions and Beyond, pp. 315–341. Oxford: Oxford University Press. von Fintel, K. and A. Gillies (2010). Must . . . stay . . . strong! Natural Language Semantics 18, 351–383. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 213 M. R. Bochnak & E. Csipak Reportative deontic modality in English and German von Fintel, K. and S. Iatridou (2009). Morphology, syntax, and semantics of modals. Lecture notes from 2009 LSA Summer Institute, University of California, Berkeley. Available online at http://kaivonfintel.org/work/. Garrett, E. (2001). Evidentiality and Assertion in Tibetan. Ph. D. thesis, University of California, Los Angeles. Gärtner, H.-M. (2012). Does Searle’s challenge affect chances for approximating assertion and quotative modal wollen? In A. Schalley (Ed.), Practical Theories and Empirical Practices, pp. 245–256. Amsterdam: John Benjamins. Heim, I. (1991). Artikel und Definitheit. In A. von Stechow and D. Wunderlich (Eds.), Semantics: An International Handbook of Contemporary Research, pp. 487–535. Berlin: de Gruyter. Hinterwimmer, S. (2013). The semantics of German sollen. Talk presented at International Congress of Linguists 19, University of Geneva. Kratzer, A. (1981). The notional category of modality. In H.-J. Eikmeyer and H. Rieser (Eds.), Words, Worlds, and Contexts: New Approaches to Word Semantics, pp. 163–201. Berlin: Walter de Gruyter. Kratzer, A. (1991). Modality. In A. von Stechow and D. Wunderlich (Eds.), Semantics: An International Handbook of Contemporary Research, pp. 639–650. Berlin: de Gruyter. Kratzer, A. (2012). Modals and Conditionals: New and Revised Perspectives. New York: Oxford University Press. Lauer, S. (2015). Performative uses and the temporal interpretation of modals. In T. Brochhagen, F. Roelofsen, and N. Thieler (Eds.), Proceedings of the 20th Amsterdam Colloquium, pp. 217–226. Available online at http://semanticsarchive.net/Archive/mVkOTk2N/. Matthewson, L., H. Davis, and H. Rullmann (2007). Evidentials as epistemic modals: Evidence from St’át’imcets. In J. van Craenenbroeck (Ed.), Linguistic Variation Yearbook, pp. 201– 254. Amsterdam: John Benjamins. Matthewson, L. and H. Truckenbrodt (2017). Modal flavor/modal force interactions in German. Talk presented at 39th DGfS, Universität des Saarlandes. Percus, O. (2006). Anti-presuppositions. In A. Ueyama (Ed.), Theoretical and Empirical Studies of Reference and Anaphora: Toward the Establishment of Generative Grammar as an Empirical Science, Report of the Grant-in-Aid for Scientific Research (B), Project No. 15320052, pp. 52–73. Washington, D.C.: Japan Society for the Promotion of Science. Portner, P. (2009). Modality. New York: Oxford University Press. Schenner, M. (2008). Double face evidentials in German: Reportative ‘sollen’ and ‘wollen’ in embedded contexts. In A. Grønn (Ed.), Proceedings of Sinn und Bedeutung 12, pp. 552–566. Oslo: ILOS. Schlenker, P. (2012). Maximize presupposition and Gricean reasoning. Natural Language Semantics 20, 391–429. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 214 Nominalized clauses and reference to propositional content1 Elizabeth BOGAL-ALLBRITTEN — University of Gothenburg Keir MOULTON — Simon Fraser University Abstract. We investigate the semantics of Korean embedded clauses that bear the nominalizer kes and declarative marker ta. Such clauses can be embedded by mit ‘believe.’ While such clauses are not factive (Shim and Ihsane 2015), we present elicitation data that shows that nominalized (ta-kes) clauses are felicitously embedded by mit only if their conveyed content was previously asserted in the context; no such restriction arises for non-nominalized clauses. Our analysis of such nominalized embedded clauses argues that they do not denote a proposition — a set of possible worlds — but rather a definite description of a discourse event — an assertion event — that carries propositional content. The use of ta-kes embedded clauses allows Korean verbs like mit to acquire felicity conditions similar to those proposed for response-stance verbs (e.g. agree, deny) (Cattell 1978, Anand and Hacquard 2014). Keywords: attitude verbs, nominalized clauses, reported discourses, Korean 1. Introduction Clause-embedding verbs are often divided into different classes based on certain aspects of the embedded clause’s interpretation. Classification schemes include those by Kiparsky and Kiparsky (1970), Hooper and Thompson (1973), Cattell (1978), Hegarty (1992), and Anand and Hacquard (2009, 2014). The classification from Cattell (1978) is given below. (1) a. b. c. Volunteered-stance / non-factive: Embedded clause introduces new idea Alice {believed/said/assumed/thought/claimed/supposed} that Ron called. Non-stance / factive: Embedded clause refers to a fact Alice {remembered/regretted/knows/forgot/realized} that Ron called. Response-stance: Embedded clause refers to a familiar idea Alice {agreed/admitted/confirmed/denied/accepted} that Ron called. Cross-linguistic investigations of clausal embedding have observed that complements to verbs classified as non-stance (1b) or response-stance (1c) often exhibit morphosyntactic properties suggestive of nominal structure. The exact nature of these properties varies across languages. In some languages, the relevant embedded clauses occupy syntactic positions otherwise reserved for nominal expressions, e.g. Dutch: (Barbiers, 2000; Haegeman and Ürögdi, 2010). In many other languages, embedded clauses are associated with (or perhaps headed by) proforms or demonstratives: such languages include English (Kiparsky and Kiparsky, 1970), German (Sudhoff, 2003; Zimmermann, 2016), Hebrew (Kastner, 2015), Greek (Roussou, 1991; Kallulli, 2006), Albanian (Kallulli, 2006), Bulgarian (Krapova, 2010), and Hungarian (Abrusán, 2011). 1 New judgments (those not otherwise attributed) for Korean reported here are from Chung-hye Han, whose input was invaluable to this project. This project was funded by SSHRC Insight Grant (#435-2015-0454) to Keir Moulton and Junko Shimoyama. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 215 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content Previous research largely agrees that apparent nominal morphosyntactic properties of embedded clauses do not strictly correlate with factivity.2 However, there is significant variation in the characterization of these complements. Among the terms used to describe them are “referential propositions” (de Cuba and Ürögdi, 2009; Haegeman and Ürögdi, 2010), “familiar” (de Cuba, 2007), “presuppositional” (Kastner, 2015), and “given” (Zimmermann, 2016). This primarily syntactic literature does not discuss in detail the contexts that license such clauses, nor does it clarify what type of semantic object these clauses denote. For example, if they denote propositions as in Haegeman and Ürögdi (2010), what exactly does it mean for a proposition — a set of possible worlds — to ‘refer’ (Bhatt, 2010; Kastner, 2015)?3 This paper begins to examine these questions by asking what it might mean for a clause to ‘refer.’ Our focus is Korean sentences like (2). The embedded clause in (2) bears the nominalizer kes in addition to the declarative mood marker ta (Kim, 2009; Yoon, 2013; Shim and Ihsane, 2015). The nominalized clause in (2) is embedded not by a factive or response-stance verb, but rather by mit ‘believe,’ a volunteered-stance verb. (2) Kibo-nun [Dana-ka i chayk-ul ilk-ess-ta-nun kes-ul] mit-ess-ta. K.-TOP D.-NOM this book-ACC read-PST-DEC-ADN kes-ACC believe-PST-DEC ‘Kibo believed (the claim) that Dana read this book.’ (Shim and Ihsane, 2015: (4b)) After §2 places sentences like (2) in the context of prior work on other types of Korean embedded clauses (Kim, 2009; Yoon, 2013; Shim and Ihsane, 2015), §3 presents new data about the contexts that license sentences like (2): (2) is only felicitous if the content conveyed by the embedded clause was previously asserted in the context. In §4, we propose that embedded clauses like (2) do not denote propositions but instead definite descriptions of assertion events that carry propositional content. When mit ‘believe’ embeds a kes-clause (2), its interpretation resembles that of sentences with response-stance verbs (2c) under Anand and Hacquard’s (2014) proposal that such verbs report discourse moves. 2. The structure and basic interpretation of kes-clauses Kim (2009) discusses three types of Korean kes-constructions: internally-headed relative clause (IHRC) (3a), perception, (3b), and factive (3c) constructions. (3) a. John-un [totwuk-i tomangka-n-un kes-ul] cap-ess-ta. J.-TOP thief-NOM run.away-IMPF - ADN kes-ACC catch-PST- DEC ‘John caught the thief that was running away.’ (Internally-headed relative clause (IHRC) construction, Kim, 2009: (1)) b. John-un [totwuk-i tomangka-n-un kes-ul] po-ess-ta. J.-TOP thief-NOM run.away-IMPF-ADN kes-ACC see-PST- DEC ‘John saw (the event) of the thief running away.’ (Perception construction, Kim, 2009: (2)) 2 For arguments that factivity is the crucial notion in Albanian and Greek, see Kallulli (2006, 2010). of reference to propositions that can be found in Asher (1993) and Chierchia (1984) are not addressed in the literature on nominalized clauses cited above. 3 Treatments Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 216 E. Bogal-Allbritten & K. Moulton c. Nominalized clauses and reference to propositional content John-un [totwuk-i tomangka-n-un kes-ul] al-ess-ta. J.-TOP thief-NOM run.away-IMPF-ADN kes-ACC know-PST- DEC ‘John knew (the fact) that the thief was running away.’ (Factive construction, Kim, 2009: (3)) In each example above, the kes-clause is an invariant string but its interpretation appears to depend on the nature of the verb that embeds it. Kim (2009) gives a compositional and largely unified account of kes-clauses where kes denotes individuals of different sorts: ordinary entities (3a), events (3b), and facts (3c). This treatment of kes is superficially supported by the translation of such Korean sentences into English using the nouns event (3b) and fact (3c).4 However, Kim (2009) does not discuss kes-clauses of the shape in (4), which are our focus: (4) Kibo-nun [Dana-ka i chayk-ul ilk-ess-ta-nun kes-ul] mit-ess-ta. K.-TOP D.-NOM this book-ACC read-PST-DEC-ADN kes-ACC believe-PST-DEC ‘Kibo believed (the claim) that Dana read this book.’ (Shim and Ihsane, 2015: (4b)) Unlike the kes-clauses in (3a)–(3c), the embedded clause in (4) contains the declarative mood marker ta in addition to nominalizer kes. The morpheme ta also occurs on verbs in main clauses that express assertions, as in mit-ess-ta ‘believed’ in (4). It is in complementary distribution with elements like the question and imperative markers. The embedded kes-clause in (4) is translated into English with the noun claim, rather than event (cf. (3b)) or fact (cf. (3c)). The main previous discussion of sentences like (4) comes from Shim and Ihsane (2015), who demonstrate that Korean verbs such as mit ‘believe’ can embed kes-clauses that contain ta (4) as well as kes-clauses of the shape in (5). The kes-clause in (5) has the same morphosyntactic form as the kes-clauses investigated by Kim (2009): (5) lacks the declarative marker ta. (5) Kibo-nun [Dana-ka i chayk-ul ilk-ess-nun kes-ul] mit-ess-ta. K.-TOP D.-NOM this book-ACC read-PST-ADN kes-ACC believe-PST-DEC ‘Kibo believed (the fact) that Dana read this book.’ (Shim and Ihsane, 2015: (4c)) In addition to both types of kes-clauses, mit also embeds clauses of the shape in (6), which bear declarative marker ta but lack kes; the clause instead bears complementizer ko, which is not nominal (does not accept case). 4 As discussed by Chae (2007) and references therein, the Korean morpheme kes has been variously characterized as a nominalizer, pronoun, and complementizer. For terminological consistency, we refer to kes as a nominalizer below. Morphological evidence that for the nominal character of kes-clauses comes from the presence of un (a relativizer or adnominalizer) and case marking (e.g. accusative marker ul). It is not possible for a kes-clause to occur without an embedding verb (i). (i) *Lee-ka hoyngryengha-ss-ta-nun kes-ul Lee-NOM embezzle-PST-DEC-ADN kes-ACC (Intended: ‘The fact, claim that Lee embezzled.’) (Yoon, 2013: (12)) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 217 E. Bogal-Allbritten & K. Moulton (6) Nominalized clauses and reference to propositional content Kibo-nun [Dana-ka i chayk-ul ilk-ess-ta-ko] mit-ess-ta. K.-TOP D.-NOM this book-ACC read-PST-DEC-ko believe-PST-DEC ‘Kibo believed that Dana read this book.’ (Shim and Ihsane, 2015: (4a)) Shim and Ihsane show that the constructions in (4) and (6) are both non-factive. The continuation ‘...but Dana didn’t read it’ was felicitous after embedded clauses containing both ta and kes (7a) and embedded clause containing both ta and ko (7b). (7) a. Kibo-nun [Dana-ka i chayk-ul ilk-ess-ta-nun kes-ul] mit-ess-ta, K.-TOP D.-NOM this book-ACC read-PST-DEC-ADN kes-ACC believe-PST-DEC kulente sasil-un Dana-nun i chayk-ul ilk-ci anh-ass-ta. but fact-TOP D.-TOP this book-ACC read-NEG-PST-DEC ‘Kibo believed (the claim) that Dana read this book, but D. didn’t read it.’ (Shim and Ihsane, 2015: (5b)) b. Kibo-nun [Dana-ka i chayk-ul ilk-ess-ta-ko] mit-ess-ta, K.-TOP D.-NOM this book-ACC read-PST-DEC-ko believe-PST-DEC kulente sasil-un Dana-nun i chayk-ul ilk-ci anh-ass-ta. but fact-TOP D.-TOP this book-ACC read-NEG-PST-DEC ‘Kibo believed that Dana read this book, but D. didn’t read it.’ (Shim and Ihsane, 2015: (5a)) The absence of factivity in (7a) and (7b) is not surprising: as a canonical volunteered-stance verb, mit ‘believe’ is not among those verbs we expect to have factive interpretations.5 However, Shim and Ihsane observe that when mit embeds clauses that contain kes but lack ta, a factive interpretation arises: (8) #Kibo-nun [Dana-ka i chayk-ul ilk-ess-nun kes-ul] mit-ess-ta, K.-TOP D.-NOM this book-ACC read-PST-ADN kes-ACC believe-PST-DEC kulente sasil-un Dana-nun i chayk-ul ilk-ci anh-ass-ta. but fact-TOP D.-TOP this book-ACC read-NEG-PST-DEC #‘Kibo believed (the fact) that Dana read this book, but D. didn’t read it.’ (Shim and Ihsane, 2015: (5c)) We elicited additional data that support the restriction of factivity for mit sentences to those whose embedded clauses contain only kes. For a false embedded proposition (that Sydney is the capital of Australia), it is infelicitous for mit to embed the clause marked with kes alone (9a). By contrast, mit can felicitously embed clauses that contain both kes and the declarative marker (realized here as la) (9b) as well as clauses that contain both ko and the declarative marker (9c). (The declarative marker is realized as la in (9) rather than ta.) 5 As Shim & Ihsane (2015) point out, sentences with yukamsuleweha ‘regret’ as the embedding verb have a factive interpretation regardless of the morphosyntax of the embedded clause. This suggests that while choice of embedded morphology may drive factivity with verbs like mit ‘believe,’ other verbs may lexically impose factivity on their complements, as in Kiparsky & Kiparsky (1970) and subsequent work. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 218 E. Bogal-Allbritten & K. Moulton (9) Nominalized clauses and reference to propositional content Context: Kibo’s stupid friend Dana told him that Sydney is the capital of Australia. Kibo missed the day of class where the children learned that Sydney is not the capital of Australia. a. # Kulayse acikto Kibo-nun [Sydney-ka Australia-uy swuto-i-n kes-ul] so still K.-TOP S.-NOM A.-GEN capital-COP-ADN kes-ACC mit-e. believe-DEC #‘Kibo still believes (the fact) that Sydney is the capital of Australia.’ b. Kulayse acikto Kibo-nun [Sydney-ka Australia-uy swuto-la-nun kes-ul] so still K.-TOP S.-NOM A.-GEN capital-DEC-ADN kes-ACC mit-e. believe-DEC ‘Kibo still believes (the claim) that Sydney is the capital of Australia.’ c. Kulayse acikto Kibo-nun [Sydney-ka Australia-uy swuto-la-ko] mit-e. so still K.-TOP S.-NOM A.-GEN capital-DEC-ko believe-DEC ‘Kibo still believes that Sydney is the capital of Australia.’ Following Shim and Ihsane (2015), we conclude that the morphosyntactic shape of clauses embedded by mit ‘believe’ correlates with the factivity of the sentence as a whole: factive interpretations arise if the embedded clause contains only kes, but not if the embedded clause contains both ta and kes or both ta and ko. 3. Licensing ta-kes-marked clauses While we agree with Shim and Ihsane (2015) that clauses with ta and kes and those with ta and ko are both non-factive, Shim and Ihsane (2015) — nor any other prior work on Korean embedded clauses, to our knowledge — do not discuss differences in the distribution or interpretation of these two types of embedded clauses. We turn to this now. 3.1. φ -ta-kes: φ previously asserted in local discourse As previously discussed, the Korean verb mit ‘believe’ can embed clauses marked with declarative ta and nominalizer kes (abbreviated φ -ta-kes) or clauses marked with ta and complementizer ko (abbreviated φ -ta-ko). In the following discourse, both utterance B1 (φ -ta-ko) and utterance B2 (φ -ta-kes) were judged felicitous. (10) A: Na-nun swukecey-lul ta ha-yess-e. Pakk-ey naka nola-to toy? I-TOP homwork-ACC all do-PST- DEC outside-at go play-also can ‘I finished my homework. Can I go outside and play?’ B: An toy. not can ‘No.’ A: Na-lul an mit-e? I-ACC not believe-INT ‘Don’t you believe me?’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 219 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content B1: Um. Na-nun [ney-ka swukecey-lul ta ha-yess-ta-ko] mit-e. Yes. I-TOP you-NOM homework-ACC all do-PST- DEC-ko believe-DEC Haciman cikum-un cenyek siksa sikan-i-ya. but now-TOP evening meal time-COP - DEC ‘Yes, I believe that you finished your homework. But it’s dinner time.’ B2: Um. Na-nun [ney-ka swukecey-lul ta ha-yess-ta-nun kes-ul] Yes. I-TOP you-NOM homework-ACC all do-PST- DEC - ADN kes-ACC mit-e. Haciman cikum-un cenyek siksa sikan-i-ya. believe-DEC but now-TOP evening meal time-COP - DEC ‘Yes, I believe (the claim) that you finished your homework. But it’s dinner time.’ In the following discourse, by contrast, only utterance B1 (φ -ta-ko) was accepted. The consultant rejected utterance B2, where mit embeds φ -ta-kes. (11) A: Cyoni-nun pakk-ey naka nola-to toy? J.-TOP outside-at go play-also can ‘Can Johnny go outside and play?’ B1: Um. Na-nun [kay-ka swukecey-lul ta ha-yess-ta-ko] mit-e. Yes. I-TOP he-NOM homework-ACC all do-PST- DEC-ko believe-DEC ‘Yes, I believe that he finished his homework.’ B2:#Um. Na-nun [kay-ka swukecey-lul ta ha-yess-ta-nun kes-ul] mit-e. Yes. I-TOP he-NOM hmwrk-ACC all do-PST- DEC-ADN kes-ACC believe-DEC #‘Yes, I believe (the claim) that he finished his homework.’ The key difference between the discourses in (10) and (11) is that only (10) contains a previous assertion that carries content comparable — if not string identical — to the φ later uttered by B: A asserts I finished my homework. In such discourses, both φ -ta-kes and φ -ta-ko were licit in utterances by B. When such a previous assertion is missing as in (11), only φ -ta-ko is licit. It is not the case that φ -ta-kes is only licensed where φ corresponds to a direct quotation. The φ uttered by B in (10) is not string identical to the string previously uttered by A: whereas A’s utterance contains a first person pronoun, B’s utterance contains a second person pronoun. This point is made even more dramatically in the discourse in (12). Here, A’s utterance of I ate peas only entails the proposition corresponding to the φ uttered by B. In addition to φ -ta-ko (B1), φ -ta-kes (B2) was also judged felicitous: (12) Context: B has a rule that A must eat vegetables before having cake. A: I ate peas! Can I have cake now? B: No, you can’t. A: But why? Don’t you believe me? Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 220 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content B1: Na-nun [ney-ka yachae-lul mek-ess-ta-ko] mit-e... I-TOP you-NOM vegetable-ACC eat-PST-DEC-ko believe-DEC ‘I believe that you ate vegetables (...but the cake’s not ready).’ B2: Na-nun [ney-ka yachae-lul mek-ess-ta-nun kes-ul] mit-e... I-TOP you-NOM vegetable-ACC eat-PST-DEC-ADN kes-ACC believe-DEC ‘I believe that you ate vegetables (...but the cake’s not ready).’ However, while φ need not be string identical to a previous assertion, the propositional content associated with φ must be consistent with the content associated with the prior assertion. The consistency requirement was met in the entailment discourse in (12). However, it is not met in the discourse in (13), in which φ occurs in the scope of negation in A’s previous assertion. As shown, A is not allowed to go on to use φ -ta-kes in a subsequent assertion. (Although not shown here, φ -ta-ko would have been licit.) (13) A: Kibo has certainly heard in his geography class that Toronto is not the capital of Canada... A: ...#Kulayto Kibo-nun [Toronto-ka Canada-uy swuto-la-nun kes-ul] even.so K.-TOP T.-NOM C.-GEN capital-DEC-ADN kes-ACC mit-e. believe-DEC ‘Even so, Kibo still believes that Toronto is the capital of Canada.’ C.H. Han’s Comment: “This sounds really odd to me, if Kibo has never heard anybody tell him that ‘Toronto is the capital of Canada’.” The prior act of assertion of φ — or material consistent with φ — is necessary for the felicity of φ -ta-kes under mit ‘believe.’ In the following discourse, we find that A’s polar question (Has Johnny finished his homework) is not sufficient to license B’s utterance of φ -ta-kes in B2, despite φ being string identical to the proposition on which A’s polar question was formed. The infelicity of φ -ta-kes in B2 contrasts with the felicity of φ -ta-ko in utterance B1. (14) A: Johnny-nun swukcey-lul ta ha-yess-ni? J.-TOP homework-ACC all do-PST-Q ‘Has Johnny finished his homework?’ B1: Na-nun [Johnny-ka swukcey-lul ta ha-yess-ta-ko] mit-nun-ta. I-TOP J.-NOM homework-ACC all do-PST-DEC-ko believe-DEC ‘I believe that Johnny finished his homework.’ B2: #Na-nun [Johnny-ka swukcey-lul ta ha-yess-ta-nun kes-ul] I-TOP J.-NOM homework-ACC all do-PST-DEC-ADN kes-ACC mit-e. believe-DEC #‘I believe (the claim) that Johnny finished his homework.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 221 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content The importance of assertion — as opposed to a question — distinguishes Korean φ -ta-kes from structures in other languages that have also been described as imposing a ‘familiarity’ requirement and exhibiting nominal morphosyntactic properties. For instance, Schwabe et al. (2016) citing Sudhoff (2003) show for German that a polar question is sufficient to license ‘familiar’ clauses, which contain the sentential proform es. (15) A: Ist Lea krank? is Lea ill ‘Is Lea ill?’ B: Max behauptet es, dass sie krank ist. Max claims it that she ill is ‘Max claims it that she is ill.’ (Schwabe, Frey, and Meinunger, 2016: (4)) We turn to a final restriction on φ -ta-kes when embedded by mit ‘believe.’ The prior assertion of φ must be familiar to the subject (attitude holder) of mit. It appears that the ‘familiarity’ requirement is satisfied if the subject of mit is among those to whom φ was asserted. In addition to [φ -ta-ko] mit (A1) being felicitous in this context, [φ -ta-kes] mit (A2) was also accepted. Here, the subject of mit is Johnny’s mother, to whom φ was previously asserted. (16) A: Johnny-ka ku-uy emma-eykey [ku-ka swukcey-lul ta ha-yess-ta-ko] J.-NOM he-GEN mother-to he-NOM homework-ACC all do-PST-DEC-ko malha-yess-ta... say-PST-DEC ‘Johnny told his mother that he finished his homework...’ A1: ...kulayse Johnny-uy emma-nun [Johnny-ka swukcey-lul ta so J.-GEN mother-TOP J.NOM homework-ACC all hay-ss-ta-ko] mit-e. do-PST-DEC-ko believe-DEC ‘...so Johnny’s mother believes that Johnny finished his homework.’ A2: ...kulayse Johnny-uy emma-nun [ku-ka swukcey-lul ta so J.-GEN mother-TOP he-NOM homework-ACC all ha-yess-ta-nun kes-ul] mit-nun-ta. do-PST-DEC-ADN kes-ACC believe-PRES-DEC ‘...so Johnny’s mother believes that he finished his homework.’ In discourse (17), however, only [φ -ta-ko] mit (B1) was accepted whereas [φ -ta-kes] mit (B2) was judged to be infelicitous. In this discourse, Johnny’s mother is once again the subject of mit ‘believe’ but φ was not asserted previously to Johnny’s mother: instead, φ was asserted to speaker A. It appears that the felicity of [φ -ta-kes] mit hinges on whether φ was asserted specifically within in the ‘reported’ or ‘local’ discourse (the one that the matrix subject participates in). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 222 E. Bogal-Allbritten & K. Moulton (17) Nominalized clauses and reference to propositional content A: Johnny told me—but hasn’t said anything to his mother—that he finished all his homework. Do you believe him? B: I don’t know, but Johnny’s mother went into his room and saw several completed assignments... B1: ...kulayse Johnny-uy emma-nun [Johnny-ka swukcey-lul ta so J.-GEN mother-TOP J.NOM homework-ACC all hay-ss-ta-ko] mit-e. do-PST-DEC-ko believe-DEC ‘...so Johnny’s mother believes that Johnny finished his homework.’ B2: #...kulayse Johnny-uy emma-nun [Johnny-ka swukcey-lul ta so J.-GEN mother-TOP J.NOM homework-ACC all ha-yess-ta-nun kes-ul] mit-e. do-PST-DEC-ADN kes-ACC believe-DEC ‘...so Johnny’s mother believes that Johnny finished his homework.’ Comment: “I feel that Johnny’s mom herself must have heard the claim that Johnny finished the homework.” In summary, whereas φ -ta-ko imposes no restrictions on discourses in which it occurs, φ -ta-kes is only felicitous under the following conditions, informally characterized: (18) The familiarity requirement of φ -ta-kes: Utterance of [φ -ta-kes] mit is felicitous just in case φ — or some utterance associated with propositional content that is consistent with φ — has been previously asserted in a local discourse (a discourse that includes the subject of mit). In §4, we arrive at these conditions by appealing to the individual contributions of declarative marker ta and nominalizer kes. φ -ta-kes presupposes the existence of a prior assertion φ (or material consistent with φ ) which is familiar to the subject of mit.6 6 Our claim that φ -ta-kes presupposes a previous assertion event of φ recalls presuppositional characterizations of reportative expressions in German and Tagalog (Schenner, 2008; Fabricius-Hansen and Sæbø, 2004; Schwager, 2010). Elements like German sollen and Tagalog daw “induce a presupposition that the prejacent has been asserted” (Schwager, 2010: 238). However, while the meanings can be described similarly, ta-kes differs from reportatives in at least three ways. First, whereas reportatives introduce this presupposition, the presupposition in Korean arises through semantic contributions of independent markers ta and kes, neither of which can itself be characterized as a reportative. Second, while reportatives can occur as main clauses that express assertions, Korean ta-kes clauses cannot (i). Third, whereas mit ‘believe’ readily embeds Korean ta-kes clauses, German glauben ‘believe’ is reluctant to embed reportative sollen (Schenner, 2008). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 223 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content 3.2. Comparison with response-stance verbs Our characterization of belief attributions with a complement of shape φ -ta-kes in (18) is strongly reminiscent of previous descriptions of Cattell’s (1978) response-stance verbs: (19) Response-stance: Embedded clause refers to a familiar idea Alice {agreed/admits/confirmed} that Ron called. Authors including Cattell (1978), Hegarty (1992), de Cuba (2007), and Kastner (2015) observe that response-stance verbs embed ‘familiar’ complements. Hegarty suggests that this familiarity requirement is satisfied when such complements express common knowledge or a point of current discussion in the reported discourse. As (20) shows, assertions with response-stance verbs that embed φ cannot be followed by a denial that φ was previously asserted. (20) Alice agreed/admits/confirmed [that Ron called]... #...but no one had said that Ron called. De Cuba (2007) and Kastner (2015) observe that Hungarian and Hebrew response-stance verbs prefer to embed clauses that exhibit nominal morphosyntactic properties, namely nominal proforms and clause-taking determiners. The same is true of Korean. The consultant readily allowed φ -ta-kes clauses to be embedded by response-stance verbs tonguyha ‘agree’ (21a), incengha ‘acknowledge, accept’ (21b), and pwuinha ‘deny, reject’ (21c). By contrast, the consultant strongly dispreferred sentences in which these verbs instead embedded φ -ta-ko clauses. (21) a. Na-nun [Lee-ka wa-ss-ta-nun kes-ey] tonguyha-n-ta. I-TOP L.-NOM come-PST-DEC-ADN kes-at agree-PRES-DEC ‘I agree (with the claim) that Lee came.’ b. kes-ul] incengha-n-ta. Na-nun [Lee-ka wa-ss-ta-nun I-TOP L.-NOM come-PST-DEC-ADN kes-ACC acknowledge/accept-PRES-DEC ‘I acknowledge/accept the claim that Lee came.’ c. Na-nun [Lee-ka wa-ssa-ta-nun kes-ul] pwuinha-n-ta. I-TOP L.-NOM come-PST-DEC-ADN kes-ACC deny/reject-PRES-DEC ‘I deny/reject (the claim) that Lee came.’ 4. Toward an account of reference to prior asserted content We propose that the parallels between Korean ta-kes clauses and clauses with responses-stance verbs are no accident, but rather that typically volunteered-stance verbs like mit ‘believe’ take on the profile of a response-stance verb by virtue of the individual semantic contributions of ta and kes. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 224 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content 4.1. The contributions of ta and kes We begin with the contribution of the declarative marker ta. As was first noted (to our knowledge) by S.S. Kim (2011), ta introduces a separate layer of embedding when found in clauses embedded under nouns, such as the relative in (22). In (22a), the clause without ta is translated as simply ‘the rumor that Chelswu told me.’ By contrast, the clause in (22b) contains ta, which is reflected in its translation with an additional verb of saying. (22) a. [Chelswu-ka na-eykey allye cwu-n] somwun C.-NOM I-DAT tell-ADN rumor ‘the rumori that Chelswu told me ti ’ b. [Chelswu-ka na-eykey allye cwu-ess-ta-nun] somwun C.-NOM I-DAT tell-PST- DEC - ADN rumor ‘the rumori that (people say that) Chelswu told me ti ’ *‘the rumori that Chelswu told me ti ’ (S.S. Kim 2011: 13a,b) We suggest that ta-clauses evoke events of assertion of p.7 We record this meaning as in (23):8 (23) J taembedded K = λ pλ e.e is an event of asserting p Next, we consider what kes-clauses do independently of ta. We rely here on M.-J. Kim (2009). Kim (2009) offers a largely unified account of three structures that feature kes: internallyheaded relative clause (IHRC) constructions (24a), perception constructions (24b), and factive constructions (24c). (24) a. John-un [totwuk-i tomangka-n-un kes-ul] cap-ess-ta. J.-TOP thief-NOM run.away-IMPF - ADN kes-ACC catch-PST- DEC. ‘John caught the thief that was running away.’ (Internally-headed relative clause (IHRC) construction, Kim, 2009: (1)) b. John-un [totwuk-i tomangka-n-un kes-ul] po-ess-ta. J.-TOP thief-NOM run.away-IMPF-ADN kes-ACC see-PST- DEC ‘John saw (the event) of the thief running away.’ (Perception construction, Kim, 2009: (2)) c. John-un [totwuk-i tomangka-n-un kes-ul] al-ess-ta. J.-TOP thief-NOM run.away-IMPF-ADN kes-ACC know-PST- DEC ‘John knew (the fact) that the thief was running away.’ (Factive construction, Kim, 2009: (3)) 7 When ta is in a root clause or combined with ko, its semantics is not as transparent. We leave a full treatment of ta for future work. 8 We treat its contribution as an entailment here, although it is possible it’s a presupposition. It’s hard to tell since ta-clauses make this contribution when embedded, and we only have examples where the embedding noun phrase carries a uniqueness presupposition, and hence determining whether the assertion component is entailed or presupposed has been challenging. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 225 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content Kim (2009) proposes that kes introduces a salient individual or situation which stands in some contextually-supplied relation R to the proposition p. (See also Kim (2007), Hoshi (1995), and Shimoyama (1999) on IHRCs.) We adopt a version of Kim’s analysis of kes, which departs from the original in largely trivial ways. Kes takes as its argument the embedded clause p (a set of situations) and returns what amounts to a definite description (25), which we characterize as a familiarity definite.9,10 (25) JkesKC = λ pι x.R(p)(x) x is in the domain of ordinary individuals or situations R is a suitable relation defined iff x is familiar in C Kim identifies several relations that are suitable for R in different kes-constructions. For IHRCs, theta-relations (26) pick out an individual from the situation denoted by the embedded clause, e.g. the thief who is the agent of the running situation described in (27). The entity denoted by the entire kesP functions as an argument to a verb in the main clause (e.g. caught). Ragent = λ p′ λ x′ .∃s[p′ (s) & Agent(x′ )(s)] Rtheme =λ p′ λ x′ .∃s[p′ (s) & Theme(x′ )(s)] (26) a. b. (27) kes-ul] cap-ess-ta. John-un [totwuk-i tomangka-n-un John-TOP thief-NOM run.away-IMPF - ADN kes-ACC catch-PST- DEC ‘John caught the thief that/while he was running away.’ kesP: e IHRC:hs,ti kes:hhs,ti,ei λ s[run.away(thief)(s)] (28) a. b. J kes K = λ pι x.Ragent (p)(x) = λ pι x.[λ p′ λ x′ .∃s[p′ (s) & Agent(x′ )(s)]](p)(x) = λ pι x.∃s[p(s) & Agent(x)(s)] J kesP K = λ pι x.∃s[p(s) & Agent(x)(s)](λ s′ .run-away(thief)(s′ )) =ι x.∃s[run-away(thief)(s) & Agent(x)(s)] ; the thief While we must constrain the possible values for R (see below), we also want to allow it a certain flexibility. As Kim (2007) shows with (29a), R can return a sum of individuals in IHRC, each with distinct thematic roles (Kim, 2007: 8). In (29b), R returns an individual that is part of a result state described by the IHRC predicate (Grosu and Landman, 2012 after (40) in Chung and Kim (2003)). 9 Further work is needed to determine if there is a uniqueness requirement. Kim, kes takes as its argument the trace left by LF movement of the embedded clause. She also separates definiteness from kes, but we have built definiteness in simply for ease of exposition. 10 For Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 226 E. Bogal-Allbritten & K. Moulton (29) Nominalized clauses and reference to propositional content a. Jinho-un [koyangi-ka cwi-lul coch-ko iss-n-un kes]-ul capassta. J.-TOP [cat-NOM mouse-ACC chase-ko COP-IMPF-ADN kes]-ACC catch-PST-DEC ‘A cat chased a mouse & J. caught {the cat/the mouse/the mouse & cat}.’ b. Jinho-un [ paci-ka teleweci-un kes-ul ] takkanay-ss-ta J.-TOP pants-NOM got.dirty-ADN kes-ACC wipe.out-PST-DEC ‘The pants got dirty and J. wiped the dirt off the pants.’ Kes-constructions arrive at factive (30) and perception (31) meanings via different values for R. Following Kim (2007) and Kratzer (2002), we treat factive complements as denoting situations that exemplify propositions; the fact-producing R (R f act ) in (30b) delivers this. Perception complements denote bare events—i.e. the individual situation described by the complement (Higginbotham 1983). The R found in such kes-clauses (31b) is simply the identity function. (30) (31) Factive construction a. John-un [totwuk-i tomangka-n-un kes-ul] al-ess-ta. J.-TOP thief-NOM run.away-IMPF-ADN kes-ACC know-PST- DEC ‘John knew (the fact) that the thief was running away.’ b. R f act = λ p′ λ x′ .x′ is a fact that exemplifies p′ (Treatment of facts after Kim (2009); Kratzer (2002)) c. JkesPK = ι x.x is a fact that exemplifies [λ s′ .run-away(thief)(s′ )] Perception construction11 a. John-un [totwuk-i tomangka-n-un kes-ul] po-ess-ta. John-TOP thief-NOM run.away-IMPF-ADN kes-ACC see-PST- DEC ‘John saw (the event) of the thief running away.’ b. Rid = λ p′ λ s′ .p′ (s′ ) c. JkesPK = ι s.run-away(thief)(s) There are questions, of course, that arise about how to constrain R. One way to constrain R would be to say that the individual x/s must refer to a (possibly non-proper) ‘part’ of the situation described by p: individuals in the situation, the situation itself (for perception), or the fact. We also note that the entries we give for R f act and Rid are closely related — or identical, in the case of R f act — to the denotations of complementizers given by Kratzer (2006), so there is precedent for linguistically encoding these functions. 4.2. Combining ta and kes It is now a matter of combining kes with a clause that contains ta. (We assume the adnominal marker un makes no semantic contribution.) If R is valued as Rid as in the perception construction, then the φ -takes structure simply denotes the set of assertion eventualities denoted by the ta-clause. For instance, the embedded clause in (32) refers to the familiar event of assertion of p in the context: 11 Kim (2007) suggests kes may pick out something more like the ‘image’ or ‘sound’ of an event. We’ve eliminated that step for simplicity. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 227 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content (32) Na-nun [kesP Johnny-ka swukcey-lul ta ha-yess-ta-nun kes-ul] mit-e. I-TOP J.-NOM homework-ACC all do-PST-DEC-ADN kes-ACC believe-DEC ‘I believe that Johnny finished his homework.’ (33) a. b. c. JtaK(that Johnny finished his homework) = λ e.e is an event of asserting that Johnny finished his homework JkesK = λ pι s.[Rid (p)(s)] JkesPK(JtaK(that Johnny finished his homework)) = ι s.s is an event of asserting that Johnny finished his homework ; the event of asserting that Johnny did his homework In §4.3, we discuss how a verb like believe combines with an individual event like the one in (33c). Even before doing so, however, we can already appreciate how treating ta-kes clauses as definite descriptions of assertion events will capture the data in §3 2–(13). When the assertion has been made in the context, it can be referred to successfully because it is familiar in the context of utterance: (34) A: B: Johnny finished his homework. (=an event of asserting p) ✓(32) In (35) (an excerpt from (14)), there is no event of asserting that Johnny did his homework (only a question): as a result, ta-kes will not be defined and will be — as attested — infelicitous. (We return in the the next section to the additional requirement of φ -ta-kes that φ have been asserted within a local discourse.) (35) A: B: Has Johnny done his homework? (not an event of asserting p) ✗(32) We can envision an alternative account, which would treat the contribution of ta as presupposition that its complement is asserted in the context, but would semantically just pass up a propositional meaning rather than introduce an event description in the object language. That presupposition would be accommodated globally when the attitude holder is a first person (utterance context participant) or locally under believe with a third person attitude holder. We explore this possibility in ongoing work. We do not pursue that approach here, however, because we do not see how it would account for the fact that ta is required for a non-factive meaning. If all ta did was place a presupposition on the propositional complement—that it was uttered—then modulo that presupposition, ta-kes clauses and kes-clauses under believe should behave alike. But that is not the case: as first demonstrated by Shim and Ihsane (2015), bare kes-clauses under believe are factive. The ta needs to make enough of a contribution to alleviate that factivity, and that is what our proposal will do. Our proposal, however, requires further elaboration to rule out R f act being used with ta-kes clauses under believe. 4.3. Response-stance believe Traditionally, we think of attitude verbs as selecting propositions. By contrast, our proposal is that a ta-kes clause refers to an event, which is not in any obvious way what a verb like believe would select. In this section, we treat ta-kes-taking predicates as response-stance verbs in a fashion similar to the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 228 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content account of such verbs developed in Anand and Hacquard (2014): in their account, verbs like claim, agree, dispute, etc. report discourse moves whose goal is to update a reported common ground, CGR , with the complement proposition. (36) JclaimKc,w,g = λ pλ e.claim’(e,w) & ∀w’ compat. with Goal(e) [∀w” ∈ CGR (w’) [p(w”)]] (Anand & Hacquard, 2014: 78) The part of their proposal we will capitalize on is the notion of updating a reported common ground: the discourse situation that the discourse move described by the verb is a part of. We suggest that response-stance believe reports acceptance of (the propositional content of) of a certain discourse move into the attitude holder’s belief set, where a discourse move is an event of assertion (whose own goal is to update the reported common ground). We sketch a denotation for response-stance believeRS in (37) which relates an attitude holder to an event of assertion e. Condition (37a) guarantees that e be uttered in the reported common ground; this accounts for the contrast in felicity between (16) and (17). Condition (37b) guarantees that e be an assertion event: the goal of e is to introduce its propositional content to the reported common ground. (37) Sketch of denotation of Response-stance (RS) believe: x believesRS e in a reported common ground (CGR ) in w iff: a. e is a discourse move in CGR b. goal(e) is to add the CONTENT(e) to CGR c. D OX(x)(w) ⊂ CONTENT(e)(w) The notion of an event’s propositional content is defined in (38b). Following Hacquard (2006) and Kratzer (2013), we take CONTENT to be a function that takes some particular with informational content (books, information sources, assertion events, belief states) and packages that informational content as a set of possible worlds. This set of worlds can then be related to the attitude holder’s doxastic alternatives in standard Hintikkan fashion. The end result is that to believe an assertion event is to believe the content of that event. (38) a. b. D OX(x)(w) = {w′ : w′ is compatible with what x believes in w} CONTENT(e)(w) = {w′ : w′ is the informational content of e in w} There are many open questions that arise from this preliminary report. Among these questions is the full range of predicates that embed ta-kes clauses. We might predict that embedding ta-kes clauses under a verb of communication like malha ‘say’ would conflict with the claim being presupposed in the CG or CGR . We also have not broached the question of what kes-clauses that lack ta mean when embedded by believe, e.g. (8). We described these as factive following Shim and Ihsane (2015), but remain agnostic as to whether they should be equated with knowledge ascriptions. 5. Conclusion We set out to examine what it could mean to say that a clause “refers,” taking as our focus Korean embedded clauses that bear the nominalizer kes and declarative marker ta. We suggested that they might not refer to propositions or even to propositional content directly (whatever that might be), but to assertion events that carry propositional content. Korean ta-kes clauses are best understood as denoting definite descriptions of an assertion event. Assertion events are easily equated with propositions, as the recent trend in projecting possible worlds from information sources (“anchors”) has demonstrated Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 229 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content (Hacquard, 2006; Kratzer, 2013). When ta-kes is present, Korean mit ‘believe’ behaves like a response stance verb, reporting a discourse move: the uptake of an assertion (Anand and Hacquard 2014). The results from Korean are interesting because things could have been different: nominalized ta-kes-clauses instead might have referred to content that was not necessarily previously asserted. Both Chierchia (1984) and Asher (1993) allow propositions to denote entities, and these can be anaphorically referred to. But nothing on that view requires there be an assertion event of the proposition. It may be useful to apply the contexts used here to other languages that have been claimed to have ‘referential clauses’ with nominal morphosyntactic properties. Our results reinforce the need to clearly distinguish factive from so-called ‘familiar’ (de Cuba, 2007), ‘referential’ (de Cuba and Ürögdi, 2009; Haegeman and Ürögdi, 2010), and ‘presuppositional’ (Kastner, 2015) clauses. When used to study embedded clauses with nominal properties in other languages, our contexts may show that such structures are best understood in terms of belief as a discourse-move reporting predicate. Preliminary results show that when Kastner’s (2015) Hebrew “presuppositional clauses” (bearing demonstrative ze) are embedded by belief verbs (39b), they have felicity conditions similar to those of Korean ta-kes clauses. (39) Hebrew a. anaxnu ma’aminim [še-yeš le-xa hetkef lev]. we believe.PL COMP-is to-you.M attack.CS heart ‘We believe that you are having a heart attack.’ b. anaxnu ma’aminim le-ze [še-yeš le-xa hetkef lev]. we believe.PL to.this COMP-is to-you.M attack.CS heart ‘We believe this that you are having a heart attack.’ (40) Discourse A: A: What’s wrong with me Doctor? B: ✓(39a), ✗(39b) (41) Discourse B: A: Don’t you believe me that I am having a heart attack? B: ✓(39a), ✓(39b) (I. Kastner, p.c.) A full-scale investigation of the semantics and pragmatics of nominalized clauses is underway. References Abrusán, M. (2011). Predicting the presuppositions of soft triggers. Linguistics and Philosophy 34, 491–535. Anand, P. and V. Hacquard (2009). Epistemics with attitude. In Proceedings of SALT 18. Anand, P. and V. Hacquard (2014). Factivity, belief and discourse. In L. Crnič and U. Sauerland (Eds.), The Art and Craft of Semantics: A Festschrift for Irene Heim, volume 1, pp. 69–90. MIT Working Papers in Linguistics. Asher, N. (1993). Reference to Abstract Objects in Discourse. Kluwer Academic Press. Barbiers, S. (2000). The right periphery in SOV languages. In P. Svenonius (Ed.), The derivation of VO and OV, pp. 181–218. John Benjamins. Bhatt, R. (2010). Comments on “Referential CPs and DPs: An operator movement account”. Theoretical Linguistics 36, 173–177. Cattell, R. (1978). The source of interrogative adverbs. Language 54, 61–77. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 230 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content Chae, H.-S. (2007). On the categorial ambiguity of the morpheme kes in Korean. Language Research 43, 229–264. Chierchia, G. (1984). Topics in the Syntax and Semantics of Infinitives and Gerunds. Ph. D. thesis, University of Massachusetts, Amherst. Chung, C. and J.-B. Kim (2003). Differences between externally and internally headed relative clause constructions. In J.-B. Kim and S. Wechsler (Eds.), Proceedings of the 9th International Conference on HPSG, pp. 43–65. Stanford. Chung, S. and W. A. Ladusaw (2004). Restriction and Saturation. MIT Press. de Cuba, C. and B. Ürögdi (2009). Eliminating factivity from syntax: Sentential complements in Hungarian. In T. Laczkó and C. O. Ringen (Eds.), Approaches to Hungarian. John Benjamins. de Cuba, C. (2007). On (Non)factivity, Clausal Complementation and the CP-field. Ph. D. thesis, Stony Brook University. Fabricius-Hansen, C. and K. J. Sæbø (2004). In a mediative mood: The semantics of the German reportative subjunctive. Natural Language Semantics 12, 213–257. Farudi, A. (2007). An anti-symmetric approach to Persian clausal complements. Ms, University of Massachusetts, Amherst. Grosu, A. and F. Landman (2012). A quantificational disclosure approach to Japanese and Korean internally headed relatives. Journal of East Asian Linguistics 21, 159–196. Hacquard, V. (2006). Aspects of Modality. Ph. D. thesis, Massachusetts Institute of Technology. Haegeman, L. and B. Ürögdi (2010). Referential CPs and DPs: An operator movement account. Theoretical Linguistics 36, 111–152. Hegarty, M. (1992). Adjunct extraction without traces. In D. Bates (Ed.), The Proceedings of the Tenth West Coast Conference on Formal Linguistics, pp. 209–222. Stanford: CSLI. Hooper, J. and S. Thompson (1973). On the applicability of root transformations. Linguistic Inquiry 4, 465–499. Hoshi, K. (1995). Structural and Interpretive Aspects of Head-Internal and Head-External Relative Clauses. Ph. D. thesis, University of Rochester. Kallulli, D. (2006). Triggering factivity: Prosodic evidence for syntactic structure. In D. Baumer, D. Montero, and M. Scanlon (Eds.), The Proceedings of the Twenty-Fifth West Coast Conference on Formal Linguistics, pp. 211-219. Somerville: Cascadilla Proceedings Project. Kallulli, D. (2010). Belief will create fact: On the relation between givenness, presupposition, and other remarks. Theoretical Linguistics 36, 199-208. Kastner, I. (2015). Factivity mirrors interpretation: The selectional requirements of presuppositional verbs. Lingua 164, 156–188. Kim, M.-J. (2007). Formal linking in internally headed relatives. Natural Language Semantics 15, 279–315. Kim, M.-J. (2009). E-type anaphora and three types of kes-construction in Korean. Natural Language and Linguistic Theory 27, 345–377. Kim, S.-S. (2011). Noun complements and clause types in Korean (and Japanese). Japanese/Korean Linguistics 18, 278–290. Kiparsky, P. and C. Kiparsky (1970). Fact. In M. Bierwisch and K. E. Heidolph (Eds.), Progress in Linguistics, pp. 143–173. Mouton. Krapova, I. (2010). Bulgarian relative and factive clauses with the invariant complementizer deto ‘that’. Lingua 120, 1240–1272. Kratzer, A. (2002). Facts: particulars or information units? Linguistics and Philosophy 25, 655-670. Kratzer, A. (2006). Decomposing attitude verbs. Semantics Archive, http://semanticsarchive. net/Archive/DcwY2JkM/attitude-verbs2006.pdf (24 June 2013). Kratzer, A. (2013). Modality for the 21st century. In S. R. Anderson, J. Moeschler, and F. Reboul Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 231 E. Bogal-Allbritten & K. Moulton Nominalized clauses and reference to propositional content (Eds.) L’interface Langage-Cognition/The Language-Cognition Interface: Actes du 19e Congrès International des Linguistes Genève, pp. 179–199. Librarie Droz. Lee, J. (2006). The Korean Internally-Headed Relative Clause Construction: Its Morphological, Syntactic and Semantic Aspects. Ph. D. thesis, The University of Arizona. Moltmann, F. (2013). Abstract Objects and the Semantics of Natural Language. Oxford University Press. Moulton, K. (2009). Natural Selection and the Syntax of Clausal Complementation. Ph. 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Schwabe, K., Werner F., and A. Meinunger (2016). Inner-sentential propositional proforms: Syntactic properties and interpretative effects. In W. Frey, A. Meinunger, and K. Schwabe (Eds.), Innersentential Propositional Proforms: Syntactic Properties and Interpretive Effects. John Benjamins. Schwager, M. (2010). On what has been said in Tagalog: Reportative daw. In T. Peterson and U. Sauerland (Eds.), Evidence from Evidentials, pp. 221–246. UBC Working Papers in Linguistics. Shim, J.Y. and T. Ihsane (2015). Facts: The interplay between the matrix predicate and its clausal complement. In A. Biggs, M. Li, A. Wang, and C. Zhang (Eds.), The Second Asian and European Linguistic Conference. Newcastle and Northumbria Working Papers in Linguistics. Shimoyama, J. (1999). Internally headed relative clauses in Japanese and E-type anaphora. Journal of East Asian Linguistics 8, 147–182. Sudhoff, S. (2003). Argumentsätze und es-Korrelate: zur syntaktischen Struktur von Nebensatzeinbettungen im Deutschen. wvb, Wiss. Verlag Berlin. Yoon, S. (2013). Embedded Root-Clause Phenonmena: ERCP in Korean vs. V2 in German. In S. Keine and S. Slogget (Eds.), Proceedings of Forty-Second Annual Meeting of the North East Linguistic Society, pp. 633–646. GLSA. Zimmermann, I. (2016). Phonological, morphosyntactic and semantic properties of es. In W. Frey, A. Meinunger, and K. Schwabe (Eds.), Inner-sentential Propositional Proforms: Syntactic properties and interpretive effects. John Benjamins. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 232 A surface-scope analysis of authoritative readings of modified numerals1 Brian BUCCOLA — The Hebrew University of Jerusalem Andreas HAIDA — The Hebrew University of Jerusalem Abstract. A sentence like You’re allowed to draw at most three cards has a so-called authoritative reading characterized by two kinds of inference: an upper-bound inference (you’re not allowed to draw more than three cards) and a free-choice inference (you’re allowed to draw any number of cards in the range [0,3]). We show that authoritative readings are available for a variety of expressions beyond just at most, and we provide the first (as far as we know) surface-scope account of such readings, building on the recursive exhaustification account of free-choice disjunction proposed by Fox (2007). Keywords: modified numerals, free-choice inferences, exhaustivity, recursive exhaustification 1. The puzzle Sentence (1) has two readings, which Büring (2008) calls a speaker insecurity reading (or ignorance reading) and an authoritative reading. On its speaker insecurity reading, the sentence conveys that the maximum number of cards you’re allowed to draw is either three or fewer than three, and the speaker is ignorant about which is true. This reading can be brought out by following the sentence with but I don’t know exactly how many. (1) You’re allowed to draw at most three cards. We will be concerned in this paper with the authoritative reading of (1), which is characterized by two kinds of inference: (i) an upper-bound (UB) inference, viz. that you’re not allowed to draw four or more cards, and (ii) a free-choice (FC) inference, viz. that you’re allowed to draw any number of cards in the range [0,3].2 Authoritative readings constitute a well-known puzzle for the semantics of modified numerals (Geurts and Nouwen, 2007; Büring, 2008; Penka, 2014), which we describe in two parts. First, on standard assumptions about the meanings of allow and at most three, a surface-scope analysis of (1) predicts a weak literal meaning, ‘There is a permissible world in which you draw three cards or fewer’, notated henceforth as ⟐[≤ 3]. Neither an UB inference (¬ ⟐ [≥ 4]) nor a FC inference (⟐[= 3] ∧ ⟐[= 2] ∧ ...) logically follows from this interpretation. Moreover, an 1. For many helpful comments, questions, and discussions, we would like to thank Luis Alonso-Ovalle, Moysh Bar-Lev, Emmanuel Chemla, Luka Crnič, Danny Fox, Doris Penka, Bernhard Schwarz, Stephanie Solt, Benjamin Spector, and Tue Trinh, as well as the audiences at the Institut Jean Nicod (École normale supérieure, LANGUAGE seminar series, July 6, 2016), at Sinn und Bedeutung 21 (University of Edinburgh, September 4–6, 2016), at Logic in Language and Conversation (LogiCon) (Utrecht University, September 19–20, 2016), and at ZAS (Semantikzirkel, September 21, 2016). This research was supported by the Israel Science Foundation (ISF 1926/14) and by the German-Israeli Foundation for Scientific Research (GIF 2353). 2. Our empirical claim regarding FC inferences deviates from that of Penka (2014), who assumes only partial, rather than total, FC: (1) conveys only that you may draw exactly three cards and may draw fewer than three cards, not that you may draw any number of cards in the range [0,3] (though the sentence is compatible with such a state of affairs). This partial view is also in line with claims about ignorance inferences, which have been argued to be partial, not total (Schwarz, 2016). We take a different stance, which is that these inferences are normally total, but in certain contexts can be partial. The system we propose will be able to account for such weakening (by ‘pruning’ certain alternatives from consideration), as we discuss at the end of the paper, in §4.4. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 233 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals inverse-scope analysis (at most three > allow) derives only the speaker insecurity reading, and the reason for this is that when at most three takes widest scope, a speaker insecurity reading obligatorily emerges. For instance, (2) is incompatible with the speaker knowing exactly how many cards Ann drew; he knows it’s either three or fewer than three, but is ignorant about which is true (Geurts and Nouwen, 2007; Büring, 2008; Nouwen, 2010, 2015; Schwarz, 2016).3 (2) Ann drew at most three cards. Second, the antonym of at most, at least, does not give rise to authoritative readings. For example, (3) cannot be used to convey that you’re allowed to draw three or more cards, with FC in the range [3,n] (for some contextually specified UB n, e.g. 52, the number of cards in a standard deck), and a lower bound (LB) that prohibits drawing two cards or fewer. To see this, notice the oddity of embedding (3) under a expression like The rules state that . . . , or of a game master uttering (3).4 (3) You’re allowed to draw at least three cards. To summarize, the puzzle has two parts: why does (1) have an authoritative reading, and why does (3) not have an authoritative reading? The most prominent and successful solution to this puzzle, as far as we are aware, is due to Penka (2014). She takes at most to be the oddity in this puzzle, and she solves it by decomposing at most into a negative component, ANT, plus at least, and giving (1) a split-scope analysis: ANT three scopes above allow, which in turn scopes above at least (hence, the scope of at most three is ‘split’). (4) a. at most three ANT + three + at least b. ANT three [λ n [allowed [at least n [λ m you draw m cards]]]] c. ∀n.n > 3 → ¬ ⟐ [≥ n] (Penka, 2014) (≡ ¬ ⟐ [≥ 4]) On this account, the literal meaning of (1) immediately entails an UB; FC then follows from neoGricean reasoning, given certain assumptions about the Horn scales responsible for generating alternatives. Together, these ingredients solve the first half of the puzzle. The second half is solved simply because at least has no analogous decomposition: parsing (3) with surface scope (allow > at least three) or with inverse scope (at least three > allow) leads only to an ignorance reading, not to a LB authoritative reading. (See Penka’s paper for details.) 2. New observations Penka’s (2014) proposal attributes the contrast between at most, which gives rise to authoritative readings, and at least, which doesn’t, to a special property of at most, namely that it’s composed of a negative part, ANT three, that can take scope separately from its remainder, at least. We 3. There are a number of proposals for how to derive ignorance readings (e.g. Geurts and Nouwen, 2007; Büring, 2008; Nouwen, 2010; Coppock and Brochhagen, 2013; Nouwen, 2015; Schwarz, 2016). Our point here is that whichever one of these accounts one adopts, the prediction is that parsing (1) with at most three taking scope above allow will necessarily derive only an ignorance reading (not an authoritative reading) by whatever mechanism the account assumes is responsible for (2). 4. One might think that an authoritative reading of (3) is somehow ‘blocked’ due to competition with the more natural and straightforward sentence You’re required to draw at least three cards. We discuss (and provide arguments against) this idea in §4.3. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 234 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals now show that a variety of expressions, beyond just at most, give rise to authoritative readings, including both members of certain other antonym pairs.5 To start, (5) has a natural authoritative reading characterized by a LB inference (the catering premises may not open earlier than 5:00 AM) and a FC inference (they may open at 5:00 AM and at any time later than that). (5) The catering premises may open at the earliest at 5:00 AM. Similarly, (6) has a natural authoritative reading characterized by an UB inference (deductions may not occur later than the time of submission) and a FC inference (they may occur at the time of submission and at any time earlier than that). (6) Deductions may occur at the latest at the time of submission. Thus, unlike at least and at most, both of at the earliest and at the latest give rise to authoritative readings.6 Furthermore, other numeral modifiers besides at most can have authoritative construals. For example, (7), with between three and seven, has both a LB inference (the Speaker is not allowed to appoint fewer than three MPs, maybe because that one or those two MPs would hold too much power) and an UB inference (the Speaker is not allowed to appoint more than seven MPs, maybe because that would give, overall, too much power to too many MPs), as well as a FC inference (the Speaker is allowed to appoint any number of MPs in the range [3,7]). (7) The Speaker is allowed to appoint between three and seven MPs to exercise his powers to issue recess writs when he is out of the country. What’s more, we find cases where at least actually does give rise to a LB authoritative reading, e.g. when conjoined with at most. For instance, (8c) conveys that the guild may not have fewer than three members, nor more than 100, and that it may have any number of members in the range [3,100]. (8) a. You’re allowed to nominate at least two and at most four authors this week! b. Each bidder is allowed to bid for at least five lots and at most fifteen lots. c. The guild may have at least three and at most 100 members. Finally, we note the robust contrast in (9). In particular, while at least in (9a) cannot be construed authoritatively, in (9b) it can be: if you choose to write a paper, then you’re not allowed to write fewer than three pages (LB inference), and you’re allowed to write exactly three, four, . . . pages (FC inference). 5. The examples in (5–8) come from Google and the Wikipedia corpus. 6. One potentially important difference between at least/most and at the earliest/latest is the presence of the definite determiner the in the latter. We’re unsure exactly what role the plays here, but we observe that adding the to at least surprisingly improves sentences intended to be interpreted authoritatively: (The rules state that) you’re allowed to draw three cards at the least, though not perfect, sounds much better to our ears than (3). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 235 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (9) The syllabus states that . . . a. # You’re allowed to write at least three pages. b. You’re allowed to (either) give a presentation or (else) write at least three pages. The LB authoritative uses of at least noted above are prima facie evidence against a decompositional account of the puzzle, i.e. an account that solves the puzzle by attributing a special property to at most. Moreover, the availability of authoritative readings for both members of antonym pairs like at the earliest and at the latest casts doubt on a decompositional explanation of the asymmetry between at least and at most. For example, while it’s possible to decompose at the earliest into something like ‘not earlier than’ and to decompose at the latest into something like ‘not later than’, doing so would undermine the explanation of the contrast between at least and at most: why not decompose at least into ‘not fewer than’?7 Finally, extending the decompositional account to non-superlative expressions would require some rather ad hoc syntactic assumptions: between three and seven would need to decompose into something like ‘not fewer than three and not more than seven’. It’s unclear to us how such an approach would proceed, nor how conceptually appealing it would be. Before concluding this section, it’s important to establish that, just like for (1), an inversescope analysis of the above examples would not account for their authoritative readings. The reason is because, just like for at most, when at the earliest, at the latest, between, and at least . . . and at most do not occur in the scope of an operator like allow, as in the examples in (10), ignorance readings obligatorily emerge, and consequently, an inverse-scope analysis would predict ignorance inferences across the board.8 7. To be more precise, the meaning of ANT, for Penka (2014), encodes the relation >: ANT d D (D a predicate of degrees) means ¬∃d ′ .d ′ > d ∧ d ′ ∈ D. Presumably, this could be extended to at the latest, where > would refer not to the ‘greater than’ ordering over degrees, but to the ‘later than’ ordering over points (or intervals) of time: ANT t T (T a predicate of points of time) would mean ¬∃t ′ .t ′ > t ∧t ′ ∈ T . However, using ANT to decompose at the earliest wouldn’t work; for that, one would need a different expression that involves the ‘earlier than’ relation, <. Call it ANT< . The point now is that one would need a principled explanation why at least does not decompose into something involving ANT< , which would lead to LB authoritative readings for sentences like (3). In other words, one would need to explain why at least is exceptional in this regard. 8. That between obligatorily implies ignorance (like superlative modifiers) is debatable. For instance, in his influential article on modified numerals, Nouwen (2010) classifies at least and at most as class B modifiers (they obligatorily imply ignorance when unembedded), but he classifies between (in contrast to from . . . to) as class A. However, Nouwen does not devote any detailed discussion to between, and we think that it patterns a lot like superlative modifiers, e.g., when it comes to Nouwen’s hexagon example: ⎧ more than three/fewer than eleven ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ #at least four/at most ten (i) A hexagon has ⎨ ⎬ sides. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ #between four and ten ⎩ ⎭ Nevertheless, as Benjamin Spector points out to us, there may still be some truth to the notion that the potential ignorance inferences associated with between are more fragile than those associated with superlative modifiers. If so, then an inverse-scope analysis of examples like (7) might be possible after all. However, one would still need to account for the rest of our new observations. Instead, we hope to show that all the observations can be subsumed under a single account. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 236 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (10) a. Bill arrived at the earliest (latest) at 8:00 AM. b. The Speaker appointed between three and seven MPs to excercise his powers to issue recess writs when he is out of the country. c. Cindy nominated at least two and at most four authors. The take-home message is that it’s not at most which is the oddity in this puzzle, nor is it at least, per se. Rather, it’s more specifically at least in just some sentences, like (3), but not (8c) or (9b). We therefore want to try to analyze all the above cases uniformly, without proposing that at most or any other expression has any special (non-standard) morphosyntax. 3. Proposal 3.1. Free-choice disjunction Our starting point is to highlight some striking similarities between authoritative readings of at most in the scope of allow and FC readings of disjunction in the scope of allow.9 Specifically, disjunction in the scope of an existential modal like allow licenses similar FC and ‘bound’ inferences. For example, in a context where the relevant desserts are cake, gelato, and pie, (11) licenses two inferences: (i) you’re not allowed to have pie (a kind of ‘bound’ inference, in the sense that, as far as desserts go, you’re bound to the set {cake, gelato}), and (ii) you’re allowed to have cake, and you’re allowed to have gelato (a FC inference) (von Wright, 1969; Kamp, 1973).10 However, similar to what we saw for (1), a surface-scope analysis of (11) predicts a weak literal meaning, ‘There is a permissible world in which you have cake or gelato’ (⟐c ∨ g), from which neither a ‘bound’ inference (¬ ⟐ p) nor a FC inference (⟐c ∧ ⟐g) logically follows. (11) You’re allowed to have cake or gelato. An influential account of FC disjunction is due to Fox (2007), who proposes that the meaning of (11) is a strengthened version of the weak surface-scope meaning ⟐(c ∨ g). Strengthening is due to the presence of a grammatical device, exh, a covert analog of only that is responsible for scalar implicatures (Chierchia et al., 2012). What exh S means is that S is true and that each ‘innocently excludable’ member of alt(S) (the set of alternatives of S) is false, where, intuitively, a proposition q ∈ alt(S) is innocently excludable (relative to ⟦S⟧) just in case the negation of q doesn’t contradict ⟦S⟧ and also doesn’t force any disjunction of members of alt(S) to be true (unless that disjunction is already entailed by ⟦S⟧).11 (12) ⟦exh S⟧ = ⟦exh⟧(alt(S))(⟦S⟧), where ⟦exh⟧(A)(p) = p ∧ ⋀{¬q ∶ q ∈ IE(p,A)}, and IE(p,A) = ⋂ {A′ ∶ A′ is a maximal subset of A s.t. {p} ∪ {¬q ∶ q ∈ A′ } is consistent} 9. Comparing superlative modifiers with disjunction is by no means a novel idea. Büring’s (2008) landmark paper established an exciting line of inquiry into how to analyze the ignorance inferences associated with at least and at most by building on well-understood accounts of the ignorance inferences associated with or. However, to our knowledge, no one has extended this line of inquiry to analyze authoritative construals of allow . . . at most along the same lines as that of FC construals of allow . . . or. 10. There is, potentially, a third inference, viz. that you’re not allowed to have both cake and gelato (¬ ⟐ (c ∧ g)). We ignore this exclusivity inference henceforth, as there is no detectable analog to it when it comes to modified numerals (it’s logically impossible to, e.g., draw exactly two cards and exactly three cards). 11. We write ‘q is IE (relative to p and A)’ to mean q ∈ IE(p,A), and we omit ‘relative to p and A’ when it’s clear from context. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 237 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals For example, suppose that alt(John ate cake or gelato) = {c ∨ g, c, g, c ∧ g} (Sauerland, 2004; Fox, 2007). Then, relative to c ∨ g, neither c nor g is IE: negating c would force g to be true, and conversely, negating g would force c to be true. (While it’s consistent with c ∨ g to negate c or to negate g, the intuition is that we can’t arbitrarily pick which of c or g to negate; thus, we don’t negate either one.) However, c ∧ g is IE, and so ⟦exh [John ate cake or gelato]⟧ = (c∨g)∧¬(c∧g), i.e. the proposition that John ate cake or gelato but not both, which corresponds to the exclusive interpretation of ordinary disjunction. Crucially, recursive application of exh is predicted to be possible. In a simple case like above, additional applications are vacuous, but when disjunction occurs in the scope of allow, recursive exhaustification is not vacuous and in fact delivers precisely the attested FC reading. To see this, consider the LF in (13). Let’s start with the constituent exh S, and assume that alt(S) = {⟐(c ∨ g), ⟐c, ⟐g, ⟐p}.12 Then, relative to ⟦S⟧ and alt(S), we see that ⟐p is IE, but neither ⟐c nor ⟐g is IE: negating ⟐c would force ⟐g to be true, and vice versa. Thus, ⟦exh S⟧ = ⟐(c ∨ g) ∧ ¬ ⟐ p, the proposition that there is a permissible world in which you have cake or gelato, and no permissible world in which you have pie. Thus, the inner exh immediately derives the ‘bound’ inference (pie is not allowed), but not the FC inferences. (13) exh [exh [S allowed [you have cake or gelato]]] Let’s move now from exh S to the entire sentence, exh exh S. Assume, along with Fox (2007), that alt(exh S) is the set of strengthened alternatives to S. (14) alt(exh S) = {⟦exh⟧(alt(S))(p) ∶ p ∈ alt(S)} Computing alt(exh S) requires computing ⟦exh⟧(alt(S))(p) for each p ∈ alt(S). This is given below. ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ (15) alt(exh S) = ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⟦exh⟧(alt(S))(⟐(c ∨ g)), ⟦exh⟧(alt(S))(⟐c), ⟦exh⟧(alt(S))(⟐g), ⟦exh⟧(alt(S))(⟐p) ⎫ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬=⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎪ ⎩ ⟐(c ∨ g) ∧ ¬ ⟐ p, ⟐c ∧ ¬ ⟐ g ∧ ¬ ⟐ p, ⟐g ∧ ¬ ⟐ c ∧ ¬ ⟐ p, ⟐p ∧ ¬ ⟐ c ∧ ¬ ⟐ g ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ Having computed alt(exh S), we are now in a position to compute ⟦exh⟧(alt(exh S))(⟦exh S⟧), i.e. ⟦exh [exh S]⟧. It’s the conjunction of ⟦exh S⟧ (computed above as ⟐(c ∨ g) ∧ ¬ ⟐ p) and the negation of all innocently excludable alternatives of exh S, i.e. the negation of the members of some subset of (15). Which subset? The answer is alt(exh S) − {⟦exh S⟧}, i.e. every proposition except the strengthened meaning of S is IE. Thus, the overall meaning is ⟦exh S⟧ conjoined with the negation of each of these alternatives. We give the negations of all the propositions in (15) below, but for clarity’s sake, we write them as material implications.13 12. We could also include the alternative ⟐(c ∧ g), which would turn out to be IE, and its negation would deliver the exclusivity inference mentioned in fn. 10. 13. This is licit because ¬(p ∧ ¬q ∧ ¬r) ≡ p → (q ∨ r). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 238 B. Buccola & A. Haida (16) a. b. c. d. A surface-scope analysis of authoritative readings of modified numerals ⟐(c ∨ g) → ⟐p ⟐c → (⟐g ∨ ⟐p) ⟐g → (⟐c ∨ ⟐p) ⟐p → (⟐c ∨ ⟐g) (contradicts ⟦exh S⟧) (already entailed by ⟦exh S⟧) Putting all the pieces together, the meaning of exh exh S is ⟐(c ∨ g) ∧ ¬ ⟐ p (the strengthened meaning of S, i.e. ⟦exh S⟧), plus the conjunction of the material implications ⟐c → (⟐g ∨ ⟐p) and ⟐g → (⟐c ∨ ⟐p). Some reflection reveals that these implications, together with ⟦exh S⟧, are equivalent to ⟐c and ⟐g.14 Thus, the overall meaning derived is the following, which is precisely the reading we wanted to derive. (17) ⟦exh [exh [S allowed [you have cake or gelato]]]⟧ = ⟐(c ∨ g) ∧ ¬ ⟐ p ∧⟐c ∧ ⟐g ´¹¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹¶ ² ´¹¹ ¹ ¹ ¹ ¹ ¹¸¹ ¹ ¹ ¹ ¹ ¹ ¶ weak meaning ‘bound’ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ FC (≡ ⟐c ∧ ⟐g ∧ ¬ ⟐ p) strengthened meaning ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ recursively strengthened meaning Our proposal in a nutshell. Given the inferential (and syntactic) similarity between (1) (You’re allowed to draw at most three cards) and (11) (You’re allowed to have cake or gelato), our goal is to provide a surface-scope analysis of (1), whereby its weak meaning is recursively strengthened as we just saw for FC disjunction. More precisely, we propose that (1) is parsed with two applications of exh, which results in an authoritative reading, as schematized in (18). (18) ⟦exh [exh [S allowed [you draw at most three cards]]]⟧ = ⟐[≤ 3] ∧¬ ⟐ [≥ 4] ∧⟐[= 3] ∧ ⟐[= 2] ∧ ... ´¹¹ ¹ ¹ ¸¹ ¹ ¹ ¹¶ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹¶ weak meaning UB ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ FC strengthened meaning ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ recursively strengthened meaning The clear similarities between (17) and (18) may give the impression that a solution to (the first half of) the puzzle is straightforward. However, as we hope to show, although there is a solution in sight, it ultimately requires a conservative, but non-trivial amendment to the theory of exhaustification. We therefore proceed in three steps: first, we present what seems like a straightforward account and show the problem it faces; second, we propose an ad hoc amendment that fixes the problem; finally, we show that our amendment can be generalized in a non-stipulative way. 14. More precisely: ⟐ (c ∨ g) ∧ ¬ ⟐ p ∧ (⟐c → (⟐g ∨ ⟐p)) ∧ (⟐g → (⟐c ∨ ⟐p)) ≡ (⟐c ∨ ⟐g) ∧ ¬ ⟐ p ∧ (⟐c → (⟐g ∨ ⟐p)) ∧ (⟐g → (⟐c ∨ ⟐p)) ≡ (⟐c ∨ ⟐g) ∧ ¬ ⟐ p ∧ (⟐c → ⟐g) ∧ (⟐g → ⟐c) ≡ (⟐c ∨ ⟐g) ∧ ¬ ⟐ p ∧ ⟐c ∧ ⟐g ≡ ⟐c ∧ ⟐g ∧ ¬ ⟐ p Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 239 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals 3.2. At most: first attempt To achieve our goal, it’s necessary (and sufficient) to show that the sets of alternatives alt(S) and alt(exh S) derived by standard means (e.g. Katzir, 2007; Fox and Katzir, 2011) deliver the right results. Demonstrating this is difficult because of the space of possible alternative sets; however, we believe that the following characterization is plausible: alt(S) is the set of propositions obtained by replacing at most with fewer than, exactly, at least or more than, plus those obtained by replacing three with any numeral, plus those obtained by doing both replacements simultaneously. Thus, we assume the following equality.15 {⟐[< n] ∶ n ∈ N0 } ∪ {⟐[≤ n] ∶ n ∈ N0 } {⟐[≤ n] ∶ n ∈ N0 } (19) alt(S) = ∪ {⟐[= n] ∶ n ∈ N0 } = ∪ {⟐[= n] ∶ n ∈ N0 } ∪ {⟐[≥ n] ∶ n ∈ N0 } ∪ {⟐[≥ n] ∶ n ∈ N0 } ∪ {⟐[> n] ∶ n ∈ N0 } The first step is to compute ⟦exh S⟧ = ⟦exh⟧(alt(S))(⟦S⟧). All alternatives of the form ⟐[= n] and ⟐[≥ n], for n ≥ 4, are IE. As a result, we negate all such alternatives, which immediately derives our UB. Moreover, alternatives that ‘overlap’ with (are compatible with) ⟐[≤ 3], e.g. ⟐[≥ 1], ⟐[≤ 2], and ⟐[= 2], are not IE; for instance, negating ⟐[= 2] would entail the disjunction ⟐[= 0] ∨ ⟐[= 1] ∨ ⟐[= 3]. So the first round of exhaustification delivers the following result. (20) ⟦exh⟧(alt(S))(⟐[≤ 3]) = ⟐[≤ 3] ∧ ¬ ⟐ [= 4] ∧ ¬ ⟐ [≥ 4] ∧ ¬ ⟐ [= 5] ∧ ¬ ⟐ [≥ 5] ∧ ... ≡ ⟐[≤ 3] ∧¬ ⟐ [≥ 4] ´¹¹ ¹ ¹ ¸¹ ¹ ¹ ¹¶ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ weak meaning UB ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ strengthened meaning Turning now to the recursive layer of exhaustification, let’s continue to assume, with Fox (2007), that alt(exh S) is the set of strengthened alternatives to S, repeated below from (14). (14) alt(exh S) = {⟦exh⟧(alt(S))(p) ∶ p ∈ alt(S)} The hope is that we now derive the desired FC inferences: ⋀{⟐[= n] ∶ n ∈ N0 ∩ [0,3]}. However, it turns out that the FC we derive is too weak. To see why, we first need to compute alt(exh S). (21) alt(exh S) = {⟦exh⟧(alt(S))(⟐[= n]) ∶ n ∈ N0 } {⟐[= n] ∧ ¬ ⟐ [< n] ∧ ¬ ⟐ [> n] ∶ n ∈ N0 } ∪ {⟦exh⟧(alt(S))(⟐[≤ n]) ∶ n ∈ N0 } = ∪ {⟐[≤ n] ∧ ¬ ⟐ [> n] ∶ n ∈ N0 } ∪ {⟦exh⟧(alt(S))(⟐[≥ n]) ∶ n ∈ N0 } ∪ {⟐[≥ n] ∧ ¬ ⟐ [< n] ∶ n ∈ N0 } Next, we must determine which members of alt(exh S) are IE relative to ⟦exh S⟧ = ⟐[≤ 3] ∧ ¬ ⟐ [≥ 4]. As before, we list all the negations as material implications. 15. We assume here that the equivalences ⟐[< n] ≡ ⟐[≤ (n − 1)] and ⟐[> n] ≡ ⟐[≥ (n + 1)] hold, i.e. that the relevant scale of numbers operative in (1) is the natural numbers. However, we believe that assuming a dense scale, as proposed by Fox and Hackl (2006), would not alter our main results. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 240 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (22) a. {⟐[= n] → (⟐[< n] ∨ ⟐[> n]) ∶ n ∈ N0 } b. {⟐[≤ n] → ⟐[> n] ∶ n ∈ N0 } c. {⟐[≥ n] → ⟐[< n] ∶ n ∈ N0 } (contradicts ⟦exh S⟧ when n ≥ 3) (contradictory when n = 0) We see that all the strengthened exactly n alternatives are IE, all the strengthened at most n alternatives for n < 3 are IE (but not for n ≥ 3), and all the strengthened at least n alternatives for n > 0 are IE (but for n ≥ 4, ⟦exh S⟧ already entails their negation). Putting all the pieces together, the meaning of exh exh S is ⟐[≤ 3] ∧ ¬ ⟐ [≥ 4] (the strengthened meaning of S, i.e. ⟦exh S⟧), plus the conjunction of the material implications below. (23) a. {⟐[= n] → (⟐[< n] ∨ ⟐[> n]) ∶ n ∈ N0 } b. {⟐[≤ n] → ⟐[> n] ∶ n ∈ N0 ∩ [0,2]} c. {⟐[≥ n] → ⟐[< n] ∶ n ∈ N0 ∩ [1,∞)} Some reflection reveals that these inferences, together with ⟐[≤ 3] ∧ ¬ ⟐ [≥ 4], are equivalent to ⟐[= 0] and ⟐[= 3]. In other words, the FC inference we derive for (1) is that you’re allowed to draw 0 cards and you’re allowed to draw exactly 3 cards, which is weaker than what we were hoping to derive: we’re missing the inferences ⟐[= 1] and ⟐[= 2]. We take it that this result is incorrect.16 3.3. At most: second attempt Intuitively, the problem we just encountered is that the members of alt(exh S) are too strong, hence their negation results in inferences that are too weak. What we need is for alt(exh S) to include weaker alternatives, whose exclusion will result in stronger inferences, namely total FC.17 Our idea is that the set of alternatives for the second exh includes not just all strengthened propositions taken from alt(S); rather, it includes all strengthened alternatives taken from the disjunctive closure of alt(S), notated as alt(S)∨ . (For now, this is just a stipulation; in the next subsection, show that if we assume that sets of alternatives are always closed under disjunction, we retain our main result for recursive exhaustification without disrupting cases of non-recursive exhaustification.) (24) alt(exh S) = {⟦exh⟧(alt(S))(p) ∶ p ∈ alt(S)∨ } (cf. (14)) By allowing p in (24) to range over propositions taken from the disjunctive closure of alt(S), we introduce weaker alternatives into alt(exh S), whose exclusion turns out to derive total FC. To see this, let p = ⟐[= 0] ∨ ⟐[= 1] ∨ ⟐[= 3]. p is not in alt(S), but it is in alt(S)∨ . ⟦exh⟧(alt(S))(p), which is now in alt(exh S), is equal to p ∧ ¬ ⟐ [= 2] ∧ ¬ ⟐ [≥ 4]. This strengthened alternative is 16. What we derive is a kind of partial FC, which is stronger than the partial FC that Penka (2014) derives (cf. fn. 2), and weaker that the total FC that we want to derive. In the oral talk version of this material, we assumed for simplicity that only the exactly alternatives were active, and we showed that this derives an even weaker FC inference than what we derive here: namely, that there are (at least) two distinct numbers m and n in [0,3] such that ⟐[= m] and ⟐[= n]. Again, we take this result to be incorrect. 17. This method is not a guaranteed recipe for deriving stronger inferences overall: the addition of weaker alternatives could instead introduce new symmetries (in the sense of Fox (2007)), which would result in fewer inferences overall. (Thanks to Emmanuel Chemla for stressing this point to us.) However, our amendment turns out not to do this, but instead has the desired effect. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 241 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals IE relative to alt(exh S) and ⟦exh S⟧. Its negation, which is equivalent to p → (⟐[= 2] ∨ ⟐[≥ 4]), and ⟦exh S⟧, which is ⟐[≤ 3] ∧ ¬ ⟐ [≥ 4], jointly entail ⟐[= 2]. Extrapolating from this example, we see that we derive ⟐[= n] for every n ∈ N0 ∩ [0,3], just as desired. Thus, the overall meaning derived for (1) is: (25) ⟦exh⟧(alt(exh S))(⟦exh⟧(alt(S))(⟦S⟧)) = ⟐[≤ 3] ∧¬ ⟐ [≥ 4] ∧⟐[= 3] ∧ ⟐[= 2] ∧ ⟐[= 1] ∧ ⟐[= 0] ´¹¹ ¹ ¹ ¸¹ ¹ ¹ ¹¶ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ weak meaning UB ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶ FC strengthened meaning ´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹¸¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹¶ recursively strengthened meaning 3.4. Generalizing the amendment Instead of stipulating something special about how alt(exh S) is computed, we now show that our amendment can be generalized in a simple way: for any sentence S, we take alt(S) to be closed under disjunction. Formally, if alt′ (S) is the set of usual alternatives of S, e.g. those derived by the algorithm proposed by Fox and Katzir (2011), then alt(S) = alt′ (S)∨ . The meaning of exh is the same as before, as given in (12), and in particular still refers to alt(S); it’s just that alt(S) has been updated to be closed under disjunction. Importantly, for a non-recursive occurrence of exh, this amendment makes no difference, in the sense that we don’t derive stronger inferences than before. For instance, assume, for some sentence S, that alt′ (S) includes p and q but not p ∨ q. Exhaustifying S now involves potentially excluding p ∨ q, since this proposition is in alt(S). However, excluding p ∨ q is possible (p ∨ q is IE) if and only if excluding both p and q is possible (p and q are both IE). And in turn, excluding p ∨ q is logically equivalent to excluding both p and q. Thus, we don’t gain anything at this level: either p and q are both IE, in which case so is p ∨ q, and negating the former is equivalent to negating the latter; or p and q are not both IE, in which case p ∨ q is not IE, and not negating both p and q is equivalent to not negating p ∨ q. (See also Spector (2017).) The effect only surfaces for recursive exh, and here’s why. The overall meaning is of exh exh S is: (26) ⟦exh⟧(alt(exh S))(⟦exh⟧(alt(S))(⟦S⟧)) Again following Fox (2007), alt(exh S) is the set of strengthened alternatives of S,18 but now we get something different from before our pre-amendment set in (14). What we get is precisely what we stipulated earlier, in (24), except now we derive it as a consequence of closing all alternative sets under disjunction. 18. Whether this set, too, is closed under disjunction doesn’t matter: closing it under disjunction doesn’t result in any additional inferences, for the same reason that closing the usual alternative set under disjunction for nonrecursive exhaustification doesn’t matter. (At least, this is true for double exhaustification. It could, in principle, matter for triple exhaustification, i.e. for a sentence of the form exh exh exh S, but we don’t pursue this line of inquiry here.) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 242 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (27) alt(exh S) = {⟦exh⟧(alt(S))(p) ∶ p ∈ alt(S)} = {⟦exh⟧(alt′ (S)∨ )(p) ∶ p ∈ alt′ (S)∨ } = {⟦exh⟧(alt′ (S))(p) ∶ p ∈ alt′ (S)∨ } = (24) Finally, we note that closing the alternative set under disjunction allows us to assume that for (1), alt′ delivers just the exactly alternatives, and this is because any at least or at most alternative can be written as a disjunction of exactly alternatives. ∨ ⎛ {⟐[≤ n] ∶ n ∈ N0 } ⎞ (28) alt(S) = ⎜ ∪ {⟐[= n] ∶ n ∈ N0 } ⎟ = {⟐[= n] ∶ n ∈ N0 }∨ ⎝ ∪ {⟐[≥ n] ∶ n ∈ N0 } ⎠ We don’t claim this is in fact what alt′ does, but making this assumption will simplify discussion of other examples in §4.2. 4. Discussion 4.1. Free-choice disjunction revisited Importantly, our amendment doesn’t disrupt the analysis of FC disjunction like (11) (You’re allowed to have cake or gelato). The reason is because, in this case, closing the alternative set under disjunction doesn’t add any new IE alternatives. For example, if, as we assumed earlier, alt′ (S) = {⟐(c ∨ g), ⟐c, ⟐g, ⟐p}, then alt(S) is as follows, where the underlined alternatives are those that we gain (relative to before) by closing the set of alternatives under disjunction:19 ⟐c, ⟐g, ⟐p ∨ ⎧ ⎪ ⎪ ⎪ ⟐c, ⟐g, ⟐p, ⟐(c ∨ g), ⟐(c ∨ p), ⟐(g ∨ p) (29) alt(S) = { } =⎨ ⟐(c ∨ g) ⎪ ⎪ ⎪ ⟐(c ∨ g ∨ p) ⎩ ⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ (30) alt(exh S) = ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ For the first round of exhaustification, none of the three new alternatives are IE, and so ⟦exh S⟧ is still ⟐(c ∨ g) ∧ ¬ ⟐ p. For the second round, we compute alt(exh S). ⟦exh⟧(alt(S))(⟐c), ⟦exh⟧(alt(S))(⟐g), ⟦exh⟧(alt(S))(⟐p), ⟦exh⟧(alt(S))(⟐(c ∨ g)), ⟦exh⟧(alt(S))(⟐(c ∨ p)), ⟦exh⟧(alt(S))(⟐(g ∨ p)), ⟦exh⟧(alt(S))(⟐(c ∨ g ∨ p)) ⎫ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬=⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎪ ⎩ ⟐c ∧ ¬ ⟐ g ∧ ¬ ⟐ p, ⟐g ∧ ¬ ⟐ c ∧ ¬ ⟐ p, ⟐p ∧ ¬ ⟐ c ∧ ¬ ⟐ g, ⟐(c ∨ g) ∧ ¬ ⟐ p, ⟐(c ∨ p) ∧ ¬ ⟐ g, ⟐(g ∨ p) ∧ ¬ ⟐ g, ⟐(c ∨ g ∨ p) The negations of all the members of alt(exh S) are provided below. As before, we write the negations of all the conjunctive alternatives as material implications. 19. Note that for any two propositions p and q, ⟐p ∨ ⟐q ≡ ⟐(p ∨ q). We use the latter form in the following set. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 243 B. Buccola & A. Haida (31) a. b. c. d. e. f. g. A surface-scope analysis of authoritative readings of modified numerals ⟐c → (⟐g ∨ ⟐p) ⟐g → (⟐c ∨ ⟐p) ⟐p → (⟐c ∨ ⟐g) ⟐(c ∨ g) → ⟐p ⟐(c ∨ p) → ⟐g ⟐(g ∨ p) → ⟐c ¬ ⟐ (c ∨ g ∨ p) (already entailed by ⟦exh S⟧) (contradicts ⟦exh S⟧) (contradicts ⟦exh S⟧) Previously, we saw that (a–b), together with ⟦exh S⟧, amount to the FC inferences ⟐c and ⟐g. Now, in addition to those, there are three potential new inferences, (e–g); however, (e) and (f), together with ⟦exh S⟧, again amount to ⟐c and ⟐g, and (g) contradicts ⟦exh S⟧. Overall, then, no new inferences are derived relative to what we derived earlier. 4.2. New observations revisited Our account extends naturally to all the new data introduced in §2. We just have to assume that the relevant exactly alternatives are available. (Other alternatives may also be available, but recall that, since we take the set of alternatives to be closed under disjunction, the exactly alternatives already generate the complete set that we’re interested in; therefore, we ignore those alternatives in what follows.) For example, the alternative set of (6) (Deductions may occur at the latest at the time of submission) must include the (meanings of) alternatives of the form Deductions may occur at (exactly) t, for some t in the set of points of time T . (32) alt(6) = {⟐[= t] ∶ t ∈ T }∨ This set is exactly the same as what we assumed for the alternative set of (1), except now we have points of time t instead of natural numbers n, and so it’s no surprise that the results here will be the same. In particular, the first round of exhaustifying the meaning of (6) (⟐[≤ time.of.submission]) will exclude all exactly alternatives involving times later than the time of submission, since those alternatives are all IE, while the second (recursive) round will derive FC inferences regarding all exactly alternatives involving times equal to or earlier than the time of submission. Similarly, let’s assume the exact same set of alternatives for (5) (The catering premises may open at the earliest at 5:00 AM). Then, in a completely parallel way, the first round of exhaustifying the meaning of (5) (⟐[≥ 5:00 AM]) will exclude all exactly alternatives involving times earlier than 5:00 AM, since those alternatives are all IE, while the second (recursive) round will derive FC inferences regarding all exactly alternatives involving times equal to or later than 5:00 AM. Finally, we turn to (7) (The Speaker is allowed to appoint between three and seven MPs), and assume the set of alternatives below. The first round of exhaustifying the meaning of (7) (⟐[3,...,7]) will exclude all exactly alternatives involving numbers less than 3 or more than 7, since those alternatives are all IE (this derives both a LB and an UB), while the second (recursive) round will derive FC inferences regarding all exactly alternatives involving numbers in the range [3,7]. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 244 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (33) alt(7) = {⟐[= n] ∶ n ∈ N0 }∨ Examples like (8c) (The guild may have at least three and at most 100 members) can be analyzed in the same way. 4.3. Open problem The reader has by now probably noticed that our account also predicts a LB authoritative reading for sentences like (3) (You’re allowed to draw at least three cards). The reason why we derive such a reading is essentially the same as the reason why we derive the attested reading of (5) (The catering premises may open at the earliest at 5:00 AM): recursive exhaustification excludes exactly alternatives with numbers below 3, and derives FC regarding all exactly alternatives with numbers greater than or equal to 3. This prediction is only partially correct. Recall the contrast in (9), repeated below. (9) The syllabus states that . . . a. # You’re allowed to write at least three pages. b. You’re allowed to (either) give a presentation or (else) write at least three pages. Unfortunately, we still have no explanation for this contrast, or more generally why at least only sometimes has a LB authoritative reading. A tempting explanation for why (3) has no LB authoritative reading is that it’s somehow ‘blocked’ by the more natural, straightforward, and seemingly equivalent sentence with required, given in (34). One rationale would be that, all else being equal, it’s more economical to use require than to use allow with recursive exhaustification. (34) You’re required to draw at least three cards. However, we’re doubtful whether a coherent and convincing story along these lines can be told, and here’s why: (3) (on what would be its LB authoritative reading) and (34) are not completely equivalent. Given the infelicity of using (3) authoritatively, this non-equivalence is hard to detect, but we can observe a clear contrast when we move to between. Specifically, (35a), on its authoritative reading, says nothing about whether the speaker is required to appoint any MPs at all; in fact, it seems to imply that not appointing any MPs at all is a possibility (it’s just that, if the Speaker decides to appoint some number of MPs, that number must fall in the range [3,7]). By contrast, (35b) clearly excludes the possibility of not appointing any MPs. (35) a. The speaker is allowed to appoint between three and seven MPs. b. The speaker is required to appoint between three and seven MPs. We can highlight the contrast even further with the minimally different pair of examples in (36). In particular, if one of the laws of Absurdistan is (36a), then presumably you won’t be breaking the law if you have no children; it’s just that, if you have children, then the number of children you have must not exceed three. By contrast, if the law is (36b), then anyone (of child-bearing age, etc.) without children is a criminal. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 245 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (36) a. In Absurdistan, you’re allowed to have between one and three children. b. In Absurdistan, you’re required to have between one and three children. The point here is that a sentence of the form allow . . . [m,n], on its authoritative reading, is not in general equivalent to required . . . [m,n] (on its strengthened, FC reading): specifically, for m > 0, the allow sentence says nothing about the ‘zero’ case, whereas the required sentence explicitly excludes it, as the between examples above illustrate. Moreover, for m = 0, judgments are clear that the resulting allow and require sentences are not only both felicitous, but also equivalent to one another, which is unexpected under a blocking account.20 (37) a. In Absurdistan, you’re allowed to have between zero and three children. ⇔ b. In Absurdistan, you’re required to have between zero and three children. 3 (38) a. Abstracts may be at most three pages long. ⇔ b. Abstracts must be at most three pages long. 3 3 3 Thus, a blocking account of the infelicity of an authoritative use of (3) that relies on semantic equivalence between the blocking sentence, (34), and the blocked sentence, (3), cannot be right, for two reasons: (3) and (34) are not actually equivalent, and cases of actual equivalence, e.g. (37a) and (37b), and (38a) and (38b), do not in fact give rise to blocking effects.21 4.4. Concluding remarks We showed that authoritative readings of sentences like (1), (7), and many others can be accounted for by assuming that their weak, surface-scope meanings are recursively strengthened in the same way that weak meanings of disjunctive permission sentences like (11) are. We conclude by addressing an important question raised by our analysis. We assumed that FC inferences are total, not partial (cf. fn. 2), and our amended system of recursive exhaustification delivers exactly this. However, there are clear cases where FC is not total. For example, (39) is a perfectly coherent two-sentence discourse, but a blind application of our proposal predicts it to be contradictory: the second sentence should entail, e.g., that you’re allowed to draw exactly five cards, which contradicts the first sentence. 20. Parallel observations arise even for FC disjunction. For instance, compare (11) (You’re allowed to have cake or gelato), which of course does not entail that you must have a dessert, and You’re required to have cake or gelato, which does. In addition, You’re allowed to have cake or gelato or neither and You’re required to have cake or gelato or neither are both intuitively equivalent, but the require sentence does not block the allow sentence. 21. Because we assume that exactly n alternatives include exactly 0 alternatives (n ranges over the set N0 , which includes 0), our account does exclude the ‘zero’ cases for sentences like (7). However, this issue can be resolved simply by assuming that a numeral like three cannot be replaced by zero, an assumption that doesn’t seem too far-feteched, given the odd nature of zero compared to all other numerals. Note that taking this route would then mean that the authoritative reading of (1), with at most, does not actually entail the possibility of drawing zero cards, but is nonetheless compatible with such a state of affairs. We think that this result is adequate and that the inference that drawing zero cards is possible (to the extent that it’s available) is either a contextual entailment or an implicature. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 246 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals (39) You’re required to draw an even number of cards. You’re allowed to draw at most ten cards. We think that our account is compatible with such observations, once we acknowledge that relevance considerations can restrict what counts as an alternative (Fox and Katzir, 2011), and/or that alternatives may, under certain conditions, be ‘pruned’ (Crnič et al., 2015). In this particular case, one effect of the first sentence is to rule out exactly n alternatives where n is odd. However, as intuitive as this resolution may appear, it must be constrained in certain ways. For example, FC regarding the numeral mentioned in the sentence seems to always be available, which suggests that the corresponding exactly alternative must always be active. Witness the oddity of the two-sentence discourse in (40): the second sentence implies that you’re allowed to draw exactly nine cards, which contradicts the first sentence. (40) #You’re required to draw an even number of cards. You’re allowed to draw at most nine cards. An obvious line to pursue is to say that if a numeral n is mentioned, then the exactly n alternative is relevant and cannot be pruned. Independent support for this approach comes from FC disjunction: each disjunct, because it’s explicitly mentioned, must be a possibility, as the oddity of the following discourse illustrates.22 (41) #You’re required to eat only green vegetables (non-green vegetables are not allowed). You’re allowed to eat broccoli, spinach, or red cabbage. References Büring, D. (2008). The least at least can do. In C. B. Chang and H. J. Haynie (Eds.), West Coast Conference on Formal Linguistics (WCCFL), Volume 26, Somerville, MA, pp. 114–120. Cascadilla Proceedings Project. http://www.lingref.com/cpp/wccfl/26/paper1662. pdf. Chierchia, G., D. Fox, and B. Spector (2012). Scalar implicature as a grammatical phenomenon. In C. Maienborn, K. von Heusinger, and P. Portner (Eds.), Semantics: An International Handbook of Natural Language Meaning, Volume 3, pp. 2297–2331. Berlin, Germany: Mouton de Gruyter. Coppock, E. and T. Brochhagen (2013). Raising and resolving issues with scalar modifiers. Semantics and Pragmatics 6(3), 1–57. https://doi.org/10.3765/sp.6.3. Crnič, L., E. Chemla, and D. Fox (2015). Scalar implicatures of embedded disjunction. Natural Language Semantics 23, 271–305. https://doi.org/10.1007/s11050-015-9116-x. Fox, D. (2007). Free choice and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and Implicature in Compositional Semantics, Palgrave Studies in 22. An important caveat: the parallelism drawn here is not perfect. In the case of FC disjunction, the non-prunable (obligatorily relevant) alternative is derived by replacing the full disjunction with a single disjunct (one of the ones mentioned); in the case of (40), the non-prunable alternative is derived by replacing at most with exactly. In some sense, the former case in more natural, insofar as the lexical material required for the alternative is fully present in the utterance (thus, the appeal to ‘mentioning’ is sensible), whereas in the latter case, it’s not (exactly was not mentioned). However, both cases involve structural manipulation of the uttered sentence, and so from a formal perspective, there’s little distinction between the two. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 247 B. Buccola & A. Haida A surface-scope analysis of authoritative readings of modified numerals Pragmatics, Language and Cognition Series, Chapter 4, pp. 71–120. New York, NY: Palgrave Macmillan. https://doi.org/10.1057/9780230210752_4. Fox, D. and M. Hackl (2006). The universal density of measurement. Linguistics and Philosophy 29(5), 537–586. https://doi.org/10.1007/s10988-006-9004-4. Fox, D. and R. Katzir (2011). On the characterization of alternatives. Natural Language Semantics 19(1), 87–107. https://doi.org/10.1007/s11050-010-9065-3. Geurts, B. and R. Nouwen (2007). At least et al.: The semantics of scalar modifiers. Language 83(3), 533–559. http://www.jstor.org/stable/40070901. Kamp, H. (1973). Free choice permission. In Proceedings of the Aristotelian Society, Volume 74, pp. 57–74. http://www.jstor.org/stable/4544849. Katzir, R. (2007). Structurally-defined alternatives. Linguistics and Philosophy 30(6), 669–690. https://doi.org/10.1007/s10988-008-9029-y. Nouwen, R. (2010). Two kinds of modified numerals. Semantics and Pragmatics 3(3), 1–41. https://doi.org/10.3765/sp.3.3. Nouwen, R. (2015). Modified numerals: The epistemic effect. In L. Alonso-Ovalle and P. Menéndez-Benito (Eds.), Epistemic Indefinites: Exploring Modality Beyond the Verbal Domain, Oxford Linguistics, Chapter 11, pp. 244–266. Oxford, England: Oxford University Press. Penka, D. (2014). At most at last. In E. Csipak and H. Zeijlstra (Eds.), Sinn und Bedeutung, Volume 19, pp. 463–480. http://nbn-resolving.de/urn:nbn:de:bsz:352-0-304168. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy 27(3), 367–391. https://doi.org/10.1023/B:LING.0000023378.71748.db. Schwarz, B. (2016). Consistency preservation in Quantity implicature: The case of at least. Semantics and Pragmatics 9(1), 1–47. https://doi.org/10.3765/sp.9.1. Spector, B. (2017). Comparing exhaustivity operators. Semantics and Pragmatics 9. https: //doi.org/10.3765/sp.9.11. von Wright, G. H. (1969). An Essay on Deontic Logic and the Theory of Action. Amsterdam, Netherlands. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 248 The Vietnamese perfect1 Thuy BUI — University of Massachusetts Amherst Abstract. The paper seeks to advance understanding of cross-linguistic variation in the semantics of tense and aspect by investigating the distribution and interpretation of the temporal marker da in Vietnamese. The study first explores the possibility of accounting for such a marker as an optional past tense. By testing this hypothesis against empirical data, this paper argues that da is neither a referential nor a quantificational past tense, but a perfect marker in Vietnamese. The second part of the paper provides a formal analysis of da. Based on da’s interaction with different adverbial phrases, this study suggests that da behaves similarly to the German perfect rather than the English perfect. The discussion relates directly to recent approaches to other languages and offers data from a superficially tenseless language to the discussion on the cross-linguistic semantic variation in ‘perfect puzzle.’ Keywords: tense, aspect, Vietnamese. 1. Introduction Vietnamese lacks obligatory overt tense morphology. Out of the blue, finite matrix clauses with temporally unmarked verbs are compatible with past and present temporal reference, and their viewpoint aspect is perfective, as illustrated in (1): (1) Boba lam viec cho Jabba. Boba do work for Jabba ‘Boba works / worked for Jabba.’ There is nonetheless a temporal marker that one may be tempted to describe as a tense: da. As shown in (2), if da appears in the sentence in (1), that sentence appears to receive a past interpretation: (2) Boba da lam viec cho Jabba. Boba DA do work for Jabba ‘Boba worked / had worked for Jabba.’ The goal of this paper is to explore the meaning of da and its contribution to the temporal interpretation of Vietnamese clauses. The organization of the paper is as follows. In Section 2, I present the background framework for tense and aspect, the basic data for Vietnamese temporal expressions, as well as the semantic proposed for superficially tenseless languages. Then, in Sections 3 and 4, I focus on the puzzle concerning past interpretations in Vietnamese, and show that da is neither a referential nor a quantificational past tense, respectively. Section 5 discusses cross-linguistic variation in the ‘perfect puzzle,’ and demonstrates that da behaves 1 For their helpful advice and extended discussions on this topic, I would like to thank Seth Cable and Barbara Partee. I am also grateful to the participants of the UMass Semantics Workshop as well as the audience at Sinn und Bedeutung 21 for their insightful comments. Particular thanks go to Alex Göbel and Ai Taniguchi for providing judgements for German and Japanese, respectively. Responsibility for shortcomings rests with me. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 249 T. Bui The Vietnamese perfect more similarly to the German perfect than the English one. Then, in Section 6, I propose a formal analysis of the perfect marker da, and demonstrate how the proposed semantics captures certain key facts. Section 7 concludes the paper. 2. Formal semantic and linguistic background 2.1. The framework Tense and aspect are conceptualized in the framework of Reichenbach (1947) and Klein (1994). Following Reichenbach (1947), this paper assumes a three-way distinction between the utterance time (UT), the reference time (RT), and the event time (ET): (3) a. b. c. UT: The time at which the sentence is uttered. ET: The time for which the predicate holds of the subject. RT: The time about which the claim is made. Furthermore, following Klein (1994), this paper assumes tense express a relation between the RT and the UT. In particular, while past tense encodes the precedence relation between the two (RT < UT), present tense locates the RT at the UT (RT = UT), and future tense locates the RT after the UT (RT > UT). In contrast, aspect morphology contributes information regarding the relationship between the RT and the ET. An aspect is perfective when the ET is included within the RT (ET ⊂ RT). On the other hand, an aspect is imperfective when the inclusion relation between the ET and the RT is reversed (RT ⊂ ET). Moreover, this study presumes the pronominal approach to the semantics of tense provided in Kratzer (1998). In this framework, the Tense (T) head, which is of type i, is proposed to be sister to the Aspect Phrase (A SP P), which denotes a property of times. As a result, the whole Tense Phrase (TP) denotes a proposition, as illustrated in (4) below: (4) The Syntax for Tense and Aspect in English (Kratzer, 1998): TP hs, ti T A SP P hii hi, hs, tii 2.2. Temporal reference in Vietnamese Given that there is no obligatory grammaticalized expressions that impose constraints on the temporal relation between the RT and the UT in Vietnamese, one may be tempted to describe Vietnamese as a superficially tenseless language. Bare verb sentences describe events that are located before or at the UT. When uttered out of the blue, such sentences are only compatible with present or past frame adverbials, as illustrated in (5): Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 250 T. Bui (5) The Vietnamese perfect Hom qua / Bay gio / #Ngay mai Chewie bay den Endor. yesterday / now / tomorrow Chewie fly to Endor ‘Chewie flew / flies to Endor yesterday / now / #tomorrow.’ Following Matthewson’s (2006) analysis of Lillooet, the non-future temporal reference observed in the Vietnamese sentences in (1) and (5) will be assumed to be contributed by a phonologically empty NONFUT tense morpheme whose semantics is shown in (6): (6) The Semantics for Tense in Superficially Tenseless Sentences (Matthewson, 2006): J NONFUTi Kg, c is only defined if g(i) ≤ tc If defined, J NONFUTi Kg, c = g(i) Under Matthewson’s (2006) analysis, the example in (5) is translated by the formula in (7): (7) J (5) Kg, c = λ w ∃e [ fly-to-Endor(e)(w) & agent(Chewie)(e)(w) & τ(e) ⊆ g(i) ] (where g(i) < tc ) ‘There is an event e of Chewie flying to Endor, whose flying τ is included in the contextually salient past time g(i).’ The semantics correctly predicts that superficially tenseless sentences like (5) are compatible only with past or present time reference. In consequence of this semantic restriction, future time reference in Vietnamese must always be marked overtly with the marker se, which will not be addressed in the discussion of this paper. 3. Not a referential past 3.1. Referential tense hypothesis Duffield’s (2007) study on the syntax of Vietnamese clausal structure claims that Vietnamese expresses assertion independently of tense or aspect. While he does not focus on the semantics of tense and aspect in Vietnamese, he does propose that Vietnamese is not a tenseless language, and that da is a past tense whose marking is almost always optional, which contrasts with the obligatory presence of tense morphology in English. According to Duffield (2007), Vietnamese tense morphemes, including da, have the same syntactic distribution as English ones, but are without the assertion (A SR) component associated with English finite auxiliaries. As a result, Duffield (2007) suggests that the tense morphemes in Vietnamese occupy the Tense node, with lexical verbs remaining in vP, as illustrated below: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 251 T. Bui (8) The Vietnamese perfect The Syntax for Tense in Vietnamese (Duffield, 2007): TP A SR P T da N EG khong A SR vP [+ NEG] [+ EMPH] [−WH] If da is an optional past tense morpheme realized as a Tense head, then it is expected to restrict the temporal reference of a sentence to be past. In this case, da requires the RT to temporally precede the evaluation time (E VALT), which is the UT in matrix clauses. Then, under the view in which Vietnamese has a referential tense system, the semantics of a temporally unmarked verb (∅) should be similar to (9a), while that of da should be like (9b): (9) The Semantics for Referential Tenses in Vietnamese: a. b. J ∅ K = J PRESi Kw, t, g, c = [ λ Phi, ti : ∃t’ . t’ = t & P(t’) = T ] ‘There is a time t’ such that t’ equals the E VALT t and P is true at t’.’ J DA K = J PSTi Kw, t, g, c = [ λ Phi, ti : ∃t’ . t’ < t & t’ ∈ g(i) & P(t’) = T ] ‘There is a time t’ such that t’ is before the E VALT t and within the interval g(i), and P is true at t’.’ This semantics explains the difference in meaning between (1) and (2). Since da imposes a precedence relation between the RT and the E VALT, it plays a role in excluding the present time reference from the matrix clause in (2). Despite the fact the analysis seems to provide a satisfactory record for the contrast in (1) and (2), it still fails to account for many other data points in the language. By showing the behavior of da in the sequence of tense constructions in Vietnamese, I argue against the claim that da is a referential past tense marker. 3.2. Embedded da in complement clauses Firstly, when the main verb in the matrix clause and the embedded verb in the complement clause are both temporally unmarked (Unmarked-under-Unmarked), the sentence appears to be ambiguous, allowing for either a simultaneous or a back-shifted reading, as illustrated in (10): (10) Unmarked-under-Unmarked in Vietnamese Complement Clauses: a. Nam 1980 Obi-Wan ∅ noi la Luke ∅ song o Tatooine luc do. year 1980 Obi-Wan ∅ say that Luke ∅ live on Tatooine time that ‘In 1980, Obi-Wan said that Luke lived on Tatooine then.’ (Lit.: ‘In 1980, Obi-Wan says / said that Luke lives / lived on Tatooine then.’) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 252 T. Bui The Vietnamese perfect b. Nam 1980 Obi-Wan ∅ noi la Luke ∅ song o Tatooine nam 1977. year 1980 Obi-Wan ∅ say that Luke ∅ live on Tatooine year 1977 ‘In 1980, Obi-Wan said that Luke lived on Tatooine in 1977.’ (Lit.: ‘In 1980, Obi-Wan says / said that Luke lives / lived on Tatooine in 1977.’) This is one of the cases showing that the presence of da is not obligatory in Vietnamese clauses. Both the matrix and the embedded clauses can obtain the past readings with a temporally unmarked verb. Furthermore, the event in the embedded clause can be anchored at the matrix time as well as any point of time before that. This contrasts to the behaviors of referential tenses in English, as illustrated in the case of Present-under-Present sentences like (11) below: (11) Present-under-Present in English Complement Clauses: a. *In 1980, Obi-Wan says that Luke lives on Tatooine then. b. *In 1980, Obi-Wan says that Luke lives on Tatooine in 1997. When both of the the matrix and the embedded verbs denote present tense, the sentences are unacceptable whether the embedded time is located at or prior to the matrix time. The same behavior also shows when a past tense morpheme is embedded under a present tense matrix verb, as illustrated below: (12) Past-under-Present in English Complement Clauses: a. *In 1980, Obi-Wan says that Luke lived on Tatooine then. b. *In 1980, Obi-Wan says that Luke lived on Tatooine in 1997. In this case, whenever the matrix time happens before the UT in English, the matrix verb cannot be in present tense. Secondly, Vietnamese sentences in which an unmarked verb is embedded in a complement clause under da, which appears in the matrix clause, (Unmarked-under-Da), also allow for either a simultaneous or a back-shifted reading, as shown in (13): (13) Unmarked-under-Da in Vietnamese Complement Clauses: a. b. Nam 1980 Obi-Wan da noi la Luke ∅ song o Tatooine luc do. year 1980 Obi-Wan DA say that Luke ∅ live on Tatooine time that ‘In 1980, Obi-Wan said that Luke lived on Tatooine then.’ (Lit.: ‘In 1980, Obi-Wan said that Luke lives / lived on Tatooine then.’) Nam 1980 Obi-Wan da noi la Luke ∅ song o Tatooine nam 1977. year 1980 Obi-Wan DA say that Luke ∅ live on Tatooine year 1977 ‘In 1980, Obi-Wan said that Luke lived on Tatooine in 1977.’ (Lit.: ‘In 1980, Obi-Wan said that Luke lives / lived on Tatooine in 1977.’) (13) shows that when da appears in the matrix clause, a temporally unmarked verb in the embedded clause can still locate the event of Luke living on Tatooine at or prior to the past matrix time. In contrary to the flexibility shown in the Vietnamese data, it is unacceptable for Present-under-Past sentences in English to have a present tense embedded verb when the ET denoted in the embedded clause occurs before the UT: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 253 T. Bui (14) The Vietnamese perfect Present-under-Past in English Complement Clauses: a. *In 1980, Obi-Wan said that Luke lives on Tatooine then. b. *In 1980, Obi-Wan said that Luke lives on Tatooine in 1997. However, in English complement clauses, the interpretation of a past tense morpheme under another past tense morpheme (Past-under-Past) is ambiguous between a simultaneous reading and a back-shifted reading (Ogihara and Sharvit, 2012), as indicated in (15) below: (15) Past-under-Past in English Complement Clauses: a. b. In 1980, Obi-Wan said that Luke lived on Tatooine then. In 1980, Obi-Wan said that Luke lived on Tatooine in 1977. Similarly, in Hebrew, a language that makes use of referential tenses like English, Past-UnderPast sentences also allow for simultaneous readings (Ogihara and Sharvit, 2012), as shown in (16) below: (16) Past-under-Past in Hebrew Complement Clauses: Han xasav se Leia ahava oto az. Han thought that Leia loved him then ‘Han thought that Leia loved him then.’ If da behaves like a referential past tense, Da-under-Da sentences in Vietnamese should also allow simultaneous readings like the Past-under-Past ones in English and Hebrew. Nevertheless, in Vietnamese, sentences in which da is embedded under another da (Da-under-Da) never allows for a simultaneous reading, as shown in (17): (17) Da-under-Da in Vietnamese Complement Clauses: a. *Nam 1980 Obi-Wan da noi la Luke da song tren Tatooine luc do. year 1980 Obi-Wan DA say that Luke DA live on Tatooine time that ‘In 1980, Obi-Wan said that Luke lived on Tatooine then.’ b. Nam 1980 Obi-Wan da noi la Luke da song tren Tatooine nam 1977. year 1980 Obi-Wan DA say that Luke DA live on Tatooine year 1977 ‘In 1980, Obi-Wan said that Luke lived on Tatooine in 1977.’ A da embedded under another da in complement clauses always forces a back-shifted reading. This fact suggests that da does not behave similarly to the referential past tenses in English and Hebrew. As a result, the possibility of da being a referential past tense is ruled out. The behavior of da in embedded contexts is further investigated with the sequence of tense cases observed in relative clauses. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 254 T. Bui The Vietnamese perfect 3.3. Embedded da in relative clauses Similarly to the Unmarked-Under-Unmarked cases in complement clauses, sentences in which unmarked verbs are present in both the matrix clause and the relative clause allow for either a simultaneous or back-shifted reading, as shown in (18): (18) Unmarked-under-Unmarked in Vietnamese Relative Clauses: a. b. Nam 1980 Obi-Wan ∅ gap mot nguoi ∅ song o Tatooine luc do. year 1980 Obi-Wan ∅ meet one person ∅ live on Tatooine time that ‘In 1980, Obi-Wan met a person who lived on Tatooine then.’ (Lit.: ‘In 1980 Obi-Wan meets / met a person who lives / lived on Tatooine then.’) Nam 1980 Obi-Wan ∅ gap mot nguoi ∅ song o Tatooine nam 1977. year 1980 Obi-Wan ∅ meet one person ∅ live on Tatooine year 1977 ‘In 1980, Obi-Wan met a person who lived on Tatooine in 1977.’ (Lit.: ‘In 1980 Obi-Wan meets / met a person who lives / lived on Tatooine in 1977.’) Likewise, sentences in which an unmarked verb is embedded in a relative clause under a matrix verb marked with da are also ambiguous, allowing for either a simultaneous or back-shifted interpretation, as illustrated in (19): (19) Unmarked-under-Da in Vietnamese Relative Clauses: a. b. Nam 1980 Obi-Wan da gap mot nguoi ∅ song o Tatooine time that. year 1980 Obi-Wan DA meet one person ∅ live on Tatooine time that ‘In 1980, Obi-Wan met a person who lived on Tatooine then.’ (Lit.: ‘In 1980, Obi-Wan met a person who lives / lived on Tatooine then.’) Nam 1980 Obi-Wan da gap mot nguoi ∅ song o Tatooine year 1977. year 1980 Obi-Wan DA meet one person ∅ live on Tatooine year 1977 ‘In 1980, Obi-Wan met a person who lived on Tatooine in 1977.’ (Lit.: ‘In 1980, Obi-Wan met a person who lives / lived on Tatooine in 1977.’) The key fact shown in (19) is that Vietnamese allows a simultaneous reading, even when da appears in the matrix clause. This is where an important difference between English and Vietnamese manifests itself. In particular, in English relative clauses, the availability of a simultaneous reading of the present depends on the matrix tense (Ogihara and Sharvit, 2012). In Present-under-Past sentences, a matrix past blocks a simultaneous reading, as in (20): (20) Present-under-Past in English Relative Clauses: a. *In 1980, Obi-Wan met a person who lives on Tatooine then. b. In 1980, Obi-Wan met a person who lives on Tatooine now. The fact that an indexical reading is allowed in (20b) shows that the time of the embedded event is required to overlap the present. In Vietnamese, however, such restriction does not exist in the relative clauses. Moreover, this availability of simultaneous readings of ∅-under-Da sentences in Vietnamese, a superficially tenseless language, shares parallels to the patterns observed in Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 255 T. Bui The Vietnamese perfect Japanese, a tensed language. In particular, Japanese sentences in which a past tense morpheme in a relative clause in embedded under a present tense matrix verb also allows for both the simultaneous and indexical readings, as demonstrated in (21): (21) Present-under-Past in Japanese Relative Clauses: a. b. 1980-nen-ni Obi-Wan-wa Tatooine-ni sono-toki sun-deiru hito-ni 1980-year-DAT Obi-Wan-TOP Tatooine-DAT that-time live-PRES person-DAT at-ta. meet-PST ‘In 1980, Obi-Wan met a person who lived on Tatooine then.’ (Lit.: ‘In 1980, Obi-Wan met a person who lives on Tatooine then.’) 1980-nen-ni Obi-Wan-wa Tatooine-ni genzai sun-deiru hito-ni 1980-year-DAT Obi-Wan-TOP Tatooine-DAT now live-PRES person-DAT at-ta. meet-PST ‘In 1980, Obi-Wan met a person who lives on Tatooine now.’ The behavior of the embedded da in relative clauses once again shows that da does not behave like the English past, further supporting the claim that da is not a referential past tense. However, the embedded da in Vietnamese appears to share similarities with the embedded past tense in Japanese. This pattern then raises a possibility that tenses in Vietnamese behave like those in Japanese. If this is the case, then it is plausible for da to be argued to function similarly to a quantificational past tense. 4. Not a quantificational past 4.1. Quantificational tense hypothesis If tenses in Vietnamese behave like those in Japanese, then they are ambiguous, and may get quantificational interpretations (Ogihara and Sharvit, 2012). In particular, one can assume that unmarked verbs are by default interpreted in the present, and thus can have similar semantics to Japanese present tense. Meanwhile, since da is more temporally marked than an unmarked verb, past temporal reference is more strongly preferred. As a result, under this quantificational tense approach, the semantics of temporally unmarked verbs as well as da in Vietnamese is as follows: (22) The Semantics for Quantificational Tenses in Vietnamese: a. b. J ∅ K = J PRES Kw, t, g, c = [ λ Phi, ti : [ λ t’ : ∃t” . t” = t’ & P(t”) = T ] ] ‘There is a time t” such that t” equals the time t’ and P is true at t”.’ J DA K = J PST Kw, t, g, c = [ λ Phi, ti : [ λ t’ : ∃t” . t” < t’ & P(t”) = T ] ] ‘There is a time t” such that t” is before the time t’ and P is true at t”.’ In this case, the quantificational tenses in (23) are of type hhi, ti, hi, tii. In movement of quantificational tense, the lambda created by movement is λ t. Moreover, the trace of movement is [t*], which always denotes E VALT. In other words, J t* Kw, t, g, c equals t. Then, the sentence Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 256 T. Bui The Vietnamese perfect in (19a) has the Logical Form (LF) structure as well as the predicted truth conditions as follows: (23) In 1980, Obi-Wan met a person who lives / lived on Tatooine then. a. t* DA λt t* Obi-Wan gap ‘meet’ mot.nguoi ‘a.person’ 2 b. ∅ t2 song.o.Tatooine ‘live.on.Tatooine’ J (19a) Kw, t, g, c = ∃t’ . t’ < t & ∃x . x is a person in w & x lives on Tatooine in w at t’ & Obi-Wan meets x in w at t’. ‘There is a time t’ such that t’ is before the time t, and there is an x such that x is a person in world w, and x lives on Tatooine in w at t’, and Obi-Wan meets x in w at t’.’ The semantics of da as a quantificational past tense correctly predicts that the UnmarkedUnder-Da cases in Vietnamese relative clauses should allow for a simultaneous reading. This analysis further rejects the hypothesis that da is a referential past tense. In this case, the function of da has now been narrowed down to be either that of a quantificational past tense or a perfect. I then argue that da is not a quantificational tense, since not only does da is shown to have the ability to arrange events in a sequence but it also felicitously appears in future contexts. 4.2. Event ordering When it comes to arranging events in a sequence, the presence of da is mandatory. As demonstrated in (24) below, da puts one event further into the past than the other. In particular, when it is uttered in the scenario described in (24), (24a) is infelicitous because it denotes that the two events occur simultaneously. On the other hand, (24b) is felicitous because da puts the event of R2-D2 fixing C-3PO before the event of Lando entering the room. (24) Context: Lando walks into the room, and he finds R2-D2 standing next to a newly repaired C-3PO. a. #Lando di vao phong. Chewie sua C-3PO. Lando walk into room Chewie fix C-3PO ‘Lando walked into the room. Chewie fixed C-3PO.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 257 T. Bui The Vietnamese perfect b. Lando di vao phong. Chewie da sua C-3PO. Lando walk into room Chewie DA fix C-3PO ‘Lando walked into the room. Chewie had fixed C-3PO.’ In this case, the first sentence, which has a NONFUT tense, sets up the RT for the next sentence. Da then requires the second sentence to be interpreted within the past of the event of the first sentence. Then, da appears to function similarly to a perfect marker. Furthermore, the fact that the presence of da is acceptable in cases like (25) provide further evidence supporting the claim that da is a perfect rather than a tense. (25) Lando di vao phong luc 2 gio. Den 2 gio 15 phut, R2-D2 da sua C-3PO. Lando walk into room at 2 hour. By 2 hour 15 minute R2-D2 DA fix C-3PO ‘Lando walked into the room at 2. By 2:15, R2-D2 had fixed C-3PO.’ In (25), the first sentence does not set up the RT for the sentence that follows it. In fact, it is the temporal adverbials den 2 gio 15 phut ‘by 2:15’ that sets up the RT for the second sentence. Given that da can combine with this adverbial phrase, it suggests that da does not pick out one particular point of time in the past. Rather, da contributes an interval of time running from one salient point in the past up until 2:15. Then, the possibility of da being a quantificational tense has been ruled out. 5. The ‘present perfect’ puzzle 5.1. Modification by ‘yesterday’ In English, the present perfect is not compatible with specific past time adverbs like ‘yesterday’ (Pancheva and von Stechow, 2004), as demonstrated in (26) below: (26) Luke: “Why is Yoda tired?” a. Obi-Wan: “He trained hard yesterday.” b. Obi-Wan: *“He has trained hard yesterday.” c. Obi-Wan: #“He had trained hard yesterday.” In the scenario in which Luke asks a question like the one in (26), the only acceptable answer that Obi-Wan can utter is (26a). Since the question is put in present tense, it sets up the present time reference for the whole discourse. Since there is no past time in the discourse to impose a pluperfect interpretation, (26c) is infelicitous when uttered in this context. Meanwhile, even though the present perfect does not encounter such problem, the sentence in (26b) is still illformed. This problem in English, which arises due to the incompatibility between the present perfect and adverbs like ‘yesterday’, has been discussed in the literature as the ‘present perfect puzzle’. In order to account for the unacceptability in cases like (26b), Pancheva and von Stechow (2004) proposes three main ingredients, which are the Perfect Time Span (PTS), the perfect aspect (PERF), and the semantics for ‘yesterday’, as illustrated below: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 258 T. Bui (27) The Vietnamese perfect The ingredients for the ‘present perfect puzzle’ (Pancheva and von Stechow, 2004): a. b. c. PTS(t’, t) = t is a final subinterval for t’ J PERF Kw, t, g, c = [ λ Phi, ti : [ λ t’ : ∃t” . PTS(t”, t’) & P(t’) ] ] ‘There is a time t” such that t’ is a final subinterval for t” and P is true at t’.’ J yesterday Kw, t, g, c = [ λ t’ : t’ ⊆ the day preceding c(time) ] ‘t’ is a subinterval of the day preceding the context time.’ Then, the LF structure as well as the predicted truth conditions for the sentence in (26b) without the modification of the adverbial phrase ‘yesterday’ are as follows: (28) Yoda trained hard. a. TP hti T A SP1 P hi,.ti PRES A SP1 A SP2 P hi,.ti PERF A SP2 PFV b. Kw, t, g, c VP hε,.ti Yoda train hard = ∃t’ . PTS(t’, c(time)) & ∃e . train(e, w) & Ag(e, w) = Yoda & J (26b) T(e) ⊆ t’ ‘There is a time t’ such that the context time is a final subinterval for t’, and there is an e such that e is an event of training in world w, and the agent of e is Yoda, and the time of e is a subinterval of t’.’ Given the semantics in (27), there is nowhere in (28) that the adverb ‘yesterday’ can be added consistently. In particular, if ‘yesterday’ modifies Asp1 P, its contribution is an internal contradiction, as illustrated in (29): (29) [ ∃t’ . PTS(t’, c(time)) & ∃e . train(e, w) & Ag(e, w) = Yoda & T(e) ⊆ t’ & c(time) ⊆ the day preceding c(time) ] Meanwhile, if ‘yesterday’ modifies Asp2 P, its contribution contradicts the statement that the context time is a final subinterval for t’, as demonstrated in (30): (30) [ ∃t’ . PTS(t’, c(time)) & ∃e . train(e, w) & Ag(e, w) = Yoda & T(e) ⊆ t’ & t’ ⊆ the day preceding c(time) ] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 259 T. Bui The Vietnamese perfect As a result, it is not possible to combine the present perfect with specific past time adverbials in English. However, unlike English, in Vietnamese, a sentence containing da can also contain ‘specific’ past time adverbs like hom qua ‘yesterday,’ as illustrated in (31): (31) Hom qua Yoda da luyen tap cuc kho. yesterday Yoda DA train hard ‘Yoda trained hard yesterday.’ (Lit.: ‘Yoda trained / has trained hard yesterday.’) As discussed above, because the question that Luke asks sets up the present tense for the discourse, da cannot be interpreted as a pluperfect. Consequently, da functions as a present perfect in this case. Therefore, this behavior of da as a perfect marker contrasts what has been observed in the English perfect. Nevertheless, this pattern of da is remarkably similar to the German perfect, as illustrated in (32) below: (32) Yoda hat gestern hart trainiert. Yoda have.3SG.PRES yesterday hard trained.PTCP ‘Yoda trained hard yesterday.’ (Lit.: ‘Yoda has trained hard yesterday.’) Similar to Vietnamese da, the German perfect is also compatible with specific past time adverbials like ‘yesterday.’ This suggests that the ‘present perfect puzzle’ that is present in English and other languages is absent in German and Vietnamese. As a result, da is more alike to the German perfect than the English one. 5.2. Interaction with ‘always’ In English, even when a past tense morpheme co-occurs with the adverb ‘always,’ it still indicates that the event discussed is no longer true at the UT. In contrast, when the present perfect appears with the adverb ‘always,’ it ends up entailing that the state in question still holds at the present (Pancheva, 2004), as demonstrated in (33) below: (33) a. b. Finn always was a Stormtroope. Finn has always been a Stormtrooper. In this case, Finn is no longer a Stormtrooper in (33a). On the other hand, (33b) entails that he is still a Stormtrooper. The semantics for (33a) and (33b) is provided in (34a) and (34b), respectively: (34) a. J (33a) Kw, t, g, c = [ ∃t’ . t’ < c(time) & ∀ t” . t” ∈ t’ → ∃e . Finn-is-aStormtrooper(e, w) & T(e) ⊆ t’ ] ‘There is an interval t’ which completely precedes c(time), every subpart of which contains an eventuality of Finn being a Stormtrooper.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 260 T. Bui The Vietnamese perfect b. J (33b) Kw, t, g, c = [ ∃t’ . PTS(t’, c(time)) & ∀t” . t” ∈ t’ → ∃e . Finn-is-aStormtrooper(e, w) & T(e) ⊆ t’ ] ‘There is an interval t’ which contains c(time), every subpart of which contains an eventuality of Finn being a Stormtrooper.’ The semantics in (34) correctly predicts that (33a) can be followed consistently with the phrase ‘until he ran away from the First Order,’ while (33b) cannot, as illustrated in below: (35) a. Finn always was a Stormtrooper, until he ran away from the First Order. b. *Finn has always been a Stormtrooper, until he ran away from the First Order. On the other hand, besides da’s interaction with ‘yesterday’ discussed earlier, the combination between da and luon ‘always’ shows that the function of da is distinct from that of the English perfect. In particular, when da appears with luon ‘always,’ it does not end up entailing that the state in question also holds at the present, as illustrated in (36): (36) a. b. Finn da luon la Stormtrooper. Finn DA always COP Stormtrooper ‘Finn has always been / had always been / always was a Stormtrooper.’ Finn da luon la Stormtrooper cho den khi no chay khoi First Order. Finn DA always COP Stormtrooper for till when 3SG ran away First Order ‘Finn always was a Stormtrooper until he ran away from the First Order.’ (Lit.: ‘Finn has always been / had always been / always was a Stormtrooper until he runs / ran away from the First Order.’) In (36a), like English, the combination of da as a perfect marker and adverbials like luon ‘always’ entails that the state in question also holds at the present. Nevertheless, unlike what has been observed in the English sentence in (35b), the Vietnamese sentence in (36b) is not ungrammatical at all. In this case, the state in question only holds until the time at which Finn ran away from the First Order. The fact that sentences like (36b) are acceptable further demonstrates that da in Vietnamese behaves more like the German perfect, as shown in (37): (37) Finn ist immer ein Sturmtruppler gewesen bis er vor des Ersten Finn is.3SG.PRES always a Stormtrooper been until he from the First Ordnung wegrannte Order ran-away.3SG.PST ‘Finn always was a Stormtrooper until he ran away from the First Order.’ (Lit.: ‘Finn has always been a Stormtrooper until he ran away from the First Order.’) Based on the interaction of da with different types of adverbs such as hom qua ‘yesterday’ and luon ‘always’, it is shown that if da is indeed a perfect, then it shares similarities to the German perfect rather than the English perfect. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 261 T. Bui The Vietnamese perfect 6. Formal analysis 6.1. Proposal Based on the language data as well as the comparisons with other languages, a formal analysis for the Vietnamese perfect is proposed. Firstly, as for the syntax, a NONFUT tense morpheme occupies the head of the TP, and da is the head of the A SP P, as illustrated below: (38) The Syntax for Tense and Aspect in Vietnamese: TP T NONFUT ∅ λw S UBJ A SP1 P A SP1 A SP2 P A SP2 PERF da VP {PFV} ∅ {IMPFV} dang Secondly, the semantics for da is provided below: (39) The Semantics for the Perfect in Vietnamese: J DA Kw, t, g = [ λ Phi, ti : [ λ t’ : ∃t” . t” ≤ t’ & P(t”) ] ] ‘There is an interval t” that either strictly precedes t’ or has t’ as a final subinterval such that P(t”) = T.’ The proposed semantics captures certain key facts in Vietnamese, including the availability of simultaneous readings with complement clauses, as well as the semantic consequences of interactions with different adverbial phrases. 6.2. Availability of simultaneous readings As mention earlier in the paper, the simultaneous reading can be obtained in Unmarked-underDa in Vietnamese complement clauses, as in (13a). Meanwhile, Da-under-Da sentences like (17a) always forces a back-shifted reading. These crucial cases showing the different temporal interpretations when it comes to sequences of tense in Vietnamese are repeated below: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 262 T. Bui (40) The Vietnamese perfect Nam 1980 Obi-Wan da noi la Luke ∅ song o Tatooine luc do. year 1980 Obi-Wan DA say that Luke ∅ live on Tatooine time that ‘In 1980, Obi-Wan said that Luke lived on Tatooine then.’ b. *Nam 1980 Obi-Wan da noi la Luke da song o Tatooine luc do. year 1980 Obi-Wan DA say that Luke DA live on Tatooine time that ‘In 1980, Obi-Wan said that Luke had lived on Tatooine then.’ a. Under the proposed semantics, the contrast between these two sentences is correctly predicted. In particular, in (40a), a simultaneous reading can be obtained via a de re NONFUT tense. Meanwhile, in (40b), the embedded PERF da places the PTS t’ prior to the E VALT t. The semantics of the embedded clause in (40b) is then proposed to be as follows: (41) J (50b) Kw, t, g, c = [ λ w’ : [ λ t’ : ∃t” . t” ≤ t’ & ∃e . Luke-live-on-Tatooine(e, w’) & T(e) ⊆ t” ] ] ‘There is an interval t” which could completely precede t’, every subpart of which contains an eventuality of Luke living on Tatooine.’ As a result, under this semantics, the state of being a Stormtrooper does not properly overlap the E VALT in sentences like (40b). This means that the semantics proposed for da correctly predicts that it is impossible to get the simultaneous reading when da is embedded in the lower clause. 6.3. Semantic consequences of modification by ‘yesterday’ Furthermore, the proposed semantics can also account for the interaction between da and specific past time adverbials like hom qua ‘yesterday’ (Pancheva, 2004), as shown in cases like (31), repeated as (42) below: (42) Hom qua Yoda da luyen tap cuc kho. yesterday Yoda DA train hard ‘Yoda trained hard yesterday.’ (Lit.: ‘Yoda trained / has trained hard yesterday.’) The syntax for the sentence in (42) without the modification of the adverbial phrase yesterday is as follows: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 263 T. Bui (43) The Vietnamese perfect Yoda has trained hard. TP T NONFUT λw S UBJ Yoda A SP1 P A SP1 da A SP2 P A SP2 VP PFV luyen tap cuc kho ‘trained hard’ With the structure proposed in (43), if the adverbial phrase hom qua ‘yesterday’ modifies A SP1 P, its contribution still leads to an internal contradiction. This is because in matrix clause, the time t equals the context time, as demonstrated in (44): (44) [ ∃t’ . t’ ≤ t & ∃e . train(e, w) & Ag(e, w) = Yoda & T(e) ⊆ t” & t ⊆ the day preceding c(time) ] Nevertheless, if the adverbial phrase (A DV P) hom qua ‘yesterday’ modifies Asp2 P, its contribution is consistent, since it locates the PTS, and so the ET, within the day preceding the context time, as demonstrated in (45) below: (45) [ ∃t’ . t’ ≤ t & ∃e . train(e, w) & Ag(e, w) = Yoda & T(e) ⊆ t” & t’ ⊆ the day preceding c(time) ] Following the logic presented in (45), then the syntax as well as the predicted truth conditions for the sentence in (42) is as follows: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 264 T. Bui (46) The Vietnamese perfect Yoda has trained hard yesterday. a. TP T NONFUT λw S UBJ Yoda A SP1 P A SP1 da A DV P hom qua ‘yesterday’ A SP2 P A SP2 VP PFV b. luyen tap cuc kho ‘trained hard’ J (52) Kw, t, g, c = [ ∃t’ . t’ ≤ t & ∃e. come(e, w) & Ag(e,w) = Yoda & T(e) ⊆ t’ & t’ ⊆ the day preceding c(time) ] ‘There is an interval t’ which could completely precede the context time t by one day, every subpart of which contains an eventuality of Yoda training hard.’ As a result, with the semantics for ‘yesterday’ in (27c), the proposed semantics of da in (39) correctly predicts that the contribution of adverbs like hom qua ‘yesterday’ is consistent. 6.4. Semantic consequences of interaction with ‘always’ Lastly, the proposed semantics of da also captures the fact that the interaction between da and luon ‘always’ does not necessarily entail that the state in question holds at the present. Instead, it can just hold up until some point of time in the past, as shown in cases like (36). Then, the semantics for (36a) is as follows: (47) J (36a) K = [ ∃t’. t’ ≤ t & ∀t” . t” ∈ t’ → ∃e. Finn-is-a-Stormtrooper(e,w) & T(e) ⊆ t’ ] ‘There is an interval t’ which could completely precede the context time t, every subpart of which contains an eventuality of Finn being a Stormtrooper.’ The semantics in (36a) accounts for the fact that the sentence in (36b) does not entail that Finn is a Stormtrooper now. 7. Conclusion In this study, I have investigated the behavior of the morpheme da in both matrix and embedded contexts, and argued that da in Vietnamese functions similarly to neither a referential past tense Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 265 T. Bui The Vietnamese perfect in English nor a quantificational one in Japanese. Then, based on the role it plays in a sequence of events, I have concluded that da in Vietnamese is a perfect marker. Furthermore, after examining da’s interaction with different adverbial phrases, I suggested that da is more alike to the German perfect than the English perfect. This discussion relates directly to recent approaches to other languages such as English or German, and contributes data from Vietnamese to the discussion on the semantic variation on the ‘present perfect puzzle’ across languages. References Duffield, N. (2007). Aspects of Vietnamese clausal structure: Separating tense from assertion. Linguistics 45, 765–814. Klein, W. (1994). Time in Language. London: Routledge. Kratzer, A. (1998). More structural analogies between pronouns and tense. In D. Strolovitch and A. Lawson (Eds.), SALT 8, pp. 92–110. CLC. Matthewson, L. (2006). Temporal semantics in a supposedly tenseless language. Linguistics and Philosophy 29, 673–713. Ogihara, T. and Y. Sharvit (2012). Embedded tenses. In R. Binnick (Ed.), The Oxford Handbook of Tense and Aspect, pp. 638–668. Oxford: OUP. Pancheva, R. (2004). Another perfect puzzle. In V. Chand, A. Kelleher, A. Rodrı́guez, and B. Schmeiser (Eds.), WCCFL 23, pp. 621–634. Cascadilla Press. Pancheva, R. and A. von Stechow (2004). On the present perfect puzzle. In K. Moulton and M. Wolf (Eds.), NELS 34, pp. 469–484. GLSA. Reichenbach, H. (1947). Elements of Symbolic Logic. Berkeley: UCP. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 266 Loose talk, negation and commutativity: A hybrid static-dynamic theory1 Sam CARTER — Rutgers, The State University of New Jersey Abstract. This paper investigates the interaction of phenomena associated with loose talk with embedded contexts. §1 introduces core features associated with the loose interpretation of an utterance and presents a sketch of how to theorise about such utterances in terms of a relation of ‘pragmatic equivalence’. §2 discusses further features of loose talk arising from interaction with ‘loose talk regulators’, negation and conjunction. §§3-4 introduce a hybrid static/dynamic framework and show how it can be employed in developing a fragment which accounts for the data surveyed in §§1-2. Keywords: loose talk, order effects, dynamic semantics, pragmatic equivalence, inexactness, granularity, imprecision, slack regulators, non-literal language use. 1. Introduction: Loose talk phenomena Loose talk is an example of the non-literal use of language. In cases of loose talk, the communicated content of an utterance (i.e., the proposition with which a hearer can be expected to update their doxastic state) deviates from its literal content (i.e., the proposition corresponding to the truth conditions of the utterance). Relatedly, the conditions under which the uttered sentence is true can differ from the conditions under which an utterance of that sentence is felicitous. This paper examines a number of ways in which the communicated content and felicity conditions of loose utterances interact with operators and logical connectives in English. In particular, it is argued that, while sensitive to conversational context, the communicated content of such utterances can be derived compositionally in a dynamic framework and is dependent upon aspects of the lexical meaning of constituent expressions which outstrip their contribution to truth conditions. An utterance of (1) in its specified context can be expected to exhibit loose talk phenomena. (1) The British Library owns 14 million books. Context.1: The interlocutors are trying to determine roughly how many books are owned by a range of major world libraries. Circumstances.1: The British Library owns (approximately) 13,950,000 books.2 In Context.1, the communicated content of (the utterance of) (1) will be a proposition true iff the number of books owned by the British Library falls within some non-trivial interval of 14 million. Whereas the literal content of the utterance will be false if the British Library in fact 1 Thanks to Nick Asher, Simon Charlow, Simon Goldstein, Veronica Gomez-Sanchez, Daniel Hoek, Hans Kamp, Jeff King, Peter Lasersohn, Sven Lauer, Ernie Lepore, Caleb Perl, Kyle Rawlins, Craige Roberts, Mandy Simons, Todd Snider, Stephanie Solt, Matthew Stone and Tim Williamson for invaluable discussion, as well as audiences at NASSLLI’16 and SuB21. 2 British Library thirty-seventh annual report and accounts 2009/10. ⟨https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/247725/0153.pdf⟩ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 267 S. Carter Loose talk, negation and commutativity owns 13,950,000, its communicated content will be true. Similarly, the utterance of (1) in Context.1 and Circumstances.1 appears felicitous, despite the falsehood of its literal content. 1.1. Pragmatic equivalence The degree to which the communicated content of a loose utterance differs from its literal content depends, in part, upon the conversational interests of the interlocutors. In Context.1, since the conversational participants are trying to determine only roughly how many books each major library owns, (1) can be expected to communicate a proposition which is true if it owns 13,950,000 books. In contrast, let Context.2 be a context in which the conversational participants are trying to determine whether the British Library owns more books than the Library of Congress, which owns, say, 13,990,000. In Context.2, the proposition communicated by (1) can be expected to be false. Say that two worlds are pragmatically equivalent at a context iff they do not differ in any way which is relevant to the conversational interests of the interlocutors. For example, at Context.1, a world in which the BL owns 13,950,000 and one in which it owns 14 million will be pragmatically equivalent. In contrast, at Context.2, they will not, since the worlds differ with respect to a state of affairs relevant to the interlocutors’ interests, namely whether the BL owns more books than the Library of Congress. Pragmatic equivalence can be expected to be reflexive and symmetric, but need not be transitive. No world differs from itself in ways which are pragmatically relevant, and if w does not differ from w′ in any way which is pragmatically relevant, then w′ does not differ from w in any way which is pragmatically relevant. However, w may differ from w′′ in ways which are pragmatically relevant, despite being pragmatically equivalent to some w′ which is itself pragmatically equivalent to w′′; pragmatically irrelevant differences can add up to form a pragmatically relevant difference. Given the relation of pragmatic equivalence, we can outline an approach to thinking about the communicated content and felicity conditions of loose utterances of simple sentences such as (1). A loose utterance of a simple sentence φ is felicitous at a context C and world w iff there is some world pragmatically equivalent to w at C at which the literal content of φ is true.3 At any world in which the BL owns 13,950,000 books, a loose utterance of (1) would be felicitous at Context.1, but infelicitous at Context.2. Stated succinctly, a loose utterance of a simple sentence is felicitous iff any difference between the world of utterance and one in which the sentence is true is pragmatically irrelevant. Correspondingly, a loose utterance of a simple sentence φ at a context C and world w communicates the proposition true at all worlds w′ such that there is some world pragmatically equivalent to w′ at which the literal content of φ is true. If determining the number of books owned by major libraries were exhaustive of the conversational interests in Context.1, then (1) might be expected to communicate the proposition that the number of books the BL owns is between 13.5×106 and 14.5×106. Likewise, if determining whether the 3 Strictly speaking, only the left-to-right direction of the biconditional is true, since other conditions on felicity unrelated to loose talk might fail to be satisfied. For present purposes, we can treat the biconditional as embedded under a ceteris paribus clause. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 268 S. Carter Loose talk, negation and commutativity British Library or the Library of Congress owns more books were exhaustive of the conversational interests in Context.2, then (1) might be expected to communicate the proposition that the number of books owned by the BL exceeds 13,990,000. For simple sentences, the truth of φ at a world pragmatically equivalent to the world of utterance appears necessary and sufficient for both the felicitous utterance of φ and the truth of that utterance’s communicated content. However, as §2 demonstrates, the same generalisations cannot be extended to account for the loose utterance of complex constructions. 2. Loose talk: Further data 2.1. LT-regulators As has been noted elsewhere (Lasersohn, 1999; Sauerland and Stateva, 2011; Solt, 2014; a.o.), there exist a range of expressions which function lexically to modify the relation between the communicated and literal contents of loose utterances. Call such expressions loose talk (LT-) regulators.4 The class of LT-regulators can be subdivided into LTstrengtheners (e.g., ‘exactly’ in (2a)) and LT-weakeners (e.g., ‘roughly’ in (2b)). (2) a. b. The British Library owns exactly 14 million books. The British Library owns roughly 14 million books. As Lasersohn notes, in contrast to (1), when uttered in context the communicated contents of sentences like (2a)-(2b) coincide with their literal content (1999: 545). The communicated content of an utterance of (2a) is strictly stronger than (i.e. asymmetrically entails) the communicated content of (1) and the utterance is, intuitively, infelicitous if the BL owns less than 14 million books. In contrast, the literal content of (2b) is strictly weaker than (i.e., asymmetrically entailed by) the literal content of (1), and the utterance is, intuitively, true if the BL owns 13,950,000 books. Stated informally, the effect of the LT-strengthener in (2a) is to assimilate the communicated content of the utterance to its literal content, whereas the effect of the LT-weakener in (2b) is to assimilate the literal content of the utterance to its communicated content.5 Note that ‘exactly’ also appears to have an effect on the truthconditional meaning of numerical determiners, making them ‘upper-bounded’. For present purposes, this effect can be set aside. Note that despite differing in felicity, both (1) and (2a) communicate a literal content which is false in Circumstance.1, regardless of whether the numerical determiner is upper-bounded. Hence the effect of LT-strengtheners on numerical determiners is clearly not exhausted by their truth-conditional contribution. As the contrast between (3a-b) suggests, LT-regulators such as ‘exactly’/‘roughly’ do not function as sentential operators, but rather take sub-clausal complements: 4 Lasersohn uses the terminology ‘slack regulators’ whereas Solt, following Sauerland and Stateva, adopts ‘approximators’. 5 LT-weakeners also appear to have a non-trivial effect on the communicated content of loose talk utterances. For example, the communicated content and felicity of (ia-b) differ: (i) a. ?? The British Library does not own exactly 14 million books, but it does own 14 million. b. The British Library does not own exactly 14 million books, but it does own roughly 14 million. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 269 S. Carter (3) Loose talk, negation and commutativity a. b. Exactly/roughly 100 libraries own 1 million books. 100 libraries own exactly/roughly 1 million books. This suggests that whatever treatment of LT-regulators is developed, it will need to account for the contrast between (3a-b) compositionally, in terms of the difference in constituent structure. In (2a-b), the LT-regulator combines with numerical determiner ‘14 million’.6 However, we can also identify apparent LT-regulators taking quantified DPs (e.g. (4b)), PPs (e.g., (5b)), adjectives/APs (e.g. (6b)), and temporal NPs (e.g. (7b)) as complements. (4) a. b. Everybody likes the new Scorsese film. Absolutely/pretty much everybody likes the new Scorsese film. (5) a. b. The helicopter landed in the centre of the field. The helicopter landed precisely/roughly in the centre of the field. (6) a. b. The bin is full.7 The bin is completely/effectively full. (7) a. b. Katja arrived at 6pm. Katja arrived at exactly/roughly 6pm. Correspondingly, the potential for contrast in felicity between utterances of (4-7a) and (4-7b) suggests that, in appropriate contexts, (4-7a) all permit a loose interpretation. While many of the features of loose talk and LT-regulators addressed above have been discussed in previous work, most notably in Lasersohn (1999), little attention has been paid 6 The ability of ‘exactly’ and ‘roughly’ to combine with numerical determiners as in (3a) might be thought to motivate an analysis on which they take ‘6’ as their complement in (2a-b), before combining with ‘pm’ to form a temporal NP. On this account, ‘exactly’/‘roughly’ could be understood as univocally taking numerical arguments. However, constructions such as (i) demonstrate the possibility of their combining directly with temporal NPs, and suggest that they are equivocal across (3a-b). (i) Katja arrived at exactly/roughly the same time as Jonas. 7 Here I follow Kennedy (2007) and Kennedy and McNally (2005) in assuming that, as constructions such as (i) suggest, absolute gradable adjectives such as ‘full’ require their subject to possess a maximal degree of the relevant property. (i) ??The bin is full but it could be more full. They argue that the possibility of felicitously of predicating such adjectives of subjects with only a close-tomaximal degree of the relevant property then needs to be explained in terms of loose talk. Correspondingly, in (6b) and (ii), ‘completely’ will need to be understood as an LT-regulator rather than a degree modifier. Similar examples with non-gradable adjectives can be constructed (as in (iii)): (ii) The bin is full but it is not completely full. (iii) The result is (effectively) unprecedented, but it is not completely unprecedented. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 270 S. Carter Loose talk, negation and commutativity to their behaviour in complex constructions. §2.2-3 survey novel phenomena involving the interaction of loose talk with negation and conjunction. 2.2. Negation As uttered in context, the communicated content of (1) is asymmetrically entailed by its literal content. This has frequently been taken to be amongst the defining features of loose talk (Lasersohn, 1999; Yablo, 2014; Lauer, 2012; though cf. Davis, 2007: 411). For example, Lauer claims that “loose talk is a phenomenon in which the communicated content is weaker than the semantic content” (p. 389). However, the loose utterances of sentences embedded under negation generate counterexamples to this claim.8 If the communicated content of an utterance of φ is weaker than its literal content, the communicated content of an utterance of ¬φ will be stronger than its literal content. (8) The British Library doesn’t own 14 million books.9 In Context.1, the communicated content of (the utterance of) (8) is a proposition true iff the number of books owned by the BL does not fall within some non-trivial interval of 14 million. Whereas the literal content of the utterance will be true if the library owns 13,950,000 books, its communicated content will, plausibly, be false. Similarly, whereas in Context.1, an utterance of (1) is felicitous despite being false, in the same context, an utterance of (8) will be infelicitous but true. The observed effect of negation suffices to demonstrate that the explanation of communicated content/felicity conditions for loose utterance of simple sentences in terms of literal truth at a pragmatically equivalent world cannot be trivially generalised to the utterance of sentences embedded under negation. There if the BL owns 13,950,000 books, then there is a world pragmatically equivalent at Context.1 to w in which the literal content of (8) is true (since every world is trivially pragmatically equivalent to itself). Nevertheless, under these 8 Not all counter-examples to the claim involve negation, and not all utterances of sentences embedded under negation constitute counter-examples to the claim. The communicated content of loose utterances of sentences such as (ia-b) involving minimal standards gradable adjectives will be strictly stronger than their literal content (in an appropriate context): (i) a. b. The stick is curved. The road is wet. Correspondingly, the communicated content of loose utterances of their negations will be strictly weaker than the literal content. 9 The same effect can be elicited in other constructions which exhibit loose talk phenomena in appropriate contexts: (i) (ii) (iii) (iv) Not everybody likes the new Scorsese film. The helicopter did not land in the centre of the field. The bin is not full. Katja did not arrive at 6pm. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 271 S. Carter Loose talk, negation and commutativity circumstances its utterance would be infelicitous in Context.1 and its communicated content false. 2.3. Commutativity The felicity of loose utterances of certain conjunctive sentence is dependent upon to order of the conjuncts. Whereas (9a) is felicitous in any context in which the LH-conjunct has a true communicated content but a false literal content, (9b) is infelicitous in every context. (9) a. The British Library owns 14 million books, though it does not own exactly 14 million. b. ?? The British Library does not own exactly 14 million books, though it does own 14 million.10 We can describe this phenomenon by saying that conjunction fails to commute with respect to the felicity of loose utterances. The felicity of a loose utterance of φ∧ψ does not entail the felicity of a loose utterance of ψ∧φ. §3, below, introduces a framework in which to theorise about loose talk, employing both a static and dynamic interpretation function. §4 presents a fragment in this framework and shows how it accounts for the phenomena in §2. 3. Dynamic Loose Talk (DLT) 3.1 Overview This section presents a hybrid static-dynamic framework for theorising about loose talk. The primary idea behind the framework is that the lexically encoded meaning of a loose utterance of a sentence is not exhausted by its truth conditions. For example, (1) and (2a) have the same truth conditions, but they differ in total compositional meaning. In addition to explaining the difference in their felicity conditions/communicated content, this difference in meaning can account for the difference in the effect they have in embedded contexts, as demonstrated in (8) and (9a-b). 10 The same effect can be elicited in constructions with LT-regulators taking expressions of different lexical categories: (i) a. Everybody, but not absolutely everybody, likes the new Scorsese film. b. ?? Not absolutely everybody, but everybody, likes the new Scorsese film. (ii) a. The helicopter landed in the centre of the field but it did not land precisely in the centre. b. ?? The helicopter did not land precisely in the centre of the field, but it landed in the centre. (iii) a. The bin is full, but it is not completely full. b. ?? The bin is not completely full, but it is full. (iv) a. Katja arrived at 6pm, but she did not arrive at exactly 6pm. b. ?? Katja did not arrive at exactly 6pm, but she arrived at 6pm. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 272 S. Carter Loose talk, negation and commutativity This idea can be seen as analogous to observations made in dynamic treatments of anaphora (e.g., Kamp, 1981; Heim, 1982, 1983; Roberts, 1989; Groenendijk and Stokhof, 1991a; a.o.), modals (e.g., Veltman, 1996; Roberts, 1989; Groenendijk and Stokhof, 1991b; a.o.) and presupposition (Karttunen, 1973; Heim, 1983; a.o.). For example, on the basis of the contrast between (10a-b), Heim concludes that “the salience-shifting potential of an utterance is not predictable from its truth-conditions and the surrounding circumstances alone” (1982, 22). (10) a. b. I dropped ten marbles and found all of them, except for one. It is probably under the sofa. I dropped ten marbles and found only nine of them. ??It is probably under the sofa.11 That is, in (10a-b) the first sentences of the discourses are truth-conditionally equivalent, but differ in meaning. In the Dynamic Loose Talk (DLT) framework, every utterance of a sentence is treated as playing a dual role: (i.) it expresses a proposition, corresponding to its literal content; and (ii.) it modifies, potentially trivially, the relation of pragmatic equivalence at the context. Since the effect of an utterance on the relation of pragmatic equivalence is not a function of its literal content, it must be included independently as an additional part of the lexically encoded meaning of the sentence uttered.12 A DLT-model contains two interpretation functions: a static interpretation function ⟦⋅⟧, mapping a sentence to its literal content, and a dynamic interpretation function [⋅], mapping it to its effect on a context. The static denotation of a sentence is a proposition – a function from worlds to truth values. The dynamic denotation of a sentence is a context change potential - a function from contexts to contexts. In DLT, a context C is identified with an accessibility relation RC – a relation between worlds. Intuitively, ⟨w,w′⟩∈RC iff w′ is pragmatically equivalent to w in C. Sentences are evaluated in DLT relative to a pair ⟨w,R⟩ consisting of world and accessibility relation. Where ⟦φ⟧(w)=1, we say that φ is true-at-⟨w,R⟩. Where R[φ](w) is non-empty, we say that φ is consistent-at-⟨w,R⟩. Stated alternatively, a sentence is consistent-at-⟨w,R⟩ iff R[φ] – the result of updating R with [φ] – relates w to at least one world. An utterance of φ is held to be felicitous in a conversation C and world w iff φ is consistent-at-⟨w,RC⟩. The communicated content of a sentence φ at R is (the characteristic function of) the set of worlds at which φ is consistent relative to R. 3.2. DLT-models The set Τ of DLT-types is defined recursively from basic types s, e, and t (corresponding to worlds, individuals and truth-values, respectively). 11 Attributed to Partee, p.c., Heim (ibid). Grice’s non-detachability constraint, which states that any content conveyed in a non-conventionalised manner by an utterance must be conveyed by any utterance with the same conventionalised meaning (with a proviso for implicatures generated by Manner) (1975, 43-6), can be seen as articulating this point. 12 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 273 S. Carter Loose talk, negation and commutativity (DEF.1) s, e, and t are DLT-types. If τ,τ′ are DLT-types, then ⟨τ,τ′⟩ is a DLT-type. Nothing else is a DLT-type. A DLT-model ℳ is a tuple consisting of a set 𝒟ℳ of domains of each DLT-type, plus static and dynamic interpretation functions, ⟦⋅⟧ℳ and [⋅]ℳ, which map a set ℒ of expressions into the corresponding domain. Indexation to a model is disregarded where no confusion arises. (DEF.2) ℳ=⟨𝒟, ⟦⋅⟧,[⋅]⟩ is a DLT-model, s.t.: - 𝒟=⋃{𝒟τ: τ∈Τ} - 𝒟s, 𝒟e and 𝒟t are pairwise disjoint non-empty sets. - 𝒟t={0,1}. - 𝒟⟨τ,τʹ⟩= 𝒟τ →𝒟τ′. - ⟦⋅⟧: ℒ→𝒟. - [⋅]: ℒ→𝒟. Contexts are identified with accessibility relations. (DEF.3) Let ⟨s⟨s,t⟩⟩=σ. - R,R′,…∈𝒟σ are accessibility relations. (DEF.4) Where φ∈ℒ is a sentential expression: - ⟦φ⟧∈𝒟⟨s,t⟩ - [φ]∈𝒟⟨σ,σ⟩. The static denotation of a sentential expression φ∈ℒ is a proposition – a function from worlds to truth values. The dynamic denotation of a sentential expression φ∈ℒ is a context change potential (CCP) – a function from accessibility relations R,R′,…∈𝒟σ to accessibility relations. A sentential expression denotes an update iff for some w,R, it returns a non-empty subset of R(w) when the result of applying it to R is applied to w. It denotes a test iff for all w it returns either R(w) or ∅ when the result of applying it to R is applied to w.13 (DEF.5) Where [φ]∈𝒟⟨σ,σ⟩: − [φ] is an update iff ∃R,w: ∅⊂R[φ](w)⊂R(w). − [φ] is a test iff ∀R,w: R[φ](w)=R(w) ∨ R[φ](w)=∅. Truth, ⊨T, and consistency, ⊨C, are defined relative to world,context-pairs. Where w,R⊨Tφ, we say that φ is true-at-⟨w,R⟩. Where w,R⊨Cφ, we say that φ is consistent-at-⟨w,R⟩. Γ⊨Tφ iff φ is true at ⟨w,R⟩ only if every ψ∈Γ is true-at-⟨w,R⟩. Mutatis mutandis for Γ⊨Cφ. (DEF.6) Where w∈𝒟S and R∈𝒟σ: - w,R⊨Tφ iff ⟦φ⟧(w)=1. - w,R⊨Cφ iff R[φ](w)≠∅. Under the requirement that, for all φ, [φ] is eliminative (i.e., R[φ]⊆R), every sentential expression denotes either an update or a test. 13 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 274 S. Carter Loose talk, negation and commutativity - Γ⊨Tφ iff ∀w,R, (∀ψ∈Γ w,R⊨Tψ)⊃w,R⊨Tφ. - Γ⊨Cφ iff ∀w,R, (∀ψ∈Γw,R⊨Cψ)⊃w,R⊨Cφ. For every R∈𝒟σ, 𝒞R is a function from sentential expressions φ∈ℒ into 𝒟⟨st⟩. 𝒞R(φ) is the proposition which maps w to 1 iff φ is consistent-at-⟨w,R⟩. (DEF.7) Let 𝒞R(φ)∈𝒟⟨s,t⟩ be the communicated content of φ at R: - 𝒞R(φ)=(λw. w,R⊨Cφ) §4 presents a fragment of English in the DLT-framework and shows how it is able to account for the data presented in §1-2. 4. Fragment 4.1. Basic sentences We assume that the static and dynamic interpretation functions coincide for singular terms, verbs and common nouns in the fragment. Singular terms are treated as denoting individuals (type e), whereas common nouns and verbs denote (intensions of) properties (type ⟨e⟨st⟩⟩) and relations (type ⟨e⟨e⟨st⟩⟩⟩), respectively. (I.) a. b. c. ⟦The British Library⟧=[The British Library]=THE BRITISH LIBRARY. ⟦book⟧=[book]=λxλw. BOOK(x)(w). ⟦owns⟧=[owns]=λxλyλw. OWN(y)(x)(w). The static and dynamic interpretation functions diverge in value for numerical determiners. The static denotation assigned to ‘14 million’ will be its standard value as a determiner (type ⟨⟨e⟨st⟩⟩⟨e⟨st⟩⟩t⟩). For simplicity, we will assume the upper-boundedness of bare numerical determiners. In contrast, the dynamic denotation of ‘14 million’ will be a function from a pair of (intensions of) properties to a CCP. Let F,G,… be variables over 𝒟⟨e⟨st⟩⟩: (II.) a. b. ⟦14 million⟧= λFλGλw. | λx(F(x)(w)) ∩ λx(G(x)(w)) | = 1.4×107. [14 million]=λFλGλRλwλw′. w′∈R(w) ∧ R(w)∩(λw.⟦14 mil.⟧(F)(G)(w))≠∅. The static denotation specified in (II.) maps a pair of properties to the proposition true at a world w iff the cardinality of their intersection at w is 14,000,000. The dynamic denotation specified in (II.) maps a pair of properties to a CCP (a function from accessibility relations to accessibility relations). Assuming the DP to undergo QR out of direct object position, (1) is assigned the simplified LF in (11), generating the static and dynamic denotations in (12)-(13) respectively:14 (11) [14 million books [λ1 [ [ the BL] [owns t1]]]]. 14 Slanted brackets, [ ], are used to represent constituent structure in order to avoid confusion with the dynamic interpretation function, [⋅]. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 275 S. Carter Loose talk, negation and commutativity (12) ⟦(11)⟧=λw. |λx. (BOOK(x)(w))∩ λx.(OWN(THE BL)(x)(w))|=14,000,000. (13) [(11)]=λRλwλw′. w′∈R(w) ∧ R(w)∩⟦(11)⟧≠∅. The static denotation of (11) is the proposition true at w iff the number of individuals which are both books at w and owned by the British Library at w is 14,000,000. The dynamic denotation of (11) is a test. Given an accessibility relation R it returns the relation R[(11)] such that, for all w, R[(11)](w)=R(w) if there is some R-accessible world from w at which ⟦(11)⟧ is true; otherwise R[(11)](w)=∅. Identifying the felicity of the utterance of φ at a world w and context C with the consistency of φ at ⟨w,RC⟩, this correctly predicts the felicity judgements regarding (1) in §1. Where RC is the relation of pragmatic equivalence at C, an utterance of (11) will be felicitous at w and C iff there is some world RC-accessible from w at which the British Library owns 14 million books. Alternatively stated, felicitous utterance of (11) requires that the actual world does not differ from one in which the British Library owns 14 million books in any ways which are pragmatically relevant. For example, let C± be a context in which any difference between the number of books owned by the BL and the number of books owned by the BL when rounded to the nearest million is pragmatically irrelevant.15 That is, w′∈RC±(w) iff ∀n∈ℕ: 106(n)−|λx. (BOOK(x)(w′)) ∩ λx.(OWN(THE BL)(x)(w′))|≤±500,000 iff 106(n)−|λx. (BOOK(x)(w))∩λx.(OWN(THE BL)(x)(w))| ≤±500,000. Let w* be a world at which there are 13,950,000 books owned by the library. Then an utterance of (11) is predicted to be felicitous at w*, since there exists a world w′ RC±-accessible from w such that ⟦(11)⟧(w*)=1.16 By (DEF.7), the communicated content of (11) at C± will be strictly weaker than its literal content. For all R, 𝒞R((11))(w)=1 iff there is some world w′ R-accessible world from w such that ⟦(11)⟧(w′)=1. Thus, an utterance of (11) at C± communicates the proposition true at a world w iff the number of books owned by the British Library in w falls within the interval [1.35×107, 1.45×107]. Clearly, this proposition is asymmetrically entailed by the literal content of (11). 15 Assume in addition that the books owned by the British Library is the only thing of pragmatic relevance at C±. 16 Note that, for all that has been said, an utterance of (i) at C± and w is predicted to be equally felicitous: (i) The British Library owns 14 million and one books. Furthermore, the conjunction of (1) and (i) is predicted to be felicitous at certain contexts. In order to accommodate the apparent infelicity of (i) at C± and w* (and the infelicity of its conjunction with (1) at all contexts), we can posit that the choice of numerical determiner in (i) is treated as evidence that the speaker is presupposing a stricter relation of pragmatic equivalence than would be indicated by the utterance of (1). If certain numerical determiners (such as ‘14 million’) are taken to be preferred over others (such as ‘14 million and one’), then the contrast between (i) and (1) can be explained in terms of optimality maximisation (Krifka, 2002, 2007; Klecha, 2014). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 276 S. Carter Loose talk, negation and commutativity 4.2. LT-regulators Let ↓ be a function from (intensions of) properties to CCPs. (DEF.8) ↓=λFλRλwλw′. w′∈R(w) ∧ (λx.F(x)(w))=(λx.F(x)(w′)). For any F such that for some x, λw.F(x)(w) is a non-constant function,17 ↓F is an update. Given an accessibility relation R, it returns that R′⊆R such that w′ is R′-accessible from w iff w′ is R-accessible from w and for all x, F(x)(w′)=1 iff F(x)(w)=1. That is, R(↓F) is the subset of R which relates only worlds which agree regarding the extension of F. For convenience, we adopt postfix notation for ↓F, so that R(↓F) denotes the result of applying ↓F to R. The LT-regulator ‘exactly’ is treated as a determiner-modifier. Let Q, Q′… and 𝒬, 𝒬′,… be variables over D⟨⟨e⟨st⟩⟩⟨e⟨st⟩⟩t⟩ and D⟨⟨e⟨st⟩⟩⟨e⟨st⟩⟩⟨σ,σ⟩⟩ (i.e., the static and dynamic denotations of determiners respectively): (III.) a. b. ⟦exactly⟧ = λQλFλGλw. Q(F)(G)(w). [exactly] = λ𝒬λFλGλRλwλw′: w′∈R(↓G) (w). w′∈R(↓G)(𝒬(F)(G))(w). The static denotation of ‘exactly’ is the identity function for functions of type ⟨⟨e⟨st⟩⟩⟨e⟨st⟩⟩t⟩; ⟦exactly NDET⟧=⟦NDET⟧. The dynamic denotation of ‘exactly’ is a function mapping functions of type ⟨⟨e⟨st⟩⟩⟨⟨e⟨st⟩⟩⟨σ,σ⟩⟩⟩ (that is, the type of the dynamic denotation of determiners) to functions of the same type. (2a) can be assigned the LF in (14), generating the static and dynamic denotations in (15) and (16), respectively. (14) [[[Exactly 14 million] books] [λ1 [ [ the BL] [owns t1]]]]. (15) ⟦(14)⟧= ⟦(11)⟧. (16) [(14)] = λRλwλw′: w′∈R(↓( λx.λw OWN(THE BL)(x)(w))) (w). R(↓(λxλw. OWN(THE BL)(x)(w))) [(11)]. (11) and (14) statically denote the same proposition. However, the CCPs dynamically denoted by (11) and (14) differ. Unlike (11), the dynamic denotation of (14) is divisible into two components: an ‘at-issue’ update on the input relation R and a ‘not-at-issue’ domain restriction on the output of this update. The ‘not-at-issue’ effect of [(14)] is to make the relation returned by the CCP only partially defined in its second argument place. Given an input R, [(14)] returns a relation R[(14)] such that, for all w, R[(14)](w) is defined on w′ iff the set of entities owned by the British Library in w and w′ are the same (and w′∈R(w)). That is, for all w, the domain of R[(14)](w) is {w′∈R(w): (λx.OWN(THE BL)(x)(w′)) = (λx.OWN(THE BL)(x)(w′))}. Unlike its counterpart (11) (which constitutes only a test on contexts), update with [(14)] restricts the output relation so that it is only defined on worlds which agree with respect to the 17 That is, any F such that F does not correspond to an essential property. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 277 S. Carter Loose talk, negation and commutativity extension of the property denoted by the scope of its determiner. By treating the effect of LTregulators as partially consisting in a domain restriction, this effect is made accessible to higher operators such as negation. The ‘at-issue’ update associated with [(14)] can be further sub-divided into two component operations. First, it restricts its input R to that subset which relates w and w′ iff the set of entities owned by the BL is the same in w and w′. Intuitively, this can be thought of as a modification of the input context which makes any difference with respect to what the BL owns pragmatically relevant. Second, it applies the test denoted by [(11)] to this relation. Thus, R[(14)](w)=∅ if there is no world w′ R-accessible from w at which the things owned by the British Library are the same at w and w′ and number of books that it owns at w′ is 14 million. Otherwise, R[(14)](w) is that subset of R(w) which agrees with w regarding the things owned by the British Library. Clearly, it follows that (14) will be consistent at ⟨w,R⟩ iff the number of books owned by the BL at w is 14 million.18 For example, consider the evaluation of an utterance of (14) at C± and w*. RC±[(14)](w*) is only defined on that subset of RC±(w*) which agrees with w* on the things owned by the British Library. R[(14)](w*)=∅ unless that subset contains a world at which the British Library owns 14 million books. Otherwise, R[(14)] relates w* to the members of the subset of RC±(w*) which agrees with w* on the things owned by the library, and is elsewhere undefined. Yet, since the British Library owns 13,950,000 books at w*, there is no world which agrees with w* regarding the things owned by the library at which it owns 14 million books. Hence, (14) is predicted to be infelicitous at C±. By (DEF.7), for any context C, the communicated content of (14) at C will be identical to the literal content of (11), since, for any C, (14) is consistent at ⟨w,RC⟩ iff ⟦(14)⟧ is true at w. Thus, we correctly predict that (14) can be felicitously uttered only if its literal content is true, and that it communicates the same proposition as it literally expresses. 4.3. Negation Let the static and dynamic denotations of negation be introduced syncategorematically: (IV.) a. b. ⟦¬φ⟧ = λw. ⟦φ⟧(w)=0. [¬φ] = λRλwλw′. w′∈R(w) ∧ R[φ](w)=∅ ∧ w′∈DOM(R[φ](w)). The static denotation of ¬φ is simply 𝒟s−⟦φ⟧. The dynamic denotation of ¬φ , given an input R, returns that relation R[¬φ] such that, for all w, w′∈R[¬φ](w) iff conditions (i.)-(iii.) are satisfied: (i.) R[φ](w)=∅; (ii.) w′∈R(w); (iii.) w′∈DOM(R[φ](w)). 18 Assuming, at least, that if x is something owned by the BL, then it is pragmatically relevant whether x is a book. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 278 S. Carter Loose talk, negation and commutativity Condition (i.) requires that φ be inconsistent at ⟨w,R⟩. If this condition fails, then R[¬φ](w)=∅. Condition (ii.) requires that w′ be R-accessible from w. Accordingly, R[¬φ](w)⊆R(w). Finally, the failures of commutativity observed in §2.3 suggest that the effects of LT-regulators project out of negation. Thus, condition (iii.) requires that R[φ](w) be defined on w′. Accordingly, R[¬φ](w) includes only those members of R(w) which satisfy the domain restrictions (if any) introduced by [φ]. Combining (i.)-(iii.), if R[φ](w)=∅, then R[¬φ](w) is that subset of R(w) in the domain of R[φ](w); otherwise R[¬φ](w)=∅. Since ⟦(11)⟧=⟦(14)⟧, the static denotations of their negations of are identical. However, the dynamic denotations of ¬(11) and ¬(14) differ substantially. To see why, consider the difference in the effect of their utterance at C± and w. Suppose, first, that ¬(11) is uttered. By condition (i.), RC±[¬(11)](w*)=∅ if RC± [(11)](w*)≠∅. Yet, as noted in §4.1, if the BL owns 13,950,000 books in w*, then there is a world w′ RC±accessible from w* at which it owns 14 million. Hence, ∅⊂RC±[(11)](w*)=RC±(w*), and, accordingly, RC±[¬(11)](w*)=∅. In contrast, suppose ¬(14) is uttered. Since, as noted in §4.2, RC±[(14)](w*)=∅, condition (i.) is satisfied. Thus, RC±[¬(14)](w*) is that subset of RC±(w*) on which RC±[(14)](w*) is defined. RC±[(14)](w*) is defined on w′ iff w′∈R(w*) and agrees with w* regarding the things owned by the BL. Thus, RC±[¬(14)](w*) is that subset of R(w*) which agrees with w* regarding the things owned by the BL. Thus, for all w′∈ RC±[¬(14)](w*), the BL owns 13,950,000 books in w′. By (DEF.7), the communicated content of ¬(11) will be strictly stronger than its literal content. For all w, there is some world RC±-accessible from w at which the BL owns 14 million books iff the number of books the library owns at w is within the interval [13.5×106,14.5×106]. Thus, an utterance of ¬(11) at C± communicates the proposition that the number of books the library owns falls outside this interval. Clearly, this proposition asymmetrically entails the literal content of ¬(11). 4.4. Conjunction and failures of commutativity Let the dynamic denotation of conjunction be introduced syncategorematically: (V.) a. b. ⟦φ∧ψ⟧=λw. ⟦φ⟧(w)=⟦ψ⟧(w)=1. [φ∧ψ]=λR. R[φ][ψ]. The static denotation of φ∧ψ is the intersection of ⟦φ⟧ and ⟦ψ⟧. The dynamic denotation of φ∧ψ, given a relation R, returns the result of sequentially updating R with [φ] and [ψ]. Say that conjunction is statically commutative iff φ∧ψ⊨Tψ∧φ; say that conjunction is dynamically commutative iff φ∧ψ⊨Cψ∧φ. Under (V.), ∧ is statically but not dynamically commutative. In particular, (11)∧¬(14)⊭C¬(14)∧(11). To see why, consider the difference in the effect of the utterance of (11)∧¬(14) and ¬(14)∧(11) at C± and w*. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 279 S. Carter Loose talk, negation and commutativity Suppose, first, that (11)∧¬(14) is uttered. As noted in §4.1, there is a world RC±-accessible from w* at which the BL owns 14 million books. Thus, RC±[(11)](w*)=RC±(w*). As such, RC±[(11)∧¬(14)](w*)=RC±[¬(14)](w*). Yet as noted in §4.3, since (14) is inconsistent at ⟨w*, RC±⟩, RC±[¬(14)](w*) is that subset of RC±(w*) which agrees with w* on the things owned by the BL. Thus, since w* is itself one such world, RC±[¬(14)](w*)≠∅. Utterances of (11)∧¬(14) are correctly predicted to be felicitous at C± and w*. In contrast, suppose that ¬(14)∧(11) is uttered. As noted, RC±[¬(14)](w*) is that subset of RC±(w*) which agrees with w* on the things owned by the BL. Thus, for any w′ which is RC±[¬(14)]-accessible from w*, the BL owns 13,950,000 books in w′. Yet, from §4.1, for any R, R[(11)](w*)=∅ unless there is some world R-accessible from w* at which the library owns 14 million books. Thus, RC±[¬(14)][(11)](w*)=∅. Utterances of ¬(14)∧(11) are correctly predicted to be infelicitous at C± and w*. More generally, (11)∧¬(14) is predicted to be consistent at any ⟨w,R⟩ such that w,R⊨C(11) but w,R⊭T(11); that is, at which (11) is false but felicitously assertable. In contrast, ¬(14)∧(11) is predicted to be inconsistent at all ⟨w,R⟩. As such, we correctly predict the contrast observed between (9a) and (9b). 5. Conclusion Loose utterances display two central features which have gone widely unobserved: First, the communicated content of certain loose utterances of negated sentences is strictly stronger than the utterance’s literal content. Second, the felicity of the loose utterance of certain conjunctions fails to commute. Under the present proposal, these features have been proposed to be related, and to arise from the interaction of negation, conjunction and LT-regulators in cases of loose talk. More generally, it has been argued that in order to account for these phenomena it is important to recognize that loose utterances are not merely dependent upon contexts for their felicity, but also serve to change the context in systematic ways. Due to the effect of LTregulators two sentences, such as (1) and (2b), which agree in their truth conditions may have different effects on context. To accommodate the role of LT-regulators, the effect of an utterance on a context must be taken to be determined by components of its meaning which outstrip its truth conditions. The fragment presented in §4 offers one way of implementing this observation. References Davis, W. (2007). Knowledge claims and context: Loose use. Philosophical Studies 132, 395–438. Grice, H. P. (1975). Logic and conversation. In P. Cole and J. Morgan (Eds.), Syntax and Semantics III: Speech Acts, pp. 41–58. New York: Academic Press. Groenendijk, J. and M. Stokhof (1991a). Dynamic Predicate Logic. Linguistics and Philosophy 14, 39–100. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 280 S. Carter Loose talk, negation and commutativity Groenendijk, J, and M. Stokhof (1991b). 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Linguistic Inquiry 4, 169–193. Kennedy, C. (2007). Vagueness and grammar: The semantics of relative and absolute gradable adjectives. Linguistics and Philosophy 30, 1–45. Kennedy, C. and L. McNally (2005). Scale structure and the semantic typology of gradable predicates. Language 81, 345–382. Klecha, P. (2014). Bridging the Divide: Scalarity and Modality. Ph. D. thesis, University of Chicago. Krifka, M. (1991). A compositional semantics for multiple focus constructions. In J. Jacobs (Ed.), Informationsstruktur und Grammatik. Opladen. Krifka, M. (2007). Approximate interpretation of number words: A case for strategic communication. In G. Bouma, I. Krämer, and J. Zwarts (Eds.), Cognitive Foundations of Interpretation, pp. 111–126. Amsterdam: Koninklijke Nederlandse Akademie van Wetenschapen. Lasersohn, P. (1999). Pragmatic halos. Language 75, 522–551. Lauer, S. (2012). On the pragmatics of pragmatic slack. In A. Aguilar, R. Nouwen, and A. Chernilovskaya (Eds.), Proceedings of SuB16, edited by. Cambridge, MA.: MIT Working Papers in Linguistics. Roberts, C. (1989). Modal subordination and pronominal anaphora in discourse. Linguistics and Philosophy 12, 683–721. Sauerland, U. and P. Stateva (2011). Two types of vagueness. In P. Égré and N. Klinedinst (Eds.), Vagueness and Language Use, pp. 121–145. London: Palgrave Macmillan. Solt, S. (2014). An alternative theory of imprecision. In Proceedings of SALT 24, pp. 514– 533. Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic 25, 221– 261. Yablo, S. (2014). Aboutness. Princeton, NJ.: Princeton University Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 281 282 Implicatures of modified numerals: quality or quantity?1 Ivano CIARDELLI — University of Amsterdam Liz COPPOCK — University of Gothenburg Floris ROELOFSEN — University of Amsterdam Abstract. This paper presents a theory of modified numerals that derives a three-way distinction in the implicature profile between superlative modifiers, comparative modifiers, and bare numerals. In contrast to the recent proposal by Schwarz (2016a), and drawing on elements from Coppock and Brochhagen’s (2013) inquisitive analysis, the proposal decouples ignorance implicatures from upper-bounding implicatures, and thereby captures an important difference between more than and at least, which differ in their ignorance implicatures but both lack an upper-bounding implicature. At the same time, it accounts for the context-sensitivity in the ignorance implicatures of modified numerals found by Westera and Brasoveanu (2014), and addresses a problem with Coppock and Brochhagen (2013) pointed out by Schwarz (2016b). The key feature of the proposal is the fact that ignorance implicatures may arise in two different ways, namely, both from the Maxim of Quantity and from the Maxim of Quality. Keywords: modified numerals, ignorance implicatures, inquisitive semantics. 1. Introduction 1.1. Empirical targets We will be concerned with three types of modified numerals: at least n, more than n, and n or more. Many authors have observed that these contrast with each other, as well as with bare numerals, in the implicatures that they give rise to. The basic empirical picture, which is assumed in most work on the topic, is as follows (where the ignorance implicature of at least six and six or more is not just that the speaker does not know exactly how many sides a hexagon has, but also that she considers it possible that it has precisely six sides). (1) a. b. c. d. A hexagon has six sides. A hexagon has more than five sides. A hexagon has at least six sides. A hexagon has six or more sides. ; exactly six 6; exactly six 6; exactly six 6; exactly six 6 ignorance ; 6; ignorance ; ignorance ; ignorance Westera and Brasoveanu (2014) argue based on experimental data that this basic empirical picture is actually a bit too simplistic. They presented experimental participants with a courtroom dialogue, in which a judge asks the witness a question (e.g. What did you see under the bed?) and the witness responds with a sentence containing a modified numeral, e.g. I saw at most 10 1 We would like to thank the audience at Sinn und Bedeutung 21 in Edinburgh, as well as Stavroula Alexandropoulou, Dominique Blok, Alexandre Cremers, Jakub Dotlačil, Sven Lauer, Yaron McNabb, Rick Nouwen, Paul Portner, and Matthijs Westera for valuable feedback and discussion. Finally, we gratefully acknowledge financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Starting Grant, agreement number 680220), and from the Riksbankens Jubileumsfond (Pro Futura Scientia scholarship). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 283 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals Figure 1: Westera and Brasoveanu’s (2014) design and results. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 284 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals diamonds under the bed. The type of question was experimentally manipulated as indicated in Figure 1 below, and the witness’s response always contained either at most 10 or less than 10. The participant is then told that the judge concludes that the witness does not know exactly how many of the relevant kind of items she saw under the bed (the ignorance inference), and asked how justified the judge is in drawing that conclusion, on a 1-5 scale. Their results (see Figure 1) show that comparative modifiers can signal ignorance (e.g. in response to ‘how many’ questions), and that ignorance can disappear for superlative modifiers (in response to certain polar questions). Note, however, that in most contexts, in particular in response to ‘how many’ questions, superlative modifiers do give rise to stronger ignorance implicatures than comparative modifiers, in line with what had been assumed in the literature. Another point to notice is that W&B’s ‘polar question’ context involves an echo response. (2) A: Did you find at most 10 of the diamonds under the bed? B: I found at most 10 of the diamonds under the bed. This may be essential for the ignorance implicature not to arise. Compare: (3) (4) A: Did Johnny eat at least four apples today? B: Yes, he ate at least four apples. A: Did Johnny eat more than three apples today? B: Yes, he ate at least four apples. 6; ignorance ; ignorance If we compare more than and at least in non-echo responses to a polar question, the latter seems to implicate ignorance but the former doesn’t: (5) Context: Johnny’s diet prescribes that he eat at most three apples per day. A: Did Johnny stick to his diet today? B: No, he ate more than three apples. 6; ignorance 0 B : No, he ate at least four apples. ; ignorance Moreover, ‘out of context’, at least signals ignorance as well, unlike more than: (6) a. I grew up with more than two parents. b. ??I grew up with at least three parents. Finally, ignorance implicatures triggered by at least, unlike implicatures triggered by more than, do not seem to be cancelable. (7) a. b. He has more than 10 cars. In fact, he has 12. He has at least 10 cars. #In fact, he has 12. So, while we concede that more than can trigger an ignorance implicature in response to a ‘how many’ question, and that the ignorance implicature for at least can disappear in the context Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 285 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals of certain polar question-answer scenarios (of the echo variety), it seems that the ignorance implicature triggered by at least arises more widely than the one triggered by more than, and it is of a more obligatory and more robust nature.2 What is the source of this difference? 1.2. Quality or quantity? At least two approaches have been explored in the literature to explain the ignorance implicatures for superlative modifiers. One approach (e.g., Mayr, 2013b; Kennedy, 2015; Schwarz, 2016a) is to derive ignorance from a particular way of computing quantity implicatures. Differences between the various kinds of bare/modified numerals are accounted for on this approach by assuming that they activate different pragmatic alternatives. Another approach (Coppock and Brochhagen, 2013) is to derive ignorance as a quality implicature. The standard Gricean quality maxim, however, does not suffice for this purpose. Rather, Coppock and Brochhagen invoke a quality maxim that is not only concerned with the informative content of the uttered sentence, but also with its inquisitive content, i.e., the semantic alternatives that it introduces. Differences between the various kinds of bare/modified numerals are accounted for on this approach by assuming that they introduce different semantic alternatives. Note that in other empirical domains (e.g., free choice effects of disjunction under modals or in the antecedent of a conditional), these two approaches have also both been pursued. We will suggest that, in the domain of modified numerals, a combination of the two approaches is in fact needed. We will develop such a combined account, and show that it improves on earlier proposals which placed the entire explanatory burden either on quantity or on quality. 2. Previous approaches 2.1. Quantity-based We will first review a specific quantity-based account of ignorance implicatures, reformulating it in a way that will allow for easy comparison with our own approach. We focus on the proposal of Schwarz (2016a), but see Mayr (2013a) and Kennedy (2015) for closely related proposals. Schwarz is concerned with at least n (not with more than n or with n or more). He assumes that h at least, only i forms a Horn scale, along with h 1, 2, 3, ... i. This yields the following set of pragmatic alternatives for Al hired at least two cooks: 2 Shortly before the deadline for submitting the present paper, we became aware of the work of Mayr and Meyer (2014), who make very similar empirical observations, and offer an alternative account of the crucial datapoints. Detailed comparison with the present approach must be left for a future occasion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 286 I. Ciardelli, E. Coppock, & F. Roelofsen [1] [2] [3] [3] ... only 1 only 2 only 3 only 4 ... Implicatures of modified numerals [1 2 [2 3 3 [3 4 4 4 [4 ... ) ... ) ... ) ... ) ... at least 1 at least 2 at least 3 at least 4 ... The meanings are visually represented in a way that brings out the fact that none of them are innocently excludable, as we will explain below. To articulate the pragmatics, we introduce the following background notions and notation: • A speaker’s information state is a non-empty set of worlds. • A state s supports a sentence ϕ iff s ⊆ [[ϕ]]. • A state s rejects a sentence ϕ iff s ∩ [[ϕ]] = 0. / • We use Aϕ to denote the set of lexically determined pragmatic alternatives for ϕ. Implicatures can be seen as imposing constraints on what the speaker’s information state might be. On Schwarz’s approach, they are derived using the following recipe, based on Innocent Exclusion. Start with the quality implicature that the speaker’s state s supports ϕ: 0ϕ := {s | s supports ϕ} Now derive primary quantity implicatures: the speaker’s state does not support any alternative ψ ∈ Aϕ that is stronger than ϕ itself. Let A⊂ ϕ be the set of those stronger alternatives: A⊂ ϕ := {ψ ∈ Aϕ | [[ψ]] ⊂ [[ϕ]]} 1ϕ := {s ∈ 0ϕ | s does not support any ψ ∈ A⊂ ϕ} Now derive secondary quantity implicatures by identifying all alternatives ψ ∈ A⊂ ϕ satisfying the following two conditions: 1. ψ is not known by the speaker according to 1ϕ . That is, no s ∈ 1ϕ supports ψ. 2. ψ is innocently excludable relative to ϕ (Gazdar, 1979; Fox, 2007). In a nutshell, ψ is innocently excludable if, whenever a set of alternatives in A⊂ ϕ has been consistently rejected we can always go on to reject ψ in addition, maintaining consistency. More precisely: for every subset A0 of A⊂ ϕ , if there are information states that validate the quality implicature and primary quantity implicatures of ϕ while rejecting every sentence in A0 , i.e., if: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 287 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals {s ∈ 1ϕ | s rejects every sentence in A0 } is non-empty then there are also information states that validate the quality implicature and primary quantity implicatures of ϕ while rejecting every sentence in A0 as well as ψ: {s ∈ 1ϕ | s rejects every sentence in A0 ∪ {ψ}} is non-empty If ψ ∈ A⊂ ϕ is not known by the speaker according to 1ϕ and innocently excludable relative to ϕ, then we say that ψ is eligible for a secondary quantity implicature. 2ϕ := {s ∈ 1ϕ | s rejects every ψ ∈ A⊂ ϕ eligible for a secondary quantity implicature} Uttering a sentence ϕ against the background of a question Q in information state s is licensed only if s ∈ 0ϕ (speaker adheres to Quality) and s ∈ 1ϕ,Q ∩ 2ϕ,Q (speaker adheres to Quantity). Since 0ϕ ⊆ 1ϕ,Q ⊆ 2ϕ,Q , this amounts to saying that s ∈ 2ϕ,Q . None of the pragmatic alternatives that Schwarz assumes for Al hired at least two cooks (see above) is innocently excludable. For instance, rejecting ‘only two’ is not consistent with rejecting ‘at least three’, given the quality assumption that ‘at least two’. So we get primary quantity implicatures, but no secondary ones. Hence ignorance is derived, and no ‘upper bounding’ implicature (exactly n) arises, as desired. Shortcomings This approach entails a very tight coupling between ignorance implicatures and upper bounding implicatures. A consequence of this is that it is unclear how to distinguish more than from at least; as mentioned above, both lack upper bounding implicatures, but behave differently with respect to ignorance. Furthermore, the effects of the QUD documented by Westera and Brasoveanu (2014) are not immediately accounted for (although Schwarz makes it clear that the theory should ultimately be refined, restricting the set of pragmatic alternatives to those that are contextually relevant). We aim to remedy both of these shortcomings in the proposal below. 2.2. Quality-based The quality-based approach that we will build on (Coppock and Brochhagen, 2013) is formulated in inquisitive semantics (Ciardelli et al., 2013). In this framework, every sentence generates a set of semantic alternatives (where each semantic alternative is a set of possible worlds). If a sentence generates two or more alternatives, it is thought of as expressing an issue as to which of these alternatives holds. Coppock and Brochhagen propose that the set of alternatives generated by an at least sentence consists of all those alternatives that are pragmatically at least as strong as one of the alternatives Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 288 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals generated by the prejacent. For example, At least two apples fell generates the set of alternatives corresponding to Two apples fell, Three apples fell, Four apples fell, etc. Assuming a one-sided analysis of bare numerals, this amounts to the following: (8) At least two apples fell: {[2,...), [3,...), [4,...), . . . } On a two-sided analysis, the denotation would be: (9) At least two apples fell: {[2], [3], [4], . . . } Coppock and Brochhagen further assume, besides the standard Gricean quality maxim, ‘Don’t claim things you don’t believe to be true’, an inquisitive quality maxim as well, which can be characterized informally as: ‘Don’t utter an inquisitive sentence if you already know how to resolve the issue that it expresses’ (cf. Groenendijk and Roelofsen, 2009). More technically, if a sentence generates multiple alternatives, then, when restricted to the speaker’s state, it should still generate multiple alternatives. This, together with the semantics in (8) or (9), derives ignorance implicatures for at least sentences. Shortcomings C&B capture the fact that at least generates ignorance implicatures but no upper bounding implicatures, and the fact that bare numerals exhibit exactly the opposite pattern. The analysis is also QUD-sensitive. However, for more than they predict that ignorance implicatures do not arise at all, which is in conflict with Westera and Brasoveanu’s (2014) experimental results. Moreover, they do not derive the lack of upper bounding implicatures for more than. This is a symptom of a deeper problem, which C&B share with the quantitybased approach: the coupling between ignorance implicatures and the lack of upper bounding implicatures is too tight. This means that it becomes difficult, if not impossible, to capture the differences and similarities between more than and at least: they behave differently with respect to ignorance, but they both lack upper bounding implicatures. Even if we focus just on at least, the C&B account is not fully satisfactory, because, as pointed out by Schwarz (2016b), the ignorance implicature that is derived for at least n is too weak: the approach predicts that a speaker uttering (9) should not know exactly how many apples fell, but not that she should consider it possible that exactly n apples fell. Finally, there is framework issue: C&B formulate their account in ‘unrestricted’ inquisitive semantics, InqU , an extension of the standard, basic inquisitive semantics framework, InqB . InqU makes more meanings available than InqB does: the latter does not allow for one alternative to be nested in another—as is the case for instance in (8)—while in InqU there are no restrictions on alternative-sets (hence the label ‘unrestricted’). However, this extra richness of InqU comes at a price. First, the resulting notion of meaning is less well-behaved from a logical point of view. In particular, it does not come with a suitable notion of entailment and therefore lacks the usual algebraic operations on meanings, like meet and join (cf., Roelofsen, 2013; Ciardelli et al., 2016). Second, InqU is arguably also less well-behaved from an empirical point of view: as discussed in detail in Ciardelli and Roelofsen (2016), while InqB straightforwardly faciliProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 289 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals tates an uniform redundancy-based account of so-called Hurford effects across declaratives and interrogatives (building on Katzir and Singh, 2013, among others), InqU seems to render such an account impossible. One question, then, is whether an analysis of modified numerals along the lines of C&B really needs the full expressive power of InqU , or whether it could also be formulated in InqB . 3. Proposal We now spell out a hybrid approach, combining insights from the quality- and quantity-based approaches, and overcoming their respective shortcomings. We provide the necessary background notions and notation from InqB in Section 3.1, spell out our lexical assumptions in Section 3.2, and then turn to the pragmatic component of the account in Section 3.3. 3.1. Background notions and notation In InqB , the meaning of a sentence ϕ, denoted [[ϕ]], is a set of propositions encoding both the information that is conveyed and the issue that is expressed by ϕ. Namely, ϕ is taken to S convey the information that the actual world is contained in info(ϕ) := [[ϕ]], and to express an issue which is resolved precisely by those propositions that are in [[ϕ]]. It is assumed that if a proposition p resolves an issue, then any stronger proposition q ⊆ p resolves that issue as well. Thus, [[ϕ]] is always downward closed: if it contains a proposition p it also contains any q ⊆ p. Furthermore, it is assumed that the inconsistent proposition, 0, / resolves any issue. Thus, [[ϕ]] always contains 0/ and is therefore always non-empty. Taken together, sentence meanings in InqB are defined as non-empty, downward closed sets of propositions. In some cases the issue expressed by ϕ is trivial, in the sense that it is already resolved by the information provided by ϕ itself. This occurs precisely if info(ϕ) ∈ [[ϕ]]. A sentence ϕ is called inquisitive just in case the issue it expresses is non-trivial, i.e., just in case info(ϕ) 6∈ [[ϕ]]. Finally, the alternatives associated with a sentence ϕ in InqB are those propositions that contain precisely enough information to resolve the issue expressed by ϕ. Technically, these are the maximal elements of [[ϕ]]: alt(ϕ) := {p ∈ [[ϕ]] | there is no q ∈ [[ϕ]] such that p ⊆ q} Note that, as remarked above, this characterization of alternatives entails that one alternative can never be properly contained in another, otherwise it could not be a maximal element of [[ϕ]]. Also note that if ϕ is non-inquisitive, it is always associated with a unique alternative, namely info(ϕ). Vice versa, if ϕ generates multiple alternatives, then it must be inquisitive.3 3 We should note here that there are several perspectives one can take on the connection between inquisitiveness, a semantic notion, and the communicative effects of sentences when uttered in discourse. The perspective assumed here, in the spirit of Groenendijk (2009) and Coppock and Brochhagen (2013), is that even if a sentence is inquisitive, i.e., even if it semantically expresses a non-trivial issue, a speaker who utters this sentence in discourse does not necessarily raise this issue. In particular, she does not necessarily request a response that addresses the issue. Under this perspective, it is possible to assume that a disjunctive declarative like John ate Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 290 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals 3.2. Lexical assumptions Following C&B, we assume that at least sentences generate multiple alternatives. However, we adopt a suggestion made by Schwarz (2016b) in his critique of C&B and analyze at least n as having the same meaning as n or more would have in inquisitive semantics.4 For example: (10) alt( At least two apples fell ) = alt( Two or more apples fell ) = { [2], [3,...) } Notice that, unlike in the C&B analysis, the alternatives for at least n are not nested within each other; in fact, they are mutually exclusive. This means that the analysis we are proposing can be formulated in the standard inquisitive semantics framework InqB , allowing us to avoid the problems that arise in the unrestricted framework InqU .5 Following C&B we assume that more than n contrasts with at least n and with n or more in that it is associated with a single semantic alternative:6 (11) alt( More than two apples fell ) = { [3,...) } Turning now to pragmatic alternatives, we assume that the lexically determined pragmatic alternatives for at least n are {at least m | m ∈ N} and {m | m ∈ N}, and similarly for n or more and for more than n: (12) Lexically determined pragmatic alternatives a. at least n: {at least m | m ∈ N} ∪ {m | m ∈ N} b. n or more: {m or more | m ∈ N} ∪ {m | m ∈ N} ∪ {more than m | m ∈ N} c. more than n: {more than m | m ∈ N} ∪ {m | m ∈ N} two or three apples (with falling intonation) is inquisitive, just like the corresponding interrogative Did John eat two apples, or three?. One could say that the former is used to make an assertion and the latter to ask a question, and that in making an assertion, speakers do not raise the issue that the uttered sentence expresses (perhaps their assertion still ‘evokes’ the issue, but the effect is weaker than in the case of a question). Another perspective that one could take (see, e.g., Farkas and Roelofsen, 2016) is that the issue expressed by a sentence is always raised when the sentence is uttered in discourse. Under this perspective, it does not make sense to treat a disjunctive declarative as being inquisitive, on a par with the corresponding disjunctive question. This perspective allows for a more economical interface between semantics and discourse pragmatics, but is not directly compatible with the present proposal. 4 The idea of treating at least n on a par with n or more goes back to Büring (2008). 5 The meaning for at least n given here should, of course, be obtained from a general analysis of at least, one that allows us to analyze at least in combination with arguments other than numerals. Building on Solt (2011) and Coppock (2016), we assume that an expression of the form at least P is interpreted relative to a context providing (i) a comparison class, which is a set Φ of propositions, including the proposition associated with the prejacent P and (ii) a pragmatic strength ordering, which is a partial order on Φ, possibly but not necessarily coinciding with entailment. Relative to such a context, at least P is associated with two semantic alternatives: one is the exhaustification of the prejacent P with respect to the stronger propositions in Φ; the other is the union of all propositions in Φ which are strictly stronger than P. The meaning that we assume in this paper for at least n is obtained from this general account by taking the comparison class to be Φ = {[0], [1], [2], . . . }, where the strength ordering corresponds to the usual ordering on natural numbers. 6 The account of more than n given here can be lifted to a general treatment of more than, allowing for arguments other than numerals, in a way similar to the one sketched in footnote 5 for at least. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 291 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals In general, we assume that the lexical pragmatic alternatives for an expression ϕ are obtained either by deleting parts of ϕ, or by replacing a scalar item in ϕ with an element of the same scale.7 This makes our pragmatic assumptions less stipulative that those of Schwarz (2016a), and more in line with general theories of pragmatic alternatives (see, in particular, Katzir, 2007). Following Kennedy (2015), we assume that numerals are ambiguous between a one-sided and a two-sided reading, and the choice between these readings is determined by which yields a stronger interpretation. A two-sided meaning is stronger in a simple positive context, so that is what the m alternatives amount to in such a context. 3.3. Pragmatic assumptions 3.3.1. Quality Following C&B and earlier work on inquisitive pragmatics (Groenendijk and Roelofsen, 2009), we assume that Quality pertains both to the informative and the inquisitive content of the sentence that is uttered. Informative sincerity (Gricean Quality) requires that if a speaker utters a sentence ϕ, her information state s should support the informative content of ϕ:8 s ⊆ info(ϕ). On the other hand, inquisitive sincerity requires that a speaker should not utter an inquisitive sentence if she already knows how to resolve the issue that the sentence expresses. That is, if ϕ is inquisitive, then the speaker’s information state s should not already resolve the issue expressed by ϕ:9 s 6∈ [[ϕ]]. Together: (13) s ∈ sincere(ϕ) iff s ⊆ info(ϕ) and if ϕ is inquisitive, then s 6∈ [[ϕ]] 3.3.2. Quantity Following Schwarz (2016a) and many others, we assume that the maxim of quantity is concerned with alternative expressions that the speaker could have used. However, only expressions that are relevant to the question under discussion should be taken into consideration. Thus, unlike Schwarz, we distinguish lexical pragmatic alternatives from contextual prag7 Strictly speaking, this means that expressions of the form m and more also count as alternatives for n or more. However, since such expressions are inconsistent, their presence does not affect the predictions of the theory. Therefore, they are left out of consideration and not listed above. 8 Of course, this maxim and the ones below are only assumed to be in force in a specific type of conversation, namely one in which the participants exchange information in a fully cooperative way. 9 The original formulation of the inquisitive sincerity maxim in Groenendijk and Roelofsen (2009) makes reference to the common ground: “If a speaker utters a sentence ϕ that is inquisitive w.r.t. the common ground, then ϕ should be inquisitive w.r.t. the speaker’s information state as well.” For our current purposes this qualification is not necessary. Note also that Coppock & Brochhagen operate with a stronger sincerity maxim, which they call the maxim of interactive sincerity. On their account this is needed because the predictions that inquisitive sincerity delivers are too weak. On our present account, inquisitive sincerity delivers the right predictions, and interactive sincerity would do so as well; indeed, interactive sincerity boils down to inquisitive sincerity in InqB. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 292 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals matic alternatives. The set of lexical pragmatic alternatives for a sentence ϕ is denoted as Aϕ . The set of contextual pragmatic alternatives for ϕ relative to a question under discussion Q, denoted Aϕ,Q , contains only those lexical pragmatic alternatives that are relevant to Q: (14) Aϕ,Q = {ψ ∈ Aϕ | ψ is relevant to Q} What does it mean for ψ to be relevant to Q? Recall that the semantic alternatives in alt(Q) are propositions that contain precisely enough information to resolve the issue expressed by Q. They can be thought of, then, as wholly relevant, complete resolutions of Q. Similarly, any union of two or more such alternatives can be thought of as a wholly relevant, partial resolution of Q. Thus, we say that ψ is relevant to Q if and only if info(ψ) coincides with the union of a set of semantic alternatives in alt(Q). For our current purposes we will stay as close as possible to Schwarz’s Innocent Exclusionbased recipe for deriving implicatures. The only serious change is that the standard Gricean Quality requirement is replaced by the requirement that the speaker be both informatively and inquisitively sincere; we also restrict attention to relevant alternatives. So the recipe runs as follows: The first step, as before, is to compute the quality implicature: 0ϕ = {s | s ∈ sincere(ϕ)} Next, also as before, we compute primary quantity implicatures, based on the assumption that any pragmatic alternative for ϕ that would have been more informative was apparently not sincerely utterable, either the speaker’s information state doesn’t support its informative content, or because the speaker can already resolve the issue that it expresses. We restrict the set of pragmatic alternatives here to those that are relevant, Aϕ,Q . Let A⊂ ϕ,Q be the set of such ⊂ alternatives that are stronger than ϕ itself: Aϕ,Q = {ψ ∈ Aϕ,Q | info(ψ) ⊂ info(ϕ)}. 1ϕ,Q = {s ∈ 0ϕ | for all ψ ∈ A⊂ ϕ,Q : s 6∈ sincere(ψ)} Finally, again as before, we compute secondary quantity implicatures. The recipe for doing so is the same as on Schwarz’s proposal, except that we now take Q into consideration. That is, we identify all pragmatic alternatives ψ in A⊂ ϕ,Q such that: 1. ψ is not known by the speaker according to 1ϕ,Q . That is, no s ∈ 1ϕ,Q supports info(ψ). 2. ψ is innocently excludable relative to ϕ and Q. The second condition is satisfied just in case for every subset A0 of A⊂ ϕ,Q , if there are information states that validate the quality implicature and primary quantity implicatures of ϕ while rejecting every sentence in A0 , i.e., if: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 293 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals {s ∈ 1ϕ,Q | s rejects every sentence in A0 } is non-empty then there are also information states that validate the quality implicature and primary quantity implicatures of ϕ while rejecting every sentence in A0 as well as ψ: {s ∈ 1ϕ,Q | s rejects every sentence in A0 ∪ {ψ}} is non-empty If ψ ∈ A⊂ ϕ,Q is not known by the speaker according to 1ϕ,Q and innocently excludable relative to ϕ and Q, then we say that ψ is eligible for a secondary quantity implicature. 2ϕ,Q = {s ∈ 1ϕ,Q | s rejects any ψ ∈ A⊂ ϕ,Q eligible for a secondary quantity implicature} As before, uttering a sentence ϕ against the background of a question Q in information state s is licensed only if s ∈ 2ϕ,Q , that is, only if the speaker adheres to Quality and Quantity. 4. Predictions We now discuss the predictions that our account makes for sentences involving bare or modified numerals. 4.1. Predictions in the context of a how many question Suppose the question under discussion is (15a), which we take to be associated with the set of alternatives in (15b). (15) a. b. How many apples did John eat? Q = {[0], [1], [2], [3], [4], [5], . . .} Bare numerals First let us consider our predictions for the sentence (16a), involving the bare numeral three. Again, following Kennedy (2015), we assume that numerals are scopally ambiguous between a one-sided interpretation (e.g. [3, . . . )) and a two-sided one (e.g. [3]), and that the interpretation that yields the strongest meaning is the one that is chosen. This means that the basic interpretation of the bare numeral example in (16a) is an ‘exactly’ reading: (16) a. b. ϕ: John ate three apples. alt(ϕ) = {[3]} Since this sentence is not inquisitive, quality simply requires the speaker to believe that the number of apples that John ate is indeed three. (17) 0ϕ = sincere(ϕ) = {s | s ⊆ [3]} Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 294 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals It is easy to see that, given this strong quality implicature, quantity implicatures cannot lead to any stronger conclusion about the speaker’s state. Thus, for (16a) we predict an exact interpretation, and no ignorance implicature. Superlative modifiers Next, let us consider the sentence (18a), involving the superlative modifier at least. The semantic alternatives for this sentence in our account are given in (18b). (18) a. b. ϕ : John ate at least three apples. alt(ϕ) = {[3], [4, . . . )} Consider the quality implicatures that are drawn about the state s of the speaker. As before, sincerity requires that s ⊆ info(ϕ), that is, s ⊆ [3, . . . ). However, since ϕ is inquisitive, now sincerity also requires s 6∈ [[ϕ]]; that is, it requires s not to be included in either of the alternatives for ϕ; in other words, the speaker should not believe that the number of apples was exactly three, nor should she believe that the number is larger than three. Formally, we have: (19) 0ϕ = sincere(ϕ) = {s | s ⊆ [3, ...) and s 6⊆ [3] and s 6⊆ [4, ...)} So, from quality considerations we already infer not only that the speaker believes that the number of apples John ate is at least 3, but also that she considers it possible that this number is exactly 3, and that she considers it possible that it is larger than 3. Next, consider quantity implicatures. We have assumed that the lexical pragmatic alternatives for ϕ are sentences of the form ψn = John ate at least n apples or of the form χn = John ate n apples, for n ∈ N. All of these sentences are relevant for the question Q, and therefore they qualify as contextual pragmatic alternatives. Thus, A⊂ ϕ,Q consists of the sentences ψn with n > 3, as well as χn with n ≥ 3. Primary quantity implicatures require that none of these sentences could be sincerely uttered by the speaker. However, this is already guaranteed by quality. For take any state s ∈ 0ϕ . Since s 6⊆ [4, ...), whenever n > 3 we have that s 6∈ sincere(ψn ) and s 6∈ sincere(χn ), because informative sincerity fails for these sentences. Moreover, since s 6⊆ [3], we also have s 6∈ sincere(χ3 ). What this shows is that 1ϕ,Q = 0ϕ , which means that nothing new is concluded by drawing primary quantity implicatures. Finally, we will show that no contextual alternative in A⊂ ϕ,Q is eligible for a secondary quantity implicature. Consider for example the ‘at least’ sentence ψ5 , John ate at least 5 apples. This alternative is not innocently excludable. To see this, consider the set A0 = {χ4 }, where χ4 = John ate 4 apples, which receives an two-sided (‘exactly’) interpretation in this context because the two-sided interpretation is stronger than the one-sided one. Rejecting χ4 is consistent with the primary quantity implicatures; some information states in 1ϕ,Q reject it (as a witness, take the state [3] ∪ [5]). But, given the primary and secondary implicatures, rejecting χ4 is not consistent with rejecting our candidate alternative ψ5 (John ate at least 5 apples); no information state in 1ϕ,Q rejects both. In a nutshell, since rejecting ψ5 forces acceptance of χ4 , the former is not innocently excludable. Similar reasoning holds for all of the other ‘at Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 295 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals least’ formulas ψn with n > 3.10 Similarly, to show that each bare numeral alternative χn is not innocently excludable we can take A0n = 0/ if n = 3, and A0n = {χm | m ≥ 4, m 6= n} if n > 3. This shows that no element of A⊂ ϕ,Q is eligible for a secondary quantity implicature, which means that 2ϕ,Q = 1ϕ,Q . This means that no secondary quantity implicatures are derived, or more precisely, nothing new is concluded about the state of the speaker by drawing secondary quantity implicatures. In conclusion, we have 2ϕ,Q = 0ϕ = {s | s ⊆ [3, ...) and s 6⊆ [3] and s 6⊆ [4, ...)}. Thus, we predict that, from an utterance of (18a) in the context of question (15a), an ignorance implicature is drawn, and no upper bounding implicature. Importantly, the relevant ignorance implicature is not just that the speaker does not know exactly how many apples John ate, but also that the speaker does not know whether John eat exactly three apples or more. n or more Disjunctions of the form n or more are predicted to behave in a parallel fashion to at least n. They have the same denotation: (20) a. b. ϕ: John ate three or more apples. alt(ϕ) = {[3], [4, ...)} The lexical alternatives are sentences of the form m, m or more, and more than m for all natural numbers m. All of these will be relevant in the context of a ‘how many’ question, and none of them will be innocently excludable for reasons parallel to the ones just given for at least. Thus, once again we will predict a strong ignorance implicature, and no upper bounding implicatures. Comparative modifiers Finally, consider (21a). We have assumed that this sentence has a unique semantic alternative, given in (21b). (21) a. b. ϕ : John ate more than two apples. alt(ϕ) = {[3, . . . )} Let us compute what implicatures are predicted for ϕ in the context of Q. First consider quality implicatures: since ϕ is not inquisitive, only the condition s ⊆ info(ϕ) is relevant to sincerity. Therefore, we have: (22) 0ϕ = sincere(ϕ) = {s | s ⊆ [3, . . .)} So, from quality we infer that the speaker believes that John ate at least three apples. Now let us turn to quantity implicatures. The set of lexical pragmatic alternatives to ϕ consists 10 To see this, consider the set A0n = {χ4 , . . . , χn−1 } (in particular, take A04 = 0). / Some information states in 1ϕ,Q reject all elements of A0n : if n = 4, this holds trivially, as A04 = 0; / if n > 4, we can take as a witness the state [3] ∪ [n]. However, no information state in 1ϕ,Q rejects all elements of A0n in addition to ψn . Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 296 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals of all sentences of the form ψn = John ate more than n apples or χn = John ate n apples for n a natural number. All of these pragmatic alternatives are relevant to the question Q we are considering, and therefore qualify as contextual pragmatic alternatives. Therefore, Aϕ,Q = {ψn | n ∈ N} ∪ {χn | n ∈ N} and A⊂ ϕ,Q = {ψn | n ≥ 3} ∪ {χn | n ≥ 3}. Just like ϕ, all pragmatic alternatives ψn are non-inquisitive, nor are the pragmatic alternatives χn , which means that the sincerity condition boils down to s ⊆ info(ψn ) and s ⊆ info(χn ). Therefore, we have the following primary quantity implicatures: (23) 1ϕ,Q = {s ∈ 0ϕ | s 6∈ sincere(ψn ) for n ≥ 3} ∩ {s ∈ 0ϕ | s 6∈ sincere(χn ) for n ≥ 3} = {s ⊆ [3, . . . ) | s 6⊆ [n, . . . ) for n > 3} ∩ {s ⊆ [3, . . . ) | s 6⊆ [n] for n ≥ 3} = {s | s ⊆ [3, . . . ) and s 6⊆ [3] and s 6⊆ [4, . . . )} Thus, from the primary quantity implicatures we infer that the speaker does not know the exact number of apples that John ate and, in fact, that she does not know whether John ate exactly three apples or more. Finally, consider secondary quantity implicatures. Clearly, each pragmatic alternative ψ ∈ A⊂ ϕ,Q is not known by the speaker according to 1ϕ,Q . But none of these alternatives is innocently excludable, for reasons parallel to those given for at least above. Thus, we have 2ϕ,Q = 1ϕ,Q , that is, nothing new is inferred in drawing secondary quantity implicatures. Summing up, for (21a) in the context of the ‘how many’ question (15a) we predict an ignorance implicature and no upper bounding implicature. While the relevant ignorance inference is exactly the same that was derived above for (18a), there is a crucial difference between the two cases: the inference is derived as a quantity implicature for (21a), but as a quality implicature for (18a). Quality implicatures are viewed as being of a more fundamental nature than other kinds of implicatures.11 Moreover, they are difficult to cancel (as exhibited by the oddness of Moore sentences) and there is no reason to imagine that they would depend on the question under discussion any more than the content of the utterance does. We take this to account for our observations in Section 1.1, which show that in the case of at least, ignorance implicatures arise more robustly and more widely, and are harder to cancel, than in the case of more than.12,13 4.2. Predictions in the context of a polar question Let us now consider a context in which not all of the lexical pragmatic alternatives to our sentences are relevant, and therefore available in the computation of quantity implicatures. 11 For instance, Grice (1975: p.27) writes: “It is obvious that the observance of some of these maxims is a matter of less urgency than is the observance of others; a man who has expressed himself with undue prolixity would, in general, be open to milder comment than would a man who has said something he believes to be false”. 12 Lauer (2014) argues that the ignorance implicatures generated by disjunctions are also of a mandatory nature. 13 Interestingly, note that in the case of (18a), even if an addressee does not derive the inference as a quality implicature (i.e., if she takes it for granted that the speaker adheres to informative sincerity, but not necessarily to inquisitive sincerity as well), then she would still derive ignorance as a quantity implicature, in a way parallel to what we discussed for (21a). This, we suggest, lends additional robustness to the ignorance implicature of at least in comparison to that of more than. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 297 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals Suppose that John’s diet prescribes that he eat at most two apples per day, and does not prescribe anything else. Consider the polar question in (24a). Given our contextual assumptions, the alternatives for this question are the ones displayed in (24b). (24) a. b. Did John stick to his diet today? Q = {[0, 2], [3, . . . )} Compare the following responses to (24a): (25) a. b. No, he ate more than two apples. No, he ate at least three apples. Intuitively, upon hearing the response (25a) we do not conclude that the speaker is ignorant as to the number of apples that John ate, whereas we do so upon hearing (25b). In other words, the ignorance implicature associated with (25b) still arises in this context, but the implicature stemming from (25a) does not. This is indeed predicted on our account. To see why, first consider (25b): we have seen above that for this sentence, the ignorance inference arises as a quality implicature; since quality implicatures are context-independent on our account, this implicature is still predicted in the present setting.The same holds for n or more. The situation is different for (25a). For this sentence, an ignorance inference in the context of question (15a) was derived as a quantity implicature. However, on our account the computation of quantity implicatures is sensitive to the question Q under discussion: only lexical pragmatic alternatives which are relevant to Q are taken into account. In the present context, no lexical alternative to ϕ—except for the sentence ϕ itself—is relevant to Q. Thus, A⊂ / which ϕ,Q = 0, means that no primary or secondary quantity implicatures are derived. Thus, we predict that the ignorance implicature that we found above for (25a) disappears in the context of the polar question (24a).14 5. Conclusion The proposal we have made here allows us to overcome the shortcomings of previous accounts. It achieves a three-way contrast between superlative modifiers, comparative modifiers, and numerals, in contrast to Schwarz (2016a). It furthermore accounts for the QUD-sensitivity observed by Westera and Brasoveanu (in contrast to both Schwarz and C&B). It predicts ignorance with respect to the prejacent of at least (overcoming Schwarz’s critique of C&B). And it brings C&B’s approach in line with recent theorizing on inquisitive semantics, where one alternative can never entail another. Most importantly, we account for the following facts: more than indeed can imply ignorance in how many contexts, as observed by Westera & Brasoveanu, but the ignorance implicature 14 In addition, notice that, due to the absence of contextually relevant alternatives, we still correctly predict the lack of upper bounding implicatures for both (25a) and (25b). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 298 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals of at least is more robust, as witnessed by (i) the fact that it is perceived to be stronger than the ignorance implicature of more than in how many contexts; (ii) the fact that it persists in non-echoic responses to polar questions; and (iii) the fact that it contrasts with more than ‘out of context’, as in the following example, repeated from the introduction: (26) a. I grew up with more than two parents. b. ??I grew up with at least two parents. To obtain these results, it is crucial to be able to derive ignorance implicatures through two distinct routes: quality for at least, and quantity for more than. References Büring, D. (2008). The least at least can do. In Proceedings of the 26th West Coast Conference on Formal Linguistics, pp. 114–120. Ciardelli, I., J. Groenendijk, and F. Roelofsen (2013). Inquisitive semantics: a new notion of meaning. Language and Linguistics Compass 7(9), 459–476. Ciardelli, I. and F. Roelofsen (2016). Hurford’s constraint, the semantics of disjunctions, and the nature of alternatives. To appear in Natural Language Semantics. Ciardelli, I., F. Roelofsen, and N. Theiler (2016). Composing alternatives. Linguistics and Philosophy. DOI:10.1007/s10988-016-9195-2. Coppock, E. (2016). Superlative modifiers as modified superlatives. In Semantics and Linguistic Theory, Volume 26, pp. 471–488. Coppock, E. and T. Brochhagen (2013). Raising and resolving issues with scalar modifiers. Semantics and Pragmatics 6(3), 1–57. Farkas, D. F. and F. Roelofsen (2016). Division of labor in the interpretation of declaratives and interrogatives. Forthcoming in Journal of Semantics. Fox, D. (2007). Free choice disjunction and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and implicature in compositional semantics, pp. 71– 120. Basingstoke: Palgrave Macmillan. Gazdar, G. (1979). Pragmatics: Implicature, presupposition, and logical form. Academic Press New York. Grice, H. (1975). Logic and conversation. In P. Cole and J. Morgan (Eds.), Syntax and Semantics, Volume 3, pp. 41–58. Harvard University Press. Groenendijk, J. (2009). Inquisitive semantics: Two possibilities for disjunction. In P. Bosch, D. Gabelaia, and J. Lang (Eds.), Seventh International Tbilisi Symposium on Language, Logic, and Computation. Springer-Verlag. Groenendijk, J. and F. Roelofsen (2009). Inquisitive semantics and pragmatics. Presented at the Workshop on Language, Communication, and Rational Agency at Stanford. Katzir, R. (2007). Structurally-defined alternatives. Linguistics and Philosophy 30(6), 669– 690. Katzir, R. and R. Singh (2013). Hurford disjunctions: embedded exhaustification and structural economy. In Proceedings of Sinn und Bedeuting 18, pp. 201–216. Kennedy, C. (2015). A “de-Fregean” semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics 8, 1–44. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 299 I. Ciardelli, E. Coppock, & F. Roelofsen Implicatures of modified numerals Lauer, S. (2014). Mandatory implicatures in Gricean pragmatics. In N. Goodman, M. Franke, and J. Degen (Eds.), Proceedings of the Formal & Experimental Pragmatics Workshop, pp. 21–28. Mayr, C. (2013a). Downward monotonicity in questions. In Proceedings of Sinn und Bedeutung 17, pp. 345–362. Mayr, C. (2013b). Implicatures of modified numerals. In I. Caponigro and C. Cecchetto (Eds.), From Grammar to Meaning: The Spontaneous Logicality of Language, pp. 139–171. Cambridge: Cambridge University Press. Mayr, C. and M.-C. Meyer (2014). More than at least. Slides presented at the Two days at least workshop, Utrecht. Roelofsen, F. (2013). Algebraic foundations for the semantic treatment of inquisitive content. Synthese 190(1), 79–102. Schwarz, B. (2016a). Consistency preservation in quantity implicature: The case of at least. Semantics and Pragmatics 9(1), 1–47. Schwarz, B. (2016b). At least and ignorance: a reply to Coppock & Brochhagen (2013). To appear in Semantics and Pragmatics. Solt, S. (2011). How many most’s? In I. Reich, E. Horsch, and D. Pauly (Eds.), Proceedings of Sinn und Bedeutung 15, pp. 565–580. Saarland Unversity Press. Westera, M. and A. Brasoveanu (2014). Ignorance in context: The interaction of modified numerals and QUDs. In Semantics and Linguistic Theory (SALT), Volume 24, pp. 414–431. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 300 Discourse-structuring conditionals and past tense1 Eva CSIPAK — Universität Konstanz Abstract. In this paper I present some data that challenges the view that a unified semantics of biscuit conditionals and hypothetical conditionals is possible. There is a class of biscuit conditionals that cannot occur with past temporal reference. In these cases, the antecedent serves to structure the discourse and as such must be true of the discourse situation. I argue that this is the reason why the past tense is incompatible with these conditionals, and therefore we can nevertheless maintain a unified semantics for hypothetical and biscuit conditionals. Keywords: biscuit conditionals, conditionals, (past) tense, discourse structure. 1. Introduction The literature on conditionals generally distinguishes between hypothetical conditionals as in (1) and biscuit conditionals as in (2). (1) If Alex went shopping this morning, there are biscuits on the sideboard. (2) If you are hungry, there are biscuits on the sideboard. The default interpretation of (1) includes the notion that the speaker is not committed with respect to whether the consequent there are biscuits on the sideboard holds in the actual world w0 . We typically assume that conditionals reason about what could be the case, for example if Alex went shopping in the morning. By contrast, it is generally understood that the speaker of (2) is in fact committed to it being true in w0 that there are biscuits on the sideboard. So it is intuitively clear why we consider (1) as a conditional: the speaker doesn’t know whether the antecedent holds, but she is willing to commit to the consequent holding just in case the antecedent does. The status of (2) is less clear since the speaker is taken to be committed to the truth of the consequent whether the antecedent holds or not. Still, in recent years a number of authors have proposed analyses which allow for a uniform semantics of sentences like (1) and (2), such as Franke (2009), Francez (2015) and Csipak (2015). There are two main arguments for why we may want a unified analysis: the form of both (1) and (2) is if p, q, and moreover, we observe that cross-linguistically many languages use the same form to express both meanings. This suggests that this is not simply a coincidence of the English language, but a systematic extension of the form from hypothetical conditionals to biscuit conditionals. The literature on biscuit conditionals typically discusses examples that are similar in spirit to (2) and its ancestor There are biscuits on the sideboard if you want them (discussed first in Austin 1956). This paper is concerned with another type of example that sometimes gets mentioned in connection with biscuit conditionals, but is not treated in more detail. This type of conditional 1I would like to thank Marı́a Biezma, Ryan Bochnak, Regine Eckardt, Kai von Fintel, Arno Goebel, Sven Lauer, Viola Schmitt, Frank Sode, Thomas Weskott, Hedde Zeijlstra, and Sarah Zobel for much helpful discussion. I thank Thomas Weskott for help with the experimental design and statistics. I would also like to thank the audiences at the LSA 2016 annual conference and Sinn und Bedeutung 21 for their insights. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 301 E. Csipak Discourse-structuring conditionals and past tense is exemplified in (3). (3) If I may be frank, you look awful. This paper will be dedicated to identifying the ways in which conditionals like (3) differ from biscuit conditionals such as (2), and whether it is possible to come up with a unified analysis that captures the properties of both. The rest of the paper is structured as follows. In section 2, I discuss the relevant data. Section 3 discusses why we cannot extend the existing analyses to account for the data in 2. Section 4 contains my analysis. Section 5 takes a brief detour into the realm of counterfactuals, and sketches how the data presented here also present a challenge to theories of counterfactuals. Section 6 concludes. 2. The empirical picture A first glance at sentences like (3) suggests that they share two properties with biscuit conditionals: they have the form if p, q, and the speaker uttering them is taken to be committed to the truth of q. We will take this seriously and assume that sentences like (3) are in fact a species of biscuit conditional. For reasons that will become apparent below, we will call them discoursestructuring conditionals. The insight that biscuit conditionals can fulfill different functions in the discourse is not new; for instance Günthner (1999) proposes to distinguish between the categories of discourse-structuring conditionals, meta-communicative conditionals, and relevance conditionals. The goal of the present section is to investigate the properties of hypothetical conditionals, biscuit conditionals, and discourse-structuring conditionals, and to identify which properties are shared and which are not. I will use the term biscuit conditional to refer to conditionals which can co-occur with past reference, but which have a biscuit interpretation (i.e., whose speaker is taken to be committed to the truth of the consequent in the actual world), and reserve the term discourse-structuring conditional to the conditionals that are the focus of this paper. We observe that hypothetical and biscuit conditionals, but not discourse-structuring conditionals, can occur with past temporal reference. Consider first the hypothetical conditionals in (4) and the biscuit conditionals in (5). (4) H YPOTHETICAL CONDITIONAL a. If Alex is in San Francisco right now, she is having iced coffee. b. If Alex was in San Francisco yesterday, she was having iced coffee. (5) B ISCUIT CONDITIONAL a. If you are hungry right now, there are biscuits on the sideboard. b. If you were hungry yesterday, there were biscuits on the sideboard. In the (b) variants of both (4) and (5) the antecedent refers to a time prior to the utterance time, and both sentences are perfectly acceptable even out of the blue. Now compare this to (6) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 302 E. Csipak Discourse-structuring conditionals and past tense through (9). In these cases, the (a) variant with the antecedent referring to the present utterance time are perfectly acceptable. The (b) variants whose antecedents refer to a time prior to the time of utterance are unacceptable, at least on a biscuit conditional interpretation. Note that when these conditionals are presented out of the blue, it is difficult to imagine a context in which a hypothetical conditional interpretation is available (more on this in section 4). (6) a. If I am being frank, you look awful. b. #If I was being frank yesterday, you looked awful. (7) a. If you promise not to tell anyone, I ran into Alex last week. b. #If you promised not to tell anyone yesterday, I ran into Alex last week. (8) a. If you ask me, Alex is getting ready to leave. b. #If you asked me yesterday, Alex was getting ready to leave. (9) a. Alex is a little odd if you know what I mean. b. #Alex was a little odd if you knew what I meant yesterday. What properties do (6)–(9) have in common, apart from not being able to occur with past temporal reference? In all of these cases the antecedent refers to the present discourse situation instead of facts outside of the discourse situation. Typically, the antecedents of hypothetical and biscuit conditionals refer to facts outside of the discourse situation, such as if you get hungry or if Alex went shopping this morning. But reference to the current discourse situation is not what makes discourse-structuring conditionals special. Hypothetical conditionals, for instance, can also refer to the utterance situation. In these cases, their antecedents remain compatible with past reference, as illustrated in (10) and (11). (10) a. b. If I am being frank, you should tell me. If I was being frank yesterday, you should have told me. (11) a. b. If you understand why this is important, I present the next example. If you understood why this was important, I presented the next example. Another property that discourse-structuring conditionals have is that whether their antecedents are true in the actual world can be decided directly by the interlocutors. Interlocutors can immediately agree on whether I may be frank or You promise not to tell anyone are true in w0 . Typical antecedents of hypothetical or biscuit conditionals are not like this. (12) If Alex gets hungry later, there are biscuits on the sideboard. (13) If Alex went shopping, there are biscuits on the sideboard. In these cases, the interlocutors cannot decide immediately whether Alex will get hungry later or whether Alex went shopping earlier. Importantly, while hypothetical and biscuit conditionals can also have antecedents whose truth in the actual world can be decided on the spot, discourseProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 303 E. Csipak Discourse-structuring conditionals and past tense structuring conditionals necessarily have this type of antecedent. There are no discoursestructuring conditionals where the interlocutors cannot decide on the truth of the antecedent based on the current discourse situation. Finally, discourse-structuring conditionals have one more property in common, to the exclusion of other biscuit conditionals and hypothetical conditionals: the proposition expressed by their antecedents is taken to be true of the discourse situation. Moreover, it corresponds to an action that is taken to have been committed by the interlocutors. For antecedents such as if I am being frank this is easy to see: simply by uttering the conditional itself, the speaker is being frank. Moreover, she can decide herself – on the spot, for a given discourse situation – whether to frankly communicate or not. Below we will discuss more tricky cases, such as if we now turn to page 5 or if you promise not to tell anyone where the interlocutors together have to decide to make the antecedent true. Note moreover that the construction is quite productive: any proposition commenting on the current discourse situation that is taken to be true by the interlocutors can be used as the antecedent of a discourse-structuring conditional.2 Moreover, they can be combined with consequents that are questions and imperatives as well as declaratives. (14) a. b. c. d. e. If we are discussing people’s teeth, have you noticed Alex’s new crown? If you want to hear my opinion, leave him already! If I can add to this, Alex is also never on time. If I may introduce a new topic, I have finally booked my vacation. If we take it one step further, I suggest we invite Alex. In sum, we have seen that discourse-structuring conditionals have the following properties. can occur with past tense q taken to be true in w0 p can refer to discourse situation truth of p in w0 decided immediately p taken to be true in w0 hypothetical conditional biscuit conditional 3 3 discoursestructuring conditional 7 7 3 3 3 3 3 7 7 3 7 7 3 3. A unified analysis? The literature on biscuit conditionals consists of two main lines of argument. Several authors have argued that there is a fundamental difference in the syntax and semantics of hypothetical 2 The antecedent and consequent propositions also have to be conditionally independent in the sense of Franke (2009) as discussed in section 3.2. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 304 E. Csipak Discourse-structuring conditionals and past tense conditionals and biscuit conditionals (e.g., Iatridou 1994, Ebert et al. 2008, 2014, Scheffler 2008, and Siegel 2006). Others argue that both kinds of conditionals share the same syntax and semantics, and propose pragmatic mechanisms that cause the difference in interpretation (e.g., Franke 2009, Francez 2015, Lauer 2015, Biezma and Goebel this volume). The data presented in section 2 pose a puzzle for the view that biscuit conditionals have the same syntax and semantics as hypothetical conditionals: if discourse-structuring conditionals are a species of biscuit conditional, and biscuit conditionals have the same syntax and semantics as hypothetical conditionals, then it should follow that discourse-structuring conditionals are acceptable under the same circumstances where hypothetical conditionals are acceptable. In particular, we would expect them to be acceptable with past temporal reference, since hypothetical conditionals and biscuit conditionals are compatible with it. On a non-unified view, we could simply stipulate that discourse-structuring conditionals are not compatible with past temporal reference, or move away even farther from a unified analysis by claiming that the data in (6) through (9) are simply not conditionals at all. This view is unattractive in light of the fact that many languages use the form if p, q to express discourse-structuring conditionals. The arguments in Franke (2009) and Francez (2015) for a unified analysis for hypothetical and biscuit conditionals are convincing. Still, the present section aims to add some additional empirical arguments for a unified analysis. Section 4 then sketches how we can account for the puzzling data in section 2 even within a Franke-style unified analysis. 3.1. A different syntax and semantics Let us first take a look at some of the empirical differences that are claimed to exist between biscuit conditionals and hypothetical conditionals. Iatridou (1991, 1994) argues that biscuit conditionals in English do not allow then-insertion, unlike hypothetical conditionals. (15) a. b. If Alex went shopping, then there are biscuits on the sideboard. If you are hungry, (#then) there are biscuits on the sideboard. Crucially, her analysis rests on this fact: the presence of then is what allows the hearer to interpret the consequent with respect to the worlds selected by the antecedent. Conversely, when then cannot occur, this interpretation is impossible and a biscuit interpretation is required instead. A more recent discussion of the (pragmatic) role of then is found in Biezma (2014), which mostly sets aside the issue of biscuit conditionals. Here I present some conditionals that clearly have a biscuit interpretation even though they contain then. (16) If you are hungry then there is a Sainsbury’s just behind the main complex that does a reasonably priced breakfast. http://www.lancaster.ac.uk/colleges/graduate/wp-content/uploads/2016/09/DAY-TRIP-TO-CHESTER CHESHIRE-OAKS.pdf Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 305 E. Csipak (17) Discourse-structuring conditionals and past tense If you are hungry, then there is a tempting menu. http://www.newsshopper.co.uk/news/10879271.PubSpy reviews The Rose and Crown Green Street Green/ Thus the empirical claims on which this analysis is based do not hold. Another empirical difference that is claimed to exist between biscuit conditionals and hypothetical conditionals applies to German (the claim originates in Davison 1983 and is widely cited, e.g. in Iatridou 1994 and Ebert et al. 2008, 2014). It is claimed that word order in the consequent determines whether a conditional receives a biscuit interpretation or a hypothetical conditional interpretation. For conditionals with a preposed antecedent, the verb can occur either as the second constituent (directly following the antecedent) or as the third constituent (following the antecedent and one more constituent). Davison claims that V2 (i.e., with the verb directly following the antecedent) word order in the consequent only allows a hypothetical conditional interpretation, whereas V3 word order (with the verb following the antecedent and another constituent) only allows a biscuit interpretation. (18) Wenn du mich brauchst, bin ich in meinem Büro. if you me need am I in my office ‘If you need me, I will be in my office.’ V2 WORD ORDER (19) Wenn du mich brauchst, ich bin in meinem Büro. if you me need I am in my office ‘If you need me, I will be in my office.’ V3 WORD ORDER Davison reports that (18) only has an interpretation as a hypothetical conditional, whereas (19) only has an interpretation as a biscuit conditional. The literature further claims that whenever a conditional with V2 consequent word order occurs where only a biscuit interpretation makes sense, speakers reject the conditional. Some analyses, such as Ebert et al. (2008), crucially rely on this difference for their analysis. They propose that the V3 word order in the consequent of biscuit conditionals is not a speaker preference, but rather grammaticalized. Thus, the consequent V3 word order triggers an obligatory biscuit interpretation even in contexts where world knowledge suggests that this does not make sense. In the same way they propose that consequent V2 word order forces a hypothetical conditional interpretation, again even in contexts where world knowledge suggests only a biscuit interpretation makes sense. Empirically these claims do not hold. Naturally occurring data suggests that speakers do choose consequent V2 word order in contexts where a biscuit conditional interpretation is necessary, as in (20). (20) Wenn du Durst hast, habe ich etwas für dich. if you thirst have have I something for you ‘If you are thirsty, I have something for you.’ Jan Paul: Paul und die Monsterpflanze Speakers also produce consequent V3 conditionals with a clearly hypothetical conditional interpretation, as in (21). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 306 E. Csipak (21) Discourse-structuring conditionals and past tense Context: A user on a knitting website is talking about how fast knitters from Finland knit socks. Die sind so schnell, ich glaube, wenn ich das ‘trainieren’ würde, ich wäre they are so fast I believe if I that train would I would.be nie so schnell! never so fast ‘They are so fast – I think if I ‘trained’ [speed knitting] I would never be so fast!’ Furthermore there is experimental evidence against the view that syntax determines conditional intepretation. Köpcke and Panther (1989) asked speakers to rate conditional sentences with consequent V2 word order on a 5-point scale where 1 was ‘fully acceptable’ and 5 was ‘not at all acceptable’. Interestingly, speakers rated the sentence Wenn Sie mich fragen, wird es bald schneien ‘if you ask me, it’s going to snow soon’ on average at 1.85. The same sentence was rated at 1.73 when dann ‘then’ was inserted. Other biscuit conditionals were less acceptable for the speakers, e.g. Wenn du durstig bist, ist Bier im Kühlschrank ‘If you are thirsty, there is beer in the fridge’ was rated at 2.68 without dann ‘then’, and 2.73 with dann. In Csipak (2015) I report on an acceptability judgment study I conducted with 24 speakers of Standard German from Göttingen (Lower Saxony). These speakers were asked to rate the acceptability of biscuit conditionals and hypothetical conditionals on a 7-point scale, with 7 being completely acceptable and 1 being completely unacceptable. The results showed that speakers found conditionals with a hypothetical conditional interpretation with the (atypical) V3 word order less acceptable than with V2 word order, both by subject (F1 (1,23)=218.8, p<.001, ηG 2 =.79) and by item (F2 (1,11)=195.2, p<.001, ηG 2 =.89). However, the lowest rated conditionals (hypothetical conditionals with V2 consequent word order) were still significantly more acceptable than ungrammatical filler sentences that contained word order violations (F1 (1,23)=42.00, p<.001, ηG 2 =.19). For the biscuit conditionals, there was a marginal preference for V3 word order. Thus, while speakers do display a preference for hypothetical conditionals to occur with V2 consequent word order, they do not seem to exhibit a preference for consequent word order for biscuit conditionals. We conclude that speakers are able and willing to assign the less preferred interpretation to both kinds of conditionals where world knowledge makes it necessary. This suggests that the speaker preference for one or the other word order, to the extent that it exists, is not grammaticalized, and it should not be the basis from which we derive an obligatory syntactic or semantic difference between hypothetical and biscuit conditionals. 3.2. The pragmatic view The previous section has shown that a syntactic or semantic difference between biscuit and hypothetical conditionals runs into empirical problems. We therefore turn to an alternative story proposed in Franke (2009). He argues that biscuit conditionals have the same semantics that we assume for hypothetical conditionals (for example a modal restrictor analysis along the lines of Kratzer 1986, 2012). The difference in interpretation that we observe between biscuit Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 307 E. Csipak Discourse-structuring conditionals and past tense and hypothetical conditionals on this view is not a semantic one, but comes about pragmatically. Franke introduces the notion of conditional independence and proposes that two propositions p and q are conditionally independent if changing one’s beliefs about one will not cause a change in one’s belief about the other. On his view, hypothetical conditionals are conditionally dependent. Consider the following example. (22) If Alex went shopping, there are biscuits on the sideboard. Imagine that the speaker is undecided about whether Alex went shopping, and equally undecided about whether there are biscuits on the sideboard. Upon learning that Alex went shopping (that is, a change in belief about p), the speaker will likely also change her beliefs about whether there are biscuits on the sideboard (that is, a change in belief about q). Compare this to a biscuit conditional such as (23). (23) If you are hungry, there are biscuits on the sideboard. Will learning that the addressee is hungry change the speaker’s beliefs about whether there are biscuits on the sideboard? World knowledge suggests that it should not. Thus, the antecedent and consequent propositions are conditionally independent. Franke proposes that whenever two propositions that are conditionally independent, they are nevertheless linked via a conditional structure, the hearer undergoes the following chain of reasoning: (24) a. b. c. d. e. The speaker used a conditional to link p and q, suggesting conditional dependence. p and q are conditionally independent. The speaker knows that the hearer knows this but used the construction nonetheless. The hearer concludes that the speaker must be uncertain about the truth of p. Since p and q are conditionally independent, the speaker must have independent evidence for the truth of q. This is how the biscuit interpretation of conditionals like (23) comes about, allowing us to maintain a unified syntax and semantics for both types of conditionals. What predictions does this proposal make for discourse-structuring conditionals? World knowledge suggests that the antecedent and consequent of a discourse-structuring conditional are conditionally independent. (25) If you ask me, Alex is tall. World knowledge suggests that changing one’s belief about whether the addressee is asking to hear the speaker’s opinion will not change one’s belief about whether Alex is tall. So on Franke’s view, (25) could be treated as a biscuit conditional. On Franke’s view biscuit conditionals and hypothetical conditionals have the same syntax and semantics. This means that we expect discourse-structuring conditionals, which are essentially biscuit conditionals, to have Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 308 E. Csipak Discourse-structuring conditionals and past tense the same properties that hypothetical conditionals have. In particular, they should be able to co-occur with past temporal reference, as biscuit conditionals do (recall the examples (4) and (5) in section 1). But the examples discussed in sections 1 and 2 have shown that this is not the case. In section 4, I argue that there are independent reasons why discourse-structuring conditionals are not available with past temporal reference, and that we can in fact maintain a Franke-style unified analysis nevertheless. 3.3. Present counterfactual uses Before turning to the analysis, let us briefly consider some additional data. It is well-known that English uses past tense morphology in the antecedents of counterfactual conditionals. Since section 2 has shown that run-of-the-mill past temporal reference is excluded in discoursestructuring conditionals, we might ask what is going on in counterfactuals that use past tense morphology. (26b) illustrates a present counterfactual conditional. Most importantly, we observe the simple past form was in the antecedent, and the form would be having in the consequent. (26) a. b. If Alex was in San Francisco last week, she was having iced coffee. If Alex was in San Francisco right now, she would be having iced coffee. In recent years counterfactual conditionals like (26b) have received a lot of attention. The past tense morphology in particular has been the subject of much debate. There are currently two lines of argument: some authors propose that the past tense morphology is not semantically interpreted as a ‘real’ past tense. On this view, the past tense does not refer to a past time, but instead tracks remoteness on another dimension, namely across worlds (see Iatridou 2000, Schulz 2014). Others have argued that the past tense that we observe is in fact interpreted temporally (see for instance Arregui 2009, Ippolito 2013). On this view, the past tense takes us back to a time when the consequent was still a live possibility in w0 . The two types of accounts differ slightly in the predictions that they make for the availability of discourse-structuring counterfactual conditionals. The fake tense approach assumes that the past tense in the antecedent is not interpreted temporally in counterfactuals like (27). Therefore we conclude that in principle, nothing in this approach directly predicts that discoursestructuring counterfactuals are unacceptable, so long as the antecedent refers to counterparts of the utterance time in counterfactual worlds. And we find some discourse-structuring present counterfactuals that are acceptable, as in (27). (27) If I was being frank right now, you look awful. But we also find some discourse-structuring present counterfactuals which are not acceptable, as in (28). (28) #If you promised not to tell anyone right now, Alex is getting ready to leave. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 309 E. Csipak Discourse-structuring conditionals and past tense In fact, the majority of discourse-structuring conditionals seems to behave like (28), i.e., they are unacceptable as counterfactuals as well as with run-of-the-mill past temporal reference. This unacceptability is a puzzle for the fake tense approach since on this view, ‘fake’ tense should behave differently semantically from ‘real’ past tense. The counterfactual-past-as-regular-past (‘past-as-past’) approaches run into similar but different problems. They assume that a past tense operator takes scope over the entire conditional, which causes the counterfactual interpretation. The simple past observed in the antecedent and the would in the consequent are reflexes of this higher past tense operator. Thus in principle this account would predict that neither conditionals with run-of-the-mill past temporal reference nor counterfactual conditionals should be available with a discourse-structuring flavour, and this is indeed what we find for most antecedents – except for (27), which is a puzzle for this view. But this view has a more serious problem. Speakers of English disprefer biscuit conditionals with consequents containing would, as in (29). Note that speakers seem to vary on whether they find a biscuit reading of (29) unacceptable, or whether they simply prefer (27). (29) #/?If I was being frank right now, you would look awful. This is true of biscuit conditionals more generally. For counterfactual biscuit conditionals, speakers prefer past tense morphology in the antecedent, but present tense morphology in the consequent. The past-as-past approach to counterfactuals cannot straightforwardly account for this.3 (30) a. If you wanted something to nibble on later, there are biscuits on the sideboard. b. #/?If you wanted something to nibble on later, there would be biscuits on the sideboard. Solving this puzzle goes beyond the scope of the present paper. 4. My proposal The present section will make a proposal for how to tackle discourse-structuring conditionals. A first analysis that suggests itself from examples like (3) is one in terms of self-verifying utterances in the sense of Eckardt (2012). She proposes that utterances are self-verifying iff they become true by virtue of being uttered. (31) a. b. I am using a verb. I promise to mow the lawn. It is easy to see that the speaker of (31a), by virtue of uttering (31a), is making the sentence true 3 Note that conditionals like (30) are not discussed in Swanson (2013). He only discusses examples were the consequent shows the past tense morphology that is predicted under the past-as-past analyses. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 310 E. Csipak Discourse-structuring conditionals and past tense since it contains the verb am using. The speaker of (31b) makes a promise by uttering (31b) (the word promise is being used performatively), and again it is by virtue of being uttered that (31b) becomes true. Now let us consider how to translate this to biscuit conditionals. (32) a. b. If I am being frank, you look awful. In all the worlds closest to w0 where I am being frank, you look awful. (33) a. b. c. By uttering (32a) I am being frank. Thus w0 itself is the world closest to w0 where I am being frank is true. (32a) is a biscuit conditional; thus the speaker has independent evidence for the consequent. The speaker believes that you look awful is true in w0 . (32a) is true in w0 . d. e. (34) If I am being frank, you look awful. a. ∀w’∈maxg (∩f(w0 )∪JI- AM - BEING - FRANKKw’ ): YOU - LOOK - AWFUL(w’)=1 because b. ∀w’∈maxg (∩f(w0 ) ∪(sp sends m to add and FRANK(ε, m), and R⊆t(ε) and S⊆R): ADD - LOOKS - AWFUL(w’)=1. The indexicals sp for speaker, add for addressee, m for message and ε for event receive their values relative to the utterance context. When the speaker utters if I am being frank, you look awful, there is an event ε of sending a message m, and the message counts as frank. Without going into the lexical semantics of frank in too much detail, let us assume that one of the ways in which a message counts as frank is if it is both true with respect to the speaker’s beliefs, and exceeding a contextual standard of what counts as rude. I assume that speakers will in a next step associate the message m with the consequent proposition, q. We can then verify that the speaker’s message (‘you look awful’) indeed counts as frank. Crucially, the speech time falls into the time of this event. This serves to verify the utterance. When combined with past temporal reference, the conditional no longer self-verifies the antecedent, causing oddness. (35) #If I was being frank yesterday, you looked awful. a. ∀w’∈maxg (∩f(w0 )∪JI- WAS - BEING - FRANK - YESTERDAYK): YOU - LOOKED - AWFUL (w’)=1. b. ∀w’∈maxg (∩f(w0 )∪(sp sends m to add and FRANK(ε, m), and R⊆t(ε) and R<S)): ADD - LOOKED - AWFUL (w’)=1. Here the speaker claims to have made a frank utterance prior to speech time (there was an event ε of sending a frank message m which lies before speech time). But because the event connected to the frank message lies before the speech time, it cannot serve as a witness to automatically verify the utterance. The resulting interpretation is a hypothetical conditional about the past (‘all the (relevant best) worlds in which I was frank yesterday are worlds in which you looked awful’) that is pragmatically odd. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 311 E. Csipak Discourse-structuring conditionals and past tense This proposal cannot straightforwardly account for those cases where the addressee is addressed in the antecedent: if you promise not to tell anyone; if you know what I mean or even if we now turn to page 5 are not antecedents that can self-verify; that is, the speaker cannot guarantee that by virtue of uttering the conditional, these antecedents become true. We therefore broaden the proposal to account for these cases. The intuition we are trying to capture is that by uttering a discourse-structuring conditional, the speaker uses the antecedent to communicate under which conditions she is willing to share the contents of the consequent, and then shares the consequent. This invites the inference that the speaker takes the antecedent to be true. To illustrate, we consider (36). (36) If you promise not to tell anyone, Alex is asleep. We can then assign the following semantics to (36). (37) ∀w’∈maxg (∩f(w0 )∪(promise(ε, add, ¬tell(add, m)) and S ⊆R⊆t(ε)): Alex-asleep(w’)=1 In prose, in all the (relevant best) worlds where there is a promising event happening at speech time involving the addressee not telling anyone about message m, q holds. Again I assume that the interlocutors will associate m and q; thus, in all the best worlds where the addressee promises not to tell anyone that q, q holds. Since the antecedent and q are conditionally independent, the speaker is taken to be committed to the fact that q holds in w0 . It is now up to the addressee to ensure that the entire conditional is true in w0 by simply not telling anyone about q, i.e., by keeping the promise not to tell anyone. The proposal spelled out for (36) can be extended to other antecedents: if you know what I mean (by message m), if you ask me (about message m), etc. The analysis also derives why past tense uses are odd. (38) (39) #If you promised not to tell anyone yesterday, Alex was asleep. ∀w’∈maxg (∩f(w0 )∪(promise(ε, add, ¬tell(add, m)) and R⊆t(ε) and R<S)): Alexasleep(w’)=1 In all the (relevant best) worlds where there was a promising event at some time prior to speech time that involved the addressee not telling anyone about message m, q holds. Again p and q are conditionally independent, but since the antecedent is about whether or not the addressee told anyone about a message m at a time prior to speech time, there is no reason to associate m with q. But without this connection, the conditional is simply uninterpretable on a discoursestructuring interpretation (and it is difficult to imagine a context where a hypothetical conditional interpretation is available). Before concluding, I will point out that as with other types of discourse effects, we expect that the antecedents of discourse-structuring conditionals should be acceptable with past temporal Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 312 E. Csipak Discourse-structuring conditionals and past tense reference in contexts where they are not used to refer to the present discourse and there is some other interpretation available. This prediction is indeed borne out, as illustrated with (40). (40) a. b. c. If you knew what I meant when I called Alex ‘organized’ yesterday, you will understand what I mean when I call Jesse ‘disorganized’. If I was being frank yesterday I may have offended Alex. If you asked me yesterday, I don’t recall. All of the conditionals in (40) have reasonable interpretations as hypothetical conditionals. For instance, in (40b) the speaker is unsure whether what she said yesterday counts as frank (presumably she is uncertain whether her statement exceeded the standard for rudeness), and consequently she is unsure whether she offended Alex.4 Finally, I speculate on the contextual clues that turn a conditional into a discourse-structuring (biscuit) conditional. Consider (41), which has an interpretation as a hypothetical conditional, but not as a discourse-structuring conditional. (41) If you promise not to tell anyone, I will tell you a secret. Given the right context, this example is perfectly acceptable with past temporal reference. (42) Context: After waking up with amnesia, A and B are trying to figure out what happened the night before. A: If you promised not to tell anyone, I told you a secret. On my view, the reason why (42) is acceptable and the reason why (41) is not interpreted as a discourse-structuring conditional is the same. In the antecedent, the speaker is referring to an event of the addressee not telling anyone the message m. However, the consequent proposition is both conditionally dependent on the antecedent proposition, and it is also not ‘juicy’, i.e., the interlocutors are unlikely to associate the message m with the consequent proposition. Compare this to (43). (43) If you promise not to tell anyone, I will tell Peter about the baby tomorrow. We observe that (43) is ambiguous between a biscuit interpretation on which the speaker’s telling Peter is conditionally independent from the addressee agreeing not to tell anyone. On this interpretation, the past tense reading is out. (44) #If you promised not to tell anyone last week, I told Peter about the baby the next day. But on a hypthetical conditional interpretation where the two propositions are conditionally 4 Remember that a verb like promise can be used performatively with present temporal reference, and reportatively with past temporal reference. (i) a. I promise to let you sleep in on Sunday. performative b. I promised to let you sleep in last Sunday. reportative Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 313 E. Csipak Discourse-structuring conditionals and past tense dependent, the past tense interpretation is available. (45) A and B have amnesia. Looking through the records, they see that B signed a nondisclosure agreement, but they do not find one signed by A. They also read in Peter’s diary that someone told him about the baby. A: If you promised not to tell anyone, I told Peter about the baby. Thus we conclude that given the particular interplay of context and content that is necessary for a discourse-structuring conditional interpretation, it follows that this interpretation is simply unavailable when the antecedent is interpreted with past temporal reference. But as the examples have shown, there is no reason to assume a separate syntax or semantics for discoursestructuring conditionals. Thus we can maintain a unified syntax and semantics for hypothetical and biscuit conditionals. 5. Conclusion The present paper has provided some challenging evidence for a unified account of hypothetical and biscuit conditionals: there are some biscuit conditionals that cannot co-occur with past temporal reference, namely discourse-structuring conditionals. This is unexpected given that both hypothetical conditionals and most biscuit conditionals can occur with past temporal reference. I have argued that a unified analysis of the two can be maintained. The reason why discourse-structuring conditionals are unacceptable with past temporal reference has to do with the relationship between antecedent and consequent: the antecedent refers to an event that is assumed to involve the consequent proposition. Such a relationship between antecedent and consequent is not available when the antecedent is temporally located in the past, but the consequent proposition is uttered in the present. References Arregui, A. (2009). On similarity in counterfactuals. Linguistics and Philosophy 32, 245–278. Austin, J. (1956). Ifs and cans. In Proceedings of the British Academy, Volume 42, pp. 109– 132. Biezma, M. (2014). The grammar of discourse: The case of then. In Proceedings of SALT 24, pp. 373–394. Biezma, M. and A. Goebel (this volume). The pragmatic ingredients to get perfect biscuits. In R. Truswell (Ed.), Proceedings of Sinn und Bedeutung 21. Csipak, E. (2015). Free Factive Subjunctives in German. Ph. D. thesis, Universität Göttingen. Davison, A. (1983). Linguistic or pragmatic description in the context of the performadox. Linguistics and Philosophy 6, 499–526. Ebert, C., C. Ebert, and S. Hinterwimmer (2008). A unified analysis of indicative and biscuit conditionals as topics. In T. Friedmann and S. Ito (Eds.), Proceedings of SALT XVIII, pp. 266–283. Ebert, C., C. Ebert, and S. Hinterwimmer (2014). A unified analysis of conditionals as topics. Linguistics and Philosophy 37, 353–408. Eckardt, R. (2012). Hereby explained. Linguistics and Philosophy 35, 21–55. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 314 E. Csipak Discourse-structuring conditionals and past tense Francez, I. (2015). Chimerical conditionals. Semantics and Pragmatics 8, 1–35. Franke, M. (2009). Signal to Act. Game Theory in Pragmatics. Ph. D. thesis, Amsterdam. Günthner, S. (1999). Wenn-Sätze im Vor-Vorfeld: Ihre Formen und Funktionen in der gesprochenen Sprache. Deutsche Sprache 3, 209–235. Iatridou, S. (1991). Topics in Conditionals. Ph. D. thesis, MIT. Iatridou, S. (1994). On the contribution of conditional then. Natural Language Semantics, 171–199. Iatridou, S. (2000). The grammatical ingredients of counterfactuality. Linguistic Inquiry 31, 231–270. Ippolito, M. (2013). Subjunctive Conditionals. Linguistic Inquiry Monographs Series, MIT Press. Köpcke, K.-M. and K.-U. Panther (1989). On correlations between word order and pragmatic function of conditional sentences in German. Journal of Pragmatics 13, 685–711. Kratzer, A. (1986). Conditionals. In Proceedings of Chicago Linguistics Society 22, pp. 1–15. Kratzer, A. (2012). Modals and Conditionals: New and Revised Perspectives. Oxford University Press. Lauer, S. (2015). Biscuits and provisos. In E. Csipak and H. Zeijlstra (Eds.), Proceedings of Sinn und Bedeutung 19, pp. 357–374. Scheffler, T. (2008). Relevance conditionals as utterance modifying adverbials. In O. Bonami and P. Cabredo Hofherr (Eds.), Empirical issues in syntax and semantics, pp. 373–392. Schulz, K. (2014). Fake tense in conditional sentences: A modal approach. Natural Language Semantics 22, 117–144. Siegel, M. (2006). Biscuit conditionals: Quantification over potential literal acts. Linguistics and Philosophy 29, 167–203. Swanson, E. (2013). Subjunctive biscuit and stand-off conditionals. Philosophical Studies 163(3), 637–648. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 315 316 Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec1 Amy Rose DEAL — University of California, Berkeley Julia NEE — University of California, Berkeley Abstract. How is definiteness expressed in number-marking languages lacking a definite article? May bare nouns in such languages simply be read as definites or indefinites, without constraint? Dayal (2004) demonstrates that the interpretation of bare nouns with respect to definiteness is significantly constrained in Hindi and Russian. In these languages, singular and plural bare nouns present different possibilities for indefinite interpretation, in a way that receives a natural explanation within a neo-Carlsonian theory of noun meaning (Chierchia, 1998). This makes for a close connection between the meanings of bare nouns in English and those in Hindi and Russian. Does this connection extend to the meanings of bare nouns in numbermarking languages in general, even outside of Indo-European? In this paper, we demonstrate that the answer is yes. Our evidence comes from bare noun interpretation in Teotitlán del Valle Zapotec, a language of Oaxaca, Mexico. The Zapotec findings closely replicate Dayal’s findings for Indo-European languages, providing support for the viability of the neo-Carlsonian approach as a set of constraints on semantic variation in general. Keywords: Bare nouns, plural, number, definite, pseudo-incorporation, Zapotec 1. Introduction Teotitlán del Valle Zapotec is a language with a singular/plural distinction and without a definite determiner. Arguments in this language frequently consist of just a bare noun, as in (1).2 (1) Ka-zhunih kabai / d-kabai. PROG -run horse / PL -horse The horse(s) is/are running. This paper is about the interpretation of Teotitlán del Valle Zapotec bare nouns, in particular as concerns definiteness and the role of number marking. Conventional wisdom holds that bare nouns in languages lacking definite articles are able to freely function both as definites and as indefinites.3 If true, this would make bare nouns in such languages quite different from their counterparts in Germanic languages, such as English bare plurals and bare mass nouns. Those arguments are well-known to show a highly restricted range of interpretations, differentiating them both from definites and from ordinary indefinites with the article a (Carlson, 1977). 1 Our deepest thanks are due to language consultants Enedina Bazán Chávez, Tomasa Chávez, Sergio Martı́nez, and Teresa Martı́nez Chávez. Thanks as well to audience members at SuB in Edinburgh, and at the Definiteness Across Languages conference in Mexico City. 2 The TdVZ data in this paper are written in a practical orthography that is similar in pronunciation to Spanish with a few modifications. ts and dz represent voiceless and voiced alveolar affricates, and ch and dx their postalveolar counterparts. ll is a geminate alveloar lateral. The following abbreviations are used in TdVZ glosses: ANIM animal gender, COP copula, EMPH emphatic, FUT future, HAB habitual, NEG negation, NEUT neutral (aspect), PERF perfective, PL plural, PROG progressive, PRT particle, SBJ subjunctive, Y. N yes/no question. 3 See, for instance, Lee (2006: p 9) on closely related language San Lucas Quiavinı́ Zapotec. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 317 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec The work of Dayal (2004) poses an important challenge to the conventional wisdom about languages lacking definite articles. In Hindi and Russian, Dayal shows, only definite and kindlevel readings are freely available for all arguments. All other types of interpretation are subject to significant restrictions. Bare plural arguments allow indefinite interpretations, but only weak indefinite readings are ever permitted. Bare singular arguments allow indefinite interpretations only in contexts of (pseudo-)incorporation. The distribution of definite and indefinite readings is thus significantly more complex than expected on the conventional view. What sort of theory is required to account for these restrictions on bare noun interpretation? Dayal shows that the answer is more familiar than might be expected. With only a minor modification, the range of restrictions on bare noun interpretation in Hindi and Russian falls out from Chierchia’s (1998) neo-Carlsonian theory for English bare nouns. The overall conclusion is that a unified theory of bare noun interpretation remains in reach, bringing together (numbermarking) languages with and without definite articles. This paper contributes new evidence in support of this conclusion from Teotitlán del Valle Zapotec, a language typologically and genetically distinct from the languages investigated by Dayal. Quite strikingly, the interpretation of singular and plural bare nouns in Teotitlán del Valle Zapotec shows the same intricate distribution predicted by the Dayal/Chierchia theory. In this language, too, only definite and kind-level readings are freely available to all arguments; existential readings show a complex distribution that involves both the number marking of the noun and the argument structure of the verb. Plural and mass bare nouns generally allow existential readings, though only with narrowest scope. Singular bare nouns show existential readings only with narrowest scope and only in contexts of plausible pseudo-incorporation. The findings overall lend support to the theoretical framework of Chierchia (1998) and Dayal (2004), as this approach successfully predicts both the range of readings possible for bare nouns and the way that number marking influences bare noun interpretation. Science depends on replication, and the prospects for formal semantic approaches to linguistic typology depend on teasing apart core constraints on semantic variation from accidental similarities owing to shared history or language contact. By showing that a familiar system for bare noun meaning is active in an unrelated, geographically distant language, this study suggests that core mechanisms of semantic competence are involved in regulating the interpretation of bare nouns. The paper is laid out as follows. In the next section, we introduce Chierchia’s (1998) approach to English bare nouns and consider certain of its crosslinguistic predictions, particularly in view of a modification suggested by Dayal (2004). In section 3, we present the core data on bare plural and mass nouns in Teotitlán del Valle Zapotec, showing that they behave as expected in this system. In section 4, we then discuss the special properties of singular kind terms, drawing especially on the discussion in Chierchia (1998); in section 5 we show how this approach leads to correct predictions for the analysis of Teotitlán del Valle Zapotec bare singulars. In section 6, we discuss how the numeral te ‘one’ fits into the system. Section 7 briefly concludes. We round out this introduction with some background information on Teotitlán del Valle Zapotec and the data presented in this paper. Teotitlán del Valle Zapotec is spoken in Teotitlán del Valle, a community of approximately 5000 people located 25 km outside of Oaxaca City, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 318 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Mexico. Following a Zapotecanist convention, we henceforth abbreviate the language name as TdVZ. The language shows VSO word order with SVO as a common alternant. TdVZ data in this paper were elicited from four speakers, three of whom reside in Teotitlán del Valle; one speaker belongs to the diasporic community in California. Semantic data were obtained through three methods. The primary method was standard semantic elicitation of the type described in Matthewson (2004), involving translation between TdVZ and Spanish (for speakers in Mexico) or English (for the speaker in California) as well as judgments of the felicity of TdVZ sentences in particular contexts. The secondary methods involved a prompted narrative task, where the speaker was asked to provide TdVZ descriptions for portions of a pair of wordless picture books (Mercer Meyer’s Frog on his own and A boy, a dog, and a frog), and act-out tasks, where the speaker was asked to narrate a series of actions performed by the fieldworker. 2. Interpreting bare nouns In this section we introduce Chierchia’s (1998) approach to English bare nouns and Dayal’s (2004) extension of that approach to languages lacking definite articles. 2.1. Bare nouns in English As is well-known, bare nouns in English support three major readings. On the first reading, the bare plural or mass noun functions as the name of a kind. This allows it to serve as the argument of a predicate like common, extinct or rare, which apply to kinds but not to individuals. (2) a. Cats are common. b. Gold is rare. The second reading is the closely related generic reading. The bare noun continues to describe a species or (natural) kind, but the predicate is one that may also apply to particular individuals. (3) a. Cats purr. b. Gold is shiny. The third reading is one where the bare noun is felt to contribute not a kind, but a set of instances of that kind. The sentence is understood with existential quantification over these instances. (4) a. Cats are purring. b. Gold is missing from the safe. The basic task for theories of bare noun interpretation in English is to explain how bare arguments can span this range of interpretations (but no others). In presenting the approach pursued by Chierchia (1998) and taken up by Dayal (2004), it will be helpful to start with mass nouns. Chierchia proposes that nouns like gold inherently denote kinds. Kinds are modeled as individual concepts, mapping any world or situation to the maximal sum of the relevant material (in this case, gold) in that world or situation. Once evaluated at a world or situation, a kind term is of type e. This semantic type explains why kind terms may function as arguments without the help of a determiner. The kind-level predicate simply Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 319 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec applies directly to the kind-level noun.4 (5) Gold is rare. rare(GOLD) To handle existential readings, Chierchia (developing ideas from Carlson 1977) proposes a special composition operation that applies as the kind-denoting argument combines with the predicate. This operation, ‘Derived Kind Predication’ or DKP, introduces local existential quantification over instances of the kind. In so doing, it makes use of the operator ∪ ‘Up’ which maps kinds to properties, (6). The DKP rule itself is defined as in (7). (6) Let d  be a kind. Then for any world s, (Chierchia, 1998: 350) λ x [x ≤ d ], if d is defined s s ∪d = λ x [FALSE], otherwise where ds is the plural individual that comprises all of the atomic members of the kind. (7) Derived Kind Predication (DKP): (Chierchia, 1998: 364) ∪ If P applies to objects and k denotes a kind, then P(k) = ∃x[ k(x) ∧ P(x)] The existential quantification introduced by DKP is necessarily limited in scope; it applies as soon as the predicate composes with its arguments. This explains why the existential quantification associated with bare arguments standardly fails to outscope negation (Carlson, 1977). (8) ¬∃x[∪ GOLD(x) ∧ f ind( j, x)] John didn’t find gold. Partially similar mechanisms are proposed for the generic reading, which plays a relatively more minor role in the overall system. In this case the generic operator is restricted by a description obtained from the kind-level argument via accommodation; the restriction contains a variable over instances of the kind, via the freely available shifter ∪ (Chierchia, 1998: 366-7).5 (9) Gold is shiny. Gnx,s [∪ GOLD(x) ∧C(x, s)][shiny(x, s)] For count nouns, Chierchia proposes a basic property-type denotation. Singular count nouns like cat denote singular properties (sets of cat-atoms) whereas plural count nouns like cats denote plural properties (sets of sums of cat-atoms). The plural property is similar to a mass property in that it has a supremum; we may speak, relative to a world or situation, of the maximal sum of cats or of gold in that world or situation. The intensionalization of this sum is formally identified with the kind. To map plural properties to kinds, Chierchia introduces the operator ∩ ‘Down’: (10) For any  property P and world/situation s, λ s ιx[Ps (x)], if λ s ιx[Ps (x)] is in the set K of kinds ∩P = undefined, otherwise (Chierchia, 1998: 351) 4 Here and below, we use capital letters for names of kinds. Chierchia, C is a contextual variable restricting the individual (x) and situation (s) arguments the Gn operator ranges over. 5 Following Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 320 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Application of ∩ to the plural property JcatsK produces a kind, CAT. Supposing ∩ is freely available as a type shift, bare plurals will freely shift to a kind-level interpretation. Evaluated at a particular world or situation, the noun will then be able to function as a bare argument of type e, much as mass nouns do. As a kind term, it will be able to give a kind-level reading; a narrow scope existential reading, via DKP; or a generic reading, via accommodation and ∪ . common(∩ cats) (11) Cats are common. ¬∃x[∪∩ cats(x) ∧ see(I, x)] (12) I don’t see cats. Gnx,s [∪∩ cats(x) ∧C(x, s)][purr(x, s)] (13) Cats purr. This system provides an initial explanation for why singular count nouns cannot function as bare arguments in English, in view of the definedness conditions of ∩ . This operation is undefined when applied to a singular property like JcatK, given that a single individual cannot be a kind.6 Unable to type shift, the singular noun cat thus remains strictly property-type. This explains why it cannot function as an argument without the help of a determiner or quantifier. This explanation is potentially threatened if additional type shifts beyond ∩ are available in natural language. Chierchia proposes that two additional type shifts are indeed available. One is the ι type shift, forming definite descriptions. The other is the ∃ type shift, forming existential generalized quantifiers. These type shifts cannot be applied to English bare singulars because lexical determiners the and a are available with these denotations. This result is ensured by the principle in (14). (14) Blocking Principle: (Chierchia, 1998: 360) For any type shifting operation τ and any X: *τ(X) if there is a determiner D such that for any set X in its domain, D(X) = τ(X) The Blocking Principle ensures that bare nouns in English never receive definite interpretations; this is always blocked by the. It also ensures that singular count nouns never receive indefinite GQ interpretations; this is always blocked by a. Whether indefinite GQ interpretations are expected for bare plurals depends on the analysis accorded to plural determiner some: if treated as a pure existential quantifier, it is expected to block existential readings for bare plurals. Chierchia proposes that some not be treated in this way, and thus that existential GQ readings are in principle available to bare plurals. This allows him to explain why the bare plural is associated with an existential quantifier scoping over negation in examples like (15). That example demonstrates a scope pattern which is unavailable in simpler cases like (16). (15) John didn’t fix parts of this machine. ∃x[parts-of-this-machine(x) ∧ ¬ f ix( j, x)] (16) John didn’t fix coffee machines. (= 6 On ¬∃x[coffee-machines(x) ∧ f ix( j, x)] f ix( j, x)] ) ¬∃x[∪ COFFEE-MACHINE(x) ∧ the singular definite generic, see section 4. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 321 A. R. Deal & J. Nee a) b) c) d) Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Table 1: Interpretations of English bare nouns (after Chierchia 1998) Bare mass noun Bare plural Bare singular Kind-level reading Available Available Unavailable ∩ type shift ∩ undefined N is kind-denoting Narrow scope existen- Available Available Unavailable ∩ ∩ undefined tial reading N denotation + DKP type shift + DKP Definite reading Unavailable Unavailable Unavailable ι blocked by the and ι blocked by the and ι blocked by outranked by ∩ outranked by ∩ the Wide scope existential Unavailable Unavailable Unavailable ∩ ∩ reading (∃ GQ inter- ∃ outranked by ; ∃ outranked by ; ∃ blocked by pretation) available only if ∩ is available only if ∩ is a undefined undefined Why is a wide scope existential reading available in (15) but not in (16)? Chierchia builds on Carlson’s intuition that the crucial factor is that not every plural property corresponds to a kind. Notably, coffee machines is considerably more amenable to a kind-level analysis than is parts of this machine. Suppose, therefore, that parts of this machine is undefined in combination with ∩ , as the sum of the machine’s parts is not a kind. This means that the default ∩ type shift for the bare plural cannot be applied, and an alternative option must be chosen. Chierchia proposes that the availability of alternatives is regulated by a hierarchical ranking as in (17). (17) Ranking of Type Shifts (to be revised): ∩ > {ι, ∃} Because coffee machines is capable of shifting via ∩ , this is the only possibility. The result is a kind-level denotation which may lead to an existential reading only via DKP. For parts of this machine, by contrast, the kind-level reading is off the table and the lower ranked ∃ type shift may be used. This makes parts of this machine a quantificational expression which is capable of scoping over negation in (15). The overall view of English bare nouns is summarized in Table 1; note that here and elsewhere, we set aside the generic reading.7 With that proviso, the only available readings of bare nouns are in the unshaded cells of rows (a) and (b). The unattested readings in rows (c) and (d) are absent due to the combination of the Blocking Principle and the Ranking of type shifts (in some cases redundantly), as discussed above for count nouns. The same logic may be applied to mass nouns if these nouns can shift to properties, via ∪ , from their basic kind-level denotations. 7 This omission is due both to the relatively minor role of the generic reading in the Chierchia/Dayal system and to the well-known interaction between generic readings and verbal morphology. This interaction means that significant further work on the tense/aspect/mood system of TdVZ will be necessary before major claims about generic sentences are made. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 322 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Bare singulars turn out not to make viable arguments in English in view of two factors working together. On one hand, the undefinedness of ∩ in combination with a singular prevents kindlevel readings; this prevents narrow scope existential readings by blocking the proper setup for DKP. On the other hand, the lexical determiners the and a block the application of the other two type shifts, ι and ∃, which otherwise would be available to the bare singular. 2.2. Predictions for languages lacking a definite article Several regions of Table 1 deserve special attention in connection with languages lacking definite articles. In this section, we focus on those that concern plurals and mass terms. We return to special issues in the analysis of bare singulars in section 4. The first point of interest concerns row (c), the definite reading. On Chierchia’s approach, the absence of a definite reading for English mass nouns and bare plurals is redundantly ruled out by blocking and by ranking of type shifts. Since the ι operator is ranked below ∩ , a definite reading is not expected for bare mass nouns and bare plurals even in a language lacking definite articles, so long as ∩ is defined. Dayal (2004) proposes a modification to the ranking of type shifts which speaks to this point. The proper ranking, she proposes, is not (17) but (18).8 (18) Revised Ranking of Type Shifts: {ι,∩ } > ∃ With this revision, the absence of definite readings for bare nouns in English is entirely due to the presence of a definite article in the lexicon. A language lacking a definite article is expected to allow its bare nouns to type shift via ι as well as via ∩ . Bare nouns in such a language should allow a definite reading in general, alongside the kind-level and narrow scope existential readings available for bare plurals and bare mass nouns. Dayal’s revision to the ranking of type shifts has an additional consequence in row (d), the wide scope existential reading. In a language which uses an ι type shift instead of a definite article, the ι shift, which is always defined, will always outrank ∃. This means that bare plurals and mass terms should never allow wide scope existential readings. Finally, a comment is in order on row (b), the narrow scope existential reading, for reasons external to the system itself. Many languages have some variety of incorporation construction available to objects and sometimes to unaccusative subjects. Incorporated nominals standardly receive narrow scope existential readings, just like English bare mass nouns and bare plurals.9 In languages with ‘pseudo-incorporation’ (Massam, 2001), incorporated nominals may look morphosyntactically quite similar to their non-incorporated counterparts. In such languages, 8 Dayal (2013) takes another step in this direction by proposing that ∃ type shifts are in fact not available in natural language and not implicated in examples like (15). This proposal leads to the view that ι and ∩ are freely available, unranked options available to bare nouns, making (18) unnecessary as part of the theoretical machinery. The reader is referred to Dayal’s paper for full details. Note that nothing in the present analysis depends on the decision between this view and the view discussed in the text. 9 Indeed, this similarity is at the heart of work by van Geenhoven (1998). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 323 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Table 2: Expectations for bare mass and plural nouns in languages lacking definite articles Bare mass noun Bare plural a) Kind-level reading Expected Expected ∩ type shift N is kind-denoting b) Narrow scope existen- Expected Expected tial reading N denotation + DKP ∩ type shift + DKP c) Definite reading Expected Expected ∪ + ι type shift ι type shift d) Wide scope existential Unexpected Unexpected reading (∃ GQ inter- ∃ outranked by ι ∃ outranked by ι pretation) care must be taken to tell apart those narrow scope existential readings produced by DKP versus those produced by incorporation. This may be done by consideration of the argumentstructural role of the bare nominal. Crosslinguistically, incorporation does not apply to external arguments (Mithun 1984, Baker 1988); no such restriction is placed on DKP. Therefore, a narrow scope existential reading for an external argument must be due to DKP. The main predictions discussed in this section are summarized in (19), and the overall range of interpretations expected for bare mass nouns and bare plurals in languages without definite articles is schematized in Table 2. The next section shows that the pattern in Table 2 correctly describes the behavior of bare mass and plural nouns in TdVZ. (19) A language lacking definite articles should . . . a. allow bare plurals and bare mass nouns to have definite, kind-level, and narrow scope existential interpretations. b. not allow bare nouns to have wide scope existential interpretations. c. allow bare plurals and bare mass nouns to have narrow scope existential readings both as internal arguments and as external arguments. 3. TdVZ bare mass nouns and plurals Mass nouns10 and plural count nouns in TdVZ present a proper superset of the readings available to their counterparts in English. In both languages, these nouns function freely as arguments to kind-level predicates. Various such predicates in TdVZ are Spanish borrowings. (20) a. Komuun na niis. common COP water Water is common. b. Raar-te na or. rare-EMPH COP gold Gold is rare. 10 The mass-count distinction in TdVZ appears to function in a way quite similar to English and Spanish. Mass nouns require measure phrases to combine with numerals, and show sorting/packaging coercions if pluralized. We have found one pair of quantifiers that distinguishes mass vs. count, viz. suskatih ‘how much’ vs. bel ‘how many’. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 324 A. R. Deal & J. Nee (21) a. Komuun-te na d-beez. common-EMPH COP PL-frog Frogs are common. Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec b. Guk d-beez ekstingir. become PL-frog extinct Frogs went extinct. Because mass nouns and plurals may serve as kind terms, they are expected to allow existential readings via DKP. We see an existential reading of a mass term in (22) as well as in (23), where the bare noun is an external argument (ruling out an incorporation analysis). (22) Context: You notice a water leak on the sidewalk. Ka-zhi’i niis lo neez. PROG -spill water on road Water is spilling on the road. (23) La b-ain za manch tuwai? Y. N PERF-make butter stain towel Did butter stain the towel? The existential quantifier associated with the mass noun may only have narrow scope. This is readily seen for negation, where the two scope patterns are contrasted in (24) versus (25). Example (24) presents a negative answer to an existential question. Only the ¬ > ∃ scope pattern constitutes an appropriate answer, and the bare mass noun subject is felicitously used. (24) Context: Question (23) A’a’, kedih b-ain-di za manch tuwai. no, NEG PERF-make-NEG butter stain towel No, butter didn’t stain the towel. [¬ > ∃] Example (25) presents a context where only a wide scope existential reading is appropriate; the narrow scope reading contradicts the previous discourse. The ∃ > ¬ pattern is not possible for a simple negated sentence with a mass subject, as (25a) makes clear. Instead, an apparently biclausal sentence with negation in the lower clause must be used, as in (25b).11 (25) Previous discourse: Bi-la’a te tank chikru bi-zhi’i setih. PERF-crash one tanker and PERF-spill oil A tanker crashed and oil spilled out. a. # Per kedih bi-zhi’i-di setih. But NEG PERF-spill-NEG oil But oil didn’t spill out. [Consultant: “It’s a contradiction.”] b. Per y-u’u tubru’ setih kedih bi-zhi’i-di. but NEUT-be a.little.bit oil NEG PERF-spill-NEG But some oil didn’t spill out. 11 This example instantiates a pattern of subordination without overt markers of embedded structure, which seems to be widespread both in TdVZ and in nearby Zapotecan languages. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 325 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec The same range of facts holds of bare plurals. The existential reading of a bare plural and its narrow scope with respect to negation are seen in the question-answer pair in (26). (Further examples of the bare plural scoping under negation are seen in (40a) and (41a) below.) (26) Q: La ka-yoo d-beni gushadih? Y. N PROG -eat PL -person grasshopper Are people eating grasshopper? A: Kedih ka-yoo-di d-tourist gushadih. NEG PROG -eat- NEG PL -tourist grasshopper No tourists are eating grasshopper. [¬ > ∃] Once again, narrow scope existential readings are conveyed with simple bare noun constructions, whereas wide scope constructions use a biclausal alternative, (27b). (27) a. b. # Ka-sia d-bekuh, per kedih ka-sia-di d-bekuh. PROG -howl PL-dog but NEG PROG-howl-NEG PL-dog Dogs are howling, but dogs aren’t howling. Consultant: “It’s contradicting each other.” Ka-sia d-bekuh, per y-u’u d-bekuh kedih ka-sia-di. PROG -howl PL-dog but NEUT-be PL-dog NEG PROG-howl-NEG Dogs are howling, but there are dogs not howling. In the facts reviewed thus far, TdVZ mass nouns and plurals match the range of interpretations of their English counterparts. Where the languages diverge is in the availability of the definite reading. In TdVZ, bare mass nouns and plurals freely allow definite readings. Definite readings of both plurals and mass nouns are seen in the short discourse in (28); bare nouns occur here first with existential readings, italicized, and subsequently as anaphoric definites, bolded. Examples (29) and (30) provide similar examples collected via the act-out (29) and storytelling (30) tasks. (28) Context: I am narrating what is happening in a cooking show I am watching. a. Raate d-kosiner ri-beki d-paap kun za le’n perolih. every PL-chef HAB-put PL-potato and butter in pot Every chef puts potatoes and butter in a pot. b. D-paap g-ai lo za. PL -potato FUT -cook in butter The potatoes will cook in the butter. jug, y-u’u niis. Naa gu-da’-a niis le’n vas. NEUT -be juice, NEUT -be water. I PERF -pour-1 SG water in cup I have some juice and some water. I pour the water into a cup. (29) Y-u’u Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 326 A. R. Deal & J. Nee (30) Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Context: A boy and his dog are walking through the park, carrying a frog and a turtle in a bucket. [Excerpt from Frog on his own] a. Mientr ri-zaa-d-an, gu-na-d-an d-maripoos. while HAB-walk-PL - HUMAN PERF-see-PL - HUMAN PL-butterfly While they walked, they saw butterflies. b. Beez siemprte ri-zhulazu-m r-idie-m. Gu-asia-m. frog always HAB-like-ANIM HAB-go.out-ANIM PERF-jump-ANIM B-idie-m le’n kubet. PERF-go.out- ANIM from bucket The frog always liked to go out. It jumped. It went out from the bucket. c. Mientr bekuh kin ka-ye-m d-maripoos. while dog DEM PROG-look-ANIM PL-butterfly Meanwhile that dog was looking at the butterflies. In summary, bare mass nouns and plurals in TdVZ allow kind-level readings, narrow scope existential readings, and definite readings; wide scope existential readings are absent. This means that these nouns behave in precisely the way predicted by the Chierchia/Dayal system. They may function as kind terms, giving rise to kind-level and narrow scope existential readings (the latter by DKP). Alternatively, they may type shift via ι, producing definite readings. But they may not type shift into generalized quantifiers with ∃, given that ι is higher than ∃ on the ranking of type shifts. This reveals an important sense in which the definite/indefinite distinction is not fully neutralized in this language. An important class of indefinite interpretations remains unavailable to bare plurals and bare mass nouns. 4. Interpreting bare singulars In this section we turn to the predictions of the Chierchia/Dayal system for bare singulars. This case deserves special attention in view of the fact that many languages are able to use singular arguments with kind reference. In English, this is seen as the singular definite generic: (31) a. The gopher is widespread. b. Babbage invented the computer. This construction has received a good amount of theoretical and empirical scrutiny.12 One central puzzle, originally noted by Lawler (1973), is that singular definite generics diverge from bare plurals in their allowance for existential readings. The existential reading of singular definite generics is possible only in cases where the predicate describes “something momentous or significant about the species as a whole” (Carlson, 1977); it is absent in examples like (32b), in contrast to bare plural counterpart (32a). (32) 12 See, a. Gophers are eating my tomatoes. b. The gopher is eating my tomatoes. i.a., Carlson 1977, Ojeda 1991, Wilkinson 1991, Krifka et al. 1995, Chierchia 1998, and Dayal 2004. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 327 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec A number of different approaches to this puzzle have been explored. On a view like Wilkinson’s (1991), where bare plurals are ambiguous between kind-level and indefinite readings, the facts simply show that definite singulars are not similarly ambiguous; they lack indefinite interpretations. On Carlson’s (1977) view, adopted and adapted by Chierchia (1998) and Dayal (2004), this explanation is not available; bare plurals always denote kinds. Examples like (31) show that singular definites can denote kinds, too, but (32b) seems to show that this kind-level interpretation is not always available. The approach taken by Chierchia (1998) responds to the challenge of (31)-(32) by essentially reversing Wilkinson’s explanation – treating singular definites, rather than bare plurals, as subject to an ambiguity. The core approach to singular definites is as referential expressions denoting singular collectives. To combine with a kind-level predicate, the singular definite must be mapped to the associated individual concept via abstraction over the world/situation variable. This operation is forced in examples like (31) by sortal restrictions of the predicate. When a singular definite combines with an object-level predicate, as in (32b), however, there is no sortal mismatch to be repaired by intensionalization. This leaves the singular definite without a true kind-level interpretation. It may combine with the predicate only via simple function application, not in the way mediated by DKP.13 These considerations lead to the following predictions for singular count nouns in languages lacking definite articles. We saw above that languages lacking definite articles are expected to allow all nouns to type shift via ι, given that this type shift is not lexically blocked. (See (19a).) Bare singulars should thus allow definite readings. If intensionalization is universally available as a type adjustment, then bare singulars should also allow kind-level readings. In contrast, existential readings of bare singulars are expected to be significantly limited. Wide scope existential readings are predicted to be absent, given (at least) that the ∃ type shift is outranked by ι.14 (See (19b).) Furthermore, bare singulars are expected to diverge from bare plurals in the availability of the narrow scope existential reading. Bare singulars cannot obtain narrow scope existential readings by DKP. Narrow scope existential readings for bare singulars could only arise via an independent mechanism, such as incorporation. This means that narrow scope existential readings should always be absent for singulars when they serve as external arguments, given that incorporation is not possible in this argument-structural configuration. The two predictions specific to bare singulars are summarized in (33), and the overall range of expected interpretations for bare singulars is schematized in Table 3. (33) A language lacking definite articles. . . a. should allow bare singulars to have kind-level or definite interpretations. 13 An alternative route is explored by Dayal (2004), who posits that singular definites do indeed have true kindlevel interpretations without the help of a special abstraction operation. What is key is that singular kind terms block access to their instantiation sets: “the singular kind term is an atomic entity which does not allow distributive predication to entities we intuitively associate with it. That is, it is an atomic term whose only instantiation set, when available, includes perhaps a representative or prototypical object.” This means that DKP is unavailable for singular kind terms, blocking the missing reading of (32b). As far as we can tell, this approach is equal in empirical coverage to the Chierchia 1998 view; we adopt the latter for simplicity of exposition only. 14 See section 6 for additional discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 328 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec b. should not allow bare singulars to have narrow scope existential interpretations, except via incorporation (if the language makes use of this option); narrow scope existential interpretations should always be absent for singular external arguments, which cannot incorporate. Table 3: Expectations for bare singulars in languages lacking definite articles Bare singular a) Kind-level reading Expected ι + intensionalization b) Narrow scope existential reading Unexpected (modulo incorporation) c) Definite reading Expected ι type shift d) Wide scope existential reading Unexpected (∃ GQ interpretation) ∃ outranked by ι The next section shows that this rather complex set of expectations is again borne out for TdVZ. 5. TdVZ bare singulars There are three respects in which bare singulars are expected to behave like bare plurals: in allowing kind-level readings, in allowing definite readings, and in disallowing wide scope existential readings. We begin this section with the evidence that these expectations are met. As expected, kind-level predication may be carried out in TdVZ either via the bare plural or via the bare singular. (34) a. Guk (d-)beez ekstingir. become (PL-)frog extinct Frogs/the frog went extinct. b. Komuun-te na (d-)beez lo geu. common-EMPH be (PL-)frog in river Frogs are / the frog is common in the river. Also as expected, bare singulars are amenable to definite readings just as their plural counterparts are. Anaphoric singular reference is accomplished with bare singulars in examples like (35) and (36); the relevant definite terms are bolded. (35) Rap-a te manzan, kon te manguh, per gu-zuub-an manguh lo yagzhilih. have-1 SG a apple and a mango but NEUT-sit-3 SG mango on chair I have an apple and a mango but the mango is on the chair. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 329 A. R. Deal & J. Nee (36) Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Context: A boy and his dog are walking through the park with a net, looking to see if they can catch an animal. They come across a frog sitting on a lily pad in a pond. a. “N-iu’!” n-e-m. “A te beez zu lo nis!” NEUT -look NEUT -say- ANIM PRT one frog stand on water “Look!” it [the dog] said. “There’s a frog on the water!” b. Xila’azga, xila’azga, ka-zaa-d-an te neez-d-an beez. slowly slowly PROG -walk- PL -3 PRT catch- PL -3 frog Slowly, slowly, they walked to catch the frog. Examples (37) show that bare singulars are also readily used to describe referents that are unique, whether absolutely or relatively. (37) a. Ziit-te zuub gubiizh. far-EMPH sit sun The sun is very far away. b. Rom zu-gua Paap. Rome PROG-be.located pope The pope lives in Rome. Finally, bare singulars behave like bare plurals, and as expected, in disallowing wide scope existential readings. Examples (38) and (39) show that bare singulars are rejected in a context calling for the wide scope existential reading; the consultant corrects the sentences to include the word te ‘one’ (discussed in section 6). (38) Context: there’s six frogs and five of them are in the basket. We want to say there’s one that’s not, so we say: # Kedih y-u’u-di beez le’n kanast. NEG NEUT -be- NEG frog in basket Speaker’s correction: Kedih y-u’u-di te beez le’n kanast. NEG NEUT -be- NEG one frog in basket One frog isn’t in the basket. (39) Context: I’m editing a paper for someone else, and fixing mistakes. I’m expressing my regret because I realize I’ve sent the paper off and there is a mistake I didn’t fix. a. Kedih b-ain sru-di-a te eror. NEG PERF-make good- NEG -1 one mistake I didn’t fix a mistake. b. # Kedih b-ain sru-di-a eror. NEG PERF-make good- NEG -1 mistake Consultant: “It’s more normal if you say te eror.” Discussion of example (39b) revealed that the bare singular object would be improved in this context if modified by a relative clause or a sequence of other modifiers. This additional material presumably rescues the example by improving the felicity of a definite reading, which requires a single salient referent for the object. This brings us to the point where bare singulars and bare plurals are expected to diverge, namely Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 330 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec the possibility of the narrow scope existential reading. Let us begin with those bare arguments not amenable to incorporation. Example (40) contrasts a bare singular and a bare plural subject for the unergative verb zhiiz ‘laugh’. As we saw above, the bare plural is freely able to show a narrow scope existential reading in this environment; the bare singular, however, is not. (40) Context: my husband has shared a joke with me and I told it to my class. When I get home, he asks if anyone laughed. I have to report the sad news: no laughing. a. Kedih ba-zhiiz-di d-bi’in xkuilih. NEG PERF-laugh- NEG PL-student No students laughed. b. # Kedih ba-zhiiz-di bi’in xkuilih. NEG PERF-laugh- NEG student Intended: No student laughed. Only possible reading: one student didn’t laugh. Example (40b) is acceptable only on an interpretation where the bare singular picks out a single individual – just what is expected, if it is forced to be definite when serving as an external argument of a non-kind-level predicate. Example (41) shows a similar contrast for transitive subjects. The bare plural is readily able to show the narrow scope existential reading; the bare singular has only a single-individual reading. (41) The mail carrier is often chased by dogs. Today he comes home and says: Sru guk nazhi . . . [It was a good day. . . ] a. . . . kedih bi-dieno-di d-bekuh naa. NEG PERF-chase- NEG PL-dog me No dogs chased me. b. # . . . kedih bi-dieno-di bekuh naa. NEG PERF-chase- NEG dog me Intended: no dog chased me. [Consultant: “This sounds like a specific dog.”] It is quite striking that this contrast between singulars and plurals comes out precisely as expected and essentially in parallel with the English facts in (32). The result is even more remarkable if we consider that the contrast collapses for internal arguments – a fact which we propose to attribute to (pseudo)-incorporation. The prototypical incorporated arguments are direct objects, and in TdVZ, narrow scope existential readings are freely available in this case. Example (42) shows that both singular and plural direct objects may scope under a higher intensional operator and quantificational subject. Example (43) provides an additional case of a singular direct object showing a narrow scope existential reading. (42) Context: Tourists going to Hollywood have a general desire to meet celebrities. a. Kadga tourist ri-kas gu-mbe beni famos. every tourist HAB-want SBJ-meet person famous Every tourist wants to meet a famous person. b. Kadga tourist ri-kas gu-mbe d-beni famos. every tourist HAB-want SBJ-meet PL-person famous Every tourist wants to meet famous people. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 331 A. R. Deal & J. Nee (43) Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec Context: I’m going to meet somebody and I want to describe to them what I look like. Kedih kaa-di zhumbrel kiye-’. NEG PROG .wear- NEG hat head-1 I’m not wearing a hat. Subjects of certain intransitive verbs may also show narrow scope existential readings; these verbs are plausibly analyzed as unaccusative. One of these is the (locative) copula u’u. (44) Kedih y-u’u-di beez le’n kanast. NEG NEUT -be- NEG frog in basket There’s no frog in the basket. Finally, prepositional objects may show narrow scope existential readings in examples like (28a) above, where pots covary with chefs. This range of facts shows that bare singulars may in principle have narrow scope existential readings, but only by a mechanism that does not apply to subjects of unergative intransitives (40) or to transitive subjects (41). Incorporation is a mechanism that is argument-structure sensitive in precisely this way, and thus, these facts suggest that TdVZ is a language making use of some type of incorporation construction. These facts are of special interest for the study of incorporation constructions because there is no obvious morphosyntactic difference in TdVZ between clauses with incorporated objects versus those with non-incorporated objects. There is, for instance, no difference in object marking or object agreement (by contrast to Hindi (Dayal, 2011) or Nez Perce (Deal, 2010)), no overt compounding of the verb and the object (by contrast to West Greenlandic (van Geenhoven, 1998)) and no switch from VSO to VOS (by contrast to Niuean (Massam, 2001) or Chol Mayan (Coon, 2010)). This suggests that TdVZ may be a language with purely semantic incorporation: the object composes with the verb in a way that facilitates extraordinary narrow scope (perhaps among other semantic effects; see Dayal 2011), but without any special consequence for word order or morphosyntactic marking. 6. Does TdVZ have an indefinite determiner? The theory presented thus far makes use of two central tools in regulating the interpretation of bare nouns: the Blocking Principle (14) and Ranking of Type Shifts (18). In this section, we consider and reject the possibility that Ranking may be removed from the theory by means of an analysis that reassigns some of its work to Blocking. In particular, we argue that TdVZ does not have indefinite articles (i.e. items that lexicalize the ∃ type shift) available for all types of NPs. The best candidate for such an item is te ‘one’, and we argue that this lexical item does indeed create existential GQs; however, it is restricted to singulars or partitive structures. The absence of a wide scope existential reading for mass and plural bare nouns therefore cannot be attributed to Blocking by te. The behavior of te ‘one’ with singulars is in several ways reminiscent of English indefinite article a. Like a, te gives rise to antifamiliarity and antiuniqueness implications, showing effects of Maximize Presupposition (Heim, 1991). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 332 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec (45) Nau-te te bekuh bedih lele’e. Cha-rilian (#te) bekuh. chase-EMPH one dog rooster patio. PROG-hungry one dog A dog is chasing a rooster on the patio. The dog looks hungry. [Consultant: With te, it means another dog.] (46) Rom zu-gua (#te) Paap. Rome PROG-be.located one pope The pope lives in Rome [Consultant: with te, there is more than one pope.] Te-phrases are also similar to English a-phrases in allowing variable scope with respect to clausemate negation. We have seen te-phrases with scope over negation in (38)-(39) above. An example with scope under clausemate negation is shown in (47). (47) Q: Did Maria buy a chicken? A: Ketih guzi-di Lie te bedih. NEG buy- NEG Maria one chicken Maria didn’t buy a chicken. (¬ > ∃) Overall, these facts suggest that singular te phrases, like their English a-phrase counterparts, are existential GQs. This has the consequence that the absence of a wide scope indefinite reading for TdVZ bare singulars could be attributed to Blocking, rather than Ranking, just like in English. Can the absence of the ∃ type shift in TdVZ in general be attributed to Blocking, then? No: while te can occur in plural DPs (unlike English a), te PL-N does not behave as an ordinary existential GQ. Rather, plural DPs containing te seem to be partitives, often also containing a demonstrative and presupposing the existence of an element in JPL-NK (e.g., in (48), a plurality of tortillas). Also notably, te PL-N is never used for an ordinary narrow scope existential reading, unlike in singular examples like (47); bare plurals are used instead. (48) Bell (lee) ri-ki’ini-u te d-get kan, guni-naa. If (you) HAB-need-2 S one PL-tortilla DEM, tell-1 SG If you need some of the tortillas, let me know. Consultant: This is what you say if you’ve already made the tortillas. The interaction with number suggests that te is a existential GQ only with a singular complement. Apparent plural complements, like in (48), reflect hidden partitive structure: If you need one portion of the/those tortillas.15 We conclude that blocking by te does some, but not all, of the work of ruling out wide scope existential readings for bare nouns. Both Blocking and Ranking are needed in order to fully constrain the interpretation of bare nouns in TdVZ. 7. Conclusions In this paper, we have demonstrated that TdVZ, while it may lack definite articles, is not a language where definite and indefinite readings are freely available for bare nouns. Rather, 15 The absence of an overt noun ‘portion’ here recalls Nez Perce and Yudja, on the analysis of Deal (2017). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 333 A. R. Deal & J. Nee Bare nouns, number, and definiteness in Teotitlán del Valle Zapotec (in)definiteness in TdVZ bare nouns is constrained by number and by argument-structural position, and this in precisely the way predicted by the neo-Carlsonian approach to bare noun meaning (Chierchia 1998, Dayal 2004). In corroborating this approach with evidence from Zapotecan, our results lend new support for the neo-Carlsonian theory as a characterization not of an accident of (Indo-)European heritage or history, but rather of Universal Grammar mechanisms at work in number-marking languages. References Baker, M. (1988). Incorporation. Chicago: University of Chicago Press. Carlson, G. N. (1977). Reference to Kinds in English. Ph. D. thesis, UMass Amherst. Chierchia, G. (1998). Reference to kinds across languages. Natural Language Semantics 6(4), 339–405. Coon, J. (2010). VOS as predicate fronting in Chol. Lingua 120, 354–378. Dayal, V. (2004). Number marking and (in)definiteness in kind terms. Linguistics and Philosophy 27(4), 393–450. Dayal, V. (2011). Hindi pseudo-incorporation. Natural Language and Linguistic Theory 29(1), 123–167. Dayal, V. (2013). On the existential force of bare plurals across languages. In I. Caponigro and C. Cechetto (Eds.), From Grammar to Meaning: The Spontaneous Logicality of Language. Cambridge University Press. Deal, A. R. (2010). Topics in the Nez Perce Verb. Ph. D. thesis, UMass Amherst. Deal, A. R. (2017). Countability distinctions and semantic variation. Natural Language Semantics 25(2), 125–171. Heim, I. (1991). Artikel und Definitheit. In A. v. Stechow and D. Wunderlich (Eds.), Semantik: Ein internationales Handbuch, pp. 487–535. Berlin: de Gruyter. Krifka, M., F. J. Pelletier, G. N. Carlson, A. Ter Meulen, G. Link, and G. Chierchia (1995). Genericity: an introduction. In The Generic Book, Chicago, pp. 1–124. Lawler, J. M. (1973). Studies in English Generics. Ph. D. thesis, University of Michigan. Lee, F. (2006). Remnant Raising and VSO Clausal Architecture: A Case Study of San Lucas Quiavinı́ Zapotec. Springer. Massam, D. (2001). Pseudo noun incorporation in Niuean. Natural Language and Linguistic Theory 19(1), 153–197. Matthewson, L. (2004). On the methodology of semantic fieldwork. International Journal of American Linguistics 70(4), 369–415. Mithun, M. (1984). The evolution of noun incorporation. Language 60(4), 847–894. Ojeda, A. E. (1991). Definite descriptions and definite generics. Linguistics and Philosophy 14(4), 367–3998. van Geenhoven, V. (1998). Semantic Incorporation and Indefinite Descriptions. CSLI. Wilkinson, K. (1991). Studies in the Semantics of Generic Noun Phrases. Ph. D. thesis, UMass Amherst. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 334 Clefts: Quite the contrary!1 Emilie DESTRUEL — University of Iowa David BEAVER — University of Texas at Austin Elizabeth COPPOCK — University of Gothenburg and Swedish Collegium for Advanced Study Abstract. Much of the previous literature on English it-clefts—sentences of the form ‘It is X that Z’— concentrates on the nature and status of the exhaustivity inference (‘nobody/nothing other than X Z’). This paper concerns the way in which it-clefts signal contrast. We argue that it-clefts signal a type of contrast that does not merely involve a salient antecedent, as on more traditional characterizations of contrast such as those of e.g. Kiss (1998) and Rooth (1992), but also involves a conflict between the speaker’s and the hearer’s beliefs, as under the characterization of contrast given by Zimmermann (2008, 2011), which we term contrariness. Results of a felicity judgment experiment suggest that clefts do have a preference for contrariness, and one which has a gradient effect on felicity judgments: the more strongly interlocutors appear committed to an apparently false notion, the better it is to repudiate them with a cleft. Keywords: English it-clefts, contrast, interlocutors’ expectations, existential inference. 1. Introduction As discussed by Horn (1981: 127), Halvorsen (1978) identified three meaning components for English it-clefts of the form “It is X that V-ed”. Consider the following example: (1) It’s David who smiled. a. David smiled. b. Someone smiled. c. No one other than David smiled. The cleft sentence (1) gives rise to the three implications in (1a)-(1c): the PREJACENT INFER ENCE (1a), i.e. the proposition expressed by the canonical form ‘X V-ed’, an EXISTENTIAL INFERENCE (1b) such that there exists an X who V-ed, and an EXHAUSTIVITY INFERENCE (1c), such that X identifies the sole (or maximal) entity of which V holds. A great deal of the subsequent work on clefts has been dedicated to the exhaustivity implication, aiming both to give a precise characterization of its content and to identify its discourse status, i.e. whether it is conventionally encoded within the cleft itself, or arises from pragmatic reasoning on the discourse context (e.g. Halvorsen 1978, Atlas and Levinson 1981, Wedgewood 2007, Velleman et al. 2012, Büring and Kriz 2013, Destruel et al. 2015). But clefts have also been posited to express a contrast, and indeed this tradition dates back to the work in which the term “cleft” was first introduced. Thus we find in Jespersen (1927), 1 We would like to thank the audience of the SuB 2016 conference for their helpful comments on this work. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 335 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! which is perhaps the first general treatment of clefts, “A cleaving of a sentence by means of it is (often followed by a relative pronoun or connective) serves to single out one particular element of the sentence and very often, by directing attention to it and bringing it, as it were, into focus, to mark a contrast.” (Jespersen 1927: 147f.). Later work discussing clefts’ contrastive function includes É. Kiss 1998, Patten 2012: 85ff, Destruel and Velleman 2014, and Umbach 2004, p. 4 who follows É. Kiss. In the literature, the notion of contrast is often discussed in relation to two other primitives of information structure, topic and focus. Since clefts are known to be focus-marking devices, we will be interested in contrast in focus-related contexts. We take focus to be the part of the sentence that evokes a set of alternatives relevant for the interpretation of that sentence, and which is taken to be salient by the speaker (Rooth, 1985, 1992; Krifka, 2007). Now, turning to contrastive focus, several definitions have been offered. É. Kiss (1998: 267), takes an identificational focus to have the feature [+contrastive] “if it operates on a closed set of entities whose members are known to the participants of the discourse [. . . ] In this case, the identification of a subset of the given set also identifies the contrasting complementary subset.” Rooth (1992) defines contrast as a subcase of a more general notion of focus; for Rooth, a phrase α should be taken as contrasting with a phrase β if the ordinary semantic value of β is a subset of the focus semantic value of α. But, as Zimmerman (2008) points out, the two approaches described above do not fully predict when contrast-marking constructions such as clefts will be used. In languages as diverse as Finish and Hausa, which are argued to use clefts to indicate exhaustivity or the presence of an antecedent, canonical sentences can sometimes be used when an exhaustive or a contrastive meaning is intended, and an explicit antecedent is present. This is illustrated in Hausa in example (2) (taken from Zimmerman 2008: 351), where Speaker B uttering (2b) corrects Speaker A uttering (2a). This suggests that there may not be a strict one-to-one correspondence between a certain focus interpretation, i.e. here contrastive, and the way in which it is realized grammatically. (2) a. b. You will pay 20 naira. A’a zâ-n biyaa shâ bı̀yar̃ nèe. no, FUT-1 SG pay fifteen PRT ‘No, I will pay [fifteen.] f ’ As opposed to Kiss and Rooth, Zimmerman (2008) argues for a notion of contrast that calls on hearer expectation, i.e. whereby a focused constituent α is a contrastive focus whenever the speaker assumes that “the hearer will not consider the content of α or the speech act containting α likely to be(come) common ground” (Zimmerman, 2008: 9). Since it relates to speaker and hearer belief, it can be thought of as doxastic contrast, but to avoid confusion with existing notions of contrast, we will use the term contrariness. With these distinctions in mind, let us distinguish among three imaginable hypotheses: • Hypothesis A: The meaning components identified by Halvorsen (1978) (the Halvorsen components) are sufficient to capture the significance of a cleft construction. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 336 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! • Hypothesis B: In addition to the Halvorsen components, clefts signal a non-doxastic type of contrast, of the type characterized by É. Kiss (1998) or Rooth (1992). • Hypothesis C: In addition to the Halvorsen components, clefts signal a doxastic type of contrast, i.e. contrariness. Hypothesis B is appealing, at least at first sight, because it accounts for some important judgments such as the observation that, while it-clefts often sound odd as direct answers to overt questions, as in (4) (see also results from Destruel and Velleman 2014 who find this context to lead to the lowest naturalness ratings for clefts), they often sound much better as corrections, as in (3).2 In this case, the previous utterance being corrected provides exactly the kind of antecedent that Rooth mentions for a contrastive focus. (3) A: I wonder why Alex cooked so much beans. B: Actually, it was John who cooked the beans. (4) A: Who cooked the beans? B: #It was John who cooked the beans.3 However, Hypothesis B is not without limitations. There are certain observations that it cannot explain. For instance, in contexts in which an antecedent is available, speakers may nevertheless choose not to use a cleft. Indeed, in some such contexts, clefts seem actively dispreferred, and their use sounds stilted and odd. For instance, (5b) does not strike us as good idiomatic English. This is confirmed in the rating experiment conducted by Destruel and Velleman (2014) where this particular sentence was actually given a lower naturalness rating than (6b), despite the fact that (5b) has an antecedent available (viz. Canada) and (6b) does not. (5) A: Darren sounded really excited about his vacation. I think he might be going to Canada. a. B: Actually, he’s going to Mexico. b. B: ? Actually, it’s Mexico that he’s going to. (6) A: We were planning Amy’s surprise party for weeks. I can’t believe she found out about it. Who told her about it? a. B: Ken told her about it. b. B: It was Ken who told her about it. So, we are still left with the question: If the mere presence of an antecedent is not “enough” to drive the naturalness ratings of a cleft up, what else is needed to make it-clefts good? In this paper, we will follow Zimmerman’s (2008) notion of contrast and set out to test Hypothesis 2 Indeed, our invocation of contrariness could be seen as an implementation of the notion of corrective focus: see e.g. Gussenhoven 2008. However, there are some cases where contrariness could be argued to be at play that do not involve what one would be inclined to call corrections, including “Either Mary ate the beans, or it was John who ate them.” For this reason, we take it that correction, although it is a possible use of clefts, is not what clefts mark. 3 Throughout the paper, we will indicate ungrammaticality with an asterisk (*) and infelicity with a hash (#). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 337 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! C. We will give experimental evidence showing that contrariness has a positive and gradient effect on the felicity of clefts: The more there is a contrast in expectation between the speaker and the hearer, the better clefts are. 2. Experiments The core idea behind the set of experiments presented hereafter (two pre-tests and one main study) is to test Hypothesis C described in the introduction: the more strongly an interlocutor appears committed to a (false) proposition, the better it is to repudiate them with a cleft. This means that the presence of a focal antecedent in the discourse, although maybe necessary, is not a sufficient use-condition for it-clefts. Rather, it is when they are used as a response to an (explicit) contrary claim that clefts are most felicitous. 2.1. Design and Material In all experiments below, the same source sentences were used to generate the stimuli that were provided to subjects, and the stimuli were always presented in written form. In the main study, the stimuli consisted of a short dialogue between Speaker A who provided the context, and Speaker B who provided the contrary comment. A’s part, as illustrated in (7), always contained three sentences, the first two establishing the context and the last one containing the information on which B’s comment was based. Experimental items varied depending on the form of the last sentence in A’s discourse across six possible contexts. The six different contexts were designed to vary along three dimensions: (i) CONTRADICTION, i.e. whether or not the information in B’s sentence contradicted the information stated in the last sentence uttered by A, (ii) COMMITMENT, i.e. the strength with which A was committed to their statement (as measured in a pre-test), and (iii) AT- ISSUENESS, i.e. whether or not the relevant proposition in A’s speech commented on by B was at-issue. B’s part was always either in a canonical form or a cleft form. When A’s context was non-contradictory (context 1), B’s sentence was always introduced by “Yeah,...”, while in the other contexts (contexts 2 through 6), B’s sentence was introduced by “Actually,...”. The different conditions are summarized in Table 1, and an illustrative sample is given in (7)–(8). Contradiction 1- Non-contradictory no 2- Weak at-issue yes 3- Weak non-at-issue yes 4- Strong at-issue yes 5- Strong non-at-issue yes 6- Presuppositional yes Strength of Commitment + ++ +++ ++++ +++++ ++++++ At-issueness no yes no yes no no Table 1: Conditions for A’s last sentence. (7) Contexts (sample lexicalization) Speaker A: We were planning Amy’s surprise party for weeks. I can’t believe she found out about it. [...] a. Context 1: ... I guess someone from the staff told her. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 338 E. Destruel, D. Beaver, & E. Coppock b. c. d. e. f. (8) Clefts: Quite the contrary! Context 2: ... I guess Alice must have told her. Context 3: ... And Alice—who I think, probably went and told her about it—just laughed and said it was no big deal! Context 4: ... Alice told her about it, you know. Context 5: ... And Alice—who went and told her about it—just laughed and said it was no big deal! Context 6: ... I’m annoyed that Alice told her about it! Sentences to rate (sample lexicalization) Speaker B: (Yeah/ Actually,) [...] a. Ken told her about it. b. it’s Ken who told her about it. Finally, we also controlled for the GRAMMATICAL FUNCTION of the element that B commented on, i.e. a grammatical subject or an object. Example (7) above illustrates the subject condition. An example of the object condition for context 1, i.e. the non-contradictory context, is given below in (9): (9) a. b. Speaker A: Look at John this evening! He’s all dressed up. [...] I guess he’s going out with someone from the marketing team. Speaker B: Yeah, he’s going out with Karen/ Yeah, it’s Karen he’s going out with. We created a total of 12 lexicalizations for each contexts, thus 72 experimental dialogues per grammatical function (or 144 total). Three groups of participants were recruited. Participants in the main study were asked to judge the naturalness of B’s part based on A’s. In pre-test 1 and pre-test 2, the two different groups of participants only saw and rated A’s part. The specifics of each task are discussed in more details hereafter in subsections 2.2-2.4. 2.2. Pre-test 1: Strength of existential inference Motivation: It is important for our argument that any effect we find of doxastic contrast is not an artifact of variation among items with respect to the strength of the existential inference that they give rise to. We therefore carried out a pre-test in order to measure the strength of the existential inference in A’s part, in other words, how strongly A believes that someone V-ed. Procedure: In this task, participants only saw and judged A’s discourse. A total of 65 participants, all undergraduates at the University of Iowa, were recruited from a first-year language class and given extra-credit for their participation. The test was delivered via the web-based survey site Qualtrics. Participants sat in front of a computer screen and read a total of 24 contexts (A’s part) pseudo-randomized among 24 fillers. On each trial, they saw Speaker A’s sentences and were asked to judge, on a scale from 1–7, how likely it is that the speaker thinks that somebody V-ed. So for instance, given context 1 in (7a) above, participants would be asked how likely is it that someone told Amy about her surprise party (1 corresponding to extremely unlikely, and 7 to extremely likely). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 339 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! Results: Mean naturalness ratings for the strength of the existential inference in A’s sentence are presented in Table 2. Overall, we observe that participants deem the likelihood of speaker thinking that someone V-ed lower for the context that lacks a contrast between A’s sentence and B’s response (i.e. context 1), versus other contexts. The data were analyzed using a mixed effect linear regression model to predict ratings with by-participant and by-item random intercept, and contrast as a factor (sum-coded as -1/1 for context 1 vs. others, respectively). Results reveal a significant effect of CONTRAST on existential ratings (β = 2.043, SE = 0.091, t = 22.24, p < .001), suggesting that, indeed, there was a significant difference in ratings between context 1 and the others where a conjecture was present. Context 1- Non-contradictory 2- Weak at-issue 3- Weak non-at-issue 4- Strong at-issue 5- Strong non-at-issue 6- Presuppositional Mean ratings (Subject) 4.6 6.5 6.5 6.6 6.4 6.7 Mean ratings (Object) 4.4 6.3 6.5 6.7 6.4 6.7 Overall ratings 4.5 6.4 6.5 6.7 6.4 6.7 Table 2: Mean naturalness ratings for Pre-test 1. Crucially though, focusing on the contradictory data set, we see that contexts 2-6 do not significantly differ from each other with respect to A’s commitment to existence. This is good news: If we further find that these contexts differ in the strength of A’s commitment to a statement that B will contradict (as they were designed to do and tested in pre-test 2), then we will be able to test our prediction as stated in Hypothesis C. 2.3. Pre-test 2: Strength of commitment Motivation: Recall that we designed for four levels of commitment strength, namely noncontradictory, weak, strong and presuppositional, with the underlying assumption that commitment would get increasingly stronger in these contexts. In pre-test 2 we measured commitment strength (how strongly committed A is to ‘X V-ed’) directly. This gave us a more accurate measure of this factor to use, and allowed us to confirm that the contexts we created were indeed, as they were designed to be, different from each other with respect to the strength of commitment of Speaker A to the prejacent proposition in their last utterance (the target proposition). Procedure: A total of 65 participants were recruited, different from those who took part in pre-test 1. They were all undergraduates at the University of Iowa. They were enrolled in a first-year language class and were given extra credit for their participation. The test was delivered via Qualtrics. Participants sat in front of a computer screen and read a total of 24 contexts (A’s part) pseudo-randomized among 24 fillers. On each trial, they saw Speaker A’s sentences and were asked to judge, on a scale from 1–7, how strongly Speaker A is committed to the fact that X V-ed. So for instance, given context 1 in (7a) above, participants would be asked how strongly is Speaker A committed to the proposition that someone from the staff told Amy about her surprise party (with 1 corresponding to extremely uncommitted and 7 to extremely committed). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 340 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! Results: Mean naturalness ratings are reported in Table 3. Overall, we observe that the context with the lowest rating, as predicted, is the one where there is no contradiction (context 1). We then observe a strengthening trend, with contexts 4–6—which we designed as containing a stronger commitment of A to the prejacent proposition—being rated higher than contexts 2–3, which were meant to weakly commit A to the prejacent. This result is welcome and suggests that there is indeed a difference between contexts in A’s degree of commitment to the prejacent. Context 1- Non-contradictory 2- Weak at-issue 3- Weak non-at-issue 4- Strong at-issue 5- Strong non-at-issue 6- Presuppositional Mean ratings (Subject) 2.2 3.6 2.7 6.1 5.5 5.3 Mean ratings (Object) 2 3.9 2.6 6.1 5.3 5.6 Overall ratings 2.1 3.8 2.7 6.1 5.4 5.5 Table 3: Mean naturalness ratings for Pre-test 2. The results from the two pre-tests are illustrated in relation to each other in Figure 1. Recall that contradictory contexts (2–6) all provide an antecedent and commit Speaker A to existence (illustrated by the fact that ratings on the x-axis are homogeneously high). But, importantly, we observe that they differ in the strength of A’s commitment to a statement that B will contradict, which allows us to test Hypothesis C. Figure 1: Existential * Strength of commitment. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 341 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! 2.4. Main study Goal: The overarching goal of the main study is to test Hypothesis C. We investigated the effect of four factors on participants’ naturalness ratings of clefts and canonicals: (i) EXISTENCE (results from strength of existence as reported in pre-test 1), (ii) GRAMMATICAL FUNCTION, i.e. whether the focus was a subject or an object, (iii) AT- ISSUENESS, i.e. whether or not the element in A’s speech commented on by B was at-issue and (iv) CONTRARINESS. The motivation behind including AT- ISSUENESS as a factor comes from Destruel and Velleman (2014), who also argue for the relevance of contrast in expectation in the interpretation of clefts, and argue that two types of expectations may be at play; not just expectations about the state of the world but also expectations about the shape and direction of discourse. The latter type is directly relevant here since it may involve beliefs about the direction in which the discourse is going, expressed, among other ways, by marking content as at-issue or not-at-issue. We assume that interlocutors taking part in a discourse will generally address the propositions that are currently at-issue. Thus, a move which addresses a previously not-at-issue proposition is an unexpected discourse move. Consequently, if it-clefts are more natural when there is a conflict in expectations, we expect clefts to be judged more acceptable if Speaker B is commenting on content which had previously been marked as not-at-issue (in A’s speech), thereby violating the expectation that such content will not need to be discussed further. The factor CONTRARINESS was measured as follows: In non-contradictory contexts, items were attributed a contrariness value of 0, because Speaker B does not say anything that conflicts with what Speaker A says. In contradictory contexts, the contrariness value for an item is the strength of Speaker A’s commitment to the conflicting proposition (as measured in pre-test 2). Thus, contrariness was operationalized as the product of commitment and contradiction, i.e. Contrariness = Commitment ∗ Contradiction. If Hypothesis C turns out to be borne out, we expect that clefts will be judged as more natural in contexts where contrariness is higher. Procedure: For this study, we counterbalanced the experimental dialogues across 12 lists so that each participant saw 24 items (12 subjects and 12 objects). The order of the items was pseudo-randomized among 24 fillers. A total of 64 participants were recruited on Amazon’s Mechanical Turk and paid for their participation. On each trial, participants saw a written context (Speaker A’s part), followed by Speaker B’s sentence in either a cleft or a canonical form. Participants were asked to rate “How natural is Speaker B’s sentence given A’s” on a seven point Likert scale, with endpoints labeled as “extremely natural” and “extremely unnatural”. Results: We present results by sentence form, for clefts first, then for canonicals. Visual inspection of Figure 2 suggests that clefts were overall rated as more natural when the context contains a stronger degree of contrariness (as illustrated by the upward trend in the position of the red dots) than when the context does not include a contrast at all (blue dots). We analyzed the cleft data by fitting a series of mixed effect models predicting naturalness ratings from the fixed effects of interest and random effect structures that included random by-participant and by-item intercepts. Results were obtained using the lme4 package (Bates et al., 2015) in R (R Core team 2016). We found no main effect of GRAMMATICAL FUNCTION (β = 0.376, SE = Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 342 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! 0.114, t = 1.64), suggesting that whether the focus is a subject or an object, the naturalness ratings for the cleft are not influenced. Surprisingly, we also found no effect of AT- ISSUENESS (β = -0.518, SE = 0.113, t = -1.55); when clefts were used to signal an unexpected discourse move, i.e. to contrast with an element that was part of the non-at-issue content of A’s speech, they were not drastically better than when commenting on an at-issue part of discourse. There was, however, a main effect of EXISTENCE (β = 0.91, SE = 0.061, t = 14.8), suggesting that clefts are rated significantly better in contexts where the existence of the element to be contrasted is assumed, and an effect of CONTRARINESS (β = 0.383, SE = 0.022, t = 17.36), which supports Hypothesis C. Among models that contain subsets of these factors, the model that gave the best fit to the data was one that included both factors (i.e. Judgment ∼ Existence + Contrariness, χ 2 = 69.5, p < .001) Figure 3 combines the results for clefts and canonicals, with the lighter-colored dots representing the naturalness ratings of clefts (light red) and of canonicals (light blue) in the one experimental context where there is no contradiction present. Darker-colored dots represent the naturalness ratings for both sentence forms in other contexts, plotted by the strength of contrariness attributed to these contexts (i.e. commitment results from pre-test 1 * contradiction). Figure 2: Mean naturalness ratings for clefts by ratings for contrariness. Visual inspection of Figure 3 suggests that, for canonical sentences, the trend is quite different. As opposed to clefts, when the context does not include a contradiction, canonical sentences are rated as very natural. This should come to no surprise since, in English, canonical sentences constitute an unmarked sentence form, and are commonly used to answer an explicit wh-question. The trend for canonicals is also different from clefts when looking at contexts that do include a contradiction: the felicity of canonicals does not significantly improve as the level of contrariness increases, but in fact decreases. These observations are reflected in the results of our statistical analysis: Fitting a series of mixed-effect linear regression models to the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 343 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! Figure 3: Mean naturalness ratings for canonicals vs. clefts by ratings for contrariness. subset of data for canonicals only reveals a main effect of CONTRARINESS (β = −0.092, SE = 0.017, t = -5.24), but no effect of the other predictors (GRAMMATICAL FUNCTION, t= 1.43; AT- ISSUENESS , t= -1.28 and EXISTENCE , t= 1.19). Here, a model that includes both Existence and Contrariness does not give a better fit to the data than the two models with each single predictors (χ 2 = 1.39, p = 0.23; χ 2 = 2.75, p = 0.19, respectively). One thing to note is that, in our experiment, sentences were delivered in written form, therefore without prosodic marking. It is possible that naturalness ratings could have been higher for contexts with a high level of contrariness if the stimuli had been heard with (the appropriate) pitch accent. Indeed, English commonly resorts to prosody to signal information structure, and contrastive focus is known to have a particular prosodic contour (Selkirk, 2002; Katz and Selkirk, 2011). 3. Closing Discussion Our experimental results provide clear evidence in favor of the hypothesis that the felicity of clefts is related to the presence of doxastic contrast (Hypothesis C). The goal of the present paper was to test prior hypotheses concerning clefts’ standard components of meaning. We hypothesized that the mere presence of an antecedent in discourse which the clefted element would pick up and comment on (i.e. simple contrast) would not suffice to fully explain the felicity pattern of English it-clefts. Instead, we set out to test the hypothesis that something more refined is needed, namely a notion of contrast that includes a conflict between interlocutors’ expectations. We followed Zimmermann’s notion of constrast, which relates to how strongly the addressee believes the contrary, and experimentally operationalized it. So what have we learned? Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 344 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! We have shown that the presence of an explicit alternative—or in other words of a contrast, as defined in semantic terms by the previous literature (Rooth, 1992)—does increase the naturalness of clefts. This suggests that the presence of an antecedent is a necessary condition for clefts to be felicitous. But our study shows that it is not sufficient. Instead, we have shown that the factor which leads clefts to be significantly preferred (in contrast to canonicals and controlling for other factors known to influence the acceptability of clefts such as existence) is that of contrariness as defined along the lines of Zimmermann: Clefts are more natural when there exists a metalinguistic contrast. Additionally, we have seen that one type of expectation is most relevant for this metalinguistic contrast—expectations involving interlocutors’ beliefs about the world (i.e. expectations about what content is likely to be added in the commonground). On the other hand, our study showed that a conflict with respect to the direction in which the discourse is heading, operationalized as the conflicting element being (non)-at-issue, was not relevant, as this factor did not influence naturalness ratings. In sum, our main finding is that clefts are better not only when there is an antecedent to contradict in the preceding discourse context, but crucially when this antecedent is not the one expected by the listener. This result is not captured by any existing model of clefts. Another interesting point concerns the felicity of canonical sentences, and their relation to clefts. Indeed, in many languages, clefts and canonicals are considered to be in competition in focus-related contexts. This means that, in theory, when canonicals are “bad”, clefts take over as the preferred strategy and are more felicitous. Put slightly differently, clefts’ emergence in discourse can depend on canonicals’ availability and naturalness. But this is not the case in English. Indeed, our results do not show a complete reversal in trend, whereby canonicals become drastically unnatural in contexts where clefts increase in felicity. This is not surprising given that in English, focus (including contrastive focus) is typically marked via prosodic means. Thus, canonicals are never truly bad. Clefts simply represent an additional option the language has to signal a (even more) marked interpretation, e.g. doxastic contrast, unambiguously. On the other hand, in languages where canonicals are less (or not) available, like in French, we expect clefts to be judged more natural in non-contradictory contexts, but still expect an effect of contrariness on their felicity. We leave this as an issue to be investigated in future work. Finally, the results of the present study have implications for current theories of focus. Much prior work on focus has emphasized properties that relate to the presence of some prior structure in discourse, for example the presence of a question, of an element of the same type as the target, or of a clause which exhibits structural parallelism. A quite different line of work was initiated by Pierrehumbert and Hirschberg (1990), who analyze various types of intonational contour in terms of speaker and hearer expectations. Our experiments and analysis imply that clefts have an intrinsically doxastic function. At the very least, this suggests that something like the Pierrehumbert and Hirschberg approach is the right one for analyzing the marking of information structure more generally. Our conclusion is that approaches which limit themselves to the occurrence or non-occurence of particular words or structures in a text are inherently insufficient to explain the distribution and interpretation of information-structural devices in English, and that a full theory of information structural marking must refer to doxastic notions such as the speaker’s expectation as to what the hearer believes. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 345 E. Destruel, D. Beaver, & E. Coppock Clefts: Quite the contrary! References Atlas, J. and S. Levinson (1981). It-clefts, informativeness, and logical form: Radical pragmatics (revised standard version). In P. Cole (Ed.), Radical Pragmatics, pp. 1–61. Büring, D. and M. Kriz (2013). It’s that, and that’s it! Exhaustivity and homogeneity presupposition in clefts (and definites). Semantics & Pragmatics. Destruel, E. and L. Velleman (2014). Refining contrast: Empirical evidence from the English it-cleft. In C. Piñón (Ed.), Empirical Issues in Syntax and Semantics 10, pp. 197–214. Destruel, E., L. Velleman, E. Onea, D. Bumford, J. Xue, and D. Beaver (2015). A crosslinguistic study of the non-at-issueness of exhaustive inferences. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 135–156. Springer. É. Kiss, K. (1998). Identificational focus versus information focus. Language, 245–273. Gussenhoven, C. (2008). Types of focus in English. In Topic and focus, pp. 83–100. Springer. Halvorsen, P. (1978). The Syntax and Semantics of Cleft Constructions. Ph. D. thesis, University of Texas at Austin. Horn, L. R. (1981). Exhaustiveness and the semantics of clefts. In Proceedings of NELS 11, pp. 125–142. Jespersen, O. (1927). A Modern English grammar on historical principles: Part VII: Syntax. (Completed and edited by Niels Haislund). Heidelberg: Carl Winters. Reprinted 1961 Allen & Unwin, London and Ejnar Munksgaard, Copenhagen. Katz, J. and E. Selkirk (2011). Contrastive focus vs. discourse-new: Evidence from prosodic prominence in English. Language 4(87), 771–816. Krifka, M. (2007). Basic notions of information structure. In C. Féry and M. Krifka (Eds.), Interdisciplinary Studies of Information Structure 6. Postdam. Patten, A. (2012). The English It-cleft: A Constructional Account and a Diachronic Investigation. Amsterdam: De Gruyter. Pierrehumbert, J. and J. Hirschberg (1990). The meaning of intonational contours in the interpretation of discourse. Intentions in communication. Rooth, M. (1985). Association with focus. Ph. D. thesis, UMass. Amherst. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1, 75–116. Selkirk, E. (2002). Contrastive focus vs. presentational focus: Prosodic evidence from the right node raising in english. In B. Bel and I. Marlien (Eds.), Speech Prosody 2002: Proceedings of the First International Speech Prosody Conference, pp. 643–646. Velleman, D., D. Beaver, E. Onea, D. Bumford, E. Destruel, and E. Coppock (2012). It-clefts are IT (Inquiry Terminating) constructions. In Proceedings of Semantics and Linguistic Theory (SALT) 22, pp. 441–460. eLanguage. Wedgewood, D. (2007). Identifying inferences in focus. In K. Schwabe and S. Winkler (Eds.), On Information Structure, Meaning and Form, Amsterdam. John Benjamins. Zimmerman, M. (2008). Contrastive focus and emphasis. In Acta Linguistica Hungarica, pp. 347–360. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 346 An experimental investigation of (non-)exhaustivity in es-clefts1 Joseph P. DE VEAUGH-GEISS — Universität Potsdam Swantje TÖNNIS — Universität Graz Edgar ONEA — Universität Graz Malte ZIMMERMANN — Universität Potsdam Abstract. We present an empirical study on exhaustivity inferences in German es-clefts compared to definite descriptions (pseudoclefts with an identity statement), exclusives, and focus constructions. Our study uses a novel mouse-driven picture-verification task in which the incremental updating of the context allows one to determine at which point participants take exhaustivity into consideration. Our results are compatible with a parallel analysis of clefts and definite pseudoclefts (see Percus 1997; Büring and Križ 2013; cf. DeVeaugh-Geiss et al. 2015), in so far as both structures are indeed interpreted on a par. In striking contrast to these analyses, however, we found that clefts do not systematically receive exhaustive interpretations, nor do definite pseudoclefts. We conclude that exhaustivity is not conventionally coded in either clefts nor definite pseudoclefts but rather arises through the anaphoric existence presupposition in both constructions together with a number-based implicature. Keywords: es-clefts, definite pseudoclefts, exhaustivity, number-based pragmatic implicature, experimental study 1. Introduction It has long been discussed in the literature that focus-background it-clefts (in German, es-clefts) give rise to both an existence as well as an exhaustivity inference, illustrated in (1). (For existence see Horn 1981; Delin 1992; Dryer 1996; Rooth 1999; Abrusán 2016; and for exhaustivity Halvorsen 1976, 1978; Atlas and Levinson 1981; Percus 1997; É. Kiss 1998; Velleman et al. 2012; Büring and Križ 2013, among others.) (1) Es ist M AX, der einen Cocktail gemischt hat. it is M. who a cocktail mixed has ‘It is M AX who mixed a cocktail.’ Max mixed a cocktail. → Someone mixed a cocktail. → No one except Max mixed a cocktail. (it-cleft) (canonical meaning) (existence presupposition) (exhaustivity inference) While there is general consensus that the existence inference is a presuppositon (although see the remarks in Büring and Križ 2013: Sec. 6 for arguments to the contrary), there is a longstanding debate on the semantic-pragmatic source of exhaustivity in clefts. On the one hand, 1 We would like to thank the Priority Program XPrag.de funded by DFG SPP 1727, without which this research would not be possible. We would also like to thank (in alphabetical order) David Beaver, Judith Degen, Emilie Destruel, Agata Renans, and Maribel Romero for the insightful and critical comments at various stages in this research, as well as the participants at Sinn und Bedeutung 21 and the XPrag.de annual meeting for their feedback. Anna-Christina Boell, Julia Bauermann, and Mareike Philipp were essential in preparing and running the experiments at the Universität Potsdam and Universität Göttingen. All errors are our own. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 347 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts there are accounts which take exhaustivity to be conventionally-coded and context-independent, which we will refer to as the semantic accounts. In this camp are: (a) the Definite-Semantic analyses that claim it-clefts share the presuppositional semantics of definite descriptions (Percus, 1997; Büring and Križ, 2013); and (b) the Inquiry-Terminating account, which takes clefts to encode the same discourse-semantic operators as exclusives, differing only in what is atissue and what is not-at-issue (Velleman et al., 2012). On the other hand there are the nonconventionally-coded and context-dependent exhaustivity analyses, which we refer to as the pragmatic accounts, that take the exhaustive inference to be a generalized conversational implicature (Horn, 1981, 2014) or a focus-triggered scalar implicature (DeVeaugh-Geiss et al., 2015).2 One of the crucial ways in which the two camps differ is in the predictions regarding the robustness and systematicity of the exhaustive inference. With robustness we are referring to the strength of exhaustivity in terms of its obligatoriness and cancellability; by contrast, systematicity refers to the regularity of the exhaustive inference within and across both experimental settings and participants. In short, a robust inference is context-independent and non-negotiable, and a systematic inference will show up using various experimental methods and not just for a subset of the participants. Semantic analyses predict cleft exhaustivity will be robust and systematic; pragmatic analyses generally make the opposite prediction. Another crucial way in which the theories differ is in their predictions in terms of parallelism with other exhaustivity effects, in particular for our study here, definite pseudoclefts. The definite semantic accounts of Percus 1997 and Büring and Križ 2013 make the clearest of all predictions in this respect, namely that clefts and definite pseudoclefts will pattern alike. The presuppositional account in Velleman et al. 2012, however, does not make any particular predictions regarding parallel behavior of clefts and definites. The pragmatic accounts, by contrast, predict clefts and definite pseudoclefts to elicit different response patterns, but plain focus and clefts may show comparable behavior.3 The goal of the two experimental studies presented here is to evaluate cleft exhaustivity along these three parameters, that is, robustness, systematicity, and parallelism. This paper will proceed as follows: In Section 2 we provide the theoretical and empirical background to cleft exhaustivity, and in Section 3 we describe the methods, design, and results of two joint experiments conducted on German es-clefts. Anticipating the results a bit, we find that clefts and definite pseudoclefts elicit nearly perfectly-parallel behavior, although neither showed robust nor systematic response patterns, results which no existing theory in the literature predict. In Section 4 we present two proposals which take advantage of the anaphoricity of clefts and definite pseudoclefts in order to account for the (non-)exhaustivity found in both constructions. Section 5 concludes. 2 See, however, Pollard and Yasavul 2016 for the argument that clefts do not encode exhaustivity per se. However, see DeVeaugh-Geiss et al. 2015, in which clefts are predicted to show stronger exhaustivity effects than plain focus—even in subject position—given unambiguous focus-marking in the former but not in the latter. See also Horn 1981 for the claim that cleft exhaustivity is strengthened by the speaker going “out of her way” by using the cleft construction. 3 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 348 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts 2. Background Here we provide an overview of the theoretical and experimental work on cleft exhaustivity in the literature. We first take a closer look at the semantic approaches, which we divide into two groups: (a) the Definite-Semantic approaches, in particular Percus 1997 and Büring and Križ 2013, and (b) the Inquiry-Terminating (IT) approach, namely Velleman et al. 2012. Following this we discuss the pragmatic accounts in Horn 1981, 2014, and DeVeaugh-Geiss et al. 2015. Theoretical approaches Starting with the semantic approaches, Percus (1997) proposed that it-clefts of the form It is X who P and definite descriptions of the form The one who P is X are parallel in their underlying syntax, with the former being derived from the latter syntactically through a process of extraposition (see Percus 1997 for details). Accordingly, the semantics for both constructions are claimed to be identical, with exhaustivity in clefts being equal to the uniqueness/maximality presupposition of the definite. Büring and Križ (2013), by contrast, make no claims regarding the syntax of the two constructions; rather, they employ algebraic semantics (Link, 1983) to model the exhaustivity effect for clefts as a homogeneity presupposition, which they argue accounts for the uniformity presupposition of definite descriptions as well. In this account, a cleft as in (1)—and the definite description counterpart—presupposes that Max is not one of a plurality of cocktail-mixers; i.e., either Max was the only cocktailmixer, or he did not mix a cocktail at all. Since in both of these analyses cleft exhaustivity is conventionally-coded and context-independent, they make a clear and direct prediction that exhaustivity effects will be robust and systematic, with parallel behavior predicted for their definite description counterparts. For the IT-construction approach, Velleman et al. (2012) make no particular claim about the parallelism between clefts and definites, instead taking clefts to share the same discoursesemantics with exclusives, namely by encoding the operators MIN and MAX. In particular, exhaustivity is encoded with MAX, which necessitates that no answer to the Current Question be above a certain upper bound. Thus, the answer terminates an inquiry by marking it as maximal. In exclusives MAX is at-issue, whereas in clefts it is not-at-issue. Similar to the semantic definite accounts, the IT-construction account would predict robust and systematic exhaustivity effects, given that the MAX operator is coded in the cleft-structure, but says nothing about parallel behavior between clefts and definites. Nevertheless, one problem with this approach—as pointed out by Pollard and Yasavul (2016)—is that clefts do not always provide a maximal answer, as illustrated in the following: (2) Q: Who took the last cookie? A: It was John or Mary, but I don’t remember which. Turning now to the pragmatic approaches, since exhaustivity in clefts does not appear to be as obligatory as semantic accounts might predict, Horn (1981) argued that exhaustivity in clefts is a (generalized conversational) implicature. This analysis is supported in part by data such as the following, in which—unlike the existence presupposition—the exhaustivity inference does not project out of the embedding environment, illustrated in (3). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 349 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann (3) An experimental investigation of (non-)exhaustivity in es-clefts It isn’t Max who mixed a cocktail. → Someone mixed a cocktail. ↛ No one except Max mixed a cocktail. (existence) (exhaustivity) Furthermore, cleft exhaustivity appears to be easily violable, illustrated in (4). (4) “Yes, it is bread we fight for—but we fight for roses too!” (in a poem by James Oppenheim in 1911,4 cited by Horn 2014) Horn (1981, 2014) proposes that the exhaustivity inference in clefts has parallels to exhaustivity inferences in other focus constructions, which is argued to be strengthened for clefts by the fact that the speaker has chosen the more marked structure over the canonical word order. This additional strengthening is necessary to account for differences in acceptability for cancellation of plain focus and clefts, illustrated in the following contrast. (5) a. Max has three children; indeed, he has four. b. #It was a pizza that Mary ate; indeed, it was a pizza and a calzone. (examples (18c)–(18d), pg. 133, Horn, 1981) Although DeVeaugh-Geiss et al. (2015) similarly argue exhaustivity is focus-derived, they take a different pragmatic approach from Horn 1981. In their analysis, clefts are a structural device for marking focus unambiguously, and exhaustivity is a focus-triggered scalar implicature derived from Grice’s Maxim of Quantity: that is, “[t]he focal alternatives build scales, and the quantity maxim conversationally implicates the exclusion of alternatives higher on the scale” (DeVeaugh-Geiss et al., 2015: 387). The weaker exhaustivity for plain focus is argued to be due to focus projection, since projection to a higher constituent makes the focal alternatives ambiguous. By contrast, projection out of the cleft pivot appears not to be possible, and thus it-clefts provide optimal environments for further pragmatic enrichment. These pragmatic accounts both predict that exhaustivity in clefts is context-dependent and neither robust nor systematic; furthermore, there are no predicted parallels to definite descriptions. A summary of the semantic and pragmatic approaches to cleft exhaustivity and their predictions is found in Table 1. It is worth noting that there are no accounts which predict exhaustivity to be –robust/systematic and +parallel to definites. ±robust/systematic ±parallel definite descriptions (A) Semantic Definite + + (B) Semantic IT-Construction + +/– (C) Pragmatic Accounts – – ? – + Table 1: Predictions of three theoretical approaches to cleft exhaustivity. 4 https://web.archive.org/web/20160216133611/https://en.wikipedia.org/wiki/Bread_ and_Roses#Words Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 350 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts Experimental work While the theoretical literature tends to bias toward semantic accounts of cleft exhaustivity, experimental work rather supports a pragmatic account, since cleft exhaustivity has been shown to be less robust and less systematic than would be predicted for an inference which is conventionally-coded and context-independent. Prior studies have typically taken exhaustivity in exclusives as a baseline comparison for cleft exhaustivity. One such example is Onea and Beaver (2009), who tested exhaustivity effects in Hungarian preverbal focus using the “Yes, but. . . ” test, and the subsequent studies on clefts by Destruel et al. (2015). In this paradigm, participants are presented with question-answer pairs in which, given a visual stimulus with or without an exhaustivity violation, they had to choose between three possible continuations corresponding to different exhaustivity strengths: (i) strictly exhaustive (No. . . . ), (ii) slightly exhaustive (Yes, but. . . ), and (iii) non-exhaustive (Yes, and. . . ). While exclusives elicited a majority of strictly exhaustive responses (i) in contexts depicting an exhaustivity violation, clefts in English and French elicited a majority of slightly exhaustive (ii) and non-exhaustive (iii) responses. Destruel et al. (2015) argue that the Yes, but . . . paradigm is a test of the at-issue status of an inference, and given their results, that exhaustivity in clefts is not-at-issue while in exclusives it is at-issue. However, not-at-issue inferences can have either a semantic or a pragmatic source (Horn, 2014). One diagnostic for the source of an inference traditionally found in the literature is to test whether or not an inference is defeasible: whereas semantic inferences are truth-conditional and cannot be cancelled in unembedded environments,5 pragmatic inferences are non-truthconditional and thus typically more easily cancellable, as illustrated in (5a). The cancellation diagnostic is the basis for the experimental studies in Saur 2013 and DeVeaugh-Geiss et al. 2015 on German es-clefts. In both studies, the exhaustivity inference from a cleft was followed by a violation (e.g., Es ist X, der P. Außerdem, Y P. ‘It was X that P. Furthermore, Y P,’ Saur 2013). In comparison to exclusives, clefts showed weaker exhaustivity effects when the exhaustive inference was violated: that is, participants more readily accepted cleft sentences despite the violation, which was not the case for sentences with nur ‘only.’ Based on the relative acceptability found in both studies, exhaustivity is argued not to be conventionally coded in clefts, but rather derived as a pragmatic implicature. Although most studies on exhaustivity compare clefts directly to exclusives, not all have. One such study is Byram-Washburn et al. 2013, in which the acceptability of clefts was tested using written dialogues across various conditions. They find that conditions with violations of contrastiveness led to much lower acceptability ratings than conditions with violations of exhaustivity (see also Destruel and Velleman 2014 for experimental studies on contrastiveness inferences in clefts). Based on these findings, they conclude that exhaustivity is not conventionallycoded but a conversational implicature (in line with Horn 1981). However, it is not clear that the target stimuli were in fact violating exhaustivity, since there is a possible domain narrowing given the temporal adverb yesterday found in the target but not in the context. A direct comparison to exclusives could have, in fact, served as a useful control. 5 Compare to embedded environments, in which semantic inferences, i.e., assertions and presuppositions, are (potentially) interpreted under the embedding operator, and thus cancellable; for presupposition cancellation, see, e.g., Karttunen 1971; Stalnaker 1974; Chierchia and McConnell-Ginet 1996; Abbott 2006; Abrusán 2016, among others. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 351 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts To sum up, the experimental literature has found that the at-issue status of cleft exhaustivity is different from that of exclusives, with exhaustivity in clefts being not-at-issue and that of exclusives at-issue (in line with previous claims in the theoretical literature, e.g., Horn 1981). Moreover, the results from a growing number of studies are more compatible with a pragmatic approach than a hardwired semantic approach to cleft exhaustivity, given that exhaustivity violations are generally found to be more acceptable for clefts than might be expected for a context-independent and truth-conditional inference. Cancellation of exhaustivity is nonetheless not as acceptable as might be expected for a pragmatic analysis (DeVeaugh-Geiss et al., 2015), and no study to date—as far as the authors are aware of—have directly compared cleft exhaustivity to the maximality inference of definite descriptions, a notable gap between the theoretical and experimental literature. 3. Methods & results We conducted two joint-studies on German es-clefts in order to test the robustness, systematicity, and parallelism of cleft exhaustivity when compared to exclusives, focus, and definite pseudoclefts using a mouse-guided incremental information paradigm written in Python (GNU/Linux v.3.4.2; Windows v.3.3.5) with the PyGame module (v.1.9.2a0, LGPL, Shinners 2011). Participants were presented with contextual information one box at a time in order to measure which truth-value judgment was made (‘true’ or ‘false’) as well as at which point there was enough information for participants to make their judgment. The design of both experiments was the same and will be presented together here. At the beginning of the experiment participants were introduced to four roommates, Jens, Max, Tom, and Ben, who they were told undertook various activities together. Participants were informed that only these four roommates would appear throughout the entire experiment. After a brief introduction to the experiment including three practice trials, the experiment started. At the beginning of each trial, participants heard the audio stimuli in their headphones, after which they uncovered up to four boxes revealing the various activities of the four roommates. Their task was to uncover only as many boxes as necessary to make a judgment whether the sentence they heard was true or false. An example of the four target auditory stimuli is presented in (6)–(9). Pitch accent was always on the subject, illustrated by capital letters in the example stimulus. (6) EXCLUSIVE Nur MAX hat einen Cocktail gemischt. only M. has a cocktail mixed. ‘Only Max mixed a cocktail.’ (7) PLAIN FOCUS MAX hat einen Cocktail gemischt. M. has a cocktail mixed ‘Max mixed a cocktail.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 352 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann (8) An experimental investigation of (non-)exhaustivity in es-clefts DEFINITE PSEUDOCLEFT Derjenige, der einen Cocktail gemischt hat, ist MAX. the.one who a cocktail mixed has is M. ‘The one who mixed a cocktail is Max.’ (9) CLEFT Es ist MAX, der einen Cocktail gemischt hat. it is M. who a cocktail mixed has ‘It is Max that mixed a cocktail.’ Note that in the definite pseudocleft sentences, the complex definite forms derjenige, diejenige, and dasjenige are compounds of the singular determiner elements der- ‘the.MASC,’ die- ‘the. FEM ,’ or das- ‘the. NEUT ’ plus -jenige, the latter derived etymologically from the demonstrative marker jene/jener/jenes meaning ‘that one (over there).’ We will argue that this inherent deictic or context-anaphoric meaning component will prove to be crucial for the interpretation of definite pseudoclefts in our experiments. For all stimuli in the definite pseudocleft condition, the complex-definite subject was singular and masculine, and it displayed singular nominative marking and gender agreement with the masculine proper name in predicative position. The boxes were manipulated to present information in such a way as to be informative about the source and status of the exhaustivity inference. That is, whereas Box 1 was always irrelevant to the purposes of the experiments, the two experiments differed in a critical way at Box 2. • Experiment I tested the at-issue status of exhaustivity by verifying in Box 2 the canonical meaning or prejacent of the target sentences. For example, for sentences (6)–(9) Max says: ‘I mixed a cocktail.’ If exhaustivity is at-issue, we predict that after revealing the second box participants must continue uncovering Box 3 and Box 4 in order to check that exhaustivity holds. • Experiment II tested the semantic-pragmatic source by falsifying exhaustivity in Box 2. For example, for sentences (6)–(9) someone other than Max, e.g., Ben, says: ‘I mixed a cocktail.’ We predict that if exhaustivity is semantic (asserted or presupposed), falsifying exhaustivity should be enough to judge the target sentence as false; by contrast, if it is pragmatic the exhaustivity implicature is defeasible and thus participants can continue to uncover Box 3 and Box 4 in order to check the as-yet-unverified prejacent. Although participants were free to choose which box to uncover next, we programmed the experiment such that the order was pre-determined. Moreover, once inside a box the cursor could not exit the box for at least 2000ms. This was done to keep participants from unnecessarily uncovering too many boxes, such as, e.g., by automatically mousing over all four boxes and then making a judgment. Further details of the individual experiments will be presented below. Our experiments exhibit the following important design features that will allow for a controlled and systematic study of exhaustivity inferences in clefts and definite pseudoclefts. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 353 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts 1. The experiments explicitly control for at-issue semantic exhaustivity triggered by exclusive particles, on the one hand, and for bona fide pragmatic exhaustivity, as triggered by instances of in situ prosodic focus in auditory stimuli. 2. The experiments explicitly control for domain restriction in order to rule out any attempts at explaining exhaustivity violations away in terms of a subsequent enlargement of the quantificational domain. 3. The experiments involve no scalar ordering of alternatives in order to rule out attempts at explaining exhaustivity effects away by recourse to ordering on a contextually-supplied scale. In both experiments there were two dependent variables: Early Judgment and Late Judgment. The first dependent variable was measured at Box 2 and had three values: richtig ‘correct,’ falsch ‘false,’ or ‘continue’ by uncovering Box 3. The second dependent variable was the final evaluation of the stimuli once all relevant information at the third or fourth box had been revealed. Clearly there was data for the Late Judgment only when participants chose to continue in the Early Judgment measure. There was a 1:1 target-to-filler ratio. Filler items consisted of sentences with universal quantifiers (jeder ‘everyone’), expletive constructions (es ist klar, dass . . . ‘it is clear that . . . ’), plural conjunctions (e.g., Ben und Max haben . . . ‘Ben and Max have . . . ’), and scalar constructions (weniger als drei Leute ‘fewer than three people’). There were 32 target items and 32 filler items for a total of 64 sentences. For Experiment I, we tested 32 German native speakers (24 female, 8 male), all students in Potsdam and Berlin, Germany (average age: 25.6).6 For Experiment II we tested 32 German native speakers (20 female, 12 male), most of them students in Göttingen, Germany (average age: 27.8). The experiments took part in a laboratory environment, and participants were compensated for their time. We now turn to the individual experiments and their results. Factorial design of Experiment I Experiment I involved a 4*2 factorial design, the two factors being Sentence Type (EXCLUSIVE , FOCUS , DEFINITE PSEUDOCLEFT, CLEFT) and Exhaustivity (±EXHAUSTIVE). Recall that the early judgment was at Box 2, which verified the canonical meaning or prejacent, whereas the factor Exhaustivity was measured as a late judgment in Box 3 and Box 4. For the condition +EXHAUSTIVE, exhaustivity holds. For instance, given a target sentence as in (6)–(9), in Box 2 Max says he mixed a cocktail, and in the other boxes none of the remaining roommates had the property of mixing a cocktail, as illustrated below. For the condition –EXHAUSTIVE, by contrast, one of the roommates in Box 3 or Box 4 also has the relevant property. For example, in Box 3 Jens says ‘I mixed a cocktail,’ which, for the sake of space, is not illustrated here. B OX 1: Tom ‘I fetched a straw.’ B OX 2: Max ‘I mixed a cocktail.’ B OX 3: Jens B OX 4: Ben ‘I opened a bottle.’ ‘I provided a schnaps.’ 6 There were 33 participants in Experiment I, but one participant was removed since judgments were erratic on the controls. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 354 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts Figure 1: Proportion of early judgments (judgment = 1, continue = 0) for Experiment I (left) and Experiment II (right). Experiment I results For data preparation of the target items, 1 response out of the 1024 potential responses at Box 1 was treated as an error and removed. All data at Box 2 were coded with 1 for judgment made and 0 for continue. Note that in Experiment I when a participant made a judgment at Box 2, the sentence was always judged ‘correct’; that is, no participant selected ‘false’ at this point. Exclusives elicited a judgment at Box 2 only 1% of the time (2/256 responses): most participants chose to continue uncovering Boxes 3 and 4, as expected. By contrast, clefts and definite descriptions elicited a ‘correct’ judgment 43% (110/255 responses and 41% of the time (105/256 responses), respectively, and focus 74% of the time (189/256 responses). See the left graph in Figure 1 for the proportion of judgments made per sentence type in Experiment I. Note that when participants continued and exhaustivity was violated in Box 3 or Box 4, the sentence was consistently judged ‘false,’ suggesting that the experiment was indeed sensitive to exhaustivity. We conducted a generalized linear mixed effects model (binomial family) in R with the dependent variable being the early response at Box 2 and the independent variable the sentence type (i.e., glmer(Judgment.Box2 ∼ SentType + (1|Item) + (1|Participant), family = binomial, data = ExpI)).7 Contrast coding was non-orthogonal: clefts were the baseline comparison for each of the other sentence types. There was no significant difference found between clefts and definite descriptions (SE = 0.286, p = 0.392); by contrast, there was a highly significant difference found between clefts and exclusives, and clefts and focus (p < 0.001 in all cases). Factorial design of Experiment II Experiment II again had a 4*2 factorial design, as in Experiment I, the two factors being Sentence Type (EXCLUSIVE , FOCUS , DEFINITE PSEUDO CLEFT, CLEFT ) and Canonical (± CANONICAL ). Recall that the early response was at Box 2, which falsified the exhaustive inference. The factor Canonical was measured as a late response in Box 3 and Box 4. The condition +CANONICAL means the canonical meaning or prejacent holds. For instance, for the sentences in (6)–(9) Max says in Box 3 that he in fact mixed a 7 We ignore the late response in our computation, because in this early stage of evaluation it plays no role. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 355 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts cocktail, as illustrated below. For the condition –CANONICAL, by contrast, Max in Box 3 or Box 4 says he did something other than mix a cocktail. For example, in Box 3 Max says ‘I provided a schnaps,’ which, for the sake of space, is not illustrated here. B OX 1: Jens ‘I opened a bottle.’ B OX 2: Ben ‘I mixed a cocktail.’ B OX 3: Max B OX 4: Tom ‘I mixed a cocktail.’ ‘I fetched a straw.’ Experiment II results For data preparation of the target items, there were 3/1024 ‘correct’ judgments for the falsifier at Box 2, which were treated as errors. The remaining data at Box 2 were coded with 1 for judgment made and 0 for continue. As predicted, exclusives elicited ‘false’ judgments 92% of the time (236/256 responses): most participants chose not to continue uncovering contextual information, even though the prejacent had not yet been verified. By contrast, focus elicited judgments only 15% of the time (38/256 responses): that is, most participants continued to uncover the remaining boxes to see if the canonical meaning held. Definite descriptions elicited ‘false’ judgments 50% of the time (128/255 responses), and clefts were similar in eliciting judgments 47% of the time (120/254 responses). Note that for participants who continued uncovering and found that the prejacent did not hold, they consistently judged the sentence as ‘false’; furthermore, when they found that the prejacent was verified, they consistently judged the sentence as ‘true.’ See the right graph in Figure 1 (on page 355) for the proportion of judgments made per sentence type for Experiment II. Again, we conducted a generalized linear mixed effects model in R with the dependent variable being the early response at Box 2 and the independent variable the sentence type (i.e., glmer(Judgment.Box2 ∼ SentType + (1|Item) + (1|Participant), family = binomial, data = ExpII)). Contrast coding was non-orthogonal: clefts were the baseline comparison for each of the other sentence types. Again, there was no significant difference found between clefts and definite descriptions (SE = 0.2223, p = 0.403). By contrast, there was a highly significant difference found between clefts and exclusives, and clefts and focus (p < 0.001 in all cases). Post hoc analysis In both experiments we measured whether and at which point participants made a truth-value judgment given the incremental evidence provided. Crucially, we were interested in participant response behavior at Box 2, which differed between the two experiments: in Experiment I the exhaustive inference was verified at Box 2, whereas in Experiment II the exhaustive inference was falsified at Box 2. The questions associated with the early evaluation variable are as follows. In Experiment I we established whether verifying at Box 2 that the canonical meaning holds was sufficient to make a judgment, or whether the exhaustivity inference was taken into consideration by further uncovering Boxes 3 and 4. That is, if a participant judged the sentence they heard as ‘true’ upon revealing the information at Box 2, exhaustivity did not matter (enough) to justify further investigation. By contrast, if a participant continued this means that exhaustivity was significant enough to warrant checking the upcoming information. In this case we predict participants will judge the sentence as ‘true’ in the +EXHAUSTIVE late response condition and ‘false’ in the –EXHAUSTIVE late response condition. This is precisely what we found, confirming that participants understood the logic of the experiment. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 356 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts Figure 2: Proportion of early judgments (judgment = 1, continue = 0) for Experiment I for non-exhaustive group (left) and exhaustive group (right). When analyzing participant behavior individually we found two main groups for definite pseudoclefts and clefts: either participants treated definite pseudoclefts and clefts as exhaustively as exclusives (Exp. I: 20 participants; Exp. II: 16 participants) or as non-exhaustively as focus (Exp. I: 12 participants; Exp. II: 16 participants). These categories were calculated like so: In Experiment I, if they chose ‘continue’ for definite pseudoclefts 5/8 or more times they fell into the exhaustive interpretation group, since exhaustivity was significant enough to warrant further uncovering a majority of the time; otherwise, they were in the non-exhaustive interpretation group (i.e., 4/8 or less times they chose ‘correct’ when the canonical meaning of the sentence was verified without checking the remaining boxes). In Experiment II, if they made a ‘false’ judgment for definite pseudoclefts 5/8 or more times they again fell into the exhaustive interpretation group, since falsifying exhaustivity at Box 2 was enough to judge the auditory stimuli as false; otherwise, they were in the non-exhaustive interpretation group (i.e., 4/8 or less times they chose ‘continue’ to check that the canonical meaning holds despite exhaustivity having been falsified). Again, the post hoc analysis, illustrated in Figure 2 for Experiment I (on this page) and Figure 3 for Experiment II (on page 358), shows quite clearly that definite pseudoclefts were indeed interpreted in full parallel to clefts in both the participant groups as well as in the experiments, albeit in two different ways, either entirely exhaustively or entirely non-exhaustively. It is therefore reasonable to assume that the source of the exhaustivity inference is identical, or at least very similar, in both clefts and definite pseudoclefts. 4. Analysis The experimental data are not in line with any of the major theories of cleft exhaustivity. As pointed out in connection with Table 1 on page 350, neither semantic nor pragmatic analyses would predict exhaustivity in clefts to be non-robust/unsystematic and parallel to definite pseudoclefts at the same time. The post-hoc analysis in particular indicated that our results are incompatible with semantic analyses of cleft exhaustivity (the effect being non-robust and unsystematic across speakers and experiments). Finally, it seems unlikely that the existence of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 357 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts Figure 3: Proportion of early judgments (judgment = 1, continue = 0) for Experiment II for non-exhaustive group (left) and exhaustive group (right). (unambiguously) marked focal alternatives is responsible for triggering the pragmatic exhaustivity implicature, given that there is weak exhaustivity in the plain focus condtions. In light of all this, we propose an alternative pragmatic analysis of the exhaustivity effect in clefts and definite pseudoclefts. In particular, we argue that our participants systematically differed in their assumptions regarding the potential linguistic contexts required for licensing the critical audio stimulus, in particular its existence presupposition. Anaphoric presupposition of clefts It is standardly assumed in the literature that clefts have anaphoric potential (Prince 1978; Horn 1981; Soames 1989; Delin 1992; Hedberg 2000; and many others). They introduce as part of their constructional meaning a presupposition that marks the information conveyed by the cleft as known-fact (Prince, 1978) or, simply, as anaphoric (Delin, 1992). The anaphoric potential of clefts can be formally expressed in the form of an existence presupposition, following van der Sandt 1989 and Rooth 1996. Turning next to the experimental setting of our experiments, there is no linguistic context against which to evaluate the audio stimulus. As a result, the existential presupposition of the cleft condition must be accommodated. This amounts to saying that the hearer will integrate into her discourse model some discourse referent with the relevant property described by the cleft relative that she takes the experimental speaker to (anaphorically) refer to. Crucially, we do not adopt claims in Szabolcsi 1994 (on pre-verbal focus in Hungarian) and Percus 1997 (on English it-clefts) that the existential presupposition of cleft sentences comes with an obligatory maximality effect. Instead we propose that part of what the experiment participants did was to reason about the anaphoric antecedent of the existential presupposition. On this proposal, the exhaustive group would take the presupposed discourse referent x to refer to an accommodated maximal discourse referent with property P denoted by the cleft relative. One way of constructing a suitable discourse referent x would consist in assuming the denotation of an implicit question, as provided in Pollard and Yasavul 2016. That is, participants could have assumed that the cleft addresses the issue “who P?,” thus resolving the existence Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 358 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts presupposition to a maximal discourse referent x with property P. Linking this with an identificational at-issue semantics for clefts, namely x = Pivot, the result will be that the maximal individual x with property P equals the pivot, which comes down to an exhaustivity claim. By contrast, the non-exhaustive group would accommodate a non-maximal discourse referent, as suggested by Pollard and Yasavul 2016 for indefinite antecedents. For this group the interpretation is then simply that there is some x with property P, and x = Pivot, which does not trigger an exhaustivity inference. The foregoing assumptions would, in principle, suffice in order to explain our experimental findings in terms of differences in the way in which the experimental subjects accommodated the anaphoric existence presupposition of clefts. On this analysis, the exhaustivity inference is a pragmatic effect that can be reliably predicted in a number of explicit contexts, but which leads to ambiguity in the absence of overt linguistic context. Still, an analysis along these lines is not without problems. A potential issue is that the proposed analysis relies explicitly on an identificational, as opposed to, e.g., a predicational, semantic analysis of clefts, working in tandem with the presupposed anaphoric content. Nevertheless, we do not want to dismiss the above sketch of an analysis altogether. At present, though, our experimental data do not provide sufficient and conclusive evidence in favor of this particular spell-out. Fortunately, there is no need for basing the pragmatic analysis of cleft exhaustivity on the semantic assumption that clefts are identificational. In particular, there is an additional implicature giving rise to exhaustivity even on a predicational semantics for clefts. This second implicature interacts with the existence presupposition and is triggered by the choice between singular and plural clefts. The fact that German clefts show consistent and transparent semantic marking of number is assumed to make the effect even stronger. Number implicature of German clefts As discussed in Büring and Križ 2013, there are plural and singular clefts, as shown in (10). (10) a. b. Es waren Georg und Friedrich, die Wilhelm verprügelt haben. it COP. PL Georg and Friedrich REL . MASC . PL Wilhelm beaten have ‘It was George and Frederick that beat William.’ Es war Georg, der Wilhelm und Friedrich verprügelt hat. it COP. SG Georg REL . MASC . SG Wilhelm and Friedrich beaten has ‘It was George that beat William and Frederick.’ It is reasonable to assume that the presupposed discourse referent inherits the singular or plural feature from the cleft sentence. Put differently, plural clefts presuppose the existence of a non-atomic sum-individual, while singular clefts at least give rise to the implicature that the anaphoric antecedent is not a sum individual, but rather an atomic individual. Especially in situations with zero context, as found in our experiments, we expect this implicature to give rise to an exhaustivity inference along the following lines of reasoning: By using the singular cleft, the experimental speaker implicates that there is no sum-individual antecedent with the cleft relative property P. If there actually were sum-individuals with the cleft Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 359 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts relative property P, and the speaker were aware of that fact, the listener would be in no position to identify the singular discourse referent the speaker meant to refer to, given the absence of further linguistic context. This in turn would make it impossible to assign the cleft sentence a proper interpretation, as it remains unclear which individual the cleft sentence is about. Hence, being cooperative, the speaker must have meant to convey that there are no potential plural antecedents at all. Hence, we are safe to assume that there is exactly one individual with property P in the context, which is then identified by the pivot. The core ingredients of the number-based analysis are summed up in (11): (11) Components of number-based pragmatic analysis of cleft exhaustivity: a. Asserted content: P(focus) or focus = x b. Existence presupposition: ∃x[P(x)], atomic(x) c. Singular-based implicature: ¬∃Y[sum(Y) ∧ P(Y)] Note that participants have the option to reason that the speaker is not committed to exhaustivity to a degree that is sufficient to judge the cleft sentence as true or false based on the truth or falsity of this implicature. This can happen, for instance, if a speaker has no relevant knowledge concerning the other individuals under consideration, thereby restricting the scope of the existence presupposition to the singular individual she is certain about. This explains the behavior of the non-exhaustive group. We would like to stress that the analysis sketched in the previous subsection and the numberbased analysis presented here are by no means mutually exclusive. It may very well be possible that both interpretive processes are simultaneously active: The number-contrast would create an exhaustivity implicature based on the anaphoric existential presupposition plus some reasoning over the speaker’s intention in choosing a singular over a plural cleft. And, additionally, it would also be possible to maximize the anaphoric antecedent. Definite pseudoclefts What remains to be done is to show how the pragmatic analysis developed for clefts can be extended in order to capture the parallel interpretive properties of definite pseudoclefts in our experiments. Following a long list of scholars ranging from Frege (1892) to Coppock and Beaver (2015), definite descriptions in general are commonly treated as triggering a uniqueness presupposition. However, at least for the particular definite expressions found in definite pseudoclefts in German, we argue that deriving exhaustivity in an anaphoric familiarity-based analysis à la Heim 1982 better captures the results reported here. We argue that definite pseudoclefts in German cannot be analyzed as run of the mill definite descriptions, given our experimental findings. Instead, we would like to propose that definite pseudoclefts express anaphoric reference as part of their conventional meaning, as evidenced by their discourse-semantic behavior and by their morpholexical make-up. First, note that the form -jenige shows the weak inflectional properties of prenominal modifying elements in definite contexts, but, more importantly, as a deictic expression it must anaphorically relate to a salient discourse referent in the preceding context (or at least to a perceptually salient individual in the utterance situation). We therefore propose that the strong bias for interpreting definite Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 360 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts pseudoclefts as anaphoric expressions, rather than as referentially unique expressions, follows from the explicit presence of the demonstrative (anaphoric) element as part of the complex definite determiner. Second, observe that definite peudoclefts are deviant as discourse openers, especially in comparison to their plain definite description counterparts, even if the two types of definite expressions have the same descriptive content. The relevant contrast is illustrated in (12). Example (12b) allows for easy accommodation of the fact that the lord, whoever that may be, has been murdered by someone, thereby triggering the interpretation that the gardener was the murderer. Example (12a), in contrast, resists such an interpretation. The most natural interpretation for (12a) is that it presupposes that the murder of the lord has already been the topic of discussion in the preceding discourse, either explicitly or implicitly. This being a condition on discourse structure, and not on the external world as such, it is very hard to accommodate, especially at the beginning of a story. (12) Out Of The Blue a. #Derjenige, der den Lord umgebracht hat, war der Gärtner. the.one who the lord murdered has was the gardener ‘The one who murdered the lord was the gardener.’ b. Der Mörder des Lords war der Gärtner. ‘The murderer of the lord was the gardener.’ Having established that definite pseudoclefts express an anaphoric relationship in the form of an existence presupposition rather than uniqueness in the utterance situation, we can apply the same reasoning as for the cleft-case, which gives us precisely the same predictions: With uniqueness no longer part of the semantic meaning of the definite pseudocleft expressions, we do not expect systematic or robust uniqueness or exhaustivity effects to show up with this construction. Furthermore, the singular-plural contrast is also observed with definite pseudoclefts, although oddly only in the masculine and feminine paradigm. The masculine and feminine forms derjenige and diejenige are morphosyntactically and semantically marked for singular, as opposed to their plural counterpart die-jenigen ‘the.PL-ones.’ This accounts for the parallel behavior of clefts and definite pseudoclefts in our experiments. Since we only referred to masculine referents in the experiments, the use of the singular form of the definite pseudocleft should give rise to the same number-based pragmatic reasoning procedure as laid out for the case of clefts above. By contrast, the neuter form dasjenige resembles the neuter determiner/relative form das ‘the/ which’ and the neuter wh-expression was ‘what’ in being semantically number-neutral (Zimmermann, 2011; Bayer, 2002). As a result, the neuter forms can refer to singular and plural forms alike, as illustrated in (13a), unlike their masculine and feminine counterparts, as in (13b): (13) a. Dasjenige, was Peter gekauft hat, ist Brot und Rosen. DEF. NEUT WH . NEUT Peter bought has COP. SG [bread and roses]PL ‘What Peter bought is bread and roses.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 361 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann b. An experimental investigation of (non-)exhaustivity in es-clefts *Derjenige, den Peter eingeladen hat, ist Klaus und Peter. DEF. MASC . SG REL . MASC . SG Peter invited has COP. SG [Klaus and Peter]PL (lit.) ‘The one that Peter invited is Klaus and Peter.’ The difference between masculine/feminine and neuter forms in terms of semantic number marking gives rise to another interesting prediction to be checked in future research: If the number-based pragmatic analysis of pseudoclefts is on the right track, we predict neuter definite pseudoclefts in German to be less exhaustive than their masculine or feminine counterparts. Given that the neuter singular form can refer to both singularities and sum individuals, there is no comparable contrast in the semantic number paradigm, and singular-based implicatures should be much weaker, or altogether absent. 5. Conclusion We reported the results of two offline experiments on cleft exhaustivity in the incremental information-retrieval paradigm. It was shown that clefts and definite pseudoclefts are treated on a par by the participants of a verification and a falsification experiment, in contrast to sentences with plain intonation foci and to sentences with exclusive particles. In particular, the exhaustivity inference in clefts and definite pseudoclefts is more pronounced than with plain focus, while being less systematic and less robust than with exclusive particles. We have argued that the non-systematic and non-robust nature of the exhaustivity effect is not accounted for by existing theoretical accounts, be they semantic or pragmatic. Moreover, a post hoc analysis further unveiled that about half of the participants treated both clefts and pseudoclefts systematically as exhaustive, while the other half treated both as non-exhaustive. Again, this finding poses a challenge to semantic theories of cleft exhaustivity. In response to the novel data, we argue that there must be some pragmatic component in the derivation of cleft exhaustivity. We then sketched a pragmatic analysis of cleft exhaustivity in clefts and definite pseudoclefts, which is based on two central assumptions: Both sentence types are anaphoric and introduce an existence presupposition. The choice of singular or plural in clefts and definite pseudoclefts triggers a pragmatic implicature, which is further supported by a systematic contrast in the marking of semantic singular and plural in German. The proposed analysis makes a number of interesting predictions to be investigated in future research, such as crosslinguistic differences or the special case of neuter definite pseudoclefts in German. At the same time, in its present form the proposed analysis is only a sketch, and more theoretical, experimental, and crosslinguistic work needs to be done before a fully detailed compositional analysis of exhaustivity in clefts and definite pseudoclefts is in reach. References Abbott, B. (2006). Where have some of the presuppositions gone? In B. Birner and G. Ward (Eds.), Drawing the Boundaries of Meaning: Neo-Gricean Studies in Pragmatics and Semantics in Honor of Laurence R. Horn, pp. 1–20. John Benjamins. Abrusán, M. (2016). Presupposition cancellation: Explaining the ‘soft–hard’ trigger distinction. Natural Language Semantics 24, 165–202. Atlas, J. and S. Levinson (1981). It-clefts, informativeness and logical form: Radical pragmatProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 362 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts ics. In P. Cole (Ed.), Radical Pragmatics, pp. 1–61. Academic Press. Bayer, J. (2002). Minimale Annahmen in Syntax und Morphologie. Linguistiche Arbeitsberichte 79, 277–297. Büring, D. and M. Križ (2013, August). It’s that, and that’s it! Exhaustivity and homogeneity presuppositions in clefts (and definites). Semantics and Pragmatics 6(6), 1–29. Byram-Washburn, M., E. Kaiser, and M. L. Zubizarreta (2013). The English it-cleft: No need to get exhausted. Poster: Linguistic Society of America (LSA). Chierchia, G. and S. McConnell-Ginet (1996). Meaning And Grammar: An Introduction To Semantics. MIT Press. Coppock, E. and D. Beaver (2015). Definiteness and determinacy. Linguistics and Philosophy 38, 377–435. Delin, J. (1992). Properties of it-cleft presupposition. Journal of Semantics 9(4), 289–306. Destruel, E., D. Velleman, E. Onea, D. Bumford, J. Xue, and D. Beaver (2015). A crosslinguistic study of the non-at-issueness of exhaustive inferences. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 135–156. Springer. Destruel, E. and L. Velleman (2014). Refining contrast: Empirical evidence from the English it-cleft. In C. Piñón (Ed.), Empirical Issues in Syntax and Semantics 10, pp. 197–214. DeVeaugh-Geiss, J. P., M. Zimmermann, E. Onea, and A.-C. Boell (2015). Contradicting (not-)at-issueness in exclusives and clefts: An empirical study. In Semantics and Linguistic Theory 25, pp. 373–393. Dryer, M. (1996). Focus, pragmatic presupposition and activated propositions. Journal of Pragmatics 26(4), 473–523. É. Kiss, K. (1998). Identificational focus versus information focus. Language 74(2), 245–273. Frege, G. (1892). Über Sinn und Bedeutung. Zeitschrift für Philosophie und Philosophische Kritik 100, 25–50. English Translation: On Sense and Meaning, in B McGuinness (Ed.), Frege: Collected Works, pp. 157–177. Blackwell. Halvorsen, P. K. (1976). Syntax and semantics of cleft sentences. In Proceedings from the 12th Chicago Linguistic Society. Halvorsen, P. K. (1978). The Syntax and Semantics of Cleft Constructions. Ph. D. thesis, University of Texas at Austin. Hedberg, N. (2000). The referential status of clefts. Language 76(4), 891–920. Heim, I. (1982). On the Semantics of Definite and Indefinite Noun Phrases. Ph. D. thesis, University of Massachusetts at Amherst. Horn, L. (1981). Exhaustiveness and the semantics of clefts. In V. E. Burke and J. Pustejovsky (Eds.), North Eastern Linguistic Society (NELS) 11, pp. 125–142. Horn, L. (2014). Information structure and the landscape of (non-)at-issue meaning. In C. Féry and S. Ishihara (Eds.), The Oxford Handbook of Information Structure, pp. 108–127. Oxford University Press. Karttunen, L. (1971). Some observations on factivity. Papers in Linguistics 5, 55–69. Link, G. (1983). The logical analysis of plurals and mass terms: A lattice-theoretic approach. In R. Bäuerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use, and the Interpretation of Language, pp. 303–323. de Gruyter. Onea, E. and D. Beaver (2009). Hungarian focus is not exhausted. In E. Cormany, S. Ito, and D. Lutz (Eds.), Semantics And Linguistic Theory (SALT) 19, pp. 342–359. Percus, O. (1997). Prying open the cleft. In K. Kusumoto (Ed.), North Eastern Linguistic Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 363 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts Society (NELS) 27, pp. 337–351. Pollard, C. and M. Yasavul (2016). Anaphoric it-clefts: The myth of exhaustivity. In Proceedings of Chicago Linguistic Society (CLS) 50. Prince, E. (1978). A comparison of wh-clefts and it-clefts in discourse. Language 54, 883–906. Rooth, M. (1996). On the interface principles for intonational focus. In T. Galloway and J. Spence (Eds.), SALT VI, pp. 202–226. Rooth, M. (1999). Association with focus or association with presupposition. In P. Bosch and R. van der Sandt (Eds.), Focus: Linguistic, Cognitive, and Computational Perspectives, pp. 232–244. Cambridge University Press. Saur, E.-M. (2013). Clefts: Discourse function and the nature of exhaustivity violation effects. Master’s thesis, Universität Potsdam. Shinners, P. (2011). Pygame. http://pygame.org/. Soames, S. (1989). Presupposition. In D. Gabbay and F. Guenther (Eds.), Handbook of Philosophical Logic, Volume IV, pp. 553–616. Reidel. Stalnaker, R. (1974). Pragmatic presuppositions. In M. Munitz and P. Unger (Eds.), Semantics and Philosophy, pp. 197–214. New York University Press. Szabolcsi, A. (1994). All quantifiers are not equal: The case of focus. Acta Linguistica Hungarica 42, 171–187. van der Sandt, R. (1989). Anaphora and accommodation. In R. Bartsch, J. van Benthem, and P. van Emde Boas (Eds.), Semantics and Contextual Expression. Foris. Velleman, D. B., D. Beaver, E. Destruel, D. Bumford, E. Onea, and L. Coppock (2012). It-clefts are IT (Inquiry Terminating) constructions. In A. Chereches (Ed.), Semantics And Linguistic Theory (SALT) 22, pp. 441–460. Zimmermann, M. (2011). Discourse particles. In P. Portner, C. Maienborn, and K. von Heusinger (Eds.), Semantics: Handbücher zur Sprach- und Kommunikationswissenschaft HSK 33.2, pp. 2011–2038. Mouton de Gruyter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 364 J. P. De Veaugh-Geiss, S. Tönnis, E. Onea, & M. Zimmermann An experimental investigation of (non-)exhaustivity in es-clefts A. Appendix: Target auditory stimuli Target auditory stimuli in German for narrow focus condition. In order to recreate the cleft, definite pseudocleft, and exclusive conditions, follow the examples in (6)–(9) on pages 352–3. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Tom hat einen Pullover angezogen. Max hat einen Cocktail gemischt. Jens hat einen Reifen gewechselt. Ben hat einen Koffer gepackt. Jens hat einen Flyer gedruckt. Ben hat eine Katze gestreichelt. Tom hat ein Hemd gebügelt. Max hat ein Gedicht aufgesagt. Jens hat einen Teppich gekauft. Ben hat einen Kuchen gebacken. Tom hat einen Kinderwagen geschoben. Max hat einen Kaktus gepflanzt. Tom hat eine Ziege gefüttert. Max hat eine Schürze genäht. Jens hat ein Regal getragen. Ben hat ein Märchen erzählt. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. Tom hat einen Weihnachtsbaum geschmückt. Max hat einen Brief geschrieben. Jens hat einen Ball geworfen. Ben hat einen Berg bestiegen. Jens hat eine DVD eingelegt. Ben hat eine Orange ausgepresst. Tom hat ein Steak gebraten. Max hat ein Zimmer aufgeräumt. Jens hat eine Karte gebastelt. Ben hat einen Ofen befeuert. Tom hat einen Tumor entfernt. Max hat einen Fleischspieß gegrillt. Tom hat eine Rechnung bezahlt. Max hat eine Salbe aufgetragen. Jens hat ein Loch gebohrt. Ben hat ein Schwein beobachtet. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 365 366 Cognitive vs. emotive factives: An experimental differentiation1 Kajsa DJÄRV — University of Pennsylvania Jérémy ZEHR — University of Pennsylvania Florian SCHWARZ — University of Pennsylvania Abstract. A central question in current presupposition theory is what (sub-)classes of triggers there are and how they differ from one another (Abusch 2002; Sudo 2012; Tonhauser et al. 2013; Romoli 2012; Abrusán 2016). Factives have traditionally been thought to presuppose the truth of their complements, but the potential need for further differentiation was present from the start, beginning with the distinction between semi-factives (e.g. discover) and ‘full’ factives (e.g. regret) by Karttunen (1971). However, the precise nature of the differences involved has remained elusive in theoretical terms, and key empirical properties have been difficult to pin down experimentally (e.g. Jayez et al. 2015). We present new experimental evidence confirming specific differences between emotive factives (be happy, appreciate) and cognitive factives (be aware, realize) using a yes/no-continuation acceptability rating task (Cummins et al., 2013). We spell out an analysis of the demonstrated contrast in terms of a distinction between triggers based on whether or not their presupposed content is encoded as part of the conventionally entailed content (Sudo, 2012; Klinedinst, 2010), and also discuss the broader theoretical implications of our experimental results. Keywords: semantics, experimental pragmatics, presupposition, factivity, entailment. 1. Introduction 1.1. Theoretical background A central question in current presupposition theory concerns whether and how expressions that trigger presuppositions can be classified in different categories according to their semantic and pragmatic properties (cf. Abusch 2002; Simons 2007; Simons et al. 2010; Sudo 2012; Tonhauser et al. 2013; Romoli 2012; Abrusán 2016). We investigate this question with regards to factive presupposition triggers, i.e. expressions that presuppose the the truth of their complement clause. (1)-(2) illustrate that the truth of the embedded clause – that the proposal offended them – remains part of what is conveyed even under negation. (1) a. I had discovered that the proposal offended them. b. I had not discovered that the proposal offended them. (2) a. I regretted that the proposal offended them. b. I did not regret that the proposal offended them. We present new experimental data pertaining to the difference between two types of factives: cognitive factives like discover and find out on the one hand, which convey a relation between a 1 We would like to thank the audiences at SuB21, as well as various Schwarz Lab meetings for useful comments and discussion. Work on this project has been supported by NSF-grant BCS-1349009 to Florian Schwarz. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 367 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives proposition and states or events relating to the subject’s doxastic state, and emotive factives like regret and be happy on the other hand, which communicate a relation between a proposition and the subject’s emotive affect towards it. 1.1.1. Empirical contrasts between cognitive and emotive factives It was already noted by Karttunen (1971) that what he called “semi-factives” (such as discover and find out) can easily lose their presuppositional status. For example, they do not necessarily project from the antecedents of conditionals, in contrast to other factives such as regret, as illustrated in (3). (3) a. If I discover later that the proposal offended them, I will apologize. does NOT presuppose the proposal offended them. b. If I regret later that the proposal offended them, I will apologize. presupposes the proposal offended them. (3a) conveys no commitment on part of the speaker to the proposition ‘the proposal offended them’, despite the fact that discover typically conveys the truth of its complement at a global level. Furthermore, cognitive factives can be used ‘parenthetically’ (e.g. Hooper and Thompson 1973; Simons 2007) by having the embedded clause answer a question, as shown in (4) from Simons (2007: p. 1035), whereas emotive factives typically cannot be used this way (5). (4) A: Where was Harriet yesterday? B: Henry discovered that she had a job interview at Princeton. (5) A: Where was Harriet yesterday? B: ?? Henry is happy that she had a job interview at Princeton. In (4), B introduces she had a job interview at Princeton as the embedded clause of the cognitive factive discovered and uses it to introduce new, non-presupposed information to answer the question, which can certainly not be taken for granted. By contrast, in (5) it is introduced as the embedded clause of the emotive factive is happy, and here it seems to retain its presuppositional status: B’s response is intuitively inappropriate, presumably because information that has the status of a presupposition is not suitable for addressing A’s inquiry for new information about Harriet. 1.1.2. Theoretical approaches to the contrast While the contrasts illustrated above go back to the beginnings of the linguistic literature on presuppositions, extensive discussion of explicit theoretical proposals for differentiating types of triggers only began in the early 2000’s. One prominent proposal by Dorit Abusch (2002; 2010) distinguishes between ‘soft’ and ‘hard’ triggers, and assigns cognitives to the former category and emotives like regret to the latter.2 The contrast above can then be seen as an 2 Abusch never employs the terms cognitive and emovitve, but mentions Karttunen’s discussion of discover as a case of soft trigger. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 368 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives instance of a more general pattern, as the presuppositions of soft, but not hard triggers, are thought to be easily suspendable. For example, it is seen as parallel to the contrast between the soft trigger win and the hard trigger too illustrated in (6), from Jayez et al. (2015: p. 174; but note that these authors propose their own terminology and distinction in terms of ‘strong’ vs. ‘weak’ triggers). (6) a. I don’t know whether Paul participated in the race, but if he won, he must be very proud. b. ?? I don’t know whether Paul participated in the race, but if Mary participated too, they probably had a drink together just after. The context in both cases establishes that the speaker is agnostic about Paul’s participation in the race. In (6a), this does not seem to create a critical conflict with the notion of participation conveyed by win, which typically projects (from antecedents of conditionals and other standard projection environments) and is thus taken to be a presupposition. In contrast, in (6b), the agnostic preface seems to clash with the projecting presupposition that someone else (salient in the context, with Paul as the only feasible candidate) participated in the race. Generally speaking, Abusch’s analysis follows influential work by Stalnaker (1974) in assuming that (at least) certain presuppositions can be derived pragmatically, i.e., as a general conversational inference that is not conventionally encoded at the level of lexical meaning. In particular, Abusch puts forth an account based on lexical alternatives. Under this view, soft triggers are associated with a set of lexical alternatives (e.g. win is associated with the alternative lose). In addition, a context-sensitive pragmatic principle imposes that one member from the set of sentences where the alternatives are substituted in fact holds. In the case of soft triggers, the idea is that all the alternatives share an entailment (e.g., win and lose both entail participation), which results in the entailment being true regardless of which alternative turns out to be true. The suspendability of the presuppositions of soft triggers is then explained by the context-sensitivity of this pragmatic principle: given that the content that traditionally is seen as presupposed starts off as a simple conventional entailment of the trigger, the effect of the pragmatic principle can effectively lose its force, e.g., when this entailment is locally relevant. This is what happens in (6a) where Abusch’s analysis represents the meaning of the conditional as if Paul both participated and won, and the effect of considering alternatives in the provided context does not give rise to a global notion that Paul participated. In addition to Abusch, there are several other proposals taking a conversational approach to deriving presuppositions which differ in the details. For example, Romoli (2012) proposes an alternative-based pragmatic account of presuppositions, where soft presupposition triggers are assimilated to indirect scalar implicatures. A different type of pragmatic account has grown out of work by Mandy Simons and colleagues (Simons, 2007; Simons et al., 2010; Tonhauser et al., 2013). For these authors, the presuppositional status of a trigger depends crucially on the Question Under Discussion (QUD). I.e., whether or not part of the content introduced by an expression is treated as presupposed or backgrounded is determined relative to the conversational goals and issues at stake. Like Abusch and Romoli, they assume that factives entail the truth of their complement clause. For example, if the QUD is ‘What happened?’, then the content of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 369 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives the matrix clause (Henry discovered that p) constitutes the ‘at-issue’ part of the utterance, and Harriet had a job interview at Princeton is backgrounded and treated as part of the common ground, i.e., presupposed. If the QUD is ’Where was Harriet yesterday?’, as in (4) and (5), then the content of the embedded clause Harriet had a job interview at Princeton is treated as new, at-issue information, which updates the common ground, i.e., it is not presupposed. The contrast between the cognitive and the emotive factives with respect to their ability to suspend their presupposition on this account then, would presumably need to be linked to a difference in their abilities to function parenthetically (see (4) and (5)).3 Taking a more general perspective, what’s crucial for current purposes is that all of these pragmatic approaches involve the assumption that presupposition triggers lexically entail the content that eventually gets projected as a presupposition (that the embedded clause is true), for both cognitive and emotive factives. In contrast, we argue that the experimental data presented below suggests that this only holds for cognitive factives, and that the presupposition of emotive factives is not part of what is conventionally entailed. Such a distinction between triggers has been advanced by previous authors for other triggers, in particular Sudo (2012); Dahlman (2016). 1.2. Experimental background While experimental work on presuppositions has only recently become a research area with significant growth, the aim of substantiating differences between different types of triggers has been a key driving force in it. For reasons of space, we will not attempt anything close to comprehensive coverage of this literature, but merely highlight a couple of especially relevant examples of prior research (for a recent review of experimental work on presuppositions more generally, see Schwarz 2016). One of the early studies finding differences between triggers is Tiemann et al. (2011), who detect variation in acceptability judgments in contexts that do not explicitly support the trigger’s presupposition, but are consistent with it. Similarly, Domaneschi et al. (2014) find that while some presupposition triggers leave a lasting impact – suggesting their presupposition is accommodated – others essentially seem to be ignored: after reading short texts containing various triggers followed by a distractor task, subjects are more likely to answer questions based on the contribution of triggers like stop, compared to a greater likelihood of failing to consider the presupposition such as that of the prefix re- (as in reintroduce). Tiemann (2014) and Tiemann et al. (2015) report a similar lack of consideration of the presupposition of again when answering questions, even without a delay in the task. The just mentioned studies confirm some of the differences between triggers, in that the patterns of variation across triggers at least roughly match one of the theoretical divisions between types of triggers. But other studies that are more narrowly targeted at comparisons between specific triggers falling on opposite sides of a given proposal for a theoretical divide have failed to 3 Note that while the QUD-based account certainly leaves room for differentiating triggers, it is not obvious what precisely it would say about the contrast between different types of factives. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 370 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives yield clear confirmation of expected contrasts. For example, Schwarz (2014) compares the presumed ‘soft’ trigger stop with the ‘hard’ trigger again in terms of their processing time course. The results from visual world eye tracking suggest that both soft and hard triggers are processed rapidly, contrary to what might be expected based on (one line of) results on processing conversational implicatures, which can be presumed to share crucial features with soft triggers on certain pragmatic accounts. Furthermore, various attempts at comparing soft triggers to implicatures suggest that they differ in their processing profile, providing evidence against analyses that assimilate them (Chemla and Bott, 2013; Kennedy et al., 2015: among others). Yet another attempt at assessing a key part of the empirical claim with regards to the distinction between hard and soft triggers illustrated in (6) was made by Jayez et al. (2015). Their acceptability judgment study focusing on the hard triggers too and regret suggests that these, too, can fail to project from antecedents of conditionals in contexts that globally establish ignorance with respect to the truth of the presupposition, at least with sufficient contextual support. Most relatedly to the experiments reported below, Cummins et al. (2013) and Amaral and Cummins (2015) investigate various triggers in English and Spanish and test the acceptability of Yes, although and No, because continuations, as illustrated for again and stop below:4 (7) Q: Did Brian lose his wallet again? A: Yes, although he never lost it before. A’: No, because he never lost it before. (8) Q: Did John stop smoking? A: Yes, although he never smoked before.5 A’: No, because he never smoked before. Across all triggers that they looked at, both yes and no responses of this sort are degraded relative to controls, suggesting that contradicting the presupposition comes with a cost no matter what. But interestingly, the triggers in their results seem to be grouped into two classes with regards to the extent to which yes,. . . and no,. . . responses differ from one another: for expressions such as stop and still, there is a fairly substantial, statistically significant difference in acceptability between the response options, with higher ratings for no than for yes. In contrast, expressions such as again and too yield comparable acceptability ratings for both continuations.6 Cummins et al. (2013) relate their results to the distinction between lexical and resolution triggers (Zeevat, 1992), but they broadly align with the soft-hard distinction as well. And in line with common claims about this distinction, the interpretation offered by these authors is indeed that the first set of triggers more easily allows for ‘local accommodation’ (Heim, 1983: i.e., an interpretation where presupposed content acts as if it were run-of-the4 Similar tasks involving the selection of the best answer from a set of options had previously been used to investigate clefts and focus (Onea and Beaver, 2011; Velleman et al., 2012; Destruel et al., 2015). 5 Note that Cummins et al. (2013) do not explicitly provide the continuations they used for stop, so this is our best guess at what they looked like for this question, which is listed in the materials in their appendix. 6 Note that they also found regret to pattern with the first set of triggers, exhibiting a significant difference between continuations. This is directly relevant to our findings below, and at first sight may seem incompatible with them; see footnote 12 for our take on this. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 371 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives mill entailed content), leading to relatively greater acceptability of the no-responses for these triggers. But there is a potential additional dimension to the variation as well, which can be related to Zeevat’s notion of lexical triggers, which constitute cases where the presupposition is a requirement that comes with the asserted component of the trigger. As Amaral and Cummins (2015: p. 169) put it, in these cases ‘the responses in condition [A; yes-continuation] appear self-contradictory, if we assume that the presupposition is a logical prerequisite for the at-issue content of the trigger.’ In other words, the content introduced in the question cannot be affirmed independently of the presupposition. Our experiments below build on essentially this notion, though we couch it in a slightly different theoretical context.7 2. Experiments The starting point for our investitagion is the hypothesis that we find different relationships between different subcomponents of meaning for emotive and cognitive factives. Generally speaking, both types of factives contribute (at least) two meaning components, that of the ATTITUDE involved (which relates the matrix subject’s mental state to the embedded proposition), and that of the ( EMBEDDED ) proposition P (conveying that P is true). We propose that these two components stand in a different relationship to each other for the two types of factives, such that for emotive factives, P can be disentangled from the subject’s ATTITUDE in a way that it cannot for cognitive factives. The basic intuition is that it is quite easy to imagine that one is happy about a certain state of affairs, but is simultaneously wrong about it. It is harder to see how one can discover something which is not true. Relatedly, (9a) is a coherent statement, whereas (9b) gives rise to contradiction:8 (9) a. John was happy that his parents are coming to town, although it turned out that he was in fact mistaken/although it turned out that they had to cancel. b. ?? John discovered that his parents are coming to town, although it turned out that he was in fact mistaken/although it turned out that they had to cancel. More specifically, we build on the proposal by Sudo (2012) that certain triggers (e.g., change of state verbs like stop) have their presupposition represented as part of the entailment at the lexical level, whereas others (such as gender features on pronoun or the additive presupposition of also) do not. Adapting this general approach, we hypothesize that cognitive and emotive factives differ in terms of their entailment properties — specifically, that P, while generally surfacing as projective content for both types of factives, is also part of the conventionally entailed content of cognitive factives, whereas it is not for emotive factives (Table 1). 7 Note that a further directly related notion, that of certain triggers exhibiting ‘Obligatory Local Effects,’ has been introduced in recent work by Tonhauser et al. (2013). 8 On this point, Egré (2008: p. 103) also observes that the emotive regret behaves differently from the cognitive know in false-belief environments. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 372 K. Djärv, J. Zehr, & F. Schwarz Factive Type Conventional Entailment Cognitive vs. emotive factives C OGNITIVE that P P & ATTITUDE E MOTIVE that P ATTITUDE Table 1: Our hypothesis. Cognitives, but not factives, conventionally encode their embedded proposition P as part of their entailment. We test this hypothesis using a yes/no-continuation task, similar to the above-mentioned one employed by Cummins et al. (2013) to explore differences between a range of triggers such as stop and again. The task pairs a factive question with a response of the form yes, although. . . or no, because. . . , followed by a denial of the content of the embedded proposition, as illustrated in (10). (10) Is Anna aware/happy that [ p Ryan is coming to the wedding]? / Does Anna realize/appreciate that [ p Ryan is coming to the wedding]? A1. Yes, although he isn’t. A2. No, because he isn’t. Q. While the overall approach taken here is quite similar to that of Cummins et al., our hypothesis provides a slightly different angle on the expected outcomes by focusing on whether or not an affirmative answer is possible when the presupposition is explicitly denied at the same time. Our basic assumption is that a yes-response necessarily commits the speaker to the entailed content introduced by the question. However, it may in principle be possible to deny a presupposition, to the extent that it is introduced entirely at a separate level and not part of the conventionally entailed content. This leads to diverging predictions based on our hypothesis: if the content of the embedded proposition is entailed, as we propose is the case for the cognitive factives, saying yes and then denying the content of the embedded proposition should be contradictory, and thus only no will be a viable response. But for the emotive factives, where we hypothesize that the content of the embedded proposition is not part of what is entailed, it should in principle be possible to just endorse the (emotive) ATTITUDE by responding yes, even if qualifying immediately by noting that the embedded proposition is false – i.e. singling out one aspect of the meaning (the entailed content: ATTITUDE) while contesting another aspect (P). Note that homing in on one particular aspect of meaning in your affirmation may still come at a cost, i.e., it is indeed plausible that the default impact of an affirmation involves endorsing both entailed and presupposed content, wholesale, as it were. What’s crucial for our approach is that in principle it may be possible that non-entailed presuppositions can be denied along with a yes-response, while entailed ones cannot. If so, that leads to a prediction for our hypothesized difference between cognitive and emotive factives, namely that the latter should yield a greater acceptance of yes-responses than the former. Note that the hypothesis makes no specific prediction for the relative acceptability of denials of presupposed content with no-continuations, which require targeting the presupposed content with negation (commonly analyzed as involving local accommodation). It’s possible that the different relationship between presuppositions and entailments has a reflex here, too, but this does not necessarily follow from our hypothesis. In the following, we report on two experiments to test these predictions: Experiment 1, where the participants were asked to chose which of the yes vs. no answer-options they preferred, and Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 373 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives Experiment 2, which uses acceptability ratings to home in on the acceptability of yes-responses more directly. 2.1. Experiment 1 2.1.1. Design In Experiment 1, participants were presented with questions containing a cognitive or an emotive factives and had to indicate their preference with resepct to yes and no-answer options. There were additional response options to express that ‘Both options are equally good.’ or ‘Both options are equally bad.’ (11) Q. {Did Mark find out/Was Mark surprised} that [PS his parents are visiting]? A1. Yes, although they had to cancel because of the weather. A2. No, because they had to cancel because of the weather. A3. Both options are equally good. A4. Both options are equally bad. If, as hypothesized, cognitives but not emotives entail the content of the proposition they embed, we expect that the yes-responses should be more readily available for the questions with an emotive facctive, compared to those with a cognitive one. That is, for the emotive factives, we expect both the yes and the no-responses to be in principle available. Assuming more or less comparable availability of the yes and no-responses, the both good and both bad responses should be chosen more frequently for emotive factives (depending on how the potential cost of local accommodation (for no) or targeting only one aspect of meaning (for yes) affects acceptability judgments). For the cognitive factives on the other hand, we expect these to allow only the no-responses, as these should be clearly better than yes-resonses (even if involving some cost for local accommodation). Hence, both good should be impossible with the cognitive factives, given the unacceptability of the yes-response. The both bad option might get chosen for the cognitive factives, if subjects dislike both local accommodation and cancellation/suspension. However, this is likely to be the dispreferred choice, assuming that local accommodation does make no-responses available. 2.1.2. Participants Thirty-six native speakers of English participated in the study. The participants were recruited on Prolific.ac, a crowd-sourcing tool for recruiting participants to participate in scientific studies online. Participants were paid at rate of 5.20 GBP per hour for their participation. The task took approximately 10 minutes to complete. No participant was excluded from the analyses. 2.1.3. Materials All items presented short written dialogues between two speakers. There were two variations of twenty-four experimental items, corresponding to the two predicate types: COGNITIVE (reProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 374 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives alize, find out) and EMOTIVE (be disappointed, be surprised) factives, as illustrated in (11) above. Each subject only saw a given item in one version, with item-condition pairings counterbalanced across subjects. In addition, there were twenty-four filler items where factives were paired with different continuations. Given the prediction for the critical part of the experiment, that the yes-responses should be endorsed to a greater extent in the EMOTIVE condition than in the COGNITIVE condition, the fillers were designed to yield the opposite preference. Hence, among the fillers, the emotive factives favoured a no-response, and the cognitive factive favoured a yes-response, as illustrated in (12) and (13), in order to counteract the potential risk of introducing an overall bias against the yes-responses. The both good and both bad options in (A3) and (A4) were available for the fillers, too. (12) Emotive filler: Q. Was Mike disappointed that John decided to quit football? A1. Yes, although he didn’t think John was a very good player. A2. No, because he didn’t think John was a very good player. (13) Cognitive filler: Q. Was Mary surprised that Bill got the grant? A1. Yes, although she was on the grant committee. A2. No, because she was on the grant committee. The participants were given the following instructions: “In this experiment you will read short questions. You will then be asked to choose which answer you prefer, given a choice of two answers. You also have the opportunity to say that you think that both answers are equally good or equally bad. There is not a right or a wrong answer. Simply choose the answer that you prefer, given the preceding question.” In order to control for variability stemming from the two predicate types influencing the answers across conditions, we used a block design. Thus, half of the participants saw the emotive factives in a randomized order first, and the cognitive factives in a randomized order last, and vice versa for the other half of the participants. Each block contained both fillers and critical items. Additionally, the items were divided into two groups, in order for each specific predicate to be evenly distributed across participants, thus creating a two-by-two Latin square design.9 2.1.4. Analysis The results were analyzed as logistic mixed effects regression models in R (version 3.1.2) using the glmer function of the lme4 package (version 1.1-11) and its bobyqa optimizer. Results from maximally complex converging models are reported here (Barr et al., 2013). We ran four types of models regarding the predicted outcomes: models predicting the observation of a yes-response (to the exclusion of all the others), of a no-response (to the exclusion of all the others), of a both good-response (to the exclusion of all the others) and of a both bad-response (to the exclusion of all the others). They tested for a fixed effect of predicate type (EMOTIVE, COGNITIVE ). For each of these simple-effect models, we also ran a version testing for an 9 The experiment is available at: http://spellout.net/ibexexps/SchwarzLabArchive/YesNoFact/ experiment.html Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 375 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives effect of block order (EMOTIVE-COGNITIVE, COGNITIVE-EMOTIVE) and its interaction with predicate type. Participants and items were added as random effects, with a random slope for predicate type per participant, and a random slope for predicate type and block order (in the relevant models) per item. Our different baselines exhausted the logical space of effects and interactions. The models did not include data-points for the filler items, and no other data-point was excluded. 2.1.5. Results The results are summarized in Figure 1. The response patterns for the first block showed a clear contrast between the cognitive and the emotive factives. There was a main effect of predicate type on the observation of no- and both bad-responses in the first block (resp. p = 0.00247, β = 1.2433, SE = 0.4107 and p = 0.024687, β = 1.6566, SE = 0.7375), with no-responses being more frequent for the cognitive factives and both bad-responses being more frequent for the emotive factives. There was also a significant interaction with block order for the noresponses (p = 0.02423, β = 1.3729, SE = 0.6092) but not for the both bad-responses; the significant main effects between the two types of factives disappeared in the second block (predicate type for no p = 0.7260, β = 0.12959, SE = 0.36983; predicate type for both bad p = 0.678, β = 0.3225, SE = 0.7768), suggesting that exposure to one type of factive predicate had a strong effect on the participants’ responses, potentially through priming one type of interpretation, or through adjusting the participants’ standards for evaluation. There was no such significant main effect on the observation of yes- and both good-responses (all p > 0.17, β ≤ 0.5). We observed the same results in simple models, excluding block order as a predictor: no- and both bad-responses were more frequent with cognitives than with emotives (no: p = 0.0222, β = 0.5266, SE = 0.2303; both bad: p = 0.0223, β = 0.7232, SE = 0.3165) but there was no significant effect of predicate type for yes- and both good-responses (yes: p = 0.737, β = 0.08468, SE = 0.25253; both good: p = 0.809, β = 0.07354, SE = 0.30382). Factive Overall proportion of choice Overall choice proportion Emotive 60% 40% 20% 60% a Cognitive a Emotive No No No 40% No 20% Yes Yes Yes Yes First Second Factive Overall proportion of choice Cognitive Factive a Cognitive 0% Yes No BothGood Response BothBad Emotive 60% 40% 20% Both Good Both Bad Both Good Both Bad 0% a Both Bad Both Bad 0% Block First Second Block Figure 1: Left: proportion of responses for the two types of factives in block 1, where the contrast between the cognitive and the emotive factives is significant for the no and the both bad-responses. Center and right: responses for the four response types (yes, no, both good, both bad), by block. The contrast between the two types of factives is neutralized in block 2. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 376 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives To summarize, even though the contrasts between the two verbs are subtle, and subject to influencing each other across blocks, there is nonetheless a clear contrast between the two types of factives with respect to the availability of no-responses. Even though there was no direct, visible contrast in the availability of yes-responses and both good-responses, the contrast in both bad-responses is in line with our hypothesis, according to which the two aspects of meaning identified as part of the semantics of the two types of factives (the ATTITUDE and the ( EMBEDDED ) P components) contribute to the overall semantic properties in different ways for the emotive and the cognitive factives — specifically in terms of the truth of the embedded clause being part of the conventional entailment in the case of cognitive factives, but not for the emotive factives. Under this view, participants were not sufficiently inclined to consider an interpretation where either negation targeted P directly or where an affirmative response selectively endorsed the conventionally entailed content (for emotive factives). At the same time, participants did display a sensitivity to the contrast in entailment in that they were more amenable to accepting a no-response for cognitive factives, because it should be easier to target the embedded proposition P with negation when it is conventionally entailed. However, there is at least one alternative interpretation of the results which basically attributes the contrast in no-responses to varying availability of local accommodation, and does not posit a difference between factives in terms of whether or not P is part of the conventionally entailed content. To spell out a specific version of this alternative, it might be that only emotives are lexically associated with a conventional presupposition that P (which at the same time is part of the entailed content as well). In contrast, the presuppositional status of P would result from a pragmatic derivation in the case of cognitive factives, in line with the proposals by Simons, Romoli and others. Based on these assumptions, no-responses for cognitives are expected to be easily acceptable, to the extent that the pragmatic derivation does not (or at least not necessarily) take place under negation.10 For emotives on the other hand, both a yes and a no-response would require cancellation of a hard-coded, conventional presupposition, which would lead participants to generally prefer the both bad response to indicate a presupposition failure. In order to disambiguate between these two interpretations of the results, Experiment 2 used an acceptability rating task where subjects were only presented with one answer option at a time. This allowed us to test for a contrast in the acceptability of yes-responses between the two types of factives more directly. As discussed above, our hypothesis predicts that yes-responses paired with denials of P will be more readily available for emotive factives than for cognitive factives. In contrast, the alternative interpretation we just considered does not predict such a contrast in the yes-responses, as both types of factives should yield low ratings for yes-responses, based on the crucial assumption that factives uniformly include a conventional entailment that P. 10 For Romoli in particular, the justification after no would block or cancel this derivation, in the same way that the sometimes implicature normally associated with not always does not arise in I don’t always curse because I never curse). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 377 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives 2.2. Experiment 2 2.2.1. Design Experiment 2 used an acceptability rating task to provide an independent assessment of the acctability of yes and no continuations. Participants saw only one response at a time (yes, although. . . or no, because. . . ), as shown in (14) and (15). (14) Q. {Is Maria aware /happy} that [P Mike is moving back to Chicago]? A1. Yes, although he isn’t. (15) Q. {Is Maria aware/Is Maria happy} that [P Mike is moving back to Chicago]? A2. No, because he isn’t. Specifically, the participants were asked to rate to what extent the answer sounds natural to them, in light of the question, by choosing a value between 1 (‘completely unnatural’) to 7 (‘completely natural’) by clicking the number or pressing the corresponding key. They were instructed that there was no right or wrong answer. If cognitive, but not emotive factives conventionally entail P, then we expect to see a contrast between the cognitive and the emotive factives in the yes-responses, such that yes is rated significantly lower for the cognitives than for the emotives. Again, no specific predictions were made for the no-responses. In addition to the slight change in the nature of the task, the stimuli were refined from Experiment 1 to be more uniform, in particular by consistently using future-oriented progressive forms (e.g., is moving to Chicago) in the embedded clause and expressing denial in the response-continuation via VP-ellipsis. This was done to avoid potential other pragmatic strategies of reconciling the denial with the initial affirmative or negative response, which may have given rise to additional variation in response patterns for the original set of materials. 2.2.2. Participants Sixty-two undergraduate students at the University of Pennsylvania, all native speakers of English, participated in the study for course credit through the Psychology department’s subject pool. The experiment took approximately 15 minutes, and was carried out on lab computers. 2.2.3. Materials As illustrated above, the items consisted of short dialogues between two speakers, as in (14), (15). Versions of the twenty-four critical items were created in four conditions, corresponding to the two predicate types—cognitive and emotive, and the two answer types—yes, although and no, because. We also included a between item adjective-verb manipulation, such that half of the items contained verbal factives (appreciate, realize), and half of them, adjectival factives (happy, aware). Forty-eight filler items were also included. These were designed with two purposes in mind: first, to provide a floor and a ceiling baseline for the yes- and no-responses; and second, to counterbalance the number of good and bad yes- and no-responses. Half of the fillers were therefore constructed using a non-factive matrix predicate (think), where the noProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 378 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives answers would be infelicitous, and the yes-answers would be fully acceptable, as in (16). The other half of the fillers involved a question with two conjuncts, as in (17). Here, it would be the yes-answers that were infelicitous, while no would be an acceptable response. (16) (17) Q. Does Sue think that Bill’s parents are going to the wedding? A1. #No, because they are. A2. XYes, although they aren’t. (‘Bad Control’) (‘Good Control’) Q. Is John going to Paris and Rome this summer? A1. XNo, he’s not. A2. #Yes, although he isn’t going to Rome. (‘Good Control’) (‘Bad Control’) The participants were given the following instructions: “In this experiment you will read short dialogues between two people in the form of a question and an answer. You will then be asked to rate to what extent the answer sounds natural to you in light of the question, by choosing a value between ‘completely unnatural’ (1) to ‘completely natural’ (7). There is not a right or a wrong answer. Simply make the choice based on how well you feel the answer works for the preceding question.” In contrast to Experiment 1, the factive and emotive items were randomly mixed, but answer type (yes vs. no) was separated by blocks, with order counter-balanced across groups.11 2.2.4. Analysis The ratings were analyzed using linear mixed effects regression models in R (version 3.1.2), using the lmer function of the lme4 package (version 1.1-11). All our models included predicate type (EMOTIVE, COGNITIVE) and answer type (YES, NO) as fixed effects. Given that we didn’t make predictions regarding syntactic category (ADJECTIVE, VERB) nor block order (YES - NO, NO - YES ), we fitted models excluding them both (simple models) and models including either one of them as predictors (models including both of them would not converge). We tested for the maximally complex models, including all possible interactions of predictors and all random slopes for participants and items as random effects, and our different baselines exhausted the logical space of effects and interactions. The models only included the data points of the experimental items. 2.2.5. Results The results are presented in Figure 2. Responses were similar in the first and second block (main effects t ≤ 1.35, β ≤ 0.45; two-way interactions t ≤ 0.3, β ≤ 0.15; three-way interaction t = 0.302, β = 0.13988, SE = 0.43359) and for adjectives and verbs (main effects t ≤ 1.5, β ≤ 0.35; two-way interactions t ≤ 1.63, β ≤ 0.44; three-way interaction t = 1.216, β = 0.37898, SE = 0.31167). As predicted, the response patterns showed the yes-ratings to be significantly higher for the emotive than for the cognitive factives (simple model: t = 4.954, β = 0.76, SE = 0.1534; t ≥ 3.1 and β ≥ 0.59 otherwise), with no difference in the no-ratings (simple 11 The experiment is available at: http://spellout.net/ibexexps/SchwarzLabArchive/YesNoRating/experiment.html?Home=true Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 379 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives model: t = 0.625, β = 0, 1005, SE = 0.1607; t ≤ 0.785 and β ≤ 0.1683 otherwise). There was also an interaction between predicate type and answer type (simple model: t = 4.083, β = 0.8605, SE = 0.2108; t ≥ 2.61 and β ≥ 0.67 otherwise). Yes No Score (0=Compl. unnatural, 6=Compl. natural) 6 4 2 0 Bad control Cognitive Emotive Good control Bad control Cognitive Emotive Good control Type Figure 2: Mean ratings by answer type and predicate type (merged blocks). With this experiment, we replicated the main conceptual result from Experiment 1, in that we elicited a contrast between emotive and cognitive factives. The contrast no longer consists in participants endorsing no-answers more readily as responses to cognitives than to emotives; rather, we now see that participants deem yes-answers relatively more natural as responses to emotives than to cognitives.12 Importantly, the results from Experiment 1 were not only compatible with our hypothesis, but also with an alternative hypothesis based on potential differences in the availability of local accommodation. However, the results from Experiment 2 are not in line with the predictions of such an alternative view: that view assumes that P is conventionally entailed both by cognitive and emotive factives, therefore yes-answers should be rated as low for emotive as for cognitive factive questions (under the assumption that yes commits the speaker to all the entailed content). On the other hand, our hypothesis in well in line with the results: participants were able to understand the affirmative reply as singling out the entailed content to the exclusion of the embedded proposition P to some extent for emotives. This led to an increase in acceptability of yes-continuations, in contrast to cognitives, which were visibly as low as the baseline controls in this regard. This is consistent with the idea that emotives do not, but cognitives do, conventionally entail P, given the assumption that it is in principle possible to selectively affirm the conventionally entailed content with a yes-response. 3. Discussion Taken together, the results from Experiment 1 and Experiment 2 support the hypothesis we advance, that cognitive and emotive factives differ in terms of whether the truth of the embedded 12 Cummins et al. (2013) report results for regret, which look similar to other triggers that we would see as candidates for entailing their presupposition. However, there is no direct point of comparison to other types of factives, and furthermore, their materials seem pragmatically skewed by using embedded clauses that the matrix subject is virtually guaranteed to be an informed authority on, such as Did Fiona regret buying the house?. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 380 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives clause is part of what is conventionally entailed (in addition to being presupposed). While the first experiment did not support that notion directly, the results were perfectly consistent with this notion, but they also could be explained by an alternative hypothesis that locates the difference entirely in terms of the interaction of negation (and more generally, no-answers) with different triggers. Experiment 2 sought to get a more direct comparison of the acceptability of yes-responses paired with a denial of the presupposition, and found a significant difference (and corresponding interactions) between the two types of factives. This showed that an explanation of the contrast has to extend beyond negation, which our hypothesis does but the alternative one does not provide. That said, there are various aspects of the results as well as the broader theoretical discussion that merit further consideration. The first issue to raise here is the absence of a contrast in ratings for the no-answers in Experiment 2, which contrasts with what we observed in Experiment 1. We suggested that noresponses were more likely to be selected with the cognitive factives because it is easier for negation to target the embedded proposition P when it is part of the conventionally entailed content. In the case of the emotives, this requires allowing negation to target purely presuppositional content, which may come with some cost (e.g., through local accommodation). But based on this interpretation, it may seem a bit surprising that we did not find parallel results for Experiment 2, where no difference in acceptability between no-answers for emotive and cognitive factives emerged. While we can’t offer a full-fledged explanation for this, there are a number of tentative points to offer that suggests that this need not undermine our proposal. To begin with, the two experiments differed not only in the explicit task, but also in several other details of implementation. While the choice of an appropriate response in Experiment 1 could be seen as closer to a production situation, the acceptability rating task in Experiment 2 primarily involved comprehension (plus assessment of an observed dialogue). It is at least possible that this introduces an asymmetry in terms of how likely people are to call upon a mechanism such as local accommodation: in Experiment 1, it was easy to avoid such a move by choosing a different response choice, whereas in Experiment 2, it may have offered itself as the last resort for taking the presented dialogue to be plausible. Furthermore, the block manipulations in the two experiments were different: Experiment 1 separated the two types of factives into separate blocks, whereas Experiment two had different blocks for yes and no-continuations, with factive types mixed with blocks. Thus the lack of an effect for negation in the latter may simply parallel the block order effect in Experiment 1, where no differences emerged between factive types in the second block. Finally, it is worth noting that the issue we’re addressing effectively is based on a null effect, and the absence of evidence in this regard should not be mistaken as evidence against our hypothesis. The core of our line of argument is that there is a difference between emotive and cognitive factives in terms of conventional entailment, and that we can find positive evidence for non-entailment, which we did. We should also address why no difference between types of factives in the acceptability of the yes-responses emerged in Experiment 1: both yes and both good choices were equally low there for cognitives and emotives, whereas in Experiment 2, yes-answers were judged to be more natural for emotives. As already noted in connection with the preceding point, the two experiments differed in various relevant respects, in particular with regards to choosing an appropriate response vs. providing a graded assessment of the acceptability of a fixed response. While the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 381 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives contrast between the different types of factives had an impact in both tasks, the persistent global presence of the truth of the embedded proposition for emotives seems to have decreased selection of either response in Experiment 1, suggesting that participants were reluctant to select a response with an unsupported presupposition from an emotive factive. That no-responses were much more readily selected and clearly preferred, for cognitives, fits the notion that their presuppositions are less persistent than those of emotives, echoing the claim that presuppositions of soft triggers are more easily suspendable that those of hard triggers (Abusch, 2002). As discussed earlier, expressions that have been claimed to project part of their conventionally entailed content (as we claim is the case for cognitive factives) tend to fall in the category of soft triggers, whereas expressions that have been claimed to trigger a presupposition independent from their conventionally entailed content (as we claim for emotive factives) generally fall in the category of hard triggers. Note that we here have tried to remain neutral as to the source of the projective content of factives, leaving open the possibility that in the case of cognitive factives, it could be derived as a type of implicature à la Romoli (2012) or a conversational inference more generally, based on the presence of the relevant proposition at the level of the conventionally entailed content. In contrast, this type of analysis is not available for the emotives, given our interpretation of the data. One obvious remaining option then is to posit that in the case of emotive factives, we are dealing with a conventionally encoded presupposition that is NOT simultaneously present at the level of conventionally entailed content. However, there is at least one further alternative, which relates to the question of what exactly is involved in the ATTITUDE component, in particular in the case of emotive factives.13 To spell out this option, let us first step back and return to the possibility of deriving the factive inference for cognitive factives: the original source of this content is in the conventional entailments at the lexical level, on this view. Its special status, leading to projection behavior is derived in one way or another based on the notion that one can distinguish between different pieces of meaning at this level namely i. that the subject believes (or has come to believe, etc.) that P , and ii. that P holds. In contrast, the information conveyed by an emotive factive expression like be happy that P seems to ultimately involve at least three pieces: i. that the subject has an emotionally positive attitude towards P, ii. that P holds, and iii. that the subject believes that P holds. So while there clearly is only one ingredient to the ATTITUDE component of cognitives (i), there could be any combination of (i) and (iii) that is lexically encoded to form the ATTI TUDE component of emotives. Relating this to our experimental results, note that any of these options would be compatible with our interpretation of the experimental results above, given that none of the considered ATTITUDE components entail P. Once we incorporate all three pieces of information into our considerations, further candidates for a conventionally encoded presupposition of emotives enter the picture. In addition to the option noted above that P (ii) be treated as a hard-coded presupposition, one could well imagine that emotives conventionally encode the subject’s belief that P (iii) as a presupposition and derive the stronger inference that P in fact holds conversationally, based on assumptions about the well-informedness and authority of the attitude holder. Alternatively, the ‘belief-presupposition’ (iii) could also be part of what is conventionally entailed, and emotive factives would then entail this presupposition. This would still be consistent with our interpretation of the experimental results, since neither the presuppositional nor the conventionally entailed content of emotive factives would 13 Thanks to Valentine Hacquard for discussion leading to our consideration of this possibility. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 382 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives then contribute that P holds: this would only emerge as a possibly defeasible inference from the presupposition that the subject believes P. In summary, once we think more broadly about precisely what ingredients there are to the meaning of emotive factives, more options open up, including one where a belief-presupposition of emotives is represented at the level of conventional entailments. While this would make cognitive and emotive factives more similar again on an abstract level, there would still be a substantive difference with regards to the role of the embedded proposition P (which would still be entailed for cognitives but not for emotives on the view under consideration). Regardless of where one comes down on these more intricate issues, the interpretation of our data is as follows: Our starting point was the long-standing observation that i. the complements of factives in general (i.e., both cognitive and emotive) are typically projected as true or impose restriction on the context of utterance, but ii. they differ in the extent to which they do so. Our proposal is that the content of the proposition that factives embed is also part of what is conventionally entailed in the case of cognitives, but not in the case of emotives. The experimental results we obtained and presented here support this proposal, and even the final alternative analysis we just discussed would wind up embracing it by assuming that emotives neither presuppose nor conventionally entail the truth of the proposition they embed, as it maintains that the truth of the embedded proposition could be derived from other conventionally encoded content. In the end, the various analyses that we discussed share precisely this property, while crucially differing on how the truth of the embedded proposition ends up as part of the conveyed content, with behavior that suggests it is (generally) projective and imposes constraints on the context of utterance, as presuppositions are traditionally thought to do. 4. Conclusion We presented two experiments investigating the role of the embedded proposition of both cognitive and emotive factives, using a yes/no-continuation task. Taken together, the experiments suggest that while the embedded proposition of cognitives inevitably gets embraced by affirmative responses to questions, this is not necessarily so for emotives. We interpret these results in terms of a more general distinction between presupposition triggers, where some – like cognitives – entail their presupposition, whereas others – like emotives – do not. This interpretation rules out certain pragmatic accounts of emotives, but leaves open at least two theoretical paths for introducing their factive presupposition, either in terms of conventionally encoding them at the presuppositional level (and only at the presuppositional level), or by deriving them from other ingredients, such as the belief-component that seems to be involved in emotives as well. References Abrusán, M. (2016). Presupposition cancellation: Explaining the ‘soft–hard’ trigger distinction. Natural Language Semantics 24(2), 165–202. Abusch, D. (2002). Lexical alternatives as a source of pragmatic presupposition. In B. Jackson (Ed.), Semantics and Linguistic Theory (SALT) 12, pp. 1–19. Abusch, D. (2010). Presupposition triggering from alternatives. Journal of Semantics 27, 37–80. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 383 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives Amaral, P. and C. Cummins (2015). A cross-linguistic study on information backgrounding and presupposition projection. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 157–172. Springer. Barr, D. J., R. Levy, C. Scheepers, and H. J. Tily (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language 68(3), 255–278. Chemla, E. and L. Bott (2013). Processing presuppositions: Dynamic semantics vs. pragmatic enrichment. Language and Cognitive Processes 28(3), 241–260. Cummins, C., P. Amaral, and N. Katsos (2013). Backgrounding and accommodation of presuppositions: An experimental approach. In Proceedings of Sinn und Bedeutung 17, pp. 201–218. Dahlman, R. C. (2016). Did people in the middle ages know that the earth was flat? Acta Analytica 31(2), 139–152. Destruel, E., D. Velleman, E. Onea, D. Bumford, J. Xue, and D. Beaver (2015). A crosslinguistic study of the non-at-issueness of exhaustive inferences. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 135–156. Springer. Domaneschi, F., E. Carrea, C. Penco, and A. Greco (2014). The cognitive load of presupposition triggers: Mandatory and optional repairs in presupposition failure. Language, Cognition and Neuroscience 29(1), 136–146. Egré, P. (2008). Question-embedding and factivity. Grazer Philosophische Studien 77(1), 85–125. Heim, I. (1983). On the projection problem for presuppositions. In D. P. Flickinger (Ed.), Proceedings of WCCFL 2, pp. 114–125. CSLI Publications. Hooper, J. and S. Thompson (1973). On the applicability of root transformations. Linguistic Inquiry 4(4), 465–497. Jayez, J., V. Mongelli, A. Reboul, and J.-B. Van Der Henst (2015). Weak and strong triggers. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 173–193. Springer. Karttunen, L. (1971). Some observations on factivity. Papers in Linguistics 4, 55–69. Kennedy, L., C. Bill, F. Schwarz, S. Crain, R. Folli, and J. Romoli (2015). Scalar implicatures vs. presuppositions: The view from Broca’s aphasia. In Proceedings of NELS 45. Klinedinst, N. (2010). Totally hardcore semantic presuppositions. Unpublished manuscript. Onea, E. and D. Beaver (2011). Hungarian focus is not exhausted. In Proceedings of Semantics and Linguistic Theory (SALT) 19, pp. 342–359. Romoli, J. (2012). Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification. Ph. D. thesis, Harvard University. Schwarz, F. (2014). Presuppositions are fast, whether hard or soft – evidence from the visual world. In Semantics and Linguistic Theory 24, pp. 1–22. Schwarz, F. (2016). Experimental work in presupposition and presupposition projection. Annual Review of Linguistics 2, 273–292. Simons, M. (2007). Observations on embedding verbs, evidentiality, and presupposition. Lingua 117, 1034–1056. Simons, M., J. Tonhauser, D. Beaver, and C. Roberts (2010). What projects and why. In N. Li and D. Lutz (Eds.), Proceedings of SALT 20, pp. 309–327. CLC Publications. Stalnaker, R. (1974). Pragmatic presuppositions. In M. Munitz and D. Unger (Eds.), Semantics and Philosophy, pp. 197–213. New York University Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 384 K. Djärv, J. Zehr, & F. Schwarz Cognitive vs. emotive factives Sudo, Y. (2012). On the Semantics of Phi Features on Pronouns. Ph. D. thesis, Massachusetts Institute of Technology. Tiemann, S. (2014). The Processing of wieder (‘again’) and Other Presupposition Triggers. Ph. D. thesis, Eberhard Karls Universität Tübingen. Tiemann, S., M. Kirsten, S. Beck, I. Hertrich, and B. Rolke (2015). Presupposition processing and accommodation: An experiment on wieder (‘again’) and consequences for other triggers. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 39–65. Springer. Tiemann, S., M. Schmid, N. Bade, B. Rolke, I. Hertrich, H. Ackermann, J. Knapp, and S. Beck (2011). Psycholinguistic evidence for presuppositions: On-line and off-line data. In Proceedings of Sinn und Bedeutung 15, pp. 581–597. Citeseer. Tonhauser, J., D. Beaver, C. Roberts, and M. Simons (2013). Toward a taxonomy of projective content. Language 89(1), 66–109. Velleman, D., D. Beaver, E. Destruel, D. Bumford, E. Onea, and L. Coppock (2012). It-clefts are IT (inquiry terminating) constructions. In Semantics and Linguistic Theory 22, pp. 441– 460. Zeevat, H. (1992). Presupposition and accommodation in update semantics. Journal of Semantics 9(4), 379–412. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 385 386 When is not-believing believing that not?1 Mojmı́r DOČEKAL — Masaryk University, CZ Jakub DOTLAČIL — University of Amsterdam, NL Abstract. We present two experiments that studied the licensing conditions of two Czech expressions in neg-raising and non-neg-raising environments: ani jeden ‘even one’ and až do ‘until’. English counterparts of these expressions are often treated as belonging to the same class, that of strict NPIs. However, our experiments revealed subtle differences between the two expressions, which we argue could be explained if we assume that only ani jeden ‘even one’ is a strict NPI, while až do ‘until’ is an expression sensitive to durativity of the predicate it modifies. The experiments furthermore showed that mood affects licensing of both ani jeden ‘even one’ and až do ‘until’ under neg-raising predicates. The role of mood on licensing is explained in Romoli’s theory of neg-raising. Keywords: Neg-raising, NPIs, mood, experimental semantics, Czech 1. Introduction In this article we focus on an interaction of two phenomena: Neg-raising (NR) and Negative Polarity Items (NPIs) licensing. The phenomena have been treated as connected since the first formal approaches to NR. In particular, strict NPI licensing is standardly taken as a test of NRhood (see Lakoff 1969 and Horn 1989, among others). NR is exemplified with (1): (1a) is in most contexts understood as (1b) – and this interpretation is the so-called NR reading of (1a). (1) a. b. John doesn’t believe that Mary was here. John believes that Mary wasn’t here. The article has two aims: an empirical and a theoretical one. In the empirical part, we present new experimental data from Czech on NR and NPIs. The data show that the choice of mood (indicative vs. subjunctive) has an effect on licensing expressions sensitive to negation (NPIs being one main representative of such a category). Second, the data also show that not all expressions sensitive to negation are equal: in particular, we will observe that expressions like ‘even’ have a very different behavior from expressions like ‘until’ when interacting with negation. The theoretical point of the article is the argument that the effect of mood can be captured in Romoli’s theory of NR-hood (Romoli, 2013), and that ‘until’ should not be classified in Czech as a strict NPI, in contrast to English. The main part of the article discusses two experiments on NR, NPIs and mood, and the theoretical consequences of the experimental results. Before turning to the experiments and the theory, we need to prepare the ground. We begin so by giving a necessary background on Czech expressions sensitive to negation. 1 We would like to thank organizers of the SuB conference in Edinburgh, audiences of SuB and FDSL 2016 in Berlin and the editors of the SuB proceedings. We would especially like to thank Manfred Krifka, Yasu Sudo and Hedde Zeijlstra for their comments and questions. The second author was supported by the NWO VENI grant 275.80.005 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 387 M. Dočekal & J. Dotlačil When is not-believing believing that not? 2. Czech expressions sensitive to negation In Czech, there are at least three groups of expressions sensitive to negation. First, there is a class of weak NPIs, which is represented by the NP sebemenšı́ tušenı́ ‘slightest suspicion’. We can see that it is a weak NPI since it requires a downward entailing (DE) environment in the at-issue meaning – see (2) – a standard condition for weak NPIs. There doesn’t seem to be any locality constraint between this NPI and its licensor. (2) Nikdo/málo lidı́/*někdo o tom (ne)-měl-o/-0 sebemenšı́ tušenı́. nobody/few people/*somebody about that had slightest suspicion ‘Nobody/few people/*somebody had slightest suspicion about that.’ In this article we stay agnostic as to the exact mechanism of weak NPI licensing (see, e.g., Gajewski 2011 and Crnič 2014 for two recent proposals). In fact, weak NPIs will not play any role in the following sections. The second class consists of strict NPIs. These can be represented by NPs such as ani jeden článek ‘not even one article’. Currently, several theoretical approches to strict NPIs co-exist (see Zwarts 1998, Giannakidou 2006, Gajewski 2011, Collins et al. 2014). Here, we will use that of Zwarts (1998): strict NPIs are licensed by anti-additive functions. Anti-additive functions are defined in (3). (3) A downward-entailing function f is anti-additive iff for any a and b in the domain of f, f(a) and f(b) ↔ f(a or b). The condition of anti-additivity can explain why we observe the difference between (2) where the DE quantifier málo lidı́ ‘few people’ licensed the weak NPI and (4) where the licensing of the strict NPI is invalid: (4) Nikdo/*málo lidı́/*někdo (ne)-přečetl ani jeden článek. nobody/*few people/*somebody read even one article ‘Nobody/*few people/*somebody read even one article.’ On Zwarts’ account, the explanation lies in the fact that the quantifier málo lidı́ is not antiadditive. To see this, consider a situation with six students, 3 of them dancing and (other) 3 of them singing. Assuming that 3 but not 6 is seen as a small number, the sentence Few students were dancing and few students were singing is true but the sentence Few students were dancing or singing is not – that is, the anti-additive condition is not satisfied by the DE quantifier few people). In general, since anti-additive licensors are a proper subset of DE licensors (see, e.g., Gajewski 2011) strict NPIs appear in some, but not all, environments that license weak NPIs. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 388 M. Dočekal & J. Dotlačil When is not-believing believing that not? A third class of expressions sensitive to negation are expressions of the type až do ‘until + time expression’, see (5).2 (5) Vojáci se *(ne)vystřı́dali až do půlnoci. soldiers SE neg-change till to midnight ‘The soldiers will not change until midnight.’ The English counterpart of až do is often taken as a good candidate for strict NPIs (when combining with predicates denoting episodic events). It is also widely used in testing NR properties of predicates (cf. Gajewski 2011, Romoli 2013). Nevertheless, we treat the Czech expression as a separate type. In particular, we assume it is an expression sensitive to durativity of the modified predicate (ESD), as can be seen by the fact that the Czech až do can appear with stative predicates, (6). The negative version of (5) is possible because negation changes a punctual predicate into a durative one (Krifka 1989, a.o.). We are not the first to take this position. In particular, until in English has been analyzed along this line by Smith (1974) and Mittwoch (1977). However, at least since Karttunen (1974), this type of analysis has been often challenged/substituted by an approach that postulates two types of until, one of which is sensitive to durativity and another one that appears with episodic predicates and is a strict NPI (see De Swart 1996 for a detailed discussion). (6) Vojáci zůstanou až do půlnoci. soldiers stay till to midnight ‘The soldiers will stay until midnight.’ While we have nothing to say about the English case, we do have a novel argument that the Czech až do should not be analyzed this way. As we will demonstrate in the following part of the article, Czech examples containing až do ‘until’ with punctual predicates like (5) are very different from parallel cases of strict NPIs. 3. Experiments In this section we describe the design of two experiments pertinent to the topic of the article. Both experiments targeted NR, NPI licensing and various factors influencing the licensing. 3.1. Experiment 1 The first experiment tested whether expressions sensitive to negation are accepted in clauses embedded under negated NR and non-NR predicates and how mood of the embedded predicate 2 Apart (i) from these three groups, Czech also has n-words (expressions requiring clause-mate negation): Nikdo *(ne)spal. Nobody not-slept. ‘Nobody slept.’ This class of negative expressions will not play any role in the rest of the article. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 389 M. Dočekal & J. Dotlačil When is not-believing believing that not? influences the acceptability. The experiment was a 3x2x2 design. Three types of predicates were used (Condition: PREDICATE ): 1. opinion class of NRs – see (7) for an item with a strict NPI; 2. probability class of NRs – see (8) for an item with a strict NPI; 3. non-NR predicates (mostly communication and causative verbs) – see (9) for an item with a strict NPI All predicates embedded either indicative or subjunctive mood (Condition: MOOD). Finally, two types of expressions sensitive to negation were tested: either the strict NPI ani jeden ... ‘not even one’ or the ESD až do ‘until’ (Condition: NEGATIVE EXPRESSION). While the first two conditions were tested within items, the last one was a between-item condition. This was so because it would be hard, if not impossible, to have sentences that could be fully parallel up to the NPI/ESD difference. An example with strict NPIs for opinion, probability and non-NR predicates are given here. (7) Nemyslı́m, že 0/by ani jeden z běžců může/mohl ten závod vyhrát. do-not-think-I that IND/SUBJ even one of runners can/could the race win ‘I don’t think that even one of the runners can/could win the race.’ (8) Nenı́ možné, že 0/by ani jeden z běžců může/mohl ten závod vyhrát. it’s-not possible that IND/SUBJ even one of runners can/could the race win ‘It’s not possible that even one of the runners can/could win the race.’ (9) Netvrdı́m, že 0/by ani jeden z běžců může/mohl ten závod vyhrát. do-not-say-I that IND/SUBJ even one of runners can/could the race win ‘I don’t say that even one of the runners can/could win the race.’ The example items with ESDs až do ‘until’ are shown below for the same three predicate classes. (10) Majitel toho hotelu nevı́, že 0/by kuchaři odjeli až do konce měsı́ce. owner this hotel not-knows that IND/SUBJ cooks left up to end month ‘The owner of this hotel doesn’t know that cooks would leave/left until the end of the month.’ (11) Podle majitele toho hotelu nenı́ možné, že 0/by kuchaři odjeli až do according owner this hotel not possible that IND/SUBJ cooks left up to konce měsı́ce. end month ‘According to the new owner of the hotel it’s not possible for the cooks to leave until the end of the month.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 390 M. Dočekal & J. Dotlačil (12) When is not-believing believing that not? Majitel toho hotelu se nedoslechl, že 0/by kuchaři odjeli až do owner this hotel not-hear that IND/SUBJ cooks left up to end konce měsı́ce. month ‘The owner of this hotel doesn’t hear that cooks would leave/left until the end of the month.’ The participants in this experiment judged acceptability of the items on 5-point Likert scale (5=best, 1=worst). There were 36 experimental items. 18 experimental items were constructed with the ESD až do ‘until’, 18 experimental items appeared with the strict NPI ani jeden ‘even one’. Furthermore, the experiment included 36 fillers, each of them an uncontroversially grammatical or ungrammatical sentence. All the fillers had their complexity comparable to the items. 60 Czech native speakers took part in the experiment which was run online on IBEX. 3 participants were excluded from the analysis due to their unreliable behavior in distinguishing good and bad fillers.3 3.2. Experiment 2 The second experiment also tested NR and NPI licensing in Czech. It consisted of two experimental methods – an acceptability and an inference task. For the topic of the current paper only the data from the acceptability part matter (for details of the whole Experiment 2 see Dočekal and Dotlačil 2016). In the acceptability test participants judged acceptability of ani jeden ‘even one’ and až do ‘until’. The acceptability was judged on the 5-point Likert scale (5=best, 1=worst), as in the other experiment. 5 different environments were used in the experiment (Condition: ENVIRONMENT): (a) simple positive sentences; (b) simple negative sentences; (c) clauses embedded under negated NR predicates of intention and judgment/obligation; (d) clauses embedded under negated NR predicates of opinion; (e) clauses embedded under negated non-NR predicates. 3 On average, pariticipants judged grammatical fillers as better than ungrammatical ones by more than 2 points difference on the 5-point scale (the mean of the difference between judgements on good and bad fillers was 2.21) and every participant (apart from the three excluded ones) showed at least a 1-point difference. The mean difference between good and bad fillers for the three excluded participants was smaller than 1 point (0.62, 0.37 and 0.15). Since they reported much weaker sensitivity to grammatical/ungrammatical sentences, they were not used for further analyses. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 391 M. Dočekal & J. Dotlačil When is not-believing believing that not? In the conditions (c), (d) and (e) strict NPIs and ESDs were placed in embedded clauses. One item for all conditions is shown in (13). (13) a. b. c. d. e. Ztratila se ani jedna ovce. lost SE even one sheep ‘A single sheep is missing.’ Neztratila se ani jedna ovce. neg-lost SE even one sheep ‘Not a single sheep is missing.’ Nový bača v Tatrách nechce, aby se ztratila ani jedna ovce. new shepherd in Tatras neg-wants C-SUBJ SE lost even one sheep. ‘The new shepherd in the Tatra mountains does not want a single sheep to be missing.’ Nový bača v Tatrách si nemyslı́, že se ztratila ani jedna ovce. new shepherd in Tatras SI neg-think C-IND SE lost even one sheep ‘The new shepherd in the Tatra mountains does not think that a single sheep is missing.’ Nový bača v Tatrách neřı́ká, že-IND se ztratila ani jedna ovce. new shepherd in Tatras neg-say C SE lost even one sheep ‘The new shepherd in the Tatra mountains does not say that a single sheep is missing.’ The second manipulation was the type of negative expression. As in Experiment 1, either the strict NPI ani jeden ‘even one’ or až do ‘until’ was used. There were 40 items in total: 20 items appeared with the strict NPI ‘even one’ and other 20 items used the ESD ‘until’. The experiment also included 30 fillers. The experiment was run on IBEX and 60 Czech native speakers participated in it. Both experiments were filled out by students of Masaryk University and volunteers. While we do not know whether there were people participating in both experiments, we note that there was more than half a year break between the two experiments. Furthermore, different university classes were asked to participate in the two experiments, making it unlikely that the same participant was tested more than once. 4. Results The results of Experiment 1, revealing the effect of mood and predicate type, are visualized in Figure 1.4 We analyzed the Experiment 1 using mixed-effects ordered probit models with two fixed effects: MOOD (indicative vs. subjunctive, the former being the reference level), PREDICATE (opinion (NR), probability (NR) and communication/causative (non-NR), the first one being the reference level), and their interaction. The model furthermore included intercept-only subject and item random effects. We found the following: 4 Notice transparent. that the graph focuses on just a slice of the response scale (from 2.0 to 2.7), to make the contrast more Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 392 M. Dočekal & J. Dotlačil When is not-believing believing that not? Response (1 −− worst, 5 −− best) 2.6 2.4 Subjunctive ● No Yes ● ● 2.2 ● 2.0 Non−NR Opinion Condition Probability Figure 1: Experiment 1, means and standard errors for three predicates crossed by the subjunctive/indicative mood manipulation 1. NR predicates were judged as significantly better than non-NR predicates (β = −0.22, z = −2.51, p = 0.012). Recall that the acceptability was mostly influenced by the ESDs/NPIs and their licensing by the three types of predicates interacting with the mood. 2. There was no difference between the opinion and probability class of NR predicates. 3. The subjunctive mood acted as a facilitating factor in the acceptability: ESDs/NPIs embedded in subjunctive clauses were more acceptable than the ones embedded in indicative clauses: β = 0.2, z = 2.39, p = 0.017. To study the effect of NPI type, we considered a second model, which added another fixed effect: N EGATIVE EXPRESSION (‘even one’ and ‘until’, the former being the reference level) and the interaction of this factor with MOOD and PREDICATE. The new model had a significantly better fit than the previous one (Likelihood ratio test, p < .001). The model revealed that ESDs ‘until’ were generally more acceptable than strict NPIs ‘even one’ (β = 0.4, z = 2.65, p = .008). The improvement was further strengthened in the case of probability predicates (there was a significant probability × ‘until’ interaction in the positive direction, β = 0.48, z = 2.79, p = 0.005). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 393 M. Dočekal & J. Dotlačil When is not-believing believing that not? Answer (1 −− worst, 5 −− best) 5 ● 4 ● 3 ● 2 ● ● 1 ● ● ● ● NPI even one until Negative notNR NR Positive Figure 2: Experiment 2 The graphical summary of the second experiment is presented in Figure 2.5 Recall that there were 5 environments tested in Experiment 2: NPIs/ESDs in simple positive clauses, in simple negative clauses, in clauses embedded under negated intention/judgment NR predicates, in clauses embedded under negated opinion NR predicates and in clauses embedded under negated non-NR predicates. To study the effect of these environments, we considered a mixed-effects ordered probit model with one factor, ENVIRONMENT (NR predicates of intention/judgment type were the reference level). The model also had the intercept+slope subjects and items random effects. The model showed that intention/judgement NR predicates were significantly worse than simple negative sentences (β = 3.2, z = 7.3, p < .001), and significantly better than positive sentences (β = −1.5, z = −9.2, p < .001). They were also significantly better than NPIs/ESDs embedded under non-NR predicates (β = −0.8, z = −5.6, p < .001), while there was no difference between two types of NR predicates (intention/judgement vs. opinion) (p > .1). The difference between NR and non-NR predicates seems stable – it was significant in both experiments, and we interpret it as showing that Czech has a class of neg-raising predicates, contra Bošković and Gajewski (2009) (see Dočekal and Dotlačil 2016 for the same point and more details). To study the difference between the NPI ‘even one’ and the ESD ‘until’, we ran a second model, which consisted of the factor ENVIRONMENT, the factor N EGATIVE EXPRESSION (NPI or ESD, the former being the reference level) and their interaction. The model also included the full random structure for subjects and items. 5 We did not use boxplots to summarize the results of Experiment 1 since the effects of mood are smaller than effects of NPIs and would be almost impossible to observe in such a graphical summary. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 394 M. Dočekal & J. Dotlačil When is not-believing believing that not? Replicating the results of the first experiment, the model yielded a significant effect for ESDs (β = 0.45, z = 2.3, p = 0.02), showing that ‘until’ was judged as better than ‘even one’ in the intention/judgement NR class. The positive effect was even stronger in the opinion class of NR predicates (opinion × ESD interaction – β = 0.6, z = 2.43, p = 0.02), as well as in non-NR sentences and positive sentences (non-NR × ESD interaction – β = 0.6, z = 2.17, p = 0.03; positive sentences × ESD interaction – β = 0.89, z = 2.61, p = 0.009). In our understanding, the positive interaction of ‘until’ with non-NR predicates and positive sentences shows that ESDs lead to less severe degradation than strict NPIs when appearing outside of their licensing environment. However, this would not explain why ‘until’ is better than ‘even one’ when embedded under NR predicates, since NR predicates should license both (cf., Gajewski 2005). It would also not explain the following finding: ESDs were less acceptable than NPIs when appearing in simple negative clauses (negative sentence × ESD interaction – β = −3.92, z = −4.14, p < .001). The last effect can be also observed in Fig. 2: while ‘until’ improves acceptability ratings in non-NR, NR and positive sentences compared to ‘even one’, it is clearly judged as worse than ‘even one’ in simple negative sentences. 5. Analysis and discussion There are two main points of the results we want to address: 1. Why does subjunctive mood improve the acceptability of NPIs/ESDs? 2. Why is the ESD ‘until’ less acceptable than the NPI ‘even one’ in negative sentences, but more acceptable under NR predicates? Let’s start with the first queston. We rely on Romoli (2013) and its scalar approach to NR: NR predicates contribute the at-issue meaning (universal quantification over possible worlds) and an excluded middle alternative (EM) implicature – formalized as the second alternative in (14a). Let’s illustrate its working on an example: for a NR verb like believe EM is intuitively equivalent to subject’s opinionatedness – a well-informed experiencer of the verb believes either the embedded proposition p (e.g. that it is raining) or its negation (that it is not raining). Consider now what happens when we interpret the sentence John does not believe that it is raining. Romoli, following Chierchia (2013), assumes that sentences come with an exhaustivity operator, EXH, that affirms the proposition and negates the alternatives that do not contradict the proposition (this is a slight simplification – see Romoli 2013 for the full account). Thus, when we combine the EXH operator with the sentence, the resulting meaning is as in (14b). This can be simplified into (14c). Intuitively: if John doesn’t believe that it’s raining and he’s opinionated w.r.t. raining, then he believes it is not raining. (14) a. b. c. Alt(NR) = {λ pλ x.x [p], λ pλ x.[x [p] ∨ x [¬p]]} EXH(John does not believe that it is raining) = ¬ j p ∧ ¬¬[ j p ∨  j ¬p] where p = it is raining  j ¬p Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 395 M. Dočekal & J. Dotlačil When is not-believing believing that not? The scalar theory of NR explains the acceptability of both ESDs and strict NPIs under negated NR predicates. For the former, it is crucial that negation creates a durative predicate (see, for example, Krifka 1989, a.o.). Given that it does and that the negation is interpreted on the embedded predicate, it suffices for the ESD ‘until’ to modify such a negated predicate to be licensed. For the latter, assume that strict NPIs are licensed in anti-additive environments (Zwarts, 1998). Then, they will be licensed when embedded under NR predicates. Somewhat more technically, since (15) is valid, strict NPIs are licensed under NR predicates. For more details, see Gajewski (2005). (15) x ¬p ∧ x ¬q ⇔ x ¬(p ∨ q) But why would subjunctives facilitate licensing of strict NPIs/ESDs? We follow Villalta (2008) in her description of the subjunctive mood in embedded sentences as a transferer of alternatives into matrix clauses. According to Villalta, indicative mood, unlike subjunctive, stops such a transfer. The observed effect of subjunctive follows from this approach. If alternatives can be transferred to the NR predicate, they can be computed. However, if they are not transferred (because they are stopped at the left periphery of the embedded sentence by the indicative mood), the exhaustification of the EM alternatives cannot proceed and the scope of the negation remains high. In this respect, Slavic languages reveal the dependency of NR interpretation on the availability of alternatives, which in turn supports the implicature approach to NR. The presuppositional approach (Gajewski, 2005) to NR would have to make some further assumptions to describe this type of dependency. The effect of mood could also be captured by syntactic accounts of NR (Collins et al., 2014), as subjunctives are generally more transparent for movement (Progovac, 1993). We now turn to the second question: why do the ESD ‘until’ and strict NPI ‘even one’ differ from each other? First, notice that ‘until’ in Czech shows different scopal behavior than NPIs. NPIs generally cannot c-command their licensors (De Swart, 1998), see (16). Surprisingly, the reverse is true for the ESD ‘until’: while it is degraded in (17a) it improves when až do půlnoci ‘until midnight’ precedes/outscopes negation, (17b). (16) a. Phil would not give me anything. b. *Anything Phil would not give me. (from De Swart 1998, ex. 8) (17) a. ??Petr neusnul až do půlnoci. Petr neg-fell-asleep up to midnight ‘Petr didn’t fall asleep until midnight.’ b. Až do půlnoci Petr neusnul. up to midnight Petr neg-fell-asleep ‘Until midnight Petr didn’t fall asleep.’ In our experiment we used items with ESDs linearized after negated verbs (which is the default adverb placement), as illustrated in (18) (the simple negative condition). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 396 M. Dočekal & J. Dotlačil (18) When is not-believing believing that not? Vojáci se nevystřı́dajı́ až do půlnoci. soldiers SE neg-exchange up to midnight ‘The soldiers will be not exchanged until midnight.’ Remember, that in such sentences ESDs were considered worse than strict NPIs. Changing the linearization seems to improve the acceptability of (18) considerably (although we lack a proper experimental support for our intuitions in this case). But recall that if až do ‘until’ would be an NPI, this effect would be totally unexpected. If anything, we would expect an opposite effect. This strongly suggests to us that až do ‘until’ is not a strict NPI (in contrast to what is commonly assumed about its English counterpart). More concretely, since Czech is a language in which arguments/adjuncts are often interpreted in their surface position (i.e., QR is much less common than in English), the ESD ‘until’ is interpreted as a modifier of the (non-negative) VP when appearing after the verb. This VP is punctual and thus, it cannot satisfy the requirement of ‘until’. The change in linearization as in (17b) allows a different parse, one in which ‘until’ modifies the negated event, hence the improved acceptability of the ESD in this case. But why would ‘until’ be more acceptable (as compared to the strict NPI ‘even one’) when modifying punctual predicates embedded under NR predicates? One explanation could go as follows. Negation is interpreted in the embedded clause at the logical form via pragmatic mechanisms. Since it is not syntactically present there, there is no signal from syntax whether the ‘until’ modifier should be interpreted in its scope or above it. In other words, there is no evidence from syntax that would support either interpretation. Given that, readers are free to pick the interpretation that is more suitable – and that is the one in which the ESD is interpreted above negation and the condition of the ESD is satisfied. Notice that this does not predict that ESDs should be better under NR predicates than in simple negative clauses. If the strengthening to EM is marginal to begin with (as Dočekal and Dotlačil 2016 argue), ESDs might be still less acceptable in this case than in simple negative clauses. What is (correctly) predicted is a relative difference: ESDs should be less acceptable than strict NPIs in simple negative clauses, but this difference should disappear in clauses embedded under NR predicates. Since ESDs are generally less degraded when lacking their licensor, compared to strict NPIs (as witnessed by the fact that ESDs are more acceptable than strict NPIs in positive sentences and clauses embedded under non-NR predicates), we furthermore expect that under NR predicates, ESDs should not just be as good as strict NPIs, but in fact, even more acceptable than strict NPIs – and this is correct. 6. Conclusion We discussed two experiments that studied the licensing conditions of two expressions in Czech: ani jeden ‘even one’ and až do ‘until’. English counterparts of these expressions are often treated as belonging to the same class, that of strict NPIs (Gajewski 2005 and references there). However, our experiments revealed subtle differences between the two expressions, which we argued could be explained if we assume that only ani jeden ‘even one’ is a strict NPI, while až do ‘until’ is an expression sensitive to durativity of the predicate it modifies. Aside from that, we also saw that Czech reveals effects of mood in licensing both ani jeden ‘even one’ and až do ‘until’ under NR predicates. The role of mood on licensing was explained in Romoli’s theory of NR. Both points show that experimental work on languages less often studProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 397 M. Dočekal & J. Dotlačil When is not-believing believing that not? ied (from the perspective of formal semantics) can clearly enrich our current understanding of language variation and interpretation. References Bošković, Ž. and J. Gajewski (2009). Semantic correlates of the NP/DP parameter. In Proceedings of NELS 39. Chierchia, G. (2013). Logic in Grammar: Polarity, Free Choice, and Intervention. Oxford: Oxford University Press. Collins, C., P. M. Postal, and L. R. Horn (2014). Classical NEG Raising: An Essay on the Syntax of Negation. MIT Press. Crnič, L. (2014). Against a dogma on NPI licensing. In L. Crnič and U. Sauerland (Eds.), The Art and Craft of Semantics: A Festschrift for Irene Heim, Volume 1, pp. 117–145. MITWPL. De Swart, H. (1996). Meaning and use of not. . . until. Journal of Semantics 13(3), 221–263. De Swart, H. (1998). Licensing of negative polarity items under inverse scope. Lingua 105(34), 175–200. Dočekal, M. and J. Dotlačil (2016). Experimental evidence for neg-raising in Slavic. Linguistica 56(1), 93–109. Gajewski, J. (2005). Neg-raising: Polarity and presupposition. Ph. D. thesis, MIT. Gajewski, J. R. (2011). Licensing strong NPIs. Natural Language Semantics 19(2), 109–148. Giannakidou, A. (2006). Only, emotive factive verbs, and the dual nature of polarity dependency. Language 82, 575–603. Horn, L. (1989). A Natural History of Negation. Chicago: University of Chicago Press. Karttunen, L. (1974). Until. In Proceedings of Chicago Linguistic Society 10, pp. 284–297. Krifka, M. (1989). Nominal reference, temporal constitution, and quantification in event semantics. In R. Bartsch, J. van Bentham, and P. van Emde Boas (Eds.), Semantics and Contextual Expressions. Dordrecht: Foris. Lakoff, R. (1969). A syntactic argument for negative transportation. In CLS 5, pp. 140–147. Mittwoch, A. (1977). Negative sentences with until. In Proceedings of CLS 13, pp. 410–417. Progovac, L. (1993). Subjunctive: The (mis) behavior of anaphora and negative polarity. The Linguistic Review 10(1), 37–60. Romoli, J. (2013). A scalar implicature-based approach to neg-raising. Linguistics and Philosophy 36(4), 291–353. Smith, S. (1974). Meaning and Negation. The Hague: Mouton. Villalta, E. (2008). Mood and gradability: An investigation of the subjunctive mood in Spanish. Linguistics and Philosophy 31(4), 467–522. Zwarts, F. (1998). Three types of polarity. In F. Hamm and E. W. Hinrichs (Eds.), Plurality and Quantification, pp. 177–238. Dordrecht: Springer. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 398 Focus association by movement: Evidence from binding and parasitic gaps1 Michael Yoshitaka ERLEWINE — National University of Singapore Hadas KOTEK — Yale University Abstract. Under the influential Roothian proposal for focus association, focused phrases remain in-situ at LF (Rooth, 1985, 1992). However, a recent line of work has resurrected the idea that focus association involves covert movement: specifically, the associate of English sentential only must covertly move to only, with the possibility of covert pied-piping (Drubig, 1994; Krifka, 1996, 2006; Tancredi, 1997, 2004; Wagner, 2006; Erlewine and Kotek, 2014, 2018). In this paper we contribute to this emerging consensus view with additional evidence from reflexive binding and parasitic gap licensing. Keywords: focus association, only, covert movement, binding, parasitic gaps 1. Two approaches to focus association The problem of focus association concerns the relationship between focus-sensitive operators such as only and focused constituents such as Fridays or chocolate in (1). The semantics of only quantifies over the focused constituent and its contextual alternatives: for example, (1a) asserts that there is no day other than Friday where John eats chocolate, whereas (1b) asserts that John eats nothing other than chocolate on Fridays (see e.g. Horn, 1969). (1) a. John only eats chocolate on [Fridays]F . b. John only eats [chocolate]F on Fridays. How does only’s semantics make reference to this focused constituent? One family of approaches posits the existence of covert focus movement so that the focused constituent becomes a local argument of the only operator at LF. A sample LF for example (1b) under the covert focus movement view is given in (2) below. Here we illustrate the non-quantificational subject John in its VP-internal base position. The movement in (2) makes the focus chocolate a local argument of a two-place only operator.2 (2) Covert movement
LF for (1b):
only [chocolate]F λ x . John eats x on Fridays The alternative approach — popularized by Rooth (1985, 1992) and adopted in much contemporary work on focus semantics — assumes that focused constituents remain in-situ at LF. The operator (only) makes indirect reference to the choice of focus and its alternatives through a process of alternative computation. Each syntactic node α is associated not only with its ordinary semantic denotation JαKo but also with a set of alternatives, JαK f , defined recursively as in (3) below. Focused (F-marked) constituents introduce non-trivial alternatives into their focus1 We thank Aron Hirsch and anonymous reviewers for comments on the material here. Errors are each other’s. precise geometry of this movement could vary. See footnotes 7 and 8 in Erlewine and Kotek (2018) for detailed discussion of this movement and alternative formulations. 2 The Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 399 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps alternative denotations (3c), which are then propagated up through the process of pointwise composition (3b). (3) Focus alternative computation: a. For non-focused terminal nodes: JαK f = {JαKo } b. For non-focused branching nodes (pointwise composition): n o J[α β ]K f = a ◦ b a ∈ JαK f , b ∈ Jβ K f where ◦ is the appropriate composition operation for JαKo and Jβ Ko . c. For focused nodes: JαK f is a contextually-determined subset of Dτ where τ is the type of JαKo The result of this procedure is that the contextual alternatives to chocolate in (4b) will be reflected indirectly in the set of alternatives at VP (4c), which is a local argument of only. (4) Interpreting (1b) with focus in-situ: a. only [VP John eats [chocolate]F on Fridays ] b. J[chocolate]F K f = {chocolate, fish, pizza, ...}    John eats chocolate on Fridays,  c. JVPK f = John eats fish on Fridays,   John eats pizza on Fridays, ... d. [only VP] ⇒ John doesn’t eat fish on Fridays, John doesn’t eat pizza on Fridays, ... As an empirical argument for the in-situ view, Rooth (1985) following Anderson (1972) notes that focus association is apparently insensitive to syntactic islands. For example, in (5) based on an example from Kratzer (1991), only successfully associates narrowly with the focused constituent the Zoning Board inside a relative clause island. Under the covert movement approach — so the argument goes — covert movement of the Zoning Board should be impossible, just as the corresponding overt focus movement in (6) is ungrammatical.3 (5) Focus association is apparently island-insensitive: I only contacted [island the person who chairs [the Zoning Board]F ]. (6) Corresponding overt focus movement of the Zoning Board: (Kratzer, 1991: 831) * It was [the Zoning Board]F that I contacted [island the person who chairs ]. Drubig (1994) however notes that this island-sensitivity problem can be avoided if covert focus movement can trigger pied-piping. That is, instead of the logically focused constituent moving alone to become a local argument of only, a focus-containing phrase can instead move to only. This possibility is illustrated schematically for the case of example (5) in (7) below. 3A possible response may be to say that covert (focus) movement is not sensitive to the same island constraints as overt movement, but this is ultimately incorrect. See Wagner (2006) and Erlewine and Kotek (2016, 2018) for evidence that covert focus movement is sensitive to syntactic islands. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 400 M. Y. Erlewine & H. Kotek (7) Focus association by movement: Binding and parasitic gaps LF for (5) using covert focus movement with pied-piping:

only [island the person who chairs [the Zoning Board]F ] λ x . I contacted x The interpretation of the pied-piped constituent in (7) then must utilize Rooth’s mechanism of in-situ alternative computation in order to yield the observed sensitivity to the position of focus within the pied-piped phrase. Pied-piping of the constituent in (7) is also independently observed in overt focus movement, as in example (8):4 (8) Corresponding overt focus movement with pied-piping: X It was [ island the person who chairs [the Zoning Board]F ] that I contacted (cf (6)) . This hypothetical possibility of pied-piping in covert focus movement thus defuses Rooth’s argument from island-insensitivity for the in-situ approach to focus association. Independent evidence is then necessary to adjudicate between these two possible options. A series of works in the past decade have introduced new arguments for the idea that focus association with English only necessarily involves covert focus movement with the possibility of covert piedpiping.5 The gist of each of these arguments is summarized here in (9). (9) Previous arguments for covert focus movement with pied-piping: a. Krifka (2006): Restrictions on association of only with multiple foci are sensitive to islands, in a manner predicted by the covert movement with pied-piping view. b. Wagner (2006): The distribution of NPIs licensed by adverb only is sensitive to the placement of islands, in a manner predicted by covert movement with pied-piping. c. Erlewine and Kotek (2014): The distribution of focus intervention effects (Beck, 2006) in focus association is explained by covert focus movement with pied-piping, with intervention affecting just the covertly pied-piped material. d. Erlewine and Kotek (2016, 2018): The distribution of so-called Tanglewood configurations, where alternatives apparently co-vary between a pronounced focus and within an ellipsis site (Kratzer, 1991), is sensitive to syntactic islands. Tanglewood readings are best explained using covert focus movement with pied-piping. In this paper, we contribute two new arguments to this growing body of evidence. Following related diagnostics for covert wh movement by Nissenbaum (2000a, b), we will show that covert focus movement in English can feed reflexive binding and the licensing of parasitic gaps. These effects too are unexplained by the in-situ approach to focus association. 4 In some cases, however, the pied-piping that we would need to posit for covert focus movement may be larger than what is observed with overt pied-piping. There is however independent evidence that pied-piping can be larger with covert movement than with overt movement: see Kotek and Erlewine (2016). See also Horvath (2000, 2007) for discussion of pied-piping in overt focus movement. 5 All of these works in (9) look exclusively at focus association with English sentential only. A significant open question is whether this claimed necessity of covert movement in focus association extends to other focus-sensitive operators or languages. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 401 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps 2. Binding Nissenbaum (2000b: pp. 124ff) shows that covert wh-movement in English allows reflexives to be bound by an antecedent outside of their surface local binding domain: that is, covert phrasal movement feeds reflexive binding. Consider the contrast in (10): (10) Covert wh-movement feeds reflexive binding: (Nissenbaum, 2000b: p. 126) a. * Whoi thinks [Mary was looking at a picture of himselfi ]? b. Whoi thinks [Mary was looking at which picture of himselfi ]? The masculine reflexive himself does not have a local antecedent within the embedded clause, as the ungrammaticality of the baseline (10a) indicates. However, when this reflexive is contained within an in-situ wh-phrase, it can be bound by a higher antecedent, as long as the containing wh-phrase takes scope under the antecedent. In this case, assuming that movements triggered by the same head (here: matrix C) will “tuck in” (see also Richards, 1997; Pesetsky, 2000), (10) will have a LF representation as in (11).6 (11) Covert wh-movement LF for (10): [CP Whoi [which picture of himselfi ] [TP thinks [CP Mary was looking at ]] In this higher LF position, himself is close enough to the intended antecedent, who. We therefore conclude that Binding Condition A is evaluated at LF. We can similarly use reflexive binding to test whether or not focused material — or material pied-piped together with focused material — can include reflexives bound by a higher antecedent than regularly possible, as long as it is within the scope of the associating only. We begin with the baseline in (12), where the intended antecedent of myself is the matrix subject, outside of the relevant binding domain (BD). (12) Baseline: *I want [BD the museum to display a picture of myself]. Now consider example (13), which differs minimally from (12) in the addition of only above want, associating with the F-marked picture. The reflexive myself is now successfully bound by its intended antecedent, which is outside of myself ’s surface local binding domain (cf (12)). (13) Covert focus movement feeds reflexive binding: Context: I commissioned many paintings and pictures of myself. The museum is interested in displaying both a painting and a picture that I had made, but in fact, X I only want [ BD the museum to display [a [picture]F of myself]]. The grammaticality of the reflexive binding in (13) is explained by the availability of covert focus movement with pied-piping. The proposed LF for (13) is given in (14). Here the overt 6 Following Kotek (2016), this covert wh-movement need not always move all the way up to the interpreting complementizer, but it suffices here that, in (10b) but not (10a), attraction of the surface in-situ wh-phrase has the option of covertly moving out of the embedded clause. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 402 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps A-movement of the subject from its predicate-internal position to its surface position, above only, is critical and therefore illustrated. (14) LF for (13) using covert focus movement with pied-piping:

Ii λ y . only [a [picture]F of myselfi ] λ x . y want [BD the museum to display x] If a different constituent is focused which will not trigger covert movement of the reflexive, the long-distance binding in (13) is not licensed: (15) * I only want [BD the [museum]F to display a picture of myself]. Notice that the solution here is not to simply say that focused constituents themselves can violate locality in reflexive binding: what is focused in (13) is picture, not myself. It is necessary for covert focus movement of the F-marked constituent, picture, to trigger pied-piping of the whole reflexive-containing DP, a picture of myself. Note too that it is not simply the case that focus on the head noun picture in (13) somehow allows myself to be bound long-distance, by an antecedent outside of the surface binding domain (BD). This long-distance binding facilitated in (13) is limited to the scope of only. If we attach only lower, within the surface binding domain of the reflexive, the long-distance antecedent option disappears: (16) * I want [BD the museum to only display a [picture]F of myself]. To summarize, we find that association with only feeds reflexive binding, as would be predicted by a theory of covert movement with pied-piping: the F-marked constituent moves (possibly with pied-piping) to become the first argument of only. This movement can put this constituent in a local relationship with a binder that is otherwise absent, licensing a binding relation. This result is unexpected under an in-situ account of Association with Focus, which predicts no difference between (12) and (13). 3. Parasitic gap licensing The literature on parasitic gaps has largely followed Engdahl (1983) in assuming that wh-in-situ never licenses parasitic gaps. Engdahl’s examples are reproduced in (17) below. Assuming that in-situ wh-phrases must or can move covertly (Karttunen, 1977; Huang, 1982; Pesetsky, 2000; Kotek, 2016; a.o.), this claim is commonly (re)interpreted as a claim that covert movements cannot license parasitic gaps. (17) Wh-in-situ does not license parasitic gaps: (Engdahl, 1983: p. 14) a. * John filed which articles without reading pg ? b. * Who filed which articles without reading pg ? Nissenbaum (2000a, b) shows that Engdahl’s generalization is not exceptionless: although it is true that covert movement alone does not license parasitic gaps, overt movement together Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 403 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps with covert movement through the same vP edge can together license two parasitic gaps. An in-situ wh-phrase can license a secondary parasitic gap (18), which is not simply licensed by the presence of a non-wh phrase in the same position (19). (18) Wh-in-situ licenses a secondary parasitic gap: (Nissenbaum, 2000a: p. 542) Which senatori did you persuade i to borrow which car j [after getting an opponent of pg i to put a bomb in (19) * Which senatori did you persuade i to borrow a Prius j [after getting an opponent of pg i to put a bomb in pg j ]? pg j ]? It is also possible to license an adjunct with just one parasitic gap bound by the overtly-moved wh-phrase (20a), but not with one corresponding to the in-situ wh-phrase (20b). The main clauses in both examples here are identical to that in (18). The secondary parasitic gap pg j as in (18) is, then, itself parasitic on the first parasitic gap pgi which corresponds to the overtly moved wh-phrase. (20) Secondary parasitic gap is parasitic on the first parasitic gap: (Ibid. p. 552) a. Which senatori did you persuade i to borrow which car j [after talking to pg i for an hour]? b. * Which senatori did you persuade i to borrow which car j [after putting a bomb in pg j ]? To license the adjunct with two parasitic gaps, both the overt and covert A-movement steps must cross the same vP edge. This is accomplished in (18) at the vP edge associated with persuade, as which senator is overtly A-moved from within it. Subjects which are first A-moved out of vP do not license their own parasitic gaps (Engdahl, 1983; a.o.) and similarly do not license secondary parasitic gaps: (21) * Which terroristi i persuaded the senator to borrow which car j [after getting a friend of pg i to put a bomb in pg j ]? The correct generalization regarding the licensing of parasitic gaps by covert movement is then as in (22). Nissenbaum (2000a, b) gives an explanation for this generalization in terms of the derivational timing of overt vs covert movement and adjunction of the parasitic-gap-containing adjunct. We refer interested readers to those works. (22) The Engdahl/Nissenbaum generalization: Covert A-movement by itself does not license parasitic gaps. However, covert Amovement does license a secondary parasitic gap when it crosses a vP edge that is also crossed by an overt A-movement step. We now show that focus association with only also licenses secondary parasitic gaps, as predicted by the covert focus movement approach to Association with Focus. Example (23) below is based on the ungrammatical baseline (19) above, but with the addition of an only associating Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 404 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps with the object of drive — here, a Jaguar: (23) The focus associate of only licenses a secondary parasitic gap: X Which senator could you only persuade i to drive [a [Jaguar]F ] j i [after getting an opponent of pg i to put a bomb in pg j ]? Both the overt movement of which senator and the covert movement of a Jaguar to only in (23) will cross through the vP edge associated with persuade, to which the after-adjunct adjoins. If only is introduced lower so that the path of covert focus movement does not overlap with the overt wh-movement path, as in (24), the secondary parasitic gap becomes ungrammatical, as also predicted by the generalization in (22). (24) The position of only marks the height of covert focus movement: * Which senatori could you persuade i to only drive [a [Prius]F ] j [after getting an opponent of pg i to put a bomb in pg j ]? Just as we saw with wh-movement, parasitic gap licensing by covert focus movement is only possible when crossing a vP edge that is also crossed by overt A-movement, as per the Engdahl/Nissenbaum generalization (22). The generalization also predicts that a single parasitic gap is not licensed by the covertly moved focus of only alone. This prediction is borne out in (25): (25) Covert focus movement alone does not license parasitic gaps, as predicted by (22): a. * I only criticized [[this]F book] without reading pg . b. * I only want to read [[this]F book] without buying pg . We include another set of secondary parasitic gap contrasts, similar to the examples above. Example (26a) shows the ungrammaticality of a secondary parasitic gap with a referential DP, the placebo; example (26b) shows the availability of a secondary parasitic gap with a wh-phrase in that position; and (26c) shows the parallel licensing of a secondary parasitic gap with an only associating with a focused placebo. (26) a. b. c. * Which patientsi did the doctors assign i to the placebo j [after showing the families of pg i how to administer pg j ]? Which patientsi did the doctors assign i to which drug j [after showing the families of pg i how to administer pg j ]? Context: Following FDA regulations, patients’ families were shown how to administer all the drugs that might be associated with the trial. After some patients began exhibiting unexpected symptoms, the families wrote the FDA and demanded to know: Which patientsi did the doctors only assign i to [the [placebo]F ] j [after showing the families of pg i how to administer pg j ]? In examples (19) and (26a), the secondary parasitic gap is not licensed. The presence of the secondary parasitic gap is not by itself able to force the covert movement necessary to license Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 405 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps the gap. Instead, this movement must be independently licensed — covert wh-movement in (18) and (26b) and covert focus movement in (23) and (26c). We conclude that — like in the case of covert wh-movement — parasitic gaps on F-marked material are licensed in Association with Focus constructions. This is predicted if association with only requires covert focus movement but is unexplained by the common, in-situ association approach of Rooth (1985) and others. 4. Conclusion Evidence from reflexive binding and parasitic gap licensing shows that the focus associate of only is interpreted in a higher position at LF through covert movement. This is predicted under the covert movement theory of only, where the F-marked constituent moves (possibly with pied-piping) to become the first argument of a two-place only (Drubig, 1994; Krifka, 1996, 2006; Tancredi, 1997, 2004; Wagner, 2006; Erlewine and Kotek, 2014, 2018). It is inconsistent with the influential in-situ analysis of association with only (Rooth, 1985, 1992), and hence serves as an argument against this view. References Anderson, S. R. (1972). How to get even. Language 48, 893–905. Beck, S. (2006). Intervention effects follow from focus interpretation. Natural Language Semantics 14, 1–56. Drubig, H. B. (1994). Island constraints and the syntactic nature of focus and association with focus. Arbeitspapiere des Sonderforschungsbereichs 340: Sprachtheoretische Grundlagen der Computerlinguistik 51. Engdahl, E. (1983). Parasitic gaps. Linguistics and Philosophy 6, 5–34. Erlewine, M. Y. and H. Kotek (2014). Intervention in focus pied-piping. In H.-L. Huang, E. Poole, and A. Rysling (Eds.), Proceedings of NELS 43, Volume 1, pp. 117–130. Erlewine, M. Y. and H. Kotek (2016). Tanglewood untangled. In M. Moroney, C.-R. Little, J. Collard, and D. Burgdorf (Eds.), Proceedings of SALT 26, pp. 224–243. Erlewine, M. Y. and H. Kotek (2018). Focus association by movement: Evidence from Tanglewood. Linguistic Inquiry 49, 441–463. Horn, L. R. (1969). A presuppositional analysis of only and even. In R. I. Binnick, A. Davison, G. M. Green, and J. Morgan (Eds.), Proceedings of CLS 5, pp. 98–107. Horvath, J. (2000). Interfaces vs. the computational system in the syntax of focus. In H. Bennis, M. Everaert, and E. Reuland (Eds.), Interface strategies, pp. 183–206. Royal Netherlands Academy of Arts and Sciences, Amsterdam. Horvath, J. (2007). Separating “focus movement” from focus. In Phrasal and Clausal Architecture. John Benjamins. Huang, C.-T. J. (1982). Logical Relations in Chinese and The Theory of Grammar. Ph. D. thesis, Massachusetts Institute of Technology. Karttunen, L. (1977). Syntax and semantics of questions. Linguistics and Philosophy 1(1), 3–44. Kotek, H. (2016). Covert partial wh-movement and the nature of derivations. Glossa 1(25), Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 406 M. Y. Erlewine & H. Kotek Focus association by movement: Binding and parasitic gaps 1–19. Kotek, H. and M. Y. Erlewine (2016). Covert pied-piping in English multiple wh-questions. Linguistic Inquiry 47(4), 669–693. Kratzer, A. (1991). The representation of focus. In A. von Stechow and D. Wunderlich (Eds.), Semantik: Ein internationales Handbuch der zeitgenössischen Forschung, pp. 825–834. Walter de Gruyter. Krifka, M. (1996). Frameworks for the representation of focus. In Conference on Formal Grammar at the 9th European Summer School in Logic, Language, and Information. Krifka, M. (2006). Association with focus phrases. In V. Molnár and S. Winkler (Eds.), The Architecture of Focus, pp. 105–136. Mouton de Gruyter. Nissenbaum, J. (2000a). Covert movement and parasitic gaps. In M. Hirotani, A. Coetzee, N. Hall, and J.-Y. Kim (Eds.), Proceedings of NELS 30, Volume 2, pp. 541–555. Nissenbaum, J. (2000b). Investigations of Covert Phrase Movement. Ph. D. thesis, Massachusetts Institute of Technology. Pesetsky, D. (2000). Phrasal movement and its kin. Cambridge, Mass.: MIT Press. Richards, N. (1997). What Moves Where When in Which Language? Ph. D. thesis, Massachusetts Institute of Technology. Rooth, M. (1985). Association with Focus. Ph. D. thesis, University of Massachusetts, Amherst. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1, 75–116. Tancredi, C. (1997). Focus, focus types, and associative operators. Manuscript. Tancredi, C. (2004). Associative operators. Gengo Kenkyu 125, 31–82. Wagner, M. (2006). Association by movement: Evidence from NPI-licensing. Natural Language Semantics 14(4), 297–324. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 407 408 Subjective standard-setting in gradable predicates: On the Mandarin hen structure1 Huilin FANG — University of Southern California Abstract. Canonical positive degree sentences in Mandarin Chinese are formed with a morpheme hen. In the literature, this morpheme is regarded as the positive degree morpheme pos (Kennedy, 1999; Liu, 2010; Grano, 2012; Zhang, 2015) that introduces a contextually given norm, as well as binding the degree argument. However, the traditional pos analysis cannot fully account for some behaviors of hen. First, hen sentences share several characteristics of subjective predicates like Predicates of Personal Tastes (PPTs). These features include the triggering of faultless disagreement and embedding under perceptual verb ganjue and ganjue-dao ‘feel/find’. Furthermore, when compared with other adjectival expressions, the hen form makes a weaker statement, which is related to the speaker’s subjective belief. To account for these two characteristics, I propose that hen introduces a subjective standard determined by a judge that is based on a subjective epistemic knowledge state. Keywords: degree semantics, gradable adjectives, positive degree sentences, subjectivity, Mandarin Chinese 1. Introduction This work focuses on a type of Mandarin adjectival sentence, the hen sentence, which has the basic structure like (1). It unique in that there is an obligatory morpheme hen that appears before the adjective. Afu hen gao Afu HEN tall ‘Afu is tall.’ It is hard to pinpoint the meaning of hen. By some native speakers’ intuition, this particle is a dummy marker in the sentence. Yet other speakers might think that it also means very, which indicates that the degree is high. Because of these features, hen is often regarded as the overt realization of positive degree morpheme, pos (see von Stechow, 1984; Kennedy, 1999, 2005, 2007, among many others, on pos). Pos has two functions. It introduces a contextually given standard, and the degree of the sentence exceeds this standard significantly. Second, gradable adjectives takes a degree argument, pos binds this argument to avoid type mismatches when combined with the subject. The lexical entry of pos is given in (2). The function s here is a contextually sensitive function that takes a gradable adjective g and returns a corresponding standard. An example of the derivation is given in (3). ⟦pos⟧=λgλx. g(x) > s(g) (Kennedy, 2007) 1 I would like to thank Roumyana Pancheva, Barry Schein, Andrew Simpson, Audrey Li, Robin Jesheon, who gave me valuable comments on an early version of this work. I’d also like to thank Thomas Grano, Alexis Wellwood, and the audience at Sinn und Bedeutung 21, and also the audience from WCCFL 34, who helped me to develop my work from my previous presentation there. All remaining errors are my own responsibility. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 409 H. Fang Subjective standard-setting in gradable predicates ⟦𝑝𝑜𝑠 expensive⟧ = λdλx.expensive(x) ≥ s(g) Meaning: the degree of expensiveness exceeds a contextually given degree. Implication: The degree of expensiveness stands out among a comparison class. The advantage of this analysis is straightforward. It explains why hen is obligatory with gradable adjectives, and it also accounts for certain parallels of hen sentences with positive degree sentences in English. For example, the degree of the sentence should not only exceed the standard, but it should be significant enough for the subject to stand out among the objects in a comparison class. Therefore, John is tall implies that John’s height not only exceeds a certain norm for tall people, but it also is significant enough to ‘stand out’ among them. As a support for the pos analysis of hen, this feature might be able to explain why some native speakers have an intuition that hen is similar to very, which also implies the degree to be significant. However, there are several features of hen that cannot be accounted for directly by viewing it as pos. The first one is related to the subtypes of gradable adjectives that hen can occur with, and the different meanings they trigger, followed by problems that emerge when compared with another adjectival form, the shi…-de form. Second, contrary to previous analyses, hen is only obligatory when the sentence is uttered out of the blue. When there is an existing standard from the context, it can be dropped. The hen form is also weaker than the expression where hen is dropped. Third, hen predicates are licensed by a negation form mei that only selects eventive predicates. Finally, hen shows certain features that are parallel to subjective predicates, such as Predicates of Personal Tastes (PPTs). These properties can be accounted for if one sees hen as related to a subjective standard determined by a judge’s knowledge state. In the following sections, I start by discussing the first three problems in section 2, and then move on to discuss the subjective features of hen predicates in section 3. In section 4, I discuss the characteristics of the subjectivity of hen. In section 5, I provide an analysis for the hen sentences, which is similar to Fernald’s view on verbs like appear and seem (Fernald, 2000). Section 6 concludes this work. 2. Problems with the pos analysis 2.1. Hen with absolute adjectives Gradable adjectives can be classified into two major classes, relative adjectives and absolute adjectives (Kennedy and McNally 2005). They are distinguished according to whether the scales they correspond to are bounded or open. As scales are set of ordered degrees, if a scale has no minimal or maximal degrees, it is an open scale. If it has maximal or minimal degrees, it is a closed scale. For example, the adjective tall corresponds to a scale of height, and there is no maximal or minimal degree for height. Adjectives with an open scale are relative adjectives. Some examples are given in (4). Relative adjectives: Open scales: the standard is contextually restricted Gao, ‘tall’, pang ‘fat’, chang ‘long’, kuan ‘wide’, shuai ‘handsome’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 410 H. Fang Subjective standard-setting in gradable predicates In contrast, adjectives corresponding to closed scales are absolute adjectives. They can be further classified into three types, upper-closed scales, which have a maximal degree but no minimal degree, lower-closed scales, which have only a minimal degree, and totally closed scales, which have both minimal and maximal degrees. The examples are given in (5). I assume that the same categorization works for Mandarin as well.2 Absolute adjectives: a. Upper-closed scales: standard=degreemax gan ‘dry’, ganjin ‘clean’, ping ‘flat’, zhi ‘straight’ b. Lower-closed scales: standard=degreemin shi ‘wet’, zan ‘dirty’ c. Totally-closed scales: standard=degreemax man ‘full’, xing ‘awake’, touming ‘transparent’, kai ‘opened’, kandejian ‘visible’ In English, when an absolute adjective has a maximal degree, which include upper-closed scale and totally-closed scale adjectives, the standard is set at the maximal degree. A lowerclosed scale has only a minimal degree, and the standard is set at this degree. While both positive degree sentences with absolute and relative adjectives in English use the same form, Mandarin Chinese actually grammaticalizes this distinction. The hen form is only the default form for relative adjectives, as shown in (1), while the canonical positive form for absolute adjectives is the shi…-de form. Shi is the main copula in Mandarin Chinese, and –de is a modifier marker. The shi…-de form is also the predicative form for non-gradable adjectives, as in (9). Upper-closed scales: standard=dmax Wazi shi gan-de sock COP dry-DE ‘The sock is dry.’ Implication: The dryness of the sock reaches dmax Lower-closed scales: standard=dmin Wazi shi shi-de sock COP wet-DE ‘The sock is wet.’ Implication: The sock has at least minimal wetness Totally-closed scales: standard=dmax Beizi shi man-de cup COP full-DE ‘The cup is full.’ 2 The major piece of evidence for this categorization, according to Kennedy and McNally (2005), is from modification by certain degree modifiers. An adjective like slightly modifies adjectives with lower bounds. Completely takes adjectives with upper bounds. Proportional adjectives, such as half, modify adjectives with totally-closed scales. Adjectives in Mandarin Chinese have similar properties. Due to limitations of space, I will not include the examples here. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 411 H. Fang Subjective standard-setting in gradable predicates Non-gradable adjectives Diqiu shi yuen-xing-de Earth COP round-shape-de ‘The Earth is round.’ The shi…-de form can also occur with relative adjectives, but only when there is a known standard given in the context, which sets things into categorical distinctions. Take (10) for example. When the shi…-de form is used with gao ‘tall’, it implies that there is an absolute degree that separates objects into those that are tall and those that are not. If being 6 feet tall count as tall, as long as Afu reaches this degree of height, he is a tall person. Afu does not need to ‘stand out’ in a comparison class, which is distinct from English positive degree sentences. Afu shi gao-de, Ali bu-shi. Afu COP tall-DE Ali NEG-COP ‘Afu belongs to the category of tall people, while Ali doesn’t.’ Quite unexpectedly, hen can also co-occur with absolute adjectives. Yet it only means that the degree is rather high, and it does not necessarily reach the absolute standard. It can be anywhere on the scale, as long as it is regarded as high. The sentences in (11) are examples of upper-closed scale adjectives. As shown in (11b), a hen sentence does not entail the shi…-de form, of which the standard is the maximal degree. a. b. Wazi hen shi sock HEN wet ‘The sock is very wet.’ Wazi hen gan, dan bu-shi (wanquan) gan-de sock HEN dry but NEG-COP totally dry-DE ‘The sock is very dry, but it is not (completely) dry.’ Likewise, with lower-closed adjectives, the sentence asserts that the degree is significantly high, not just reaching the minimal degree. Wazi hen shi sock HEN wet ‘The sock is very wet.’ Implication: the reference value is significantly high. As for adjectives with totally-closed scales, the standard does not need to reach the upper bound, but it is significantly high. a. b. Beizi hen man cup HEN full ‘The cup is very full.’ Beizi hen man, dan bu-shi (wanquan) man-de cup HEN full but NEG-COP totally full-DE ‘The cup is very full, but it’s not totally full.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 412 H. Fang Subjective standard-setting in gradable predicates What is the difference between the shi…-de form and the hen form when it comes to absolute adjectives? A possible analysis is that the shi…-de form introduces what is known as a conventional standard (Kennedy, 2007), while hen introduces a contextually given standard, functioning just like pos. In English, the traditional analysis of pos cannot directly account for why standards for absolute adjectives are set at the bounds. Kennedy (2007) proposes an economy principle, Interpretive Economy, which requires the interpretations of a sentence to be based on conventional understanding as much as possible. Since the standards of absolute adjectives are conventionally on the natural bounds, their standards are interpreted on these bounds, unless such interpretations are unavailable. Take wet for example. Wet has a lower-closed scale. For an expression the sock is wet, it only requires minimal wetness for things to count as wet. As a result, context-dependent standards become last resort, which emerges only when conventional standards are unavailable. It is possible that Mandarin has both types of standards irrespective of the categories of the gradable adjectives. Therefore, the hen form derives a standard from a comparison class even with absolute adjectives. Take (13) for example. It would mean that the cup’s fullness exceeds a contextually given standard of being full, which is derived from comparing the fullness of this specific cup with other objects filled to different degrees. It does not entail that it reaches the conventional standard, which is the maximal degree. In other words, absolute adjectives now behave just like relative adjectives in standard setting when hen is added. This explains why (13b) is not contradictory under the traditional pos analysis. The above analysis, however, faces a problem. If what hen introduces is a contextual standard for a thing x to count as having a property P, it would be nearly equivalent to, when expressed under that same context, that x is a P thing. This works for relative adjectives in English. In (14), once the standard for being tall is set through the context, and the girl exceeds that height, she is a girl that has the property of being tall. That girl is tall. ≈ That girl is a tall girl. This is not borne out for hen sentences with absolute adjectives, as shown in (15). For the sock to be hen-dry, it does not need to be dry at all, whether the standard is given contextually or stipulated conventionally. It only implies that the dryness of the sock is significantly high. Zhe wazi hen gan ≉ zhe wazi shi yi-zhi gan-de wazi. this sock HEN dry this sock COP one-CL dry-DE sock ‘This sock is very dry.’ ≉ ‘This sock is a dry sock.’ The data presented here seems to suggest that the hen form is a weaker statement than the attributive form in (15). Similarly, it is weaker than the shi…-de form in (13). In conclusion, the hen form is not simply the pos counterpart of English, or at least this is not the full picture. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 413 H. Fang Subjective standard-setting in gradable predicates 2.2. Comparison with the ‘bare’ form A second problem with the pos analysis is that hen is not obligatory in some marked environments.3 When a simple sentence is uttered out of the blue, it is infelicitous without hen, as in (16). Out of the blue context: A: # Afu congming. Afu smart ‘Afu is smart.’ However, hen can be omitted when the property denoted by the gradable adjective is regarded as a known fact. Women dou zhidao, Afu gao. we all know Afu tall ‘We all know, that Afu is tall.’ Furthermore, as pointed out by Liu (2010), hen can be omitted under some modals, including factive verbs such as aonao ‘regret/annoyed’ and zhidao ‘know’, and epistemic modals like renwei, as shown in (18) and (19). Factive verbs: a. Wo aonao ta (hen) wuzhi. I feel-annoyed s/he HEN ignorant ‘I feel annoyed at her/his being ignorant.’ b. Wo zhidao ta (hen) wusi. I know s/he HEN altruistic ‘I know that he is altruistic.’ (Liu, 2010) Epistemic modal renwei ‘think’: Wo renwei ta (hen) wuli. I think s/he HEN unreasonable ‘I think s/he is unreasonable.’ (Liu, 2010) Based on the analysis that hen is the realization of pos, Liu proposes that modals, as well as several other structures (see footnote 3), carry an operator that licenses a covert form of hen. However, Liu does not mention a common feature when hen is dropped in these sentences. In the bare form, there is always a strong implication that the property denoted by the adjective is already an accepted fact. This explains why the bare form is compatible with factive verbs, which trigger the presupposition that the complement proposition is true. Similarly, with 3 Liu (2010) points out that there are several structures in which hen is not obligatory, which include questions, embedding under certain modals, and in the predicative position of contrastive focus forms. He proposes that these syntactic structures license a covert counterpart of pos, and the restriction is syntactic. However, the data given in this section are not syntactically unique. A thorough study on these structures is beyond the scope of this article. I leave it for future research. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 414 H. Fang Subjective standard-setting in gradable predicates epistemic modal like (19), the bare form implies that the speaker is emphasizing a statement that is acknowledged in the context, while when hen is present, there is no such implication. In conclusion, although hen can be absent, it implies that the statement is about a given standard, or a known fact. This feature cannot be explained directly by the pos analysis. 2.3. The puzzle of negation A third puzzle regarding hen is related to negation. In Mandarin Chinese, there are two negation markers, bu and mei. Bu negates generic or habitual predicates, as in (20), and states, as shown in (21). Generic and habitual readings: Wo bu chi mugua. I NEG eat papaya ‘I don’t (generally) eat papayas.’ (Ernst, 1995: 1) States: Wo bu shi laoshi. I NEG COP teacher ‘I’m not a teacher.’ Mei negates eventive predicates and non-states (a la Lin, 2003; also see Huang, 1988; Ernst, 1995; Lee and Pan, 2001; Hsieh, 2001; a.m.o.). According to Lin, a predicate negated by mei has an episodic meaning. Therefore, compared to (21), (22) denies that there was an episode of papaya eating. Generally speaking, mei cannot negate states, as shown in (23) and (24). Wo mei chi mugua. I NEG eat papaya ‘I did not eat papayas.’ (Ernst, 1995: 1) * Afu mei shi laoshi. Afu NEG COP teacher Intended: ‘Afu is/was not a teacher.’ * Afu mei gao. Afu NEG tall Intended: ‘Afu is not tall.’ One would expect that a predicate with gradable adjectives to be negated by bu only, since it describes a state. An example is shown in (25). Hen form under bu: Afu bu hen gao. Afu NEG HEN tall ‘Afu is not tall.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 415 H. Fang Subjective standard-setting in gradable predicates However, surprisingly, when hen is present, it can be negated by mei. This is shown in (26). When hen is absent, the sentence is ungrammatical, as shown in (24). Hen form under mei: Afu mei hen gao. Afu NEG HEN tall ‘Afu is/was not very tall.’ In comparison, the shi…-de form can only be negated by bu, never by mei, as shown in (27) and (28). In fact, the copula shi only co-exist with negation marker bu. Shi…-de form: Beizi bu shi man-de. cup NEG COP full-DE ‘The cup is not full.’ * Beizi mei shi man-de cup NEG COP full-DE Table 1 is a summary of adjectival predicates in negation sentences. The major puzzle is that hen licenses the use of mei. It seems to imply that the hen form is more ‘eventive’ than the shi…-de form. This is the third phenomenon that the pos analysis cannot account for. Table 1 Types of adjectival predicates under negation Mei Bu Hen Ok Ok Shi…-de No No Bare adjectives (no hen) No Ok 3. Hen sentences are subjective 3.1. Subjectivity in adjectives In this section I propose that hen is related to a subjective reading. Subjectivity is related to people’s opinions. It is well known that certain predicates are more subjective than others. One of the widely discussed topics on subjectivity in the domain of adjectives is on Predicates of Personal Tastes (PPTs) (See Kennedy, 2013; Lasersohn, 2005, 2009; Stephenson, 2007; Pearson, 2013; among others). Adjectives like tasty and fun have truth conditions relativized to a judge. In other words, a sentence like (29a) has the truth condition of (29b), in which j refers to the judge who makes the evaluation of what counts as tasty. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 416 H. Fang Subjective standard-setting in gradable predicates a. b. The cake is tasty. The cake is tasty for j. In comparison, adjectives that have objective dimensions, such as tall, large, heavy, dry, full, long, empty, are generally not regarded as subjective. There are two commonly discussed diagnostics to identify subjective predicates. The first one is called faultless disagreement (Kölbel, 2002; Lasersohn, 2005, 2009; among many others). Faultless disagreement refers to the phenomenon that participants of a conversation can argue over whether a statement is true, without reaching a real conclusion, since both of them are entitled to their own opinions. This is shown in (30). None of them can be wrong with respect to whether chili is tasty. John: The chili is tasty. Mary: No! The chili is not tasty. (Lasersohn, 2005) Lasersohn proposes that there should be an independent judge parameter, aside from the ordinary world and time parameters. He adopts a Kaplanian (Kaplan, 1989) approach in explaining faultless disagreement. Kaplan distinguishes between characters and contents. The character of a sentence is a function from context to the contents. When the indexicality of the character is resolved, the result is the content of the sentence. Faultless disagreement is the debate over the same content, but they are evaluated by different judge parameters. The case of PPTs contrasts with sentences with other indexical expressions, such as first person indexicals, as in (31). The expression I’m a doctor has different contents when uttered by different speakers. If what John says is true, Mary’s objection here is infelicitous. John: I’m a doctor. Mary: #No, you’re not a doctor! (Lasersohn, 2005) Another feature of subjective predicates is the capability of embedding under perceptual attitude verb, such as find (Sæbø, 2009; Kennedy, 2013). The English find is a verb that expresses a person’s personal perceptions. Non-subjective adjectives, such as tall, are not acceptable under find, as shown in (32) and (33). John finds the cake tasty. #John finds Mary tall. The hen form shows both characteristics. This is explained in the following sections. 3.2. Faultless disagreement in Mandarin Chinese Similar to the PPTs, the hen form triggers faultless disagreement. This is shown in (36). Imaging the two speakers are arguing about whether Afu is a tall person. When using the hen form, it is more likely to trigger faultless disagreement than the shi…-de form, as in (35). By a native speaker’s intuition, while the hen form provides a certain vagueness related to how Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 417 H. Fang Subjective standard-setting in gradable predicates the standard is set with respect to the speaker, the shi…-de form is related to a more absolute standard that is objective, without the need for assessment from the speaker. A: Afu hen gao Afu HEN tall ‘Afu is tall.’ B: Cuo! Afu bu gao! wrong Afu NEG tall ‘Wrong! Afu is not tall.’ A: Afu shi gao-de Afu COP tall-DE ‘Afu is tall.’ B: Cuo! Afu bu-shi! wrong Afu NEG-COP ‘Wrong! Afu is not tall.’ This contrast is more obvious with absolute adjectives. When they appear with hen, there is vagueness with respect to what counts as significantly full for each individuals, which triggers faultless disagreement, as in (36). As for the shi…-de form, there is no faultless disagreement, as in (37). A: Beizi hen man. cup HEN full ‘The cup is very full.’ B: Cuo! Beizi bu hen man! wrong cup NEG HEN full ‘Wrong! The cup is not very full!’ A: Beizi shi man-de cup COP full-DE ‘The cup is full.’ B: Cuo! Beizi bu shi man-de wrong cup NEG COP full-DE ‘Wrong! The cup is not full!’ In conclusion, there is a strong intuition that the hen form triggers faultless disagreement, and this contrast is particularly obvious when compared with the shi…-de counterpart. 3.3. Embedding under ganjue and ganjue-dao ‘find/feel’ PPTs can embed under attitude verb find. Kennedy (2013) points out that only subjective predicates like PPTs can embed under find with positive forms, while non-subjective adjectives, such as big, large or small, cannot. a. b. Anna finds her bowl of pasta tasty/delicious. ? Anna finds her bowl of pasta big/large/small. (Positive sentences) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 418 H. Fang Subjective standard-setting in gradable predicates Mandarin Chinese has two similar verbs, ganjue and ganjue-dao ‘find/feel’. They have the same verb root ganjue, which literally means ‘to feel.’ They are both related to a person’s gut feelings or judgment based on personal experiences. These two verbs are generally not completely acceptable to occur with non-subjective expressions, as shown in (39) and (40) respectively. ? Afu ganjue/ganjue-dao hua shi hong-se de Afu find/feel flower COP red-color DE Int. ‘Afu finds the flower red.’ ?? Afu ganjue/ganjue-dao konglong miejue-le Afu find/feel dinosaurs extinct-PERF Int. ‘Afu find/feel that dinosaurs are extinct.’ A feature that ganjue and ganjue-dao have is that the judge often has low degree of certainty over his statements. Therefore, it is compatible with an expression in which the speaker second guesses himself. Wo ganjue/ganjue-dao Lisi hen bukekao, dan ye nanshuo. I find/feel Lisi HEN unreliable but still hard-to-say ‘I have the feeling that Lisi isn’t reliable, but it’s hard to say.’ Ganjue-dao is often related to evaluation over a specific situation, and it entails an event of direct encounter of the object. Dao is a morpheme can be literally translated as ‘to’ or ‘reach’ (Chen and Tao, 2014). When attached to a verb, dao adds the meaning that the agent expresses heightened senses and a high degree of transitivity (Chen and Tao, 2014), which is often related to direct perceptual encounters. According to Maienborn (2005), there are several often used diagnostics that can identify an event argument in the predicate position, such as the plausibility of locative and temporal modifiers, and the existence of manner adverbs. Ganjue-dao can appear with these three, as shown in (42) to (44) respectively. Locative modifiers: Zai zheli Ali ganjue-dao ta hen congming. at here Ali find/feel he HEN smart ‘Here Ali had the feeling that he was smart.’ Temporal modifiers: Xianzai Afu ganjue-dao Ali hen mei. Now Afu find/feel Ali HEN beautiful ‘Now Afu feels that Ali is beautiful.’ Manner adverbs: Afu jianjian ganjue-dao Lisi hen congming. Afu gradually feel/find Lisi HEN smart ‘Afu gradually starts to feel that Lisi is smart.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 419 H. Fang Subjective standard-setting in gradable predicates While ganjue-dao is related to direct perceptual experiences, ganjue allows guessing based on circumstantial or inferential evidence. Imagine a scenario where Afu has heard people’s description of Lisi’s build, and how he looks when he stands in a group, but Afu does not know Lisi’s exact height, and he has never met him. It is felicitous to say (45) by using ganjue. On the contrary, ganjue-dao involves an event of actually observing or perceiving the object. Therefore, it is strange to use ganjue-dao in the same situation, as shown in (46). Afu ganjue Lisi hen congming, suiran mei gen ta peng-guo mien. Afu find/feel Lisi HEN smart although NEG with him meet-EXP.PERF face ‘Afu has a feeling that Lisi is smart, although he never met him face to face.’ Afu ganjue-dao Lisi hen congming, # suiran mei gen ta peng-guo mien. Afu find/feel Lisi HEN smart although NEG with he meet-EXP.PERF face Int. ‘Afu feels that Lisi is smart, although he never met him face to face.’ In conclusion, the hen sentences are licensed under both ganjue and ganjue-dao. The hen forms can be used to describe observations of direct perceptual encounters, as in the case of ganjue-dao, and also possible to have the reading based on inferential information, as shown in the sentences with ganjue. 4. The type of subjectivity of hen What kind of subjectivity do hen sentences have? I propose that what hen contributes to the meaning is a standard that is evaluated by the judge according to his epistemic knowledge. In a sense, it is similar to subjective epistemic modals, which are statements based on speaker’s subjective view. Viewing hen as parallel to epistemic modals has a second advantage. It explains why hen makes a weaker claim than the bare form: sentences with epistemic modals are usually weaker claims than simple statements (Karttunen, 1972; Lyons, 1977; Kratzer, 1991; Groenendijk and Stokhof, 1975; von Fintel and Gillies, 2009; among others). Therefore, a sentence like (47b) is intuitively weaker than (47a), as pointed out by Karttunen (1972). a. b. John left. John must have left. This type of subjectivity is distinct from what is widely discussed in the literature of PPTs. The subjectivity related to PPTs has two well-known features. First, the judge of PPTs should be the direct perceptual experiencer of the evaluated object. Second, a PPT sentence cannot really be denied. On the contrary, the judge of a hen sentence does not need to be the direct perceptual experiencer. A hen sentence can be denied, as long as there is further evidence to object to the judge’s evaluation. These features make hen more similar to subjective epistemic modals than PPTs. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 420 H. Fang Subjective standard-setting in gradable predicates 4.1. Comparison between hen and PPTs According to Pearson (2013), PPTs requires the judge to be the direct experiencer of the described (stative) event of the object having the property attributed to it. This is shown in the infelicitous sentence (48). a. b. This cake is tasty to John. #But he hasn’t tried it. This cake is tasty to me. #But I haven’t tried it. However, hen does not have the same restriction. It is felicitous to say (49), where the judge does not have direct experiences towards Afu. Afu hen gao, dan wo mei yu-guo ta. Afu HEN tall but I NEG met-EXP.PERF him ‘Afu is tall, but I’ve never met him.’ For the speaker, to know whether Afu is tall does not require him to have perceptual experiences of Afu. This is not surprising, considering that hen can appear with a variety of gradable adjectives, not just those related to perceptual experiences. 4.2. Faultless disagreement of hen sentences Hen sentences are not really subject to faultless disagreement. If enough information is provided with respect to how the standard is set, a hen statement can still be false. This is shown in the conversation in (50). A: Afu hen gao. Afu HEN tall ‘Afu is tall.’ B: Bu juede. Afu bu gao. NEG find Afu NEG tall ‘I don’t think so. Afu isn’t tall.’ A: Zai san-nianji xiaohai limian, Afu hen gao in third-grade children among Afu HEN tall ‘Among the third grade children, Afu is tall.’ B: Cuo-le! Wo jiao-guo de yi-nianji dou bi ta gao. wrong-PERF I teach-EXP.PERF DE first-grade even COMP he tall ‘Wrong! Even the first grades I taught was taller than him.’ A: Na wo xian wo cuo-le then I think I wrong-PERF ‘Then I guess I was wrong.’ In (50), Speaker A makes a statement that Afu is tall, based on his own understanding. Since it is unclear what his criteria are, there seems to be faultless disagreement. However, when Speaker A further clarifies that he bases his judgment on a group of third graders, the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 421 H. Fang Subjective standard-setting in gradable predicates sentence can be denied by a more knowledgeable person like Speaker B. This is not the case in PPTs. It is infelicitous to negate speaker A’s original statement. A: Zhe dangao hen haochi. this cake HEN tasty ‘This cake is tasty.’ B: Cuo-le. Youde geng haochi wrong-PERF some better tasty ‘Wrong! Some are tastier.’ A: # Haoba wo jian cuo le Okay I say wrong PERF ‘Okay. What I said was wrong.’ 4.3. Similarity with subjective epistemic modality Epistemic modals can be subcategorized into subjective and objective modals. According to Lyons (1977), subjective modals are related to personal and likely more incomplete evidence. This is illustrated by a sentence like (52). It may rain tomorrow. When may is interpreted subjectively, it is reasoned according to someone’s personal experiences. When it is interpreted objectively, it can be based on more solid evidence, such as scientific data (see Lyons, 1977; Drubig, 2001; von Fintel and Iatridou, 2002; von Fintel, 2003; Papafragou 2006; among others). Specifically, Papafragou (2006) views subjective modals as the special cases such that the modal claim is based on the speaker’s personal belief alone, as opposed to beliefs shared by both the speaker and the hearer, or by a subset of people. Although subjective modals are related to the speaker’s knowledge or evidence, the statement expressed with a subjective modal can be challenged by other people when new evidence is available (Papafragou, 2006; von Fintel and Gillies, 2009; MacFarlane 2003). This is shown in an example originally from MacFarlane (2003), which is also discussed in Papafragou (2006). Sally: Joe might be in Boston. George: He can’t be in Boston. I just saw him in the hall five minutes ago. (i) Sally: Oh, then I guess I was wrong. (ii) Sally: Oh, OK. So he can’t be in Boston. Nonetheless, when I said “Joe might be in Boston”, what I said was true, and I stand by that claim. The case of hen in (50) is similar. When speaker A first makes a hen statement, he is talking about evaluation based on his own knowledge. However, when new evidence is added by speaker B about the general height for first grade students, A’s knowledge becomes irrelevant. Therefore, the hen sentence is parallel with epistemic modal yiding ‘must’, as in (54). Yet this distinction is not acceptable with PPTs, as in (51). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 422 H. Fang Subjective standard-setting in gradable predicates A: Afu yiding zai jia. Afu must at home ‘Afu must be at home.’ B: Cuo-le, Afu lian-fenzhong qian hai zai bangongshi. wrong-PERF Afu two-minute ago still at office ‘Wrong! He was in the office two minutes ago.’ A: Haoba wo cai cuo le. Ok I guess wrong PERF ‘Ok, I guess I was wrong.’ 5. Hen and parallelism with seem and appear So far, I’ve shown that the hen form has several features that need to be accounted for. First, hen shows features of subjective predicates, such as triggering faultless disagreement, or at least superficially. Second, it licenses an adjectival predicate to appear with mei. Third, it is a standard given by a judge’s knowledge state. Finally, in comparison with the bare form, the hen form makes a weaker assertion. To account for these three features, I propose that hen is subjective in the sense that it introduces a standard based on a subjective knowledge state. Hen introduces an event of evaluation, in which the judge is the evaluator. As a result, it can be licensed under mei. Hen is similar to epistemic modality in making a weaker statement when compared with the bare form. There is an interesting parallelism between hen and English verbs like appear and seem. According to Fernald (2000), these two verbs are related to speaker’s judgment over a situation in an evaluative event, and make a generalization based on his evaluation. This is shown in (55). Adopting Carlsonian sorted types, here x is a stage of John, Q is some property of John, G is the generic quantifier, y is a stage realized by z, and z are individuals that are intelligent in general. a. b. John seems to be intelligent. ∃Q, xs [perceive'(Q(x)) & R(x, j)& Q(x)& Gys , zi (Q(y)& R(y, z))[intelligent' (z)]] (Modified from Fernald, 2000: 90) The meaning of (55) is as follows. There exists some stage-level property Q, and a stage xs, which refers to the sort of stage objects, such that John is realized as x, and there is a perceiving event of x, such that x has Q, and in general, for any stage y and any individual z such that z realizes as y, if y also has the property Q, then z is regarded as intelligent. Hen can be analyzed in a similar manner. Here a judge is involved in an event of evaluation, and based on his knowledge, he could determine whether the object being evaluated possesses that property denoted by the gradable adjective. a. Afu hen gao Afu HEN tall ‘Afu is tall. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 423 H. Fang Subjective standard-setting in gradable predicates b. ∃Q, xs , vi [R(x, Afu)& Eval(Q(x))(v)& Gys , zi (Q(y)& R(y, z))[tall'(z)]] In (56), there is a property Q, a stage xs, and a judge vi, such that the subject Afu is realized as x, and there is an evaluation event in which the judge v evaluates the stage x of Afu as having the property of Q, and for any stage y, individual z, if z is realized as y, and y has the property of Q, then z is tall. 6. Concluding remarks On the surface, the Mandarin hen sentences are just the counterpart of English positive degree sentences. Yet different from English, they show properties of subjectivity. This work try to account for this property by seeing hen as introducing subjectivity in a similar manner as subjective modals. What hen does is introducing a subjective standard based on a judge’s knowledge. Although viewing hen as introducing a subjective standard is different is the traditional view that hen is pos, my analysis does not refute the idea that hen has the same function of pos in terms of binding the degree argument and avoiding type mismatches, as well as introducing a standard. The major difference of this analysis only lies in what the standard is based on. While the traditional pos analysis only requires a norm function that takes a comparison class and derives a norm from it, what hen does is to provide a norm based on a judge’s knowledge state. Syntax-wise, hen is similar to a copula for avoiding type mismatches. Some languages are known to have different copulas that contrast in terms of subjectivity (de Bruyne, and Pountain, 1995; Maienborn, 2005; Geist, 2005), and the same contrast may also lie in positive degree morphemes. References Chen, K. and H. Tao (2014). The rise of a high transitivity marker 到 dao in contemporary Chinese: Co-evolvement of language and society. Chinese Language and Discourse 5(1), 25–52. de Bruyne, J. and C. J. Pountain (1995). A Comprehensive Spanish Grammar. Blackwell. Drubig, H. B. (2001). On the syntactic form of epistemic modality. Ms., University of Tübingen. Ernst, T. (1995). Negation in Mandarin Chinese. Natural Language & Linguistic Theory 13(4), 665–707. Fernald, T. B. (2000). Predicates and Temporal Arguments. Oxford University Press. von Fintel, K. (2003). Epistemic modality and conditionals revisited. Linguistics colloquium talk, UMass Amherst. von Fintel, K. and A. S. Gillies (2009). `Might' made right. In A. Egan and B. Weatherson (Eds.), Epistemic Modality, pp. 108–130. Oxford University Press. von Fintel, K. and S. Iatridou (2002). The meanings of epistemic modality. Paper presented at Sinn und Bedeutung 7, Universität Konstanz. Geist, L. (2005). Copular sentences in Russian vs. Spanish at the syntax–semantics interface. In Proceedings of Sinn und Bedeutung 10, pp. 99–110. Grano, T. (2012). Mandarin hen and universal markedness in gradable adjectives. Natural Language & Linguistic Theory 30(2), 513–565. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 424 H. Fang Subjective standard-setting in gradable predicates Groenendijk, J. and M. Stokhof (1975). Modality and conversational information. Theoretical Linguistics 2(1–3), 61–112. Huang, C.-T. J. (1988). Wǒ pǎo de kuài and Chinese phrase structure. Language 64(2), 274– 311. Hsieh, M. L. (2001). Form and Meaning: Negation and Question in Chinese. Ph. D. thesis, University of Southern California. Kaplan, D. (1989). Demonstratives. In J. Almog, J. Perry and H. Wettstein (Eds.), Themes from Kaplan, pp. 481-563. Oxford University Press Karttunen, L. (1972). Possible and must. In J. Kimball (Ed.), Syntax and Semantics 1, pp. 1– 20. Academic Press. Kennedy, C. (1999). Projecting the Adjective: The Syntax and Semantics of Gradability and Comparison. Routledge. Kennedy, C. (2005). Parameters of comparison. Unpublished ms., University of Chicago. Kennedy, C. (2007). Vagueness and grammar: The semantics of relative and absolute gradable adjectives. Linguistics and Philosophy 30(1), 1–45. Kennedy, C. (2013). Two sources of subjectivity: Qualitative assessment and dimensional uncertainty. Inquiry 56(2–3), 258–277. Kennedy, C. and L. McNally (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language 81(2), 345–381. Kölbel, M. (2002). Truth without Objectivity. Routledge. Kratzer, A. (1991). Modality. In A. von Stechow and D. Wunderlich (Eds.), Semantics: An International Handbook of Contemporary Research, pp. 639–50. De Gruyter. Lasersohn, P. (2005). Context dependence, disagreement, and predicates of personal taste. Linguistics and Philosophy 28(6), 643–686. Lasersohn, P. (2009). Relative truth, speaker commitment, and control of implicit arguments. Synthese 166(2), 359–374. Lee, P. L. and H. Pan (2001). The Chinese negation marker bu and its association with focus. Linguistics 39(4), 703–732. Lin, J. W. (2003). Aspectual selection and negation in Mandarin Chinese. Linguistics 41(3), 425–460. Liu, C. S. L. (2010). The positive morpheme in Chinese and the adjectival structure. Lingua 120(4), 1010–1056. Lyons, J. (1977). Semantics (2 volumes). Cambridge University Press. MacFarlane, J. (2003). Epistemic modalities and relative truth. Ms., UC Berkeley. Maienborn, C. (2005). A discourse-based account of Spanish ser/estar. Linguistics 43(1), 155–180. Pearson, H. (2013). A judge-free semantics for predicates of personal taste. Journal of Semantics 30(1), 103–154. Papafragou, A. (2006). Epistemic modality and truth conditions. Lingua 116(10), 1688–1702. Sæbø, K. J. (2009). Judgment ascriptions. Linguistics and Philosophy 32(4), 327–352. Stephenson, T. C. (2007). Judge dependence, epistemic modals, and predicates of personal taste. Linguistics and Philosophy 30(4), 487–525. von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics 3(1), 1–77. Zhang, N. N. (2015). Functional head properties of the degree word hen in Mandarin Chinese. Lingua 153, 14–41. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 425 426 Coordination and focus particles (re?)united1 Jovana GAJIĆ — University of Goettingen Abstract. The aim of this paper is to sketch a unified semantics for coordination markers and focus particles. The main empirical motivation is found in the existence of some ‘multipractic’ particles in Serbian, ni and i, which serve as coordination markers, additive focus particles and scalar focus particles. A disjunction-based analysis can capture the polarity-sensitive behavior of ni, whereas i relies on a conjunction semantics. An approach that involves the exhaustification of alternatives is a crucial ingredient. Nonetheless, two types of exhaustification should be allowed — one corresponding to ‘only’ and the other one to ‘even’. Keywords: Negative Polarity Items, coordination, additive focus particles, scalar focus particles, exhaustification. 1. Introduction Most research on coordination examines different aspects of conjunction and disjunction markers, focusing on the problems of their syntactic representation and the possibilities for interpretations based on the logical properties of corresponding connectives (Rooth and Partee (1982); Partee and Rooth (1983); Progovac (1998a, b); Szabolcsi and Haddican (2004); Zamparelli (2011)). Both conjunctions and disjunctions are scope-taking elements, and it is important to determine which constituents they have in their scope, as well as how they scopally interact with other functional expressions in a sentence. Special coordination markers that emerge in negative contexts, such as English ‘neither. . . nor’ (in (1), Wurmbrand (2008)) or French (ni. . . ) ni (in (2), González and Demirdache (2015)), have sparked some interest (de Swart (2001); Doetjes (2005); Dagnac (2012); Paperno (2014)). (1) Leo ate neither the rice nor the carrots. (2) Zoé n’aime *(pas) le thé ni le café. Zoé NEG.likes NEG the tea ni the coffee ‘Zoé doesn’t like tea nor coffee.’ At the center of attention of the research on this topic is what the logical nature of such connectives is, as well as their (scope) relations with negation. In a similar way, the issue of scope relations with negation and the source of polarity sensitivity are debated for different focus particles, as well: (3) (Ian cooked the food.) He washed the dishes too/*either. 1I would like to thank the Harvard Linguistics Department, where I spent one semester as a visiting fellow, and especially professor Gennaro Chierchia. I am also thankful to Dorothy Ahn for her inspiring work. In addition, I benefited from a number of interesting suggestions from the anonymous reviewers of SuB21, as well as the participants of the conference. All errors are mine. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 427 J. Gajić (4) Coordination and focus particles (re?)united (Ian didn’t cook the food.) He didn’t wash the dishes either/? *too. Among others, Rullmann (2003) and Ahn (2015) discuss the alternation between English ‘too’ and ‘either’. An additive (existential) presupposition is identified as responsible for the contextual restrictions on the distribution of the focus particles in (3) and (4). In the case of scalar focus particles, such as English ‘even’ (in (5) and (6), Horn (1969)), there is an additional, scalar presupposition that the assertion is less likely than all of its alternatives (Karttunen and Peters (1979)). (5) Even Muriel voted for Hubert. (6) Not even Muriel voted for Hubert. Are the three phenomena related in any way and do they have some features in common? What can be observed cross-linguistically is that, in certain cases, one item can perform all of these roles. Along with a ‘plain’ conjunction marker i (8), Serbian2 disposes with a coordination marker that only surfaces in negative contexts — ni (7). Noting their apparent morphological kinship, a starting hypothesis could thus be that ni is the polarity sensitive counterpart of i. (7) Sofija *(ne) piše (ni) pesme ni priče. SofijaNOM NEG writes (ni) poemsACC ni storiesACC ‘Sofija doesn’t write poems or stories’ (8) Sofija (ne) piše (i) pesme i priče. SofijaNOM NEG writes (and) poemsACC and storiesACC ‘Sofija (doesn’t) write(s) poems and/or stories’ As shown below, the same items can also serve as focus particles (FP), with both additive and scalar interpretations available, depending on the context. (9) I Lea je uradila domaći. FP LeaNOM AUX3Sg doPART homeworkACC a. ‘Lea did the homework, too’ b. ‘Even Lea did the homework’ (10) Ni Lea nije uradila domaći. FP LeaNOM didn’t doPART homeworkACC a. ‘Lea didn’t do the homework, either’ b. ‘Not even Lea did the homework’ This calls for an investigation of the possibility for a unified analysis of all these different uses of ni and i. The present paper outlines such a unified analysis, where i is treated as a conjunc2 The language whose official name I use here, calling it Serbian, corresponds to what is (also) known as Bosnian-Croatian-Montenegrin-Serbian or Serbo-Croatian in the linguistic literature. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 428 J. Gajić Coordination and focus particles (re?)united tion, but ni is a polarity sensitive disjunction, and it is only the nature of the individual members of coordination that differs in different uses — pronounced or silent. First the coordination role of ni and i will be examined, followed by a proposal of an analysis for ni. Next, the focus particle uses of ni and i will be presented, starting with the additive interpretation and followed by the scalar one, along with the corresponding accounts. Finally, some conclusions about a unified analysis will be laid out. 2. Coordination The present section examines the particle ni as a coordination marker, comparing it to i.3 2.1. Distribution In Serbian, sentential negation is indicated by the preverbal marker ne (turning into ni- when merging with certain auxiliaries). Being a strict Negative Concord language, the presence of multiple negatively marked expressions in one clause does not yield double negation readings in Serbian (11). (11) Niko nikad ne jede ništa. NEG-person NEG-time NEG eats NEG-thing ‘Nobody ever eats anything’ The hallmark of the distribution of ni-coordination is the requirement for the presence of overt negation in the same clause. Different kinds of phrases can be coordinated by ni: DPs4 (12), NPs (13), PPs (14), VPs (15). Ni can appear as a single marker, introducing only the last member of the coordination, but it can also be reiterated, thus one ni heading each member of the coordination. When coordinated constituents are preverbal, single ni is ungrammatical5 . Even though single ni is acceptable post-verbally, reiterated ni is generally preferred in all positions. (12) a. *(Ni) Sofija ni Lea ne ide/idu u školu. ni SofijaNOM ni LeaNOM NEG goSg/goPl to schoolACC ‘Neither Sofija nor Lea go to school’ b. Sofija nije upoznala ?(ni) mog brata ni tvoju sestru. SofijaNOM didn’t meetPART ni myACC brotherACC ni yourACC sisterACC ‘Sofija didn’t meet my brother or your sister’ (13) a. *(Ni) devojčice ni dečaci ne vole španać. ni girlsNOM ni boysNOM NEG likePl spinachACC ‘Neither girls nor boys like spinach’ 3A detailed discussion of the conjunction marker i is outside of the scope of the present paper; the reader is referred to Arsenijević (2011). 4 Both singular and plural agreement on the verb are possible. 5 Nonetheless, even postverbal subjects coordinated by single ni yield strongly degraded sentences. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 429 J. Gajić Coordination and focus particles (re?)united b. Sofija ne voli ni španać ni šargarepu. SofijaNOM NEG likes ni spinachACC ni carrotsACC ‘Sofija doesn’t like spinach or carrots’ (14) Sofija ne čuva knjige ?(ni) na polici ni u fijoci. SofijaNOM NEG keep3Sg booksACC ni on shelfLOC ni in drawerLOC ‘Sofija doesn’t keep books on the shelf or in the drawer’ (15) a. Lea nije (ni) pojela sendvič ni popila jogurt. LeaNOM didn’t ni eatPART sandwichACC ni drinkPART yogurtACC ‘Lea didn’t eat a/the sandwich or drink (the) yogurt’ b. Sofija neće (ni) sašiti ni kupiti haljinu. SofijaNOM won’t ni sewINF ni buyINF dressACC ‘Sofija will neither sew nor buy a/the dress’ The conjunction marker i can coordinate all of the above phrases, but also CPs (20, 21). (16) a. (I) Sofija i Lea (ne) ide/idu u školu. and SofijaNOM and LeaNOM NEG goSg/goPl to schoolACC ‘(Both) Sofija and Lea (don’t) go to school’ b. Sofija (ni)je upoznala (i) mog brata i tvoju sestru. SofijaNOM didn’t meetPART and myACC brotherACC and yourACC sisterACC ‘Sofija (didn’t) m(e)et (both) my brother and your sister’ (17) a. (I) devojčice i dečaci (ne) vole španać. and girlsNOM and boysNOM NEG likePl spinachACC ‘(Both) girls and boys (don’t) like spinach’ b. Sofija (ne) voli (i) španać i šargarepu. SofijaNOM NEG likes and spinachACC and carrotACC ‘Sofija (doesn’t) like (both) spinach and carrots’ (18) Sofija (ne) čuva knjige (i) na polici i u fijoci. SofijaNOM NEG keep3Sg booksACC and on shelfLOC and in drawerLOC ‘Sofija (doesn’t) keep(s) books (both) on the shelf and in the drawer’ (19) a. Lea (ni)je (i) pojela sendvič i popila jogurt. LeaNOM didn’t and eatPART sandwichACC and drinkPART yogurtACC ‘Lea (didn’t) (both) eat/ate a/the sandwich and drink (the) yogurt’ b. Sofija (ne)će (i) sašiti i kupiti haljinu. SofijaNOM won’t and sewINF and buyINF dressACC ‘Sofija will (both/neither) sew and/or buy a/the dress’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 430 J. Gajić Coordination and focus particles (re?)united (20) (I) Sofija je pojela sendvič i Lea je popila jogurt. and SofijaNOM AUX3Sg eatPART sandwichACC and LeaNOM AUX3Sg drinkPART yogurtACC ‘Sofija ate a/the sandwich and Lea drank (the) yogurt’ (21) Ko je došao i šta si video? whoNOM AUX3Sg comePART and whatACC AUX2Sg seePART ‘Who came and what did you see?’ Unlike ni, i doesn’t have a restricted distribution — it is grammatical in both positive and negative environments, as shown in the examples above. Like ni, i can also appear as a single or reiterated marker. Nonetheless, single i is fully grammatical in all positions, especially when no contrastive focalisation is involved. Do the apparent morphological kinship between the two coordination markers and their similar distribution indicate that ni is to be analyzed as a conjunction? Arsenijević (2011) offers an analysis of Serbo-Croatian connectives (i, a, ali, ili, ni), focusing on their morphological make-up and the syntax and semantics that can be derived from it, as well as their information structural behavior. In his account, ni is described as a negative conjunction, but without weighing in on the possible consequences of such an analysis. 2.2. Conjunction or disjunction? Out of these two coordination markers, ni is the one whose status is debatable. For a strict NC language, such as Serbian, two questions emerge: • Is ni inherently negative or semantically non-negative? • Is it a conjunction or a disjunction? It has been proposed that ni is a negative conjunction (Arsenijević (2011)). Yet, this is only one of the four logical possibilities resulting from the combination of the two relevant questions: 1. If ni is an inherently negative disjunction, the presence of a negative operator in each disjunct would predict readings that are not attested for Serbian sentences with ni (such as: ‘Lea didn’t eat a sandwich or she didn’t drink yogurt’ for the example in (15a)). 2. If ni is a semantically non-negative conjunction, its dependence on the presence of a clausemate negative operator is problematic. 3. If ni is an inherently negative conjunction, each conjunct needs to introduce a negative operator of its own. 4. If ni is a non-negative disjunction, all disjuncts would have to be in the scope of one negative operator. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 431 J. Gajić Coordination and focus particles (re?)united Maintaining only options (3.) and (4.), we establish that they are, in fact, predicted to yield logically equivalent interpretations, as stated by one of the de Morgan’s equivalences (22): (22) [¬p] ∧ [¬q] = ¬[p∨q] This makes it impossible to tease apart an interpretation of the ni-coordination as a conjunction that has negative operators in its scope (23a) from the one where it is a disjunction in the scope of a negative operator (23b), in simple sentences like (23). At the same time, a reading available for negated ‘plain’ conjunction i (in (24)), but not for ni (in (23)), is the one where the conjunction is in the scope of sentential negation, as paraphrased in (24b),6 cf. Arsenijević (2011). (23) Sofija ne piše (ni) pesme ni priče. SofijaNOM NEG writes (ni) poemsACC ni storiesACC a. ‘Sofija doesn’t write poems and she doesn’t write stories’ [¬p] ∧ [¬q] b. ‘Sofija doesn’t write poems or stories’ ¬[p∨q] (24) Sofija ne piše (i) pesme i priče. SofijaNOM NEG writes (and) poemsACC and storiesACC a. ‘Sofija doesn’t write poems and she doesn’t write stories’ [¬p] ∧ [¬q] b. ‘Sofija doesn’t write (both) poems and stories (only one of the two)’ ¬[p∧q] Thus, not only have ni and i a similar morphological make-up, they also have one interpretation in common, in negative sentences. In the case of i, there is no reason to doubt the conjunction status of the connective, as it displays both scope orderings with respect to sentential negation. But is there a way to disentangle the two interpretations of ni ((23a) vs. (23b)) and determine whether it is a conjunction or a disjunction? 2.3. Determining the scope of ni In order to create a more transparent LF, an additional scope-taking element can be inserted in the structure. One possible way is to pick a necessity modal as a ‘scope-intervener’. This diagnostic would be parallel to the so-called split-scope readings in Germanic languages (Penka (2010); Zeijlstra (2011)). A necessity modal that is interpreted in the scope of sentential negation allows to test whether ni is unambiguously a narrow scope disjunction (25). However, if the modal is outscoped by both the sentential negation and the ni-coordination, two equivalent interpretations (26) are again possible. (25) ¬ > >[p∨q] (26) a. ¬ [[p] ∨ [q]] = b. [¬p] ∧ [¬q] The corresponding readings available for the Serbian example in (27) are paraphrased below: 6 When i is reiterated in the negated sentence in (24), only the reading (24b) is available. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 432 J. Gajić Coordination and focus particles (re?)united (27) (Sofija) ne mora ni da kuva ni da čisti. SofijaNOM NEG has-to ni FIN cook ni FIN clean a. (25): ‘it is not necessary that Sofija cooks or cleans’ b. i. (26a): ‘it is not the case that it is necessary for Sofija to cook or that it is necessary for Sofija to clean’ ii. (26b): ‘it is not necessary for Sofija to cook and it is not necessary for Sofija to clean’ These readings don’t appear to be very distinct from each other, and this is because there is an entailment relation between them: the scopal configuration in (25) entails the ones in (26). It thus needs to be verified whether the only possible reading is the one paraphrased in (27a) or whether the readings in (27b) are independently available. A potential disambiguating scenario would be the following one: (28) Sofija’s aunt owns a restaurant and she needs some extra workforce, namely for cooking and cleaning, so Sofija’s mother sends her over to help out during summer holidays. The mother thus obliged Sofija to help her aunt out in the restaurant, but without designating either of the two chores as a particular requirement. The scenario in (28) renders only (26/27b) true. Importantly, the sentence in (27) is not accepted by native speakers in this scenario, which discards the reading in (27b). This provides evidence for a narrow-scope disjunction account of ni, since the only available reading is the one (27a) where ni cannot be reanalyzed as a wide scope conjunction. Intervention with modals speaks in favor of analyzing ni as a disjunction in the scope of sentential negation. But is there any further evidence? A second test for teasing apart the two interpretations involves a quantificational adverb as the intervening element, inspired by Shimoyama (2011). An adverb that outscopes sentential negation allows to test whether ni is unambiguously a wide scope conjunction (29). Nonetheless, when the adverb outscopes both the sentential negation and the ni-coordination, two equivalent interpretations are possible (30). (29) (Qadv ¬p) ∧ (Qadv ¬q) (30) a. Qadv >(¬p ∧ ¬q) = b. Qadv >¬(p ∨ q) If ni is a conjunction that has the negative operators in its scope, the interpretation in (29) should be available for the sentence in (31). But the reading in (31b), which can be represented through two logically equivalent LFs, also seems to be available, at first glance. (31) Sofija obično nije (ni) kuvala ni čistila. SofijaNOM usually didn’t ni cookPART ni cleanPART a. (29): ‘It was usually not the case that Sofija cooked and it was usually not the case that Sofija cleaned’ b. i. (30a): ‘It was usually the case that Sofija didn’t cook and that Sofija didn’t clean’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 433 J. Gajić Coordination and focus particles (re?)united ii. (30b): ‘It was usually not the case that Sofija cooked or cleaned’ Again, there is an entailment relation between these readings: the one in (31b) entails the one in (31a). In order to check whether the configuration in which ni can only be interpreted as a conjunction scoping over negation (31a) is available independently form the other one (31b), a context incompatible with the latter needs to be construed. Such a disambiguating scenario is given in the table in (32) — this state of affairs is compatible only with the interpretation in (31a). The reading in (31b) does not correspond to the distribution given in (32) because there were only two out of six days in which Sofija neither cooked nor cleaned (namely Tuesday and Friday), and this is not the majority of days, thus insufficient for employing ‘usually’. When native speakers are asked to judge, the sentence in (31) turns out to be unacceptable in the distribution depicted in (32). This provides evidence against an analysis of ni as a conjunction that outscopes sentential negation. (32) cooking cleaning Mon yes no Tue no no Wed no yes Thu no yes Fri Sat no yes no no Tests that rely on more complex quantificational configurations, with necessity modals or quantificational adverbs as potential interveners, show that Serbian ni behaves as a disjunction in the scope of a negative operator and not as a conjunction that scopes over negative operators. An additional argument against a conjunction-based analysis comes from the observation that (ni. . . ) ni is incompatible with collective predicates, as shown in the examples (33, 34). Furthermore, a predicate of a sentence whose subjects are coordinated by ni cannot be overtly modified with ‘together’ (35). (33) * Ni Sofija ni Lea (ni Marko) se nisu sreli u biblioteci. ni SofijaNOM ni LeaNOM ni MarkoNOM REFL didn’t meetPART in libraryLOC ‘Sofija, Lea and Marko didn’t meet (each other) in the library.’ (34) * Ni Sofija ni Lea (ni Marko) nisu oformili tim. ni SofijaNOM ni LeaNOM ni MarkoNOM didn’t formPART teamACC ‘Sofija, Lea and Marko didn’t form a team (together).’ (35) * Ni Sofija ni Lea (ni Marko) ne pišu projekte zajedno. ni SofijaNOM ni LeaNOM ni MarkoNOM NEG writePl projectsACC together ‘Sofija, Lea and Marko don’t write projects together’ This would be unexpected for a conjunction-based connective, as they normally exhibit nonBoolean interpretations with coordinated subject NPs/DPs (Champollion (2016)). However, Sofija and Lea (and Marko) cannot be interpreted as a semantic plurality in the examples above. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 434 J. Gajić Coordination and focus particles (re?)united 2.4. Strong NPI ni The previous section revealed empirical evidence for a narrow scope disjunction analysis of Serbian ni, where it has been shown that this coordination marker must remain in the scope of sentential negation. This finding makes ni a good candidate for an NPI7 (Ladusaw (1979), Chierchia (2013), inter alia), as exemplified for English ‘anyone’ in (36). But NPIs are known to be grammatical in weaker, Downward Entailing (DE) environments,8 such as the scope of ‘few’ in (37). (36) Lea didn’t see anyone. (37) Few students saw anyone. Ni-coordination is ungrammatical in DE contexts, as shown in (38). But this only means that ni cannot be analyzed as a weak NPI (Zwarts (1998)). (38) *Malo dece voli (ni) španać ni šargarepu. few childrenGEN likes ni spinachACC ni carrotACC ‘Few children like spinach or carrots’ In fact, ni-coordination is grammatical only in anti-additive (39) contexts.9 This makes it a suitable candidate for a strong NPI. (39) Niko ne voli (ni) španać ni šargarepu. ni-whoNOM NEG likes ni spinachACC ni carrotACC ‘Nobody likes spinach or carrots’ What is the syntactic and semantic mechanism that is behind such polarity sensitivity of ni? 3. Proposal Building on the work of his predecessors (Kadmon and Landman (1993), Krifka (1995), Gajewski (2002)), Chierchia (2013) argues that the source of polarity sensitivity of NPIs is a logical contradiction that arises when they appear in an upward or non-monotone environment. What distinguishes NPIs from expressions that are not polarity sensitive are the obligatory alterna7 The unclear status of the ni-coordination in fragment answers makes an analysis in terms of a pure neg-word (Negative Concord Item) less appealing. (i) A: Koga si pozvao? B: ??? Ni Leu ni Sofiju. whoACC AUX2Sg invitePART ni LeaACC ni SofijaACC A: Who did you invite? B: ??? Neither Lea nor Sofija. 8 These environments allow for inferences from sets to subsets: ‘Few girls wore dresses’ → ‘Few girls wore blue dresses’. 9 Such environments satisfy the equivalence: f(X∪Y) ⇔ f(X)∩f(Y); for example — ‘No girls sang or danced’ is equivalent to ‘No girls sang and no girls danced’. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 435 J. Gajić Coordination and focus particles (re?)united tives that NPIs introduce, as well as the presence of a covert exhaustifying operator. The null head that hosts this operator must be able to value the features present on the NPI, through a feature-checking operation under c-command. The role of the operator is then to negate all the alternatives activated by the NPI that are not entailed by the assertion. In a non-DE context such exhaustification will lead to a contradiction. Understood through this framework, the polarity sensitive behavior of Serbian ni stems from the presence of two formal features [σ ,D] which need to be valued by matching features present on a c-commanding operator OS [+σ ,+D]. Once the agreement between ni[-σ ,-D] and OS [+σ ,+D] is established, the scalar (σ ) and subdomain (D) alternatives are activated for the ni-coordination. The scalar (σ ) alternative for a disjunction is a conjunction (its stronger scalemate), whereas subdomain (D) alternatives are drawn from the individual members of the ni-coordination. The role of the OS operator is to perform the exhaustification of both scalar and domain alternatives associated with the ni-coordination.10 In other words, all alternatives that are not entailed by the assertion have to be negated. The OS operator (40)11 is thus similar in effect to the focus particle ‘only’. 0 (40) k O(σ ,D)-ALT φ kg,w = k φ kg,w ∧ ∀p ∈ k φ k(σ ,D)−ALT [p → λ w’k φ kg,w ⊆ p] When (ni. . . ) ni is found in a positive sentence (41), the exhaustified alternatives end up being incompatible with the assertion (42a). Namely, the result of the exhaustification performed by OS (42e) states that neither of the individual disjuncts (p,q) is true, but the assertion says that (at least) one of them must be true (due to the meaning of the disjunction). This yields a clear contradiction, as shown in (42e). (41) *Sofija piše (ni) pesme ni priče. SofijaNOM writes (ni) poemsACC ni storiesACC ‘Sofija writes ni poems ni stories’ (42) a. b. c. d. e. Assertion: OS (p∨q) where p = ‘Sofija writes poems’ and q = ‘Sofija writes stories’ Scalar (σ ) alternatives: p∧q Subdomain (D) alternatives: p, q After EXH: (p∨q) ∧ ¬(p∧q) ∧ ¬p ∧ ¬q Sets of scalar and subdomain alternatives are posited for the ‘plain’ disjunction (such as English ‘or’), as well (Sauerland (2004); Fox (2007)). What makes the difference in the case of NPIs, such as ni, is that these alternatives are always present and must invoke the presence of an exhaustifying operator. This is due to the agreement operation between the covert ONLYoperator and ni, which is required for the syntactic grammaticality of the sentence. But this restricts a ni-coordination to anti-additive contexts, such as the sentential negation in (43), since it is logically sustainable only in such scale-reversing environments. Plain disjunction 10 Arsenijević (2011) also mentions a ‘Domain-Broadening effect’, referring to Chierchia (2006), introduced by the combination of the negative marker component n- and the additive i in ni. 11 Modified from Chierchia (2013), p.138. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 436 J. Gajić Coordination and focus particles (re?)united ‘or’, for example, does not have such a restricted distribution, since its sets of alternatives are not necessarily active. (43) Sofija ne piše (ni) pesme ni priče. SofijaNOM NEG writes (ni) poemsACC ni storiesACC ‘Sofija doesn’t write poems or stories’ (44) a. b. c. d. e. Assertion: OS ¬(p∨q) where p = ‘Sofija writes poems’ and q = ‘Sofija writes stories’ Scalar (σ ) alternatives: ¬(p∧q) Subdomain (D) alternatives: ¬p, ¬q After EXH: ¬(p∨q) In contrast, when a negative environment hosts ni-coordination (43), the exhaustification of alternatives turns out to be vacuous (44e). This time, the assertion (44a) is the strongest of all the alternatives, i.e. it entails all the other alternatives — scalar (44c), as well as subdomain (44d), so there is no alternative to be negated. Crucially, after the syntactic agreement is effectuated and the sets of alternatives activated, no logical contradiction arises. 3.1. Why ‘strong’? If a scale-reversing context prevents the logical contradiction to arise due to the presence of an NPI, it is still unclear why ni-coordination needs an anti-additive environment and why it is not acceptable in a weaker DE context. Following Gajewski (2011), Chierchia (2013) argues that it is not the anti-additivity to be held responsible for this. He introduces a parametric switch manifested in the so-called strong exhaustification, performed by OS . Instead of exhaustifying only subdomain alternatives,12 OS is sensitive to the scalar alternatives as well. But, once it is invoked, the OS operator cannot remain blind to the potential alternatives of other scalar elements that can be found in the same sentence. As a result, when found in the scope of an alternative-sensitive operator at LF, even scalar items which do not obligatorily carry active sets of alternatives, such as the quantifier ‘few NP’, have their scalar alternatives activated, for example, ‘some NP’. For this reason, (ni. . . ) ni is ungrammatical in DE contexts such as the scope of ‘few NP’ in (45) — ‘few children like x’ gives rise to an additional implicature that ‘some children like x’ and this positive implicature provokes a contradiction, as shown in (46e).13 (45) * Malo dece voli (ni) španać ni šargarepu. few childrenGEN likes ni spinachACC ni carrotACC ‘Few children like spinach or carrots’ 12 This would, in fact, be sufficient to account for weak NPIs, since negating their scalar alternative in a positive context wouldn’t lead to a contradiction — ‘It is not the case that Sofija writes poems and stories’ is not incompatible with ‘Sofija writes poems or stories’, it is merely an implicature that would arise obligatorily. 13 Along with its scalar alternatives, subdomain alternatives are also triggered for FEW, however, this is not exemplified here, as scalar alternatives suffice to make the point. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 437 J. Gajić Coordination and focus particles (re?)united (46) a. Assertion: OS FEWch (P OR Q) b. where P = ‘like spinach’, Q = ‘like carrots’, and FEWch = ‘few children’ c. Scalar (σ ) alternatives: FEWch (P AND Q); NOch (P OR Q), NOT-ALLch(P OR Q),. . . d. Subdomain (D) alternatives: FEWch P, FEWch Q e. After EXH: FEWch (P OR Q) ∧ FEWch (P AND Q) ∧ ¬NOch (P OR Q) ∧ NOTALLch(P OR Q) = FEWch (P OR Q) ∧ FEWch (P AND Q) ∧ SOMEch (P OR Q) ∧ NOT-ALLch (P OR Q) Strong exhaustification thus takes into account not only the truth-conditional component of the meaning, but also the presuppositions and the implicatures. This is why strong NPIs are not acceptable in DE contexts, since additional scalar implicatures may arise and yield a contradiction after exhaustification. In contrast, weak NPIs are not coupled with an operator that performs strong exhaustification OS , but with a ‘plain’ operator O, which looks only at the truth-conditional component of meaning and neglects presuppositions and implicatures. 3.2. What about i? The conjunction i does not carry obligatory sets of scalar and subdomain alternatives (for whose activation the formal features [σ ] and [D] are in charge). Therefore, as a coordination marker, i does not depend on the presence of an exhaustification operator, nor a scale-reversing environment for that matter. Activation of these alternatives is, nonetheless, possible, the difference with respect to ni being that it is not obligatory for i. 4. Focus particles As exemplified in the introduction of this paper, both i and ni can serve as focus particles. Depending on whether the set of focal alternatives entailed by the previous context is ordered on a likelihood scale or a simple unordered set, the contribution to the interpretation is, respectively, that of a scalar or an additive focus particle. The present section argues that an ‘even’-based exhaustification is thus needed for both particles in their scalar focus particle incarnation. 4.1. Additive focus particles i and ni As an additive focus particle, i can associate with constituents of different kinds and activate the corresponding unordered sets of focus alternatives ((47a) for the example in (47b)).14 Following Ahn (2015)’s analysis of English ‘too’, i is analyzed as a conjunction which, this time, takes as its arguments the host proposition p and a silent anaphor q (48), where q is a member of the focus value (Rooth (1992)) of p. This means that, when the conjunction i lacks overt multiple conjuncts, one of its members of coordination remains covert, and this is the null anaphor. Due to the presence of the anaphor, a salient antecedent must be available in the preceding context 14 Serbian is a pro-drop language. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 438 J. Gajić Coordination and focus particles (re?)united in order for the sentence with an additive i to be felicitous. The anaphor q thus must be entailed by a member of the set of alternatives in the focus value of p (Rullmann (2003)), and this alternative must be distinct from p (Kripke (2009)). No exhaustification takes place, since i does not carry any formal features in charge of activating scalar and subdomain alternatives. (47) a. ‘She washed the dishes’, ‘She fed the dog’, ‘She practised the piano’. . . b. I domaći je uradila. also homeworkACC AUX3Sg doPART.F ‘She also did the homework’ (48) Assertion: p∧q Ni also serves as an additive focus particle, but one that only appears in anti-additive contexts, similar to English ‘either’. In this use, single ni attaches to a focalized constituent and activates the corresponding unordered set of alternatives ((49a) for (49b)). Additive focus particle ni is infelicitous in the absence of a negative contextual antecedent. (49) a. ‘She didn’t wash the dishes’, ‘She didn’t feed the dog’, ‘She didn’t practise the piano’. . . b. Ni domaći nije uradila. (n)either homeworkACC didn’t doPART.F ‘She didn’t do the homework, either’ This is due to the presence of a silent anaphor in the semantics of focus particle ni, which must be entailed by a member of the set of focus alternatives of the host proposition. Ni is analyzed as a disjunction which takes as its arguments the host proposition p and the silent anaphor q (following Ahn (2015)’s proposal for ‘either’ in English). The difference between ni-coordination and ni additive particle is that in the latter case one disjunct is covert. The polarity sensitivity of the additive focus particle ni is predicted by its disjunctive nature. Even in the absence of overt multiple members of the coordination, ni carries the formal features [σ ,D] in charge of activating scalar and subdomain alternatives. The same exhaustification mechanism is at work and it applies vacuously in a negative environment (50), such as in the example in (49b). This is due to the fact that the assertion (50a) is the strongest alternative (50e). (50) a. b. c. d. e. Assertion: OS ¬(p∨q) where p = ‘She did the homework’ and q∈[[p]]F Scalar (σ ) alternatives: ¬(p∧q) Subdomain (D) alternatives: ¬p, ¬q After EXH: ¬(p∨q) Additive focus particle ni is unacceptable in a positive sentence (51) for the same reason as the coordination marker ni — a contradiction arises between the assertion and the exhaustified Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 439 J. Gajić Coordination and focus particles (re?)united alternatives (52e). (51) * Ni domaći je uradila. (n)either homeworkACC AUX3Sg doPART.F ‘*She did the homework, either’ (52) a. b. c. d. e. Assertion: OS (p∨q) where p = ‘She did the homework’ and q∈[[p]]F Scalar (σ ) alternatives: p∧q Subdomain (D) alternatives: p, q After EXH: (p∨q) ∧ ¬(p∧q) ∧ ¬p ∧ ¬q It turns out that the coordination and the additive focus particle use of (n)i can be treated on a par, if the status of the arguments that they take as a conjunction or a disjunction is allowed to be different — either an overt member of the coordination or a silent anaphor. 4.2. Scalar focus particles i and ni When used as focus particles, ni and i can have either an additive or a scalar contribution to the meaning of the sentence. The flip from the former to the latter is made once the set of focus alternatives becomes ordered on a likelihood scale, as exemplified for i in (53) and for ni in (54). (53) a. ‘She did the homework’ <‘She washed the dishes’ <‘She fed the dog’. . . b. (Čak) i domaći je uradila. even even homeworkACC AUX3Sg doPART.F ‘She even did the homework’ (54) a. ‘She didn’t do the homework’ <‘She didn’t wash the dishes’ <‘She didn’t feed the dog’. . . b. (Čak) ni domaći nije uradila. even even homeworkACC didn’t doPART.F ‘She didn’t even do the homework’ The importance of the context is essential — the distinction between an additive and a scalar use of these particles depends solely on whether the alternatives are ordered or not, and this information can be retrieved from the context. The interpretation of ni and i as scalar focus particles requires emphasis and heavy stress is needed on the associate of the particle. Some other circumstances that can enforce this are information structural effects and the addition of an ‘even’-like particle in Serbian — čak.15 As for the latter, the presence of čak is possible, but 15 In the case of the scalar focus particle i, the universal quantifier sve (= ‘everything’) can marginally be used instead of čak. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 440 J. Gajić Coordination and focus particles (re?)united not necessary. As a rough generalization, this additional particle is needed when the constituent that (n)i is attached to is topicalized.16 Is there an account for the scalar uses of i and ni that would be parallel to the one proposed in the previous section for the additive uses? Recall that we made use of conjunctions and disjunctions of the assertions and some propositional anaphors, respectively. ONLY-exhaustification was then used to explain the restricted distribution of ni. The difference that exists between the additive and the scalar use of these focus particles requires a different operator, one that can capture the scalar ordering of alternatives. An operator modelled after ‘even’ has been proposed by Chierchia (2013): (55) EALT(p) = p ∧ ∀q ∈ ALT [p <µ q] where ‘p <µ q’ says that p is less likely than q with respect to some contextually relevant probability measure µ When applied to the examples above ((53) and (54)), such EVEN-exhaustification looks like (56) and (57), respectively. (56) Scalar focus particle i a. Assertion: E(p∧q) b. where p = ‘She did the homework’ and q∈[[p]]F c. After EXH: p ∧ q ∧ p<µ q (57) Scalar focus particle ni a. Assertion: ¬ES (p∨q) b. where p = ‘She did the homework’ and q∈[[p]]F c. Scalar (σ ) alternatives: ¬(p∧q) d. Subdomain (D) alternatives: ¬p, ¬q e. After EXH: ¬(p ∨ q ∨ p<µ q) = ¬p ∧ ¬q ∧ ¬p<µ ¬q The E operator is invoked to signal that the assertion is the least likely among the relevant alternatives. Such a mechanism is needed both for the scalar focus particle i (56) and for the scalar focus particle ni (57). This is the first time that some sort of exhaustification is needed for both the polarity sensitive (ni) and the ‘plain’ item (i). Note that, distributionally, these two expressions obey the same restrictions when they are scalar focus particles, as when they are additive focus particles — that is, ni is only grammatical in anti-additive contexts. As a disjunction bearing [-σ ,-D] features, ni gets checked and valued by a c-commanding E[+σ ,+D] operator. ES activates a set of parallel, focus alternatives, ordered with respect to some contextually salient probability measure µ. In the case of the scalar use of i, the result of the exhaustification (56c) assures not just that both the assertion and the propositional anaphor hold (as with the additive use), but also that the former is less likely than the latter. As for the 16 It feels more natural to have the word order used in the examples (53b) and (54b) when scalarity is invoked without the help of the ‘even’-like particle čak, although other word orders are also seem to be possible. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 441 J. Gajić Coordination and focus particles (re?)united scalar use of ni, after exhaustification we get that not only the assertion and the propositional anaphor do not hold, but also the assertion not holding is less likely than any focus alternative not holding. This proposal would capture one of the two possible interpretations of (53b), namely the scalar one, where Lea did the homework, she did something else as well, and Lea doing the homework was the least likely thing she could do. As for (54b), its scalar interpretation corresponds to: it is not the case that Lea did the homework, it is not the case that she did something else, and Lea not doing the homework was the least expected thing. What is the link between the ONLY and the EVEN-exhaustification? In other words, why are these two mechanisms united in different interpretations of the same expressions? At first glance, there is nothing connecting the two types of exhaustification or the natural language expressions they are modelled after (‘only’ and ‘even’). But notice that ‘only’ can acquire emphasis and receive a richer meaning than the one that is canonically attributed to it: (58) I can only imagine what it looked like! (59) He managed to read only one book (out of 50 that were on the list)! In the above examples we see that the focus particle ‘only’ can, in addition to its regular exceptive meaning, implicate that the alternative that constitutes the assertion is the most likely. It means that this focus particle is also capable of expressing scalar ordering between different alternatives, under heavy emphasis, although it represents the mirror image of ‘even’ in positive contexts (‘least likely’ vs. ‘most likely’). However, in the case of additive focus particles ni (‘either’) and i (‘also’), we are not dealing with an overt ‘only’ particle, but with an ‘only’-like exhaustification whose mechanism is fixed (40). It is thus still unclear how the switch from ONLY to EVEN exhaustification happens in one and the same item, if their mechanisms are fixed and essentially different form each other (with or without a probability measure). 5. Conclusions This paper tried to provide a unified analysis for ni as a coordination marker and ni as a focus particle, since the source of their polarity sensitivity is identified as the same — their disjunctive nature in combination with the sets of alternatives they obligatorily introduce. Serbian particle ni is analyzed as a strong NPI disjunction that is always found in the scope of a negative operator and whose alternatives must be exhaustified. Scope diagnostics with necessity modals and quantificational adverbs provide additional evidence for the disjunction-based analysis of ni. Its polarity sensitive behavior results from its lexical specification — the particle must agree with a c-commanding silent operator, which makes the subdomain and scalar alternatives active and subject to exhaustification. The present account of different roles in grammar performed by ni is related to the distributionally non-restricted conjunction i, which also acts as an additive and a scalar focus particle. The paper shows, on the case of ni, that an alternatives and exhaustification approach can also Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 442 J. Gajić Coordination and focus particles (re?)united be useful for analyzing polarity sensitive coordination markers. Crucially, it fits with the rest of the framework, since the lowest scalar elements exhibit negative polarity in all described cases (indefinites, modals, and now a disjunction). Diachronic studies in the field of coordination strategies cross-linguistically report a common additive origin for a number of Indo-European conjunctions and additive particles (Goldstein (2016)), Old Church Slavonic i being among them. The reasoning is the following: if the additive particle is indeed a binary operator, as soon as the antecedent of the silent anaphor is immediately preceding the host in the discourse, the additive particle is easily reanalyzed as a conjunction. However, the opposite reasoning could also hold — such particles are used as coordinators at first (as advanced by Szabolcsi (2016)), and once the structure is left with only one member of the coordination, another one must be understood as silent, in order to rescue the meaning of the sentence. References Ahn, D. (2015). The semantics of additive either. In E. Csipak and H. Zeijlstra (Eds.), Proceedings of SuB 19. Arsenijević, B. (2011). Serbo-Croatian coordinative conjunctions at the syntax-semantics interface. The Linguistic Review 28, 175–206. Champollion, L. (2016). Ten men and women got married today: Noun coordination and the intersective theory of conjunction. Journal of Semantics 33(3), 561–622. Chierchia, G. (2006). Broaden your views: Implicatures of domain widening and the spontaneous logicality of language. Linguistic Inquiry 37(4), 535–590. Chierchia, G. (2013). Logic in Grammar. Polarity, Free Choice and Intervention. OUP. Dagnac, A. (2012). Gapping as vP-coordination: an argument from French strict NPI licensing. Paper presented at Ellipsis, University of Vigo. de Swart, H. (2001). Négation et coordination: la conjonction ni. In R. Bok-Bennema, B. de Jonge, B. Kampers-Manhe, and A. Molendijk (Eds.), Adverbial Modification, pp. 109– 124. Brill. Doetjes, J. (2005). The chameleonic nature of French ni: Negative coordination in a negative concord language. In E. Maier, C. Barry, and J. Huitnik (Eds.), Proceedings of SuB 9. Fox, D. (2007). Free choice disjunction and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and Implicature in Compositional Semantics, pp. 71– 120. Palgrave Macmillan. Gajewski, J. (2002). L-analyticity and natural language. Ms., University of Connecticut. Gajewski, J. (2011). Licensing strong NPIs. Natural Language Semantics 19(2), 109–148. Goldstein, D. (2016). Conjunction strategies in Indo-European. Talk at the Oberseminar, English Linguistics, University of Goettingen. González, A. and H. Demirdache (2015). Negative coordination: Single vs. recursive ni in French. In Proceedings of 44th LSRL, Western University. Horn, L. (1969). A presuppositional analysis of only and even. In Proceedings of the 5th Annual Meeting of the Chicago Linguistic Society, pp. 97–108. Kadmon, N. and F. Landman (1993). Any. Linguistics and Philosophy 15, 353–422. Karttunen, L. and S. Peters (1979). Conventional implicature. In C.-K. Oh and D. A. Dinneen Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 443 J. Gajić Coordination and focus particles (re?)united (Eds.), Syntax and Semantics 11: Presupposition, pp. 1–56. Academic Press. Krifka, M. (1995). The semantics and pragmatics of polarity items. Linguistic Analysis 25, 209–257. Kripke, S. (2009). Presupposition and anaphora: Remarks on the formulation of the projection problem. Linguistic Inquiry 40(3), 367–386. Ladusaw, W. (1979). Polarity Sensitivity as Inherent Scope Relations. Ph. D. thesis, University of Texas at Austin. Paperno, D. (2014). An alternative semantics for negative conjunction in Russian. In Proceedings of FASL 23. Partee, B. and M. Rooth (1983). Generalized conjunction and type ambiguity. In R. Bäuerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use and Interpretation in Language, pp. 361–383. De Gruyter. Penka, D. (2010). Negative Indefinites. OUP. Progovac, L. (1998a). Structure for coordination, part I. GLOT International 3(7), 3–9. Progovac, L. (1998b). Structure for coordination, part II. GLOT International 3(8), 3–8. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1, 75–116. Rooth, M. and B. Partee (1982). Conjunction, type ambiguity, and wide scope ‘or’. In M. M. Daniel P. Flickinger and N. Wiegand (Eds.), Proceedings of the first West Coast Conference on Formal Linguistics, pp. 353–362. Rullmann, H. (2003). Additive particles and polarity. Journal of Semantics 20(4), 329–401. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy 27(3), 367–391. Shimoyama, J. (2011). Japanese indeterminate negative polarity items and their scope. Journal of Semantics 28, 413–450. Szabolcsi, A. (2016). Hybrid negative concord, and quantifier-internal vs. clausal particles. Ms., lingbuzz/003114. Szabolcsi, A. and B. Haddican (2004). Conjunction meets negation: A study in cross-linguistic variation. Journal of Semantics 21(3), 219–249. Wurmbrand, S. (2008). Nor: Neither disjunction nor paradox. Linguistic Inquiry 39(3), 511– 522. Zamparelli, R. (2011). Coordination. In K. von Heusinger, C. Maienborn, and P. Portner (Eds.), Semantics. An International Handbook of Natural Language Meaning, Volume 2, pp. 1713–1741. De Gruyter Mouton. Zeijlstra, H. (2011). On the syntactically complex status of negative indefinites. Journal of Comparative German Linguistics 14, 111–138. Zwarts, F. (1998). Three types of polarity. In F. Hamm and E. Hinrichs (Eds.), Plurality and Quantification, pp. 177–238. Kluwer Academic Publishers. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 444 A uniqueness puzzle: How many-questions and non-distributive predication1 Francesco Paolo GENTILE — McGill University Bernhard SCHWARZ — McGill University Abstract. We discuss a novel observation about the meaning of how many-questions, viz. a uniqueness implication that arises in cases that feature non-distributive predicates, such as How many students solved this problem together?. We attempt an analysis of this effect in terms of Dayal’s (1996) Maximal Informativity Presupposition for questions. We observe that such an analysis must be reconciled with the unexpected absence of uniqueness implications in cases where the non-distributive predicate appears under a possibility modal. We explore two possible solutions: (i) the postulation of a scopally mobile maximality operator in degree questions of the sort proposed in Abrusán and Spector (2011); (ii) the proposal that the informativity to be maximized is based on pragmatic, contextual, entailment rather than semantic entailment. We explain why neither solution is satisfactory. We also observe that a Maximal Informativity Presupposition fails to capture uniqueness implications in how many-questions with predicates that are weakly distributive in the sense of Buccola and Spector (2016), such as How many students in the seminar have the same first name?. We conclude that uniqueness implications in how many-questions must have a source that is independent of Dayal’s (1996) Maximal Informativity Presupposition. Keywords: how many-questions, uniqueness presuppositions, non-distributive predication, Maximal Informativity Presupposition. 1. Introduction Recent work posits that questions come with a Maximal Informativity Presupposition (MIP, Dayal 1996). The MIP is stated informally in (1), where an answer is to be understood as a member of the question extension under the Hamblin/Karttunen analysis of questions, the set of so-called Hamblin/Karttunen answers (Hamblin 1973, Karttunen 1977). (1) Maximal Informativity Presupposition (MIP) A question presupposes that it has a true answer that semantically entails any other true answer. Dayal (1996) proposed the MIP in order to capture the uniqueness presupposition carried by singular which questions. It has since played a prominent role in the analysis of so-called weak islands (Fox and Hackl 2006, Schwarz and Shimoyama 2011, Abrusán and Spector 2011, Abrusán 2011, 2014). 1 For comments and discussion, we would like to thank audiences at the 9th Toronto-Ottawa-Montreal Semantics Workshop, Sinn und Bedeutung 21, and Theoretical Linguistics at Keio (TaLK) 2016, especially Itai Bassi, Aron Hirsch, Manfred Krifka and Mats Rooth; the members of the Semantics Research Group at McGill, especially Junko Shimoyama and Michael Wagner; and Brian Buccola. This research was supported by the Social Sciences and Humanities Research Council of Canada (SSHRC, grants #435-2016-1448 and #435-2013-0592). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 445 F. P. Gentile & B. Schwarz A uniqueness puzzle In this paper, we discuss a phenomenon which, at first sight, is naturally interpreted as another symptom of the MIP, viz. uniqueness presuppositions that arise from how many-questions with non-distributive predicates. The phenomenon is illustrated by (2). (2) How many students solved this problem together? A questioner who already assumes that two or more student groups of different sizes solved the problem will not consider (2) a fully appropriate vehicle for requesting information about the exact sizes of those groups; and an addressee who believes that two or more student groups of different sizes solved the problem will likewise judge (2) as not fully appropriate. In short, the question is judged to carry the presupposition that there is a unique size of student groups who solved this problem.2 Under familiar assumptions about how many-questions (Beck and Rullmann 1999), the set of Hamblin/Karttunen answers to (2) contains, for any cardinality n, the propositions that there is a group of n students who solved this problem together. We note that none of these Hamblin/Karttunen answers are related by semantic entailment. For different cardinalities n and m, the propositions that there is a group of n students who solved this problem together and the propositions that there is a group of m students who solved this problem together are semantically independent. As a consequence, the MIP is true if and only if exactly one of these Hamblin/Karttunen answers is true, hence if and only if there is exactly one cardinality n such that there is a group of n students who solved this problem together. This straightforwardly captures the uniqueness effect described above, which therefore appears to present a novel instantiation the MIP in (1). A puzzle arises under this analysis from the study of examples that feature modal operators. In (3), example (1) is modified by embedding the wh-phrase’s scope under the deontic possibility modal allowed. Clearly, this question does not presuppose that there is only one cardinality n such that it is allowed that a group of n students solves this problem. (3) How many students are allowed to solve this problem together? Yet this unattested uniqueness presupposition is precisely what the MIP derives. The reason is that in this case, too, the Hamblin/Karttunen answers are not related by entailment. For different cardinalities n and m, the propositions that it is allowed for n students to solved this problem together and the propositions that it is allowed for m students to solved this problem together are again semantically independent. What, then, accounts for the contrast between (2) and (3)? In this paper, we explore two answers to this question. The first answer enriches the syntaxsemantics of how many questions by positing a scopally mobile maximality operator of the 2 We are not the first to study how many-questions with non-distributive predicates (Beck and Rullmann 1999, Abrusán 2014). However, to our knowledge previous work confined attention to examples with possibility modals, such as Beck and Rullmann’s example How many people can play this game?. As we will discuss shortly, possibility modals obviate the uniqueness effect just described, which explains why no uniqueness effects were reported in those works. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 446 F. P. Gentile & B. Schwarz A uniqueness puzzle sort posited in Abrusán and Spector (2011); the second answer proposes that for the purposes of the MIP, the proper notion of informativity is contextually supported entailment rather than semantic entailment. Unfortunately, however, we find that both solutions fall short of properly characterizing the relevant data, mischaracterizing the conditions under which the uniqueness effect arises in (2) or (3). In addition, we observe that a Maximal Informativity Presupposition fails to capture uniqueness implications in how many-questions with predicates that are weakly distributive in the sense of Buccola (2015) and Buccola and Spector (2016), such as How many students in the seminar have the same first name?. We conclude that, despite initial appearance, uniqueness implications in how many-questions must have a source that is independent of Dayal’s (1996) Maximal Informativity Presupposition. 2. On the syntax-semantics of how many-questions We adopt assumptions about the syntax and semantics of how many-questions familiar from, for example, Beck and Rullmann (1999). We assign to our running example (2) the logical form in (4), where spt abbreviates solved this problem together. (4) how λ n[ [∃ [n many] students] spt] In (4), the wh-phrase how has extracted from the argument position of many; wh-movement leaves behind a trace n ranging over degrees or, more specifically, cardinalities; the phrase n many students is taken to form an existential generalized quantifier, headed by the silent existential determiner ∃; finally, wh-movement of how creates a derived predicate of cardinalities. Again following Beck and Rullmann (1999), we take many to denote a relation between cardinalities and individual sums in the sense of Link (1983), which for ease of exposition we also refer to as groups. (Note that a group may consist of just one atomic individual.) As shown in (5), we take many to relate a cardinality n to a group x just in case the cardinality of x (i.e., the number of atomic individuals in x) equals n. (5) JmanyK = λ nd . λ xe . λ ws . |x| = n The lambda abstract in (4) will accordingly denote the property of cardinalities in (6), which maps any cardinality n to the proposition that there is a group of size n that solved this problem. (6) λ nd . λ ws . ∃x[JstudentsK(x)(w) ∧ JsptK(x)(w) ∧ |x| = n] For ease of exposition, we adopt the so-called functional approach to the semantics of questions (Krifka 2011), that is, we assume that the property in (6) is also the denotation of the question in (2) as a whole. Under this assumption, the set of Hamblin/Karttunen answers to a how manyquestion (or any wh-question) is the set of propositions that forms the range of the question’s denotation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 447 F. P. Gentile & B. Schwarz A uniqueness puzzle 3. The uniqueness effect Before we turn to the analysis of the uniqueness effect described in section 1, we briefly elaborate on the nature of this effect. According to our description above, (2) presupposes that there is a unique size of student groups that solved the problem together. However, some speakers judge (2) to even carry the presupposition that there is a unique group of students who solved the problem together. We will refer to these two presuppositions as the uniqueness of size and the uniqueness of group presupposition, respectively. Note that the uniqueness of group presupposition is stronger than the uniqueness of size presupposition: if there is only one group who solved the problem, then there is a unique size of student groups who solved it, viz. the size of that unique group; however, the reverse entailment does not hold, as there could be several groups of the same size who solved the problem. Whether or not (2) indeed carries an (obligatory) uniqueness of group presupposition, we will in this paper focus on the weaker uniqueness of size presupposition, whose existence we take not to be in doubt. However, we will briefly return to the potential uniqueness of group presupposition, and its significance for the puzzle we describe, in section 9 at the very end of this paper. 4. An account of the uniqueness effect For any given question, the MIP stated in (1) requires that the question have a true Hamblin/Karttunen answer that entails any other true Hamblin/Karttunen answer. Under the functional question semantics that we have adopted, the MIP can be characterized as the proposition that there is a true proposition in the question denotation’s range that entails any other true answer in the range. This is stated in (7), where the variable x ranges over members of the domain of the question denotation, which in the case of how many-questions is the set of cardinalities. (7) For any (functional) question denotation Q: MIP(Q) = λ ws . ∃x[Q(x)(w) ∧ ∀y[Q(y)(w) → Q(x) ⊆ Q(y)] ] We observed in section 1 that the Hamblin/Karttunen answers to (2) are not related by entailment. For the denotation in (6), this means that it is non-ordering in the sense of (8): no proposition in the question denotation’s range entails any other proposition in that range. (8) Non-orderingness f is non-ordering :⇔ ∀x,y[f(x) 6= f(y) → f(x) * f(y)] The denotation in (6) is non-ordering because, as noted, for different cardinalities n and m, the proposition that there is a group of n students that jointly solved this problem and the proposition that there is a group of m students that jointly solved this problem are semantically independent. The central observation, as stated in (9), is now that for a non-ordering question denotation, the MIP encodes a uniqueness presupposition: if all the propositions in the range of the question Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 448 F. P. Gentile & B. Schwarz A uniqueness puzzle denotation are unrelated by entailment, then the MIP requires that there be at most (and at least) one of them that is true. (9) For any non-ordering question denotation Q: MIP(Q) = λ ws . ∃x[Q(x)(w) ∧ ∀y[Q(y)(w) → Q(x) = Q(y)] ] For (2), the MIP therefore yields the proposition that exactly one proposition in the range of (6) is true, which we can describe as in (10), as the proposition that there is exactly one cardinality n such that a group of n students solved this problem together. In other words, the MIP delivers the uniqueness of size presupposition described above. (10) λ ws . ∃!n[∃x[JstudentsK(x)(w) ∧ JsptK(x)(w) ∧ |x|=n] ] Note that the non-orderingness of the denotation of (2) is due to the semantic behaviour of the predicate solved this problem together. The property expressed by this predicate is itself non-ordering: for any two distinct groups x and y, the proposition that the members of x solved the problem together fails to entail the proposition that the members of y solved the problem together. Of course, not all predicates are non-ordering. To illustrate, we contrast (2) with (11), where solved this problem together is replaced by laughed. (11) How many students laughed? The properties expressed by laugh and students are distributive in the sense of (12), where v is the mereological part-of relation between groups of individuals. For any two groups of individuals x and y such that x is included in y, the proposition that y are students (or is a student) who laughed entails the proposition that x are students (or is a student) who laughed. This keeps the denotation of the logical form (13a), shown in (13b), from being non-ordering. In fact, distributivity ensures that (13b) is downward scalar in the sense of (14) (Beck and Rullmann 1999).3 (12) Distributivity f is distributive :⇔ ∀x,y[xvy → f(y) ⊆ f(x)] (13) a. b. (14) Downward scalarity f is downward scalar :⇔ ∀n,m[m≤n → f(n) ⊆ f(m)] 3 Since how λ n[ [∃ [n many] students] laughed] λ nd . λ ws . ∃x[JstudentsK(x)(w) ∧ JlaughedK(x)(w) ∧ |x| = n] it presupposes reference to the intrinsic ordering of cardinalities or other degrees, the notion of downward scalarity selectively applies to the denotations how many-questions and other degree questions, not to question in general. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 449 F. P. Gentile & B. Schwarz A uniqueness puzzle The denotation in (13b) is downward scalar because, given distributivity of students and laughed, the existence of a group of n students who laughed guarantees the existence of a group of m students who laughed, for any m≤n; hence for any such n and m, the proposition that there is a group of n students who laughed semantically entails the proposition that there is a group of m students who laughed. Consider now the set of cardinalities that a given downward scalar question denotation maps to a true proposition. Suppose that this set has a (unique) maximal element. The downward scalar function will map that maximal element to a proposition that entails all the other true propositions in its range, and hence the MIP will be met; so, as stated in (15), the MIP will merely require that the set of cardinalities that the question denotation maps to a true proposition have a maximal member in terms of the intrinsic ordering of cardinalities. (15) For any downward scalar question denotation Q: MIP(Q) = λ ws . ∃n[Q(n)(w) ∧ ∀m[Q(m)(w) → m≤n] ] But in order for a set of cardinalities to have a (unique) maximal member, all it takes is for that set to be non-empty and finite. Applied to the downward scalar denotation of (11) in (13b), the MIP therefore yields the proposition stated in (16), the presupposition that there is a group of students of some (finite) size who solved this problem together. (16) λ ws . ∃n[∃x[JstudentsK(x)(w) ∧ JlaughK(x)(w) ∧ |x|=n] ] So in this case, the MIP amounts to a mere existence presupposition. The content of the MIP is predicted to be more obvious, however, in cases that feature non-ordering properties, as illustrated by the correctly predicted uniqueness of size presupposition for (2). 5. The puzzle: modal obviation of the uniqueness effect Under the MIP-based account for the uniqueness of size presupposition in how many-questions, an interesting puzzle emerges from examples that feature modal expressions such as deontic required and allowed. Consider the pair of questions in (17), where (17b) repeats (3). Extrapolating from our analysis of (2), we arrive at assigning to these questions the logical forms in (18a) and (19a) and the denotations in (18b) and (19b).4 (17) a. b. How many students are required to solve this problem together? How many students are allowed to solve this problem together? (18) a. b. (19) a. b. how λ n[ required [ [∃ [n many] students] spt ] ] λ nd . λ ws . ∀v[v∈ACC(w) → ∃x[JstudentsK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] 4 We how λ n[ allowed [ [∃ [n many] students] spt ] ] λ nd . λ ws . ∃v[v∈ACC(w) ∧ ∃x[JstudentsK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] only consider the “de dicto” readings of the relevant questions (Cinque 1990), where the existential generalized quantifier containing many plus modified noun is interpreted within the scope of the modal. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 450 F. P. Gentile & B. Schwarz A uniqueness puzzle So, the denotation assigned to (17a), shown in (18b), maps any cardinality n to the proposition that in every permissible world, there is a group of students of size n who solved the problem together; likewise the denotation of (17b), shown in (19b), maps any cardinality n to the proposition that there is a permissible world in which there is a group of students of size n who solved the problem together. Note that the non-orderingness of the denotation of solve this problem together ensures that the question denotations in (18b) and (19b), too, are once again non-ordering. For any distinct cardinalities n and m, the proposition that in every permissible world there is a group of n students who solved the problem together does not entail the proposition that in every permissible world there is a group of m students who solved the problem together; likewise the proposition that there is a permissible world where a group of n students solved the problem together does not entail the proposition that there is a permissible world where a group of m students solved the problem together. This means that for both of those cases the MIP once again delivers a uniqueness presupposition. Given (18b), the MIP assigned to (17a), shown in (20a), is the proposition that that there is a unique cardinality such that a student group of that cardinality is required to solve the problem; and given (19b), the MIP assigned to (17b), shown in (20b), is the proposition that there is a unique cardinality such that a student group of that cardinality is allowed to solve the problem. (20) a. b. λ ws . ∃!n[∀v[v∈ACC(w) → ∃x[JstudentsK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] ] λ ws . ∃!n[∃v[v∈ACC(w) ∧ ∃x[JstudentsK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] ] For the question in (17a), this prediction appears adequate, supported by intuitions similar to those about the non-modal example in (2). A speaker using (17a) indeed seems to exclude the possibility of there being more than one cardinality such that it is required for a student group of that cardinality to solve the problem. However, for the question in (17b), the predicted uniqueness of size presupposition is clearly incorrect. The question can be used very naturally in contexts where there is assumed to be a range of permissible group sizes. For example, the interlocutors’ common knowledge might entail that there is an upper bound on the permissible sizes, that this upper bound is between five and ten, and that there are no further constraints on permissible group sizes. In this case, common knowledge is consistent with there being between five and ten permissible sizes, and the speaker may use (17b) to obtain further information. So the uniqueness effect is expectedly preserved under the addition of the necessity modal, but it is unexpectedly obviated by the addition of the possibility modal. How can this obviation effect of possibility modals be accounted for? In sections 6 and 7, we examine two different conceivable strategies to answer this question that preserve the idea that the uniqueness effect is due to to a maximal informativity presupposition. 6. First try: a maximality operator We are not the first to encounter a problem of unwanted uniqueness presuppositions derived by the MIP. Abrusán and Spector (2011) describe much the same problem as they develop an analysis of degree questions that lets gradable predicates denote relations between individuals and intervals of degrees. Abrusán and Spector report that such an interval semantics comes Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 451 F. P. Gentile & B. Schwarz A uniqueness puzzle into conflict with the assumption that questions carry a maximal informativity presupposition. For example, they report that under their interval-based analysis, a degree question like (21) is incorrectly assigned the MIP that there is only one length that the paper is allowed to have. (21) How long is the paper allowed to be? This presupposition is inconsistent with intuitions about (21), which clearly indicate that the question can be used in contexts where the paper is permitted to have a range of different lengths. For example, (21) can be used in a context where the interlocutors’s common knowledge entails that there is an upper bound on the paper’s permitted lengths, that this upper bound is somewhere between 10 and 20 pages, that there is a lower bound of 6 pages, and that there are no further constraints on the on permissible lengths. In such a scenario, common knowledge is consistent with there being between 5 and 15 different permitted paper lengths (measured in terms of numbers of pages). The speaker might then use (21) to obtain further information. The problem that Abrusán and Spector (2011) describe is transparently analogous to our puzzle of modal obviation of the uniqueness of size effect in how many-questions. Therefore, since Abrusán and Spector offer a solution to the problem that arises in their interval semantics, one might hope that this solution is transferrable to our puzzle. That is the line of attack that we explore below. Abrusán and Spector propose that gradable predicates (such as long or many) introduce a scopally mobile operator Π (first defined in Heim 2006) that creates derived properties of degrees. Here we minimally adapt Abrusán and Spector’s semantics for Π to ensure consistency with our assumptions. We take Π to denote a Curryed version of a function from properties of cardinalities to properties of cardinalities, which relates any set of cardinalities that has a unique maximal member to the singleton set containing that maximal member. This denotation is spelled out in (22) (where max maps a set of cardinalities to its unique maximal member). We note that a nearly identical maximality operator has been employed for somewhat different purposes in Buccola and Spector (2016). (22) JΠK = λ md . λ Pd(st) . λ ws . max{n: P(n)(w)} = m To illustrate the syntax and the semantic effect of Π, we return to the question in (11), repeated below in (23). As shown in (24a), we assume that Π enters the syntactic derivation as part of a phrase, the Π-phrase, that also includes the wh-phrase how and that sits in the argument position of many; in (24b), the Π-phrase has extracted from its base position to the edge of the sentence, forming a derived predicate of cardinalities in its scope; and in (24c), how has subextracted from the Π-phrase, once again forming a predicate of cardinalities in its scope. (23) How many students laughed? (24) a. b. c. [∃ [ [Π how] many] students] laughed [Π how] λ n[ [∃ [n many] students] laughed] how λ m[ [Π m] λ n[ [∃ [n many] students] laughed] ] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 452 F. P. Gentile & B. Schwarz A uniqueness puzzle Given the denotation of Π shown in (22), the logical form in (24c) receives the denotation in (25). This question denotation maps any cardinality m to the proposition that m is the largest cardinality n such that there is a group of n students who laughed. More transparently, (25) maps any cardinality to the proposition that the set of all students who laughed has that cardinality. (25) λ md . λ ws . max{n: ∃x[JstudentsK(x)(w) ∧ JlaughedK(x)(w) ∧ |x| = n]} = m The propositions in the range of this function are mutually incompatible. For any distinct cardinalities n and m, the proposition that n is the number of all students who laughed contradicts the proposition that m is the number of all students who laughed. Therefore, the MIP derived from (25) is satisfied as long as there are (finitely many) students who laughed. Therefore, just like under the analysis in section 4 (where we appealed to the distributivity of the meaning of laugh) the MIP for (23) amounts to a mere existence presupposition. For completeness, we note that (23) may well be considered ambiguous between the meaning in (25) and the meaning we derived in in section 3, shown in (13b). Repurposing related hypotheses entertained in Buccola and Spector (2016), we can see two possible ways of recovering (13b). One way is to assume that the presence of Π is optional and that (13a), too, is a well-formed logical form for (23). Another option is to assume that the Π-phrase can scope within the containing noun phrase, below the existential determiner ∃. As readers are invited to verify, with such narrow scope, the presence of Π winds up having no effect on the question denotation as a whole, replicating the meaning assigned to the logical form (13a), where Π is not present in the first place. We are now ready to return to our problematic example (3), repeated again below in (26). We are focusing on a logical form for this question where the Π-phrase has moved past allowed to again take widest scope, turning (27a) into (27b), followed by short subextraction of how, yielding (27c). The denotation assigned to (27c) is shown in (28). (26) How many students are allowed to solve this problem together? (27) a. b. c. (28) λ md . λ ws . max{n: ∃v[v∈ACC(w) ∧ ∃x[JstK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] } = m allowed [ [∃ [ [Π how] many] students] spt] [Π how] λ n[allowed [ [∃ [n many] students] spt] ] how λ m[ [Π m] λ n[allowed [ [∃ [n many] students] spt] ] ] This denotation maps any cardinality m to the proposition that m is the largest cardinality n such that in some permissible world, there is a group of n students who solved this problem together. More transparently, (28) maps any cardinality m to the proposition that m is the largest permitted size of groups of students that solve this problem. Since there can be at most one such largest permitted group size, the propositions in the range of (28) are again pairwise incompatible. Therefore, the MIP once again yields a mere existence presupposition, though in Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 453 F. P. Gentile & B. Schwarz A uniqueness puzzle this case the presupposition that there is a largest permitted size of student groups solving the problem. So the Π-phrase scoping over the possibility modal in (26) has the welcome effect of preempting the derivation of the unattested uniqueness of size presupposition, that is, the presupposition that there is a unique permitted size of student groups solving the problem. Moreover, the weaker MIP now derived for (26) appears weak enough to be consistent with intuitions about the meaning of the question. This might be an encouraging finding, especially since the Π operator employed here, or some version of it, may have independent support from domains other than how many-questions (Heim 2006, Buccola and Spector 2016, Abrusán and Spector 2011, Kennedy 2015). However, there remains an obvious open question that the proposal as stated fails to answer. Why is the obviation of the uniqueness effect tied to the presence of a possibility modal? After all, one might expect that the questions in (2) and (17a), repeated below in (29a) and (29b), also allow for logical forms where the Π-phrase takes wide scope, that is, the logical forms in (30). (29) a. b. How many students solved this problem together? How many students are required to solve this problem together? (30) a. b. how λ m[ [Π m] λ n[ [∃ [n many] students] spt] ] how λ m[ [Π m] λ n[required [ [∃ [n many] students] spt] ] ] These logical forms, too, would preempt the uniqueness of size presuppositions described in sections 1, 3, and 5. The MIP that the logical form in (30a) would give rise to is the proposition that there is a largest size of student groups who solved the problem. But once again, this proposition amounts to a mere existence presupposition. Whenever there is at least one student group (of finite size) who solved the problem, there is guaranteed to be exactly one that is as large as any of the others. Hence the Π-phrase in (30a) incorrectly obviates the very uniqueness of size presupposition that served as the starting point of our investigation. Similarly, the MIP based on (30b) is the proposition that there is a largest cardinality such that it is required for there to be a student group of that cardinality that solves the problem. Once again, this is weaker than the uniqueness presupposition described above, namely the proposition that there is a unique required cardinality of student groups solving the problem. Therefore, if a MIP-based account of the uniqueness effects in (29a) and (29b) is to be preserved, logical forms like those in (30) must be excluded as well-formed inputs to semantic interpretation. Unfortunately, however, there appears to be no independent rationale for such exclusion. In particular, it is not promising to explore the hypothesis that there is something wrong with the syntactic distance that the moving Π-phrase has travelled in the logical forms in (30), since an equal or greater distance is covered by the Π-phrase movement posited in the logical form in (27c). We conclude that, as long as the uniqueness of size effect is sought to be accounted for in terms of the MIP, the obviation of this effect by a scopally mobile Π-phrase must be excluded, which presumably requires excluding the logical form in (27c) along with Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 454 F. P. Gentile & B. Schwarz A uniqueness puzzle those in (30). We then require a different account of the puzzling obviation of the uniqueness of size effect by possibility modals. 7. Second try: contextual entailment Having reverted to the position that the relevant question denotations are as initially presented in sections 2 and 5, we now target the MIP itself for revision. Our formulation of the MIP in (7) above follows Dayal (1996) and subsequent literature in that it construes the relevant notion of informativity as semantic entailment. We will now explore the consequences of instead construing informativity for the purposes of the MIP as pragmatic, contextual, entailment. Let c be the context set in the sense of Stalnaker (1978). As stated in symbols in (31), we say that a proposition p contextually entails a proposition q in context set c just in case q is semantically entailed by p in conjunction with c. (31) Contextual Entailment p ⊆c q :⇔ p ∩ c ⊆ q We use this definition to minimally revise the statement of the MIP in (7) as shown in (32), relativizing it to the context set and substituting contextual entailment for semantic entailment. (32) For any (functional) question denotation Q and context set c: MIPc (Q) = λ ws . ∃x[Q(x)(w) ∧ ∀y[Q(y)(w) → Q(x) ⊆c Q(y)] ] The immediate benefit of this revision is that the problematic modal obviation example in (3), repeated once more in (33), is no longer predicted to carry a uniqueness of size presupposition in all contexts. (33) How many students are allowed to solve this problem together? Under (32), the felicity of (33) is expected to be consistent with the existence of multiple true Hamblin/Karttunen answers, as long as there is one among them that contextually entails all the others. The most natural contexts of this sort are contexts that ensure that the denotation of (33) in (19b), repeated in (34), is contextually scalar. (34) λ nd . λ ws . ∃v[v∈ACC(w) ∧ ∃x[JstudentsK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] The denotation in (34) is contextually scalar in the intended sense in contexts where the relative contextual strength of any two Hamblin/Karttunen answers is predictable from the intrinsic ordering of the two cardinalities that (34) maps to these propositions. In particular, (34) might be contextually downward scalar in the sense defined in (35). (35) Contextual downward scalarity f is contextually downward scalar in c :⇔ ∀n,m[m≤n → f(n) ⊆c f(m)] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 455 F. P. Gentile & B. Schwarz A uniqueness puzzle According to (35), the denotation (34) is contextually downward scalar in contexts where for any cardinalities n and m such that m≤n, the proposition that there are permissible worlds where a group of n students solves the problem contextually entails the proposition that there are permissible worlds where a group of m students solves the problem. In such a context, the truth of the contextual MIP for (33) merely requires that the set of permissible student group sizes have a unique maximal member. Assuming contextual downward scalarity, the proposition that (34) maps that maximal member to will be true and will contextually entail all the other true propositions in the range of (34). We submit that contexts that make (34) contextually downward scalar are rather natural. Such a context could arise in a scenario where, for some cardinality n, the relevant authority, say, a university teacher, is known to have stated that groups of no more than n students may be formed to collaborate on solving this problem, and where it is moreover understood that there are no further restrictions on permitted group sizes. In such a scenario, the contextual downward scalarity of (34) is common knowledge: if it were to emerge, for example, that groups of five students are permitted, an interlocutor could justifiably infer that groups of four or less are permitted as well. A speaker who lacks complete information about the identity of n might appropriately use (33) in the hope of acquiring such information. Once again, the obvious question is whether the approach under consideration captures our finding that the obviation of the uniqueness of size presupposition is only observed with possibility modals. The non-modal example (2) and the case with a necessity modal in (17a) are repeated again in (36), together with their denotations in (37), repeated from (6) and (18b). (36) a. b. How many students solved this problem together? How many students are required to solve this problem together? (37) a. b. λ nd . λ ws . ∃x[JstudentsK(x)(w) ∧ JsptK(x)(w) ∧ |x| = n] λ nd . λ ws . ∀v[v∈ACC(w) → ∃x[JstudentsK(x)(v) ∧ JsptK(x)(v) ∧ |x|=n] ] The expectation is, of course, that in the examples in (36), the uniqueness effect might disappear in suitable scenarios. The most plausible conceivable cases of this sort would again be scenarios that render the denotations in (37) contextually scalar. But now, again focusing on contextual downward scalarity, let us consider what such scenarios would be like. For (37a), contextual downward scalarity would require a scenario where for any cardinalities n and m such that m≤n, the existence of a student group of size n who solved the problem contextually guarantees the existence of a student group of size m who solved the problem. In such a scenario, upon learning that there was a group of, say, six students who solved the problem together, one would be able to infer that there was also a group of five that did so, as well as a group of four, and so on. So in scenarios of this type, the existence of a group of n students who solved the problem would allow one to infer that there are at least n−1 other groups who did so as well, whose cardinalities moreover cover the entire range from 1 to n−1. We suggest that such a scenario is outlandish enough to not readily come to mind to speakers that interpret sentence (36a). The robustness of the uniqueness of size presupposition carried by Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 456 F. P. Gentile & B. Schwarz A uniqueness puzzle (36a) would then not be a matter of linguistic structure, but of the complexity and implausibility of the type of scenario under which that uniqueness presupposition would be weakened in the way it can be weakened in cases with possibility modals. This line of analysis arguably accommodates the case of (36b), as well. For the denotation in (37b), contextual downward scalarity would require a scenario where for any cardinalities n and m such that m≤n, the proposition that a group of n students solved the problem in every permissible world contextually entails the proposition that a group of m students solved the problem in every permissible world. In such a scenario, upon learning that it is required for a group of n students to solve the problem, one would be justified in drawing the inference that it is also required that n−1 other groups of students solve the problem, whose cardinalities moreover must cover the entire range from 1 to n−1. Once again, we submit that such a scenario is sufficiently implausible to not readily come to mind to speakers judging the question in (36b), which serves to account for the robustness of the uniqueness effect in that example. Thus, unlike our attempted account in terms of the Π-operator, the move to a revised MIP based on contextual entailment promises to capture the fact that the obviation of the uniqueness of size effect is limited to cases with a possibility modal. Even so, we must report that, unfortunately, this account does not seem to fully capture the conditions on the use of the case with the possibility modal. While it affords a welcome weakening of the conditions on the use of (33), we can observe that this weakening does not go far enough. Consider a scenario where a teacher is known to have stipulated, for two different cardinalities n and m, that students must form groups to solve the problem together and that each group must have one of the sizes n and m. In this scenario, without having any further beliefs about the permitted group sizes, a speaker may felicitously use (33) to learn about the identity of n and m. Yet in this scenario, no contextual entailment holds between the proposition that a group of n students solves the problem in some permissible world and the proposition that a group of m students solves the problem in some permissible world. This scenario not only conflicts with the presupposition given by the original MIP in (7) but likewise with the weaker presupposition given by the revised MIP, based on contextual entailment. So we are still left without a solution to the puzzle of modal obviation of the uniqueness of size effect. If we were to insist that this effect is a symptom of the MIP, we would still need to find a different way of understanding why the relevant how many-questions with possibility modals do not carry the expected presuppositions. In the next section, we present a type of how many-question that raises the reverse problem, by virtue of carrying a uniqueness of size presupposition that the MIP fails to derive. 8. Another problem: weak distributivity and weak downward scalarity The how many-question in (38) gives rise to a similar observation as the question in (2) that we presented as our first illustration of the uniqueness of size presupposition. That is, (38) suggests that there is only one size of groups of students in the seminar that have the same first name. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 457 F. P. Gentile & B. Schwarz (38) A uniqueness puzzle How many students in the seminar have the same first name? In support of this assessment, we present two concrete scenarios in the form of the class rosters in (39). Imagine that (39a) is the roster for the seminar and that an addressee who has access to this information is presented with the question in (38). It seems clear that the addressee’s cooperative response would be three, given that the class roster in (39a) shows a group of students with the same first name (viz. Ann), which has cardinality 3, and given that it does not show any other group of students that share their first name. (39) a. Adams, Ann Baker, Ann Collins, Ann Durant, Bill Ellis, Chris Foster, Dan b. Adams, Ann Baker, Ann Collins, Ann Durant, Bill Ellis, Bill Foster, Dan In contrast, the class roster in (39b) shows a second group of students with the same first name (viz. Bill), which has cardinality 2. We submit that an addressee who has this information would be hard pressed to answer the question in (38). While such an addressee could truthfully assert that there are groups of two and three students with the same first name, the question in (38) does not appear to be a suitable vehicle for eliciting this information. Accordingly, a speaker who takes a class roster like (39b) to be a good possibility would presumably refrain from using (38) as a request for information. These observations confirm that (38) indeed carries a uniqueness of size presupposition. Interestingly, however, this uniqueness of size presupposition cannot be understood as an instantiation of the MIP. This is a consequence of the semantic behaviour of the denotation of have the same first name and the denotation of the question in (38) as a whole. In contrast to the property expressed by solve this problem together, the property expressed by have the same first name is not non-ordering. For example, it is clear that the proposition that Adams, Baker, and Collins have the same first name semantically entails the proposition that Adams and Baker have the same first name. In fact, this example illustrates that the property expressed by have the same first name is weakly distributive in the sense of definition (40). That is, the property is distributive down to groups of at least two individuals: for any groups x and y such that x is included in y and x has cardinality 2 or more, the proposition that the individuals in y have the same first name semantically entails the proposition that the individuals in x have the same first name.5 (40) Weak distributivity f is weakly distributive :⇔ ∀x,y[xvy ∧ 2≤|x| → f(y) ⊆ f(x)] 5 What keeps the property from being distributive simpliciter is that it does not apply to any atomic individuals. Setting aside the so-called discourse anaphoric reading of same (Beck 2000), the statement that, say, Adams has the same first name is not meaningful. That some collective predicates are weakly distributive in this way was observed in, e.g., Champollion (2010), Buccola (2015), and Buccola and Spector (2016), who illustrate the phenomenon with the verb gather. We borrow the term weak distributivity from Buccola and Spector (2016) (although in a slightly different meaning). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 458 F. P. Gentile & B. Schwarz A uniqueness puzzle Under our current assumptions about the syntax and semantic of how many-questions, (38) has the logical form in (41a) and the denotation in (41b), where hsfn abbreviates have the same first name. (41) a. b. how λ n[ [∃ [n many] students] hsfn] λ nd . λ ws . ∃x[JstudentsK(x)(w) ∧ JhsfnK(x)(w) ∧ |x| = n] The weak distributivity of the denotation of have the same first name (together with the distributivity of the denotation of students) guarantees that the question denotation in (41b) is weakly downward scalar in the sense of definition (42). (42) Weak downward scalarity f is weakly downward scalar :⇔ ∀n,m[m≤n ∧ 2≤m → f(n) ⊆ f(m)] That is, for any cardinalities n and m such that m≤n and 2≤m, the proposition that a group of n students have the same first name semantically entails the proposition that a group of m students have the same first name. For an argument that will be familiar from section 4, consider now the set of cardinalities (greater than 1) that a given weakly downward scalar question denotation maps to a true proposition. Suppose that this set has a (unique) maximal element. The weakly downward scalar function will map that maximal element to a proposition that entails all the other true propositions in its range, and hence the MIP will be met; so, as stated in (43), the MIP will merely require that the set of cardinalities that the question denotation maps to a true proposition have a (unique) maximal member in terms of the intrinsic ordering of cardinalities. (43) For any weakly downward scalar question denotation Q: MIP(Q) = λ ws . ∃n[Q(n)(w) ∧ ∀m[Q(m)(w) → m≤n] ] But, again, in order for any set of cardinalities to have a maximal member, all it takes is for that set to be non-empty and finite. Applied to the weakly downward scalar denotation of (38) in (41b), the MIP therefore yields the proposition stated in (44), the presupposition that there is a group of students in the seminar of some size (greater than 1 and finite) who have the same first name. So, just like questions with (strongly) downward scalar denotations, (38) winds up with a mere existential presupposition. (44) λ ws . ∃n[∃x[JstudentsK(x)(w) ∧ JhsfnK(x)(w) ∧ |x|=n] ] This result entails that the MIP does not capture the uniqueness of size presupposition of (38), identified above. In the scenario (39b), for example, the MIP of (38) would be satisfied. In this scenario, the question has two true Hamblin/Karttunen answers, viz. the proposition that there is a group of two students who have the same first name and the proposition that there is a group of three students who have the same first name. MIP is satisfied in this scenario because, due to the weak distributivity of the property of having the same first name, the latter proposition semantically entails the former. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 459 F. P. Gentile & B. Schwarz A uniqueness puzzle We conclude that for how many-questions with weakly distributive predicates, a MIP-based account delivers a presupposition that is too weak to capture the attested uniqueness effect. 9. Conclusion To recap, we described a uniqueness presupposition carried by certain how many-questions with non-distributive predicates, such as solve this problem together. We explored an approach to this uniqueness effect that credits it to (a version of) Dayal’s (1996) Maximal Informativity Presupposition (MIP). However, we found two symmetric problems for this approach. (i) The MIP derives an overly strong presupposition for how many-questions where a non-distributive predicate is embedded under a possibility modal. For such cases, the MIP is very obviously inadequate when informativity is construed as semantic entailment, and substituting contextual entailment for semantic entailment does not go far enough in weakening the MIP. We saw that a Π-operator which can outscope the possibility modal would weaken the MIP sufficiently to be consistent with intuitions; but such a Π-operator would be expected to incorrectly remove the uniqueness effect across the board, and leave one without an explanation for why the effect is ever observed to begin with. (ii) The MIP derives a presupposition that is to weak for how many-questions with a weakly distributive predicate. Our finding about how many-questions with a weakly distributive predicate brings us back to our discussion of the uniqueness effect in section 3. There we noted that some speakers report that the question in (2), repeated one more time in (45a), does not merely carry a uniqueness of size presupposition, but a stronger uniqueness of group presupposition. That is, the relevant speakers take (45a) to presuppose that there is a unique group of students who solved the problem together. We suspect that this observation extends to (38), repeated in (45b), that is, that (45b) is naturally read as presupposing that there is only one group of students in the seminar that have the same first name. (45) a. b. How many students solved this problem together? How many students in this seminar have the same first name? So, at least for some speakers, the MIP-based approach delivers presuppositions that are overly weak in two different ways. It fails to derive attested uniqueness of size presuppositions in how many-questions with certain collective predicates, and it fails to derive uniqueness of group presuppositions across the board. The problem of predicted presuppositions being too weak becomes even more pronounced under a recent proposal in Fox (2013). In the context of analyzing so-called mention-some readings of questions, Fox proposes a revision of Dayal’s (1996) definition of the MIP. Translated into our format, Fox proposes to replace Dayal’s MIP in (7), repeated in (46), with the weaker version in (47). (46) For any (functional) question denotation Q: MIP(Q) = λ ws . ∃x[Q(x)(w) ∧ ∀y[Q(y)(w) → Q(x) ⊆ Q(y)] ] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 460 F. P. Gentile & B. Schwarz (47) A uniqueness puzzle For any (functional) question denotation Q: MIP(Q) = λ ws . ∃x[Q(x)(w) ∧ ¬∃y[Q(y)(w) ∧ Q(x) ⊃ Q(y)] ] The MIP as defined in (46) requires that the set of true Hamblin/Karttunen answers have a member that is maximal in terms of the ordering given by semantic entailment, that is, a member that entails any other member. This maximal member is necessarily unique. Hence according to (46) the MIP excludes the existence of two true Hamblin/Karttunen answers that are not related by entailment. In contrast, the MIP defined in (47) merely requires that the set of true Hamblin/Karttunen answers have at least one maximal element in terms of the ordering given by semantic entailment, that is, at least one member that is not entailed by any other member. This allows for the existence of two true Hamblin/Karttunen answers that are not related by entailment. Recall now that in all of the how many-questions with a non-distributive predicate like solve this problem together, the Hamblin/Karttunen answers are semantically unrelated. But that means that for those questions, the MIP as defined in (47) will amount to a mere existence presupposition, requiring that the question have at least one true Hamblin/Karttunen answer. Hence the weak MIP does not derive a uniqueness of size presupposition, let alone a uniqueness of group presupposition, for any of the questions we have studied in this paper. In all, the negative results that we have reported suggest that the uniqueness of size effect we set out to understand is after all not a symptom of the MIP, and that an alternative account of this effect is to be sought, one that also captures uniqueness of group presuppositions and that extends to how many-questions with weakly distributive predicates. We must leave the development of such an alternative account to future work. But we will conclude by pointing to one possible approach that may have some promise: We have analyzed many as a relational adjective, which combines with a cardinality denoting expression to form an intersective modifier. In contrast, Hackl (2000) proposes that many is a so-called parametrized determiner. Hackl takes this determiner to have existential quantificational force. Adapting Hackl’s proposal, one could think of many as being more similar to a singular definite article in that it triggers a presupposition of uniqueness. Uniqueness presuppositions would then be contributed by conventional lexical meaning, and would not be tied to the interpretation of questions in the way they are under the approach explored in this paper. We hope to spell out and evaluate this idea in future work. References Abrusán, M. (2011). Presuppositional and negative islands: a semantic account. Natural Language Semantics 19(3), 257–321. Abrusán, M. (2014). Weak Island Semantics. Oxford University Press. Abrusán, M. and B. Spector (2011). A semantics for degree questions based on intervals: Negative islands and their obviation. Journal of Semantics 28(1), 107–147. Beck, S. (2000). The semantics of different: Comparison operator and relational adjective. Linguistics and Philosophy 23(2), 101–139. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 461 F. P. Gentile & B. Schwarz A uniqueness puzzle Beck, S. and H. Rullmann (1999). A flexible approach to exhaustivity in questions. Natural Language Semantics 7(3), 249–298. Buccola, B. (2015). Maximality in the Semantics of Modified Numerals. Ph. D. thesis, McGill University. Buccola, B. and B. Spector (2016). Maximality and modified numerals. Linguistics and Philosophy. Champollion, L. (2010). Parts of a whole: Distributivity as a bridge between aspect and measurement. Ph. D. thesis, University of Pennsylvania. Cinque, G. (1990). Types of A’-Dependencies. Cambridge, Massachusetts: MIT Press. Dayal, V. (1996). Locality in Wh Quantification. Dordrecht: Kluwer. Fox, D. (2013, February). Mention some readings. Unpublished lecture notes, Massachusetts Institute of Technology. Fox, D. and M. Hackl (2006). The universal density of measurement. Linguistics and Philosophy 29, 537–586. Hackl, M. (2000). Comparative Quantifiers. Ph. D. thesis, Massachusetts Institute of Technology. Hamblin, C. L. (1973). Questions in Montague English. Foundations of Language 10, 41–53. Heim, I. (2006). Remarks on comparative clauses as generalized quantifiers. unpublished manuscript, Massachusetts Institute of Technology. Karttunen, L. (1977). Syntax and semantics of questions. Linguistics and Philosophy 1, 3–44. Kennedy, C. (2015, May). A ”de-fregean” semantics (and neo-gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics 8(10), 1–44. Krifka, M. (2011). Questions. In Semantics. An international handbook of Natural Language Meaning. Berlin: Mouton de Gruyter. Link, G. (1983). The logical analysis of plurals and mass terms: A lattice-theoretical approach. In R. Bäuerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use, and the Interpretation of Language, pp. 302—323. Berlin: de Gruyter. Schwarz, B. and J. Shimoyama (2011). Negative Islands and Obviation by wa in Japanese Degree Questions. In N. Li and D. Lutz (Eds.), Proceedings of SALT 20, Ithaca, NY, pp. 702–719. Cornell University: CLC Publications. Stalnaker, R. (1978). Assertion. In P. Cole (Ed.), Syntax and Semantics, Volume 9, pp. 78–95. Academic Press, New York. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 462 Incrementality and Clarification/Sluicing potential1 Jonathan GINZBURG — Université Paris-Diderot (Paris 7) Robin COOPER — University of Gothenburg Julian HOUGH — Bielefeld University David SCHLANGEN — Bielefeld University Abstract. Incremental processing at least as fine grained as word-by-word has long been accepted as a basic feature of human processing of speech (see e.g., Schlesewsky and Bornkessel (2004)) and as an important feature for design of spoken dialogue systems (see e.g., Schlangen and Skantze (2009); Hough et al. (2015)). Nonetheless, with a few important exceptions (see e.g., Kempson et al. (2016)), incrementality is viewed as an aspect of performance, not semantic meaning. Moreover, it seems to entail giving up on compositionality as a constraining principle on denotations. In this paper, we point to a variety of dialogical phenomena whose analysis incontrovertibly requires a semantics formulated in incremental terms. These include cases, above all with sluicing, that call into question existing assumptions about ellipsis resolution and argue for incremental updating of QUD. The incremental semantic framework we sketch improves on existing such accounts (reviewed in Peldszus and Schlangen (2012); Hough et al. (2015)) on both denotational and contextual fronts: the contents we posit are in fact tightly constrained by a methodological principle more restrictive than traditional compositionality, namely the Reprise Content Hypothesis (Purver and Ginzburg (2004); Ginzburg and Purver (2012); Cooper (2013a)), embedded within independently motivated dialogue states (Ginzburg (2012)). Keywords: Incremental processing, dialogue, clarification potential, sluicing 1. Introduction Incremental processing at least as fine grained as word-by-word has long been accepted as a basic feature of human processing of speech (see e.g., Schlesewsky and Bornkessel (2004)) and as an important feature for design of spoken dialogue systems (see e.g., Schlangen and Skantze (2009); Hough et al. (2015)). Nonetheless, with a few important exceptions (see e.g., Kempson et al. (2016)), incrementality is viewed as an aspect of performance, not semantic meaning. Moreover, it seems to entail giving up on compositionality as a constraining principle on denotations. In this paper, we point to a variety of dialogical phenomena whose analysis incontrovertibly requires a semantics formulated in incremental terms. These include cases, above all with sluicing, that call into question existing assumptions about ellipsis resolution and argue for incremental updating of QUD. The incremental semantic framework we sketch improves on existing such accounts (reviewed in Peldszus and Schlangen (2012); Hough et al. 1 Many thanks to the insightful comments of three Sinn und Bedeutung reviewers, as well as to the audience at Sinn und Bedeutung, 2016. We acknowledge support by the French Investissements d’Avenir–Labex EFL program (ANR-10-LABX-0083) and by the Disfluences, Exclamations, and Laughter in Dialogue (DUEL) project within the Projets Franco-Allemand en sciences humaines et sociales of the Agence Nationale de Recherche (ANR) and the Deutsche Forschunggemeinschaft (DFG). For Hough and Schlangen: this work was supported by the Cluster of Excellence Cognitive Interaction Technology ’CITEC’ (EXC 277) at Bielefeld University, which is funded by the German Research Foundation (DFG). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 463 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential (2015)) on both denotational and contextual fronts: the contents we posit are in fact tightly constrained by a methodological principle more restrictive than traditional compositionality, namely the Reprise Content Hypothesis (Purver and Ginzburg (2004); Ginzburg and Purver (2012); Cooper (2013a)), embedded within independently motivated dialogue states (Ginzburg (2012)). The structure of the paper is as follows: in section 2 we introduce the data and draw from it basic specifications for incremental semantics. In section 3 we present the necessary background concerning KOS and Type Theory with Records, the frameworks we employ for representing dialogue, grammar, and semantics. In section 4, we sketch an account of dialogical incremental processing, which we apply to the data from section 2 in section 5. We end with some brief conclusions. 2. Why Semantics needs Incrementality : the Data and Initial specification (1) exemplifies the fact that at any point in the speech stream of A’s utterance B can interject with an acknowledgement whose force amounts to B understanding the initial segment of the utterance (Clark (1996)): (1) A: Move the train . . . B: Aha A: . . . from Avon . . . B: Right A: . . . to Danville. (Trains corpus) (1) requires us to be able to write a lexical entry for ‘aha’ and ‘yeah’ (and their counterparts cross linguistically, e.g., French: ‘ouais’, ‘mmh’,. . . , ) whose context is/includes “an incomplete utterance”. (2a,b,c) exemplify a contrast between three reactions to an ‘abandoned’ utterance: in (2a) B asks A to elaborate, whereas in (2b) she asks him to complete her unfinished utterance; in (2c) B indicates that A’s content is evident and he need not spell it out: (2) a. A(i): John . . . Oh never mind. B(ii): What about John/What happened to John? A: He’s a lovely chap but a bit disconnected. / # burnt himself while cooking last night. b. A(i): John . . . Oh never mind. B(ii): John what? A: # He’s a lovely chap but a bit disconnected. / burnt himself while cooking last night. c. A: Bill is . . . B: Yeah don’t say it, we know. (2a,b,c) requires us to associate a content with A’s incomplete utterance which can either trigger an elaboration query (2a), a query about utterance completion (2b), or an acknowledgement of understanding (2c). (3) is an attested example of an abandoned utterance in mid-word: (3) [Context: A is in the kitchen searching for the always disappearing scissors. As he walks towards the cutlery drawer he begins to make his utterance, before discovering the scissors once the drawer is opened.] A: Who took the sci-. . . (3) requires us to integrate within-utterance and (in this case, visual) dialogue context processing. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 464 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential (4) exemplifies two types of expressions—filled pauses and exclamative interjections—that can in principle, be inserted at any point in the speech stream of A’s utterance; the interjection ‘Oh God’ here reacts to the utterance situation conveyed incrementally. (4) Audrey: Well it’s like th- it’s like the erm (pause) oh God! I’ve forgotten what it’s bloody called now? (British National Corpus) (4) requires us to enable the coherence of a question about what word/phrase will follow, essentially at any point in the speech stream; It also requires us to enable the coherence of an utterance expressing negative evaluation of the current incomplete utterance. (5a-e) illustrate that an incomplete clause can serve as an antecedent for a sluice, thereby going against the commonly held assumption that sluicing is an instance of ‘S-ellipsis’ (Merchant (2001)): (5) a. b. c. d. The translation is by—who else?—Doris Silverstein (The TLS, Feb 2016) He saw—can you guess who?—The Dude; Queen Rhonda is dead. Long live . . . who? (New York Times, Nov 2015); A: A really annoying incident. Some idiot, B: Who? A: Not clear. B: OK A: has taken the kitchen scissors. e. A: Someone I’m not saying who / B: No, do say/Who? (5) requires us to enable either incomplete argument frames or QNPs immediately after their utterance to trigger sluices. 3. Background 3.1. KoS For our dialogical framework we use KoS (Ginzburg (1994); Larsson (2002); Purver (2006); Ginzburg (2012). KoS provides a cognitive architecture in which there is no single common ground, but distinct yet coupled Dialogue GameBoards, one per conversationalist. The structure of the dialogue gameboard (DGB) is given in table 1. The Spkr and Addr fields allow one to track turn ownership; Facts represents conversationally shared assumptions; VisualSit represents the dialogue participant’s view of the visual situation and attended entities; Pending, the nature of which we explicate in more detail below, represents moves that are in the process of being grounded and Moves represents moves that have been grounded; QUD tracks the questions currently under discussion, though not simply questions qua semantic objects, but pairs of entities which we call InfoStrucs: a question and an antecedent sub-utterance.2 This latter entity provides a partial specification of the focal (sub)utterance, and hence it is dubbed the focus establishing constituent (FEC). This is similar to the parallel element in higher order unification-based approaches to ellipsis resolution e.g. Gardent and Kohlhase (1997); and to Vallduvı́ (2015), who relates the focus establishing constituent with a notion needed to capture contrast. 2 Extensive motivation for this view of QUD can be found in (Fernández, 2006; Ginzburg, 2012), based primarily on semantic and syntactic parallelism in non-sentential utterances such as short answers, sluicing, and various other non-sentential utterances. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 465 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential Dialogue Gameboard component type Spkr Individual Addr Individual utt-time Time Facts Set(propositions) VisualSit Situation Moves List(Locutionary propositions) QUD Partially ordered set(hquestion, FECi) Pending List(Locutionary propositions) keeps track of Turn ownership Shared assumptions Visual scene Grounded utterances Live issues Ungrounded utterances Table 1: Dialogue Gameboard 3.2. TTR The logical underpinnings of KoS is Type Theory with Records (TTR) (Cooper (2012); Cooper and Ginzburg (2015)). TTR is a framework that draws its inspirations from two quite distinct sources. One source is Constructive Type Theory for the repertory of type constructors, and in particular records and record types, and the notion of witnessing conditions. The second source is situation semantics (Barwise (1989)) which TTR follows in viewing semantics as ontology construction. This is what underlies the emphasis on specifying structures in a model theoretic way, introducing structured objects for explicating properties, propositions, questions etc. It also takes from situation semantics an emphasis on partiality as a key feature of information processing. This aspect is exemplified in a key assumption of TTR—the witnessing relation between records and record types: the basic relationship between the two is that a record r is of type RT if each value in r assigned to a given label li satisfies the typing constraints imposed by RT on li : (6) record witnessing The record:  l1 l 2  . . . ln = = =  a1 is of type: a2     an  l1 l 2  . . . ln : T1 : T2 (l1 )      : Tn (l1 , l2 , . . . , ln−1 ) iff a1 : T1 , a2 : T2 (a1 ), . . . , an : Tn (a1 , a2 , . . . , an−1 ) This allows for cases where there are fields in the record with labels not mentioned in the record type. This is important when e.g., records are used to model contexts and record types model rules about context change—we do not want to have to predict in advance all information that could be in a context when writing such rules. For what follows, we require use of an analog to priority unification for record types in asymmetric merge (Cooper, 2012; Hough, 2015) defined as: given two record types R1 and R2, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 466 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential R1 ∧. R2 will yield a record type which is the union of all fields with labels not shared by R1 and R2 and the asymmetric merge of the remaining fields with the same labels, whereby R2’s type values take priority over R1’s fields, yielding a resulting record type with R2’s fields only in those cases.       a:T1 a:T1 b:T2  ∧. b:T2 = b:T2  (7) Asymmetric Merge c:T4 c:T3 c:T4 3.2.1. Conversational Rules Context change is specified in terms of conversational rules, rules that specify the effects applicable to a DGB that satisfies certain preconditions. This allows both illocutionary effects to be modelled (preconditions for and effects of greeting, querying, assertion, parting etc.), interleaved with locutionary effects. We mention here three rules used subsequently. The first two concern the incrementation of QUD. (8a)3 specifies that given the LatestMove being q, q becomes maximal in QUD, whereas (8b) concerns the effect of A asserting p: this raises the issue p?—the responder can then either decide to discuss this issue (as a consequence of the rule QSPEC introduced below as (9)) or accept it as positively resolved (as a consequence of a rule we do not mention here): (8)  a. Ask QUD-incrementation b. Assertion QUD-incrementation #  " # q : Question p : Prop pre =  pre =    LatestMove = Ask(spkr,addr,q): IllocProp  LatestMove = Assertion(spkr,addr,p): IllocProp             D E D E     ∗ ∗ effects = qud = q,r .qud : poset(Question) effects = qud = p?,r .qud : poset(Question) " QSPEC is KoS’ version of Gricean Relevance—it characterizes the contextual background of reactive queries and assertions. QSPEC says that if q is QUD-maximal, then subsequent to this either conversational participant may make a move constrained to be q-specific (i.e. either a partial answer or sub-question of q).4 3 Throughout in update rules we will use r∗ to refer to the immediately preceding information state which is required to be of the type in the field labelled by ‘pre’ or ‘preconditions’. 4 We notate the underspecification of the turn holder as TurnUnderspec, an abbreviation for the following specification which gets unified together with the rest of the rule:   n o PrevAud = pre.spkr,pre.addr : Set(Ind)      spkr : Ind   c1 : member(spkr, PrevAud)     addr : Ind     : member(addr, PrevAud) c2 ∧ addr 6= spkr Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 467 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen (9) Incrementality and clarification/sluicing potential QSPEC   D E pre = qud = i, I : poset(InfoStruc)      effects = TurnUnderspec        r : AbSemObj        R: IllocRel        ∧. LatestMove =       R(spkr,addr,r) : IllocProp     c1 : Qspecific(r,i.q) Update procedure: Using asymmetric merge, we employ the following update process for a dialogue context C and for some rule R, a record of type (10). (10)  pre : effects : RecType RecType  When updating from one context Ci to the next Ci+1 with rule R: (11) If Ci : TCi and TCi is a subtype of R.pre, then R licenses the conclusion that: Ci+1 : TCi ∧. R.effects The updates operate on various levels of information which can be arbitrarily fine-grained (even phonetic). This gives us the requisite apparatus for the incrementality discussed in section 2. 3.3. The Reprise Content Hypothesis and Generalized Quantifiers As a means of tightly constraining semantic denotations, we adopt the Reprise Content Hypothesis (RCH, Purver and Ginzburg, 2004; Ginzburg and Purver, 2012; Cooper, 2013a): (12) A fragment reprise question queries exactly the standard semantic content of the fragment being reprised. This uses the data from responses to clarification questions about a constituent as indicative of its content (e.g., A: Most students object to the proposal. B: Most students? A: Carl, Max, and Minnie.). Purver and Ginzburg (2004) and Ginzburg and Purver (2012) use such data to argue in favour of witness sets rather than higher order entities as denotations of QNPs, whereas Cooper (2013a) refines Purver and Ginzburg’s account and shows how the RCH can be maintained using a GQ-based perspective. Using the RCH as a methodological principle for positing denotations can be applied straightforwardly in an incremental setting. It offers a stronger constraint than Fregean/Montogovian compositionality which leaves underdetermined which part contributes what—it fulfills the criteria of what Milward (1991) calls incremental representation and strongly incremental interpretation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 468 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential 3.4. Grounding/Clarification interaction Conditions Much recent work in dialogue has emphasized two essential branches that can ensue in the aftermath of an utterance: • Grounding: the utterance is understood, its content is added to common ground, uptake occurs. • Clarification Interaction: some aspect of the utterance causes a problem; this triggers exchange to repair problem. KoS’s treatment of repair involves two aspects. One is straightforward, drawing on an early insight of Conversation Analysis (Schegloff (2007)), namely that repair can involve ‘putting aside’ an utterance for a while, a while during which the utterance is repaired. That in itself can be effected without further ado by adding further structure to the DGB, specifically the field introduced above called Pending. ‘Putting the utterance aside’ raises the issue of what is it that we are ‘putting aside?’. In other words, how do we represent the utterance? The requisite information needs to be such that it enables the original speaker to interpret and recognize the coherence of the range of possible clarification queries that the original addressee might make. Ginzburg (2012) offers detailed arguments on this issue, including considerations of the phonological/syntactic parallelism exhibited between CRs and their antecedents and the existence of CRs whose function is to request repetition of (parts of) an utterance. Taken together with the obvious need for Pending to include values for the contextual parameters specified by the utterance type, Ginzburg concludes that the type of Pending combines tokens of the utterance, its parts, and of the constituents of the content with the utterance type associated with the utterance. An entity that fits this specification is the locutionary proposition defined by the utterance. A locutionary proposition is a proposition whose situational component is an utterance situation, typed as in (13a) and will have the form of record (13b): (13) a. LocProp=def # " sit : Sign sit-type : RecType b. # " sit = u sit-type = Tu Here Tu is a grammatical type for classifying u that emerges during the process of parsing u. It can be identified with a sign in the sense of Head Driven Phrase Structure Grammar (HPSG, Pollard and Sag, 1994). This is operationalized as follows: given a presupposition that u is the most recent speech event and that Tu is a grammatical type that classifies u, a record pu of the form (13b), gets added to Pending. The two branches lead to the following alternative updates: • Grounding, utterance u understood: update MOVES with pu and respond appropriately (with the second half of an adjacency pair etc.) • Clarification Interaction: 1. pu remains for future processing in PENDING; 2. CQ(u), a clarification question calculated from pu , updates QUD and CQ(u) becomes a discourse topic. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 469 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential 4. An incremental perspective on grounding and clarification 4.1. Incrementalizing dialogue processing The account in section 3.4 was extended to self-repair in Ginzburg et al. (2014): the basic idea is simply to incrementalize the perspective from the turn level to the word level: as the utterance unfolds incrementally there potentially arise questions about what has happened so far (e.g. what did the speaker mean with sub-utterance u1?) or what is still to come (e.g. what word does the speaker mean to utter after sub-utterance u2?). These can be accommodated into the context if either uncertainty about the correctness of a sub-utterance arises or the speaker has planning or realizational problems. Overt examples for such accommodation are provided by self-addressed questions (She saw the . . . what’s the word?, Je suis comment dire?), as explained below. The account of Ginzburg et al. (2014) exemplified some incremental contents and explained a significant conceptual change that would need to be assumed—that Pending would have incremental utterance representations. It did not, however, begin to spell out concretely the nature of such representations, which are crucial in a third option a speaker has apart from grounding and (self)clarifying, namely prediction (see examples (2) and (3) above). We can summarize this picture of processing as in (14), the monitoring and update/clarification cycle is modified to happen at the end of each word utterance event, and in case of the need for repair, a repair question gets accommodated into QUD. (14) a. Ground: continue (Levelt (1983)). b. Predict: stop, since content is predictable. c. (Self)Clarify: generate CR given lack of expected utterance. In the rest of this section we sketch an account of incremental utterance representations, including in particular incremental semantic contents. 4.2. Update Rules for specifying syntax An essential presupposition of our approach (already in its non-incremental version, see above) is a view of syntax as speech event classification by an agent. For a very detailed exposition of such a view see Cooper (2016), a précis of which can be found in Cooper (2013b). Starting at the word level—if Lex(Tw , C) is one of the lexical resources available to an agent A (e.g., Lex(‘Beethoven’, NP) or Lex(‘a’, Det)) and A judges an event e to be of type Tw , then A is licensed to update their DGB with the type Lex(Tw ,C). Intuitively, this means that if the agent hears an utterance of the word “composer”, then they can conclude that they have heard a sign which has the category noun. This is the beginning of parsing, which Cooper shows how to assimilate to a kind of update akin to that involved in non-linguistic event perception such as route finding. The licensing condition corresponding to lexical resources like (14) is given in (15). We will return below to how this relates to gameboard update. (15) says that an agent Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 470 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential with lexical resource Lex(T , C) who judges a speech event, u, to be of type T is licensed to judge that there is a sign of type Lex(T , C) whose ‘s-event.e’-field contains u. (15) If Lex(T  , C) is aresource  available to agent A, then for any u, u :A T licenses :A Lex(T , C) ∧. s-event: e=u:T Strings of utterances of words can be classified as utterances of phrases. That is, speech events are hierarchically organized into types of speech events in a way akin to the complex event structures needed to model activities such as route finding. Agents have resources which allow them to reclassify a string of signs of certain types (“the daughters”) into a single sign of another type (“the mother”). For instance, a string of type Det⌢ N (that is, a concatenation of an event of type Det and an event of type N) can lead us to the conclusion that we have observed a sign of type NP whose daughters are of the type Det⌢ N. The resource that licences this is a rule which modelled as the function in (16a) which we represent as (16b).    (16) a. λ u : Det⌢ N . NP ∧. syn: daughters=u:Det⌢ N b. RuleDaughters(NP, Det⌢ N) ‘RuleDaughters’ is to be the function in (17). Thus ‘RuleDaughters’, if provided with a subtype of Sign+ and a subtype of Sign as arguments, will return a function which maps a string of signs of the first type to the second type with the restriction that the daughters field is filled by the string of signs: (17) λ T1 : Type . λ T2 : Type .    λ u : T1 . T2 ∧. syn: daughters=u:T1 4.3. Semantic Composition using asymmetric merge As we mentioned in section 3.2.1, we use asymmetric merge to integrate utterances into the DGB. We postulate as the denotation associated with the root of the tree the type illocutionary proposition, which is hence compatible with declarative, interrogative and imperative utterances. This gets refined as each word gets introduced using asymmetric merge, which enables us to effect a combinatory operation that synthesises function application and unification. We exemplify how this works in explicating the evolution of the speaker’s information state in example (3), repeated here as (18). (18) [Context: J is in the kitchen searching for the always disappearing scissors. As he walks towards the cutlery drawer he begins to make his utterance, before discovering the scissors once the drawer is opened.] J: Who took the sci-. . . Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 471 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential Before the first word we assume that the speaker has the question ‘who took the scissors’ (which we denote here with q0 ) on his agenda, in the private part of his information state;5 in his visual field he can see no scissors:6 (19) InfState0 : T0 where   D T0 is E D E ask(s,q ) Type 0 : private.agenda =n on o   DGB.FACTS = . . . ¬∃xIn(Vis − sit, x.scissors(x)) . . . : Type We assume that an utterance, u1 , of an interrogative NP such as who results in the update in (20). The content associated with the utterance involves projection in a sense we explicate shortly. Here it is projected to be a question of type WhPQ as in (20), a function from records that include a person x into propositions involving a predication P(x). (20)   x:Ind →RecType) ( c:person(x) P is of type Pred, that is (Ind→RecType), the type of functions from individuals to record types. The function, w, which serves as the incremental content (cf. Milward and Cooper, 1994) of who is given in (21).7 (21)   x:Ind w = λ P:Pred . λ r: . P(r.x) c:person(x) Now the updated information state is characterized in (22). (22) InfState1 : T0 ∧.     sit =u1 : Sit # "     : RecType DGB.Pending =  phon : who  sit-type=  :RecType cont = w: (Pred→WhPQ) We denote the type computed in (22) by T1 . We take content of the verb took to be (23a) (ignoring tense) of type (23b). We represent this content as ‘take′ ’. (23)   a. take′ = λ y:Ind . λ x:Ind . e:take(x,y) b. (Ind→Pred) Thus the incremental content of who took can be computed in line with Milward and Cooper (1994) as (24a) which can be expressed with reference to InfState1 as (24b). 5 This is not a necessary assumption—presumably many utterances are partially planned as their generation starts, hence the occurrence of some filled pauses to buy the speaker planning time. 6 We assume this visual field is part of the speaker’s DGB, which is again a simplification, since it need not be (quasi)-shared. 7 Milward and Cooper (1994) offer an explicit procedure that converts such lambda terms to existentially quantified propositions. Their fragment considered only declarative utterances. In the current work we could adapt their procedure to yield existentially quantified illocutionary propositions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 472 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen (24) a. λ y:Ind . w(take′ (y)) Incrementality and clarification/sluicing potential b. λ y:Ind . InfoState1 .DGB.Pending.sit-type.cont(take′(y)) We abbreviate (24b) as wt. We can compute a type for InfState2 as in (25). (25) InfState2 : T1 ∧.     sit =u2 :Sit " #     :RecType DGB.Pending =  phon : who took    sit-type= :RecType cont = wt : (Ind→WhPQ) We use T2 to represent the type computed in (25). J opens the drawer and sees the scissors there. This updates the DGB facts with a fact that the scissors are in the visual field. This, in turn, implies that no one took the scissors, and hence, given the existence of a resolving answer to the question, the original motivation for asking it is eliminated. We can now compute a type for the next information state, InfState3 , as in (26).   DE D E (26) InfState3 = T2 ∧. private.agenda = : Type             x:Ind   n o    DGB.FACTS = . . .  c:scissors(x). . . : Type           In(VisSit,x ) 4.4. Pending and charts Information included in the ‘Pending’-field of the dialogue gameboard includes a type that represents the agent’s view of the ongoing parse as the utterance unfolds. We call this type a chart-type because we appeal to a notion of chart parsing for this purpose, though as will become clear our approach is compatible with various other approaches for such representations, for instance Hough’s graph-based representation (Hough (2015)) which synthesizes a graph-based Dynamic Syntax view of parsing (Sato (2011)) with the Incremental Unit (IU) framework of Schlangen and Skantze (2011) for incremental processing. The type of Pending remains LocProp, as in (27). The issues that remains is how to explicate Tchart in order to understand how incremental content arises. # " (27) sit = s sit-type = Tchart We present here the briefest sketch of chart parsing as it is used in computational linguistics; for a recent textbook introduction to chart parsing see Jurafsky and Martin (2009), Chap. 13, whereas for its implementation in TTR see Cooper (2016). The idea of a chart is that it should store all the hypotheses made during the processing of an utterance which in turn allow us to compute new hypotheses to be added to the chart. Charts can be updated incrementally for Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 473 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential each word and they can represent several live possibilities in a single data structure. We will say that a chart is a record and we will use our resources to compute a chart type on the basis of utterance events. 4.5. Charts: a simplified example Suppose that we have so far heard an utterance of the word Dudamel. At this point we will say that the type of the chart is (28) (28)  e1 e : “Dudamel”     : e1 :start(e1 ) ⌢ e1 :end(e1 )  The main event of the chart type (represented by the e-field) breaks the phonological event of type “Dudamel” down into a string of two events, the start and the end of the “Dudamel”event.8 Thus (28) records that we have observed an event of the phonological type “Dudamel” and an event consisting of the start of that event followed by the end of that event. Given that we have the resource LexPropName (“Dudamel”, d) available, we can update (28) to (29): (29)  e1  e2   e : : :  “Dudamel”     LexPropName (“Dudamel”, d) ∧. s-event: e=e1 :Phon       e1 :start(e1 ) ⌢ e1 :end(e1 ) e2 :end(e2 ) e2 :start(e2 ) That is, we add the information to the chart that there is an event (labelled ‘e2 ’) of the type which is the sign type corresponding to “Dudamel” and that the event which is the speech event referred to in that sign type is the utterance event, labelled by ‘e1 ’. Furthermore the duration of the event labelled ‘e2 ’ is the same as that labelled ‘e1 ’. The type LexPropName (“Dudamel”, d) is a subtype of NP. Thus the event labelled ‘e2 ’ could be the first item in a string that would be appropriate for the function which we have abbreviated as (30a), which has the type (30b). (30) a. S −→ NP VP | NP′ (VP′ ) b. (NP⌢ VP → Type) Cooper (2016) argues for an analogy between non-linguistic event prediction and the prediction that occurs in parsing.9 So on observing a noun-phrase event one can predict that it might be followed by a verb phrase event thus creating a sentence event. We add a hypothesis event to our chart which takes place at the end of the noun-phrase event as in (31).10 8 These starting and ending events correspond to what are standardly called vertices in the chart parsing literature. 9 Indeed he suggests that this might extend to non-linguistic event prediction among non-humans, e.g., the prediction by a dog playing Fetch that it should run after a stick which is held up. 10 In terms of the traditional chart parsing terminology this corresponds to an active edge involving a dotted rule. The fact that the addition of this type to the chart type is triggered by finding something of an appropriate type to be the leftmost element in a string that would be an appropriate argument to the rule corresponds to what is called a left-corner parsing strategy. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 474 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen  (31) e1  e2      e  3       e : : : : “Dudamel”    LexPropName (“Dudamel”, d) ∧. s-event: e=e1 :Phon   rule=S −→ NP VP | NP′ (VP′ ):(NP⌢ VP → Type)  fnd=e2 :Sign    req=VP:Type e:required(req,rule)     e :end(e1 ) e1 :start(e1 ) ⌢  1  e2 :end(e2 ) e2 :start(e2 ) e3 :start(e3 )⌢ end(e3 ) Incrementality and clarification/sluicing potential               In the e3 -field the ‘rule’-field is for a syntactic rule, that is, a function from a string of signs of a given type to a type. The ‘fnd’-field is for a sign or string of signs so far found which match an initial segment of a string of the type required by the rule. The ‘req’-field is the type of the remaining string required to satisfy the rule as expressed in the ‘e’-field. This hypothesis event both starts and ends at the end of the event of the noun-phrase event e2 . In what follows, we will adopt a simplified version of (31), exemplified in (32). We will omit the ‘e field’. (32)   e1 : “Dudamel”    h i   e2 : LexNP (“Dudamel”) ∧. s-event : e = e1 : Phon         fnd = e2 : Sign   # "       cat = VP : Syncat   req = : Type    cont : (Ind → Prop)    e3 :       ⌢   s-event :fnd.phon req.phon         cat = S : Type proj =       cont =req.cont(fnd.cont) : Prop 5. Incremental Dialogue Processing: principles and examples With a basic means of representing utterances in progress, we can now formulate certain principles which will serve to help explicate the phenomena discussed in section 2. 5.1. Utterance Projection The first principle we introduce corresponds to the ‘stop option’ in our utterance protocol (14b)—it says that if one projects that an utterance will continue in a certain way, then one can actually use this prediction to update one’s DGB. This is of course a dangerous principle to apply in an unconstrained fashion, and would ideally be formulated using probabilities about the projection, for instance using the framework of Cooper et al. (2015), though we do not do so here. (33) is an update rule which moves a locutionary proposition from pending to LatestMove. (r∗ represents the previous information state which is required to be of the type labelled ‘preconds’.) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 475 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential Utterance Projection   # " pending.sit : Sign preconds =    pending.sit-type.proj : Type   h i   ∗ effects = TurnUnderspec ∧. LatestMove = r : LocProp (33) We exemplify an incremental view of the latest move that is being moved in (33) with a wordby-word evolution of the latest move, analogous to that in section 4.3, but this time for an initial segment of a declarative utterance: Jo. . . saw. . . (34) a. b.  sit = u1       phon : “Jo”   " #      j : Ind  dgb-params :      s0 : Rec   sit-type=        sit = s0    h i : (Pred→Prop) cont = λ P:Pred .    sit-type = c1:P(j)  sit = u2       phon : “Jo saw”   " #       j : Ind       dgb-params : s0 : Rec   sit-type=          sit = s0   h i: (Ind→Prop)  cont = λ x:Ind .    sit-type = c1:Saw(j,x) 5.2. Forward-Looking Disfluencies Forward-looking disfluencies are disfluencies where the moment of interruption is followed not by an alteration, but just by a completion of the utterance which is delayed by a filled or unfilled pause (hesitation) or a repetition of a previously uttered part of the utterance (repetitions). As we mentioned with respect to example (4) and in our discussion in section 4.1, we need a means of enabling at any point in the speech stream the emergence of a question about what is still to come in the current utterance. Forward Looking Disfluencies involve the update rule in (35)—given a context where an initial segment of utterance by A has taken place, the next speaker—underspecified between the current one and the addressee—may address the issue of what A intended to say next by providing a co-propositional utterance: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 476 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential (35) Forward Looking Utterance Rule:    spkr : Ind       addr : Ind   preconds =  " #      fnd : Sign       pending.sit-type :   req: Sign        MaxQud =          q = λ x:Ind . MeanNextUtt(r∗.spkr,r∗ .fnd,x)      no : InfoStruc      effects = TurnUnderspec ∧.  fec =      LatestMove : LocProp      c2: Copropositional(LatestMovecontent ,MaxQud) A consequence of (35), is that it offers the potential to explain cases like (36). In the aftermath of a filled pause an issue along the lines of the one we have posited as the effect of the conversational rule (35) actually gets uttered: (36) a. Carol 133 Well it’s (pause) it’s (pause) er (pause) what’s his name? Bernard Matthews’ turkey roast. (BNC, KBJ) b. They’re pretty ... um, how can I describe the Finns? They’re quite an unusual crowd actually. http://www.guardian.co.uk/sport/2010/sep/10/small-talk-steve-backley-interview On our account such utterances are licensed because these questions are co-propositional with the issue ‘what did A mean to say after u0?’. This suggests that a different range of such questions will occur depending on the identity of (the syntactic/semantic type of) u0. This expectation is met, as discussed in Tian et al. (2016), who also discuss cross-linguistic variation with SAQs in English, Chinese, and Japanese. 5.3. Prediction and Clarification for incomplete utterances We return now to (2a,b), repeated here as (37): (37) a. A(i): John . . . Oh never mind. B(ii): What about John? A: He’s a lovely chap but a bit disconnected. / # burnt himself while cooking last night. b. A(i): John . . . Oh never mind. B(ii): John what? A: burnt himself while cooking last night. / # He’ss a lovely chap but a bit disconnected. Whether (2a) or (2b) arise depends on whether one uses utterance projection or the forward looking utterance rule. For the former, as we showed in (34), an initial referential NP when prediction is applied results in (roughly) the projected content in (38). Thus, given the conversational rule QSPEC (the rule (9) above), B’s follow up questions are justified as seeking elaboration of the existentially quantified proposition ∃P IllocRel(spkr, P( j)): Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 477 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen (38) LatestMove =  Incrementality and clarification/sluicing potential sit = u1       phon : “John”  " #       dgb-params : j : Ind      s0 : Rec  sit-type=          sit = s0   h i: (Pred→Prop) cont = λ P:Pred .     sit-type = c1:P(j) As for (2b), this follows by applying the forward looking utterance rule, where the addressee takes over. 5.4. Sluicing, incrementally We assume, following Cooper (2013a) that a QNP such as ‘someone’ has a content of the form (39), where q-params constitute descriptive content that, in contrast to the dgb-params, does not require instantiation. (39)  " # restr = person: Ppty  q-params:   witness : ∃(restr)      P : Ppty  " #    scope = P :Ppty cont = : Rtype c1 = witness : ∃(restr,scope)  We assume a constructional specification for a sluice as in (40), deriving from Ginzburg (2012). A sluice denotes a question (i.e., a function from records into propositions) whose domain is the type denoted by the wh-phrase and whose range is that given by MaxQUD’s proposition where the wh-phrase’s variable is substituted for that associated with the antecedent: (40) sluice-int-cl.cont = (whP.rest)MaxQUD.prop[antecedent.x 7→whP.x] The sluice is triggered by utterance prediction that LatestMove is A asserts that Someone P’ed. This gives rise to QUD update, via Assertion QUD-incrementation with (41a) as maximal element of QUD and the antecedent for a sluice, as in (41b), which is predicted to mean (41c) immediately after it is uttered: (41) a. ?∃x, P[Person(x) ∧ P(x)] b. A: Someone . . . B: Who? c. ‘Who is that person (that has some as yet uninstantiated property)?’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 478 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential 6. Conclusions and further Work In this paper we provide data related to the potential for clarification, repair, and sluicing in mid-utterance. This data shows that the “competence grammar” must be formulated in a way that enables incremental (minimally word by word and even mid-word) semantic composition to be effected. In particular, this data constitutes an argument for incremental access to the contextual repository QUD. This approach has parallels to Dynamic Syntax (Kempson et al., 2001), and particularly recent dialogue-friendly versions (Purver et al., 2011; Kempson et al., 2016), where the central idea is online, incremental construction of meaning representations. However, the incremental account presented here not only allows the representation of utterances, but the internal state of a dialogue agent, including background beliefs and the events in the situated context, to be updated online for entire interactions. In a more detailed presentation we will present a small grammar/context fragment. In future work we hope to investigate experimentally the processing of data of the kind presented here. References Barwise, J. (1989). The Situation in Logic. CSLI Lecture Notes. Stanford: CSLI Publications. Clark, H. (1996). Using Language. Cambridge: Cambridge University Press. Cooper, R. (2012). Type theory and semantics in flux. In R. Kempson, N. Asher, and T. Fernando (Eds.), Handbook of the Philosophy of Science, Volume 14: Philosophy of Linguistics. Amsterdam: Elsevier. Cooper, R. (2013a). Clarification and generalized quantifiers. Dialogue and Discourse 4, 1–25. Cooper, R. (2013b). Update conditions and intensionality in a type-theoretic approach to dialogue semantics. In Proceedings of SemDial 2013 (DialDam), pp. 15–24. Citeseer. Cooper, R. (2016). Type theory and language: From perception to linguistic communication. Book Draft. Cooper, R., S. Dobnik, S. Larsson, and S. Lappin (2015). Probabilistic type theory and natural language semantics. Linguistic Issues in Language Technology 10(4). Cooper, R. and J. Ginzburg (2015). Type theory with records for natural language semantics. In C. Fox and S. Lappin (Eds.), Handbook of Contemporary Semantic Theory, 2nd edition. Oxford: Blackwell. Fernández, R. (2006). Non-Sentential Utterances in Dialogue: Classification, Resolution and Use. Ph. D. thesis, King’s College, London. Gardent, C. and M. Kohlhase (1997). Computing parallelism in discourse. IJCAI, 1016–1021. Ginzburg, J. (1994). An update semantics for dialogue. In H. Bunt (Ed.), Proceedings of the 1st International Workshop on Computational Semantics. Tilburg: ITK, Tilburg University. Ginzburg, J. (2012). The Interactive Stance: Meaning for Conversation. Oxford: Oxford University Press. Ginzburg, J., R. Fernández, and D. Schlangen (2014). Disfluencies as intra-utterance dialogue moves. Semantics and Pragmatics 7(9), 1–64. Ginzburg, J. and M. Purver (2012). Quantification, the reprise content hypothesis, and type theory. In L. Borin and S. Larsson (Eds.), From Quantification to Conversation: Festschrift for Robin Cooper on the occasion of his 65th Birthday, pp. 85–110. College Publications. This paper appeared in an online version of this collection in 2008. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 479 J. Ginzburg, R. Cooper, J. Hough, & D. Schlangen Incrementality and clarification/sluicing potential Hough, J. (2015). Modelling Incremental Self-Repair Processing in Dialogue. Ph. D. thesis, Queen Mary, University of London. Hough, J., C. Kennington, D. Schlangen, and J. Ginzburg (2015). Incremental semantics for dialogue processing: Requirements, and a comparison of two approaches. In Proceedings of the 11th International Conference on Computational Semantics (IWCS). Jurafsky, D. and J. H. Martin (2009). Speech and Language Processing (2nd ed.). New Jersey: Prentice Hall. Kempson, R., R. Cann, E. Gregoromichelaki, and S. Chatzikyriakidis (2016). Language as mechanisms for interaction. Theoretical Linguistics 42(3-4), 203–276. Kempson, R., W. Meyer-Viol, and D. Gabbay (2001). Dynamic Syntax: The Flow of Language Understanding. Oxford: Blackwell. Larsson, S. (2002). Issue based Dialogue Management. Ph. D. thesis, Gothenburg University. Levelt, W. J. (1983). Monitoring and self-repair in speech. Cognition 14(4), 41–104. Merchant, J. (2001). The Syntax of Silence. Oxford: Oxford University Press. Milward, D. (1991). Axiomatic Grammar, Non-Constituent Coordination and Incremental Interpretation. Ph. D. thesis, University of Cambridge. Milward, D. and R. Cooper (1994). Incremental interpretation: Applications, theory, and relationship to dynamic semantics. In Proceedings of the 15th conference on Computational linguistics-Volume 2, pp. 748–754. ACL. Peldszus, A. and D. Schlangen (2012). Incremental construction of robust but deep semantic representations for use in responsive dialogue systems. In Proceedings of the Coling Workshop on Advances in Discourse Analysis and its Computational Aspects. Pollard, C. and I. A. Sag (1994). Head Driven Phrase Structure Grammar. Chicago: University of Chicago Press and CSLI. Purver, M. (2006). Clarie: Handling clarification requests in a dialogue system. Research on Language & Computation 4(2), 259–288. Purver, M., A. Eshghi, and J. Hough (2011). Incremental semantic construction in a dialogue system. In J. Bos and S. Pulman (Eds.), Proceedings of the 9th IWCS, pp. 365–369. Purver, M. and J. Ginzburg (2004). Clarifying noun phrase semantics. Journal of Semantics 21(3), 283–339. Sato, Y. (2011). Local ambiguity, search strategies and parsing in dynamic syntax. The Dynamics of Lexical Interfaces, 205–233. Schegloff, E. (2007). Sequence Organization in Interaction. Cambridge: Cambridge University Press. Schlangen, D. and G. Skantze (2009). A general, abstract model of incremental dialogue processing. In Proceedings of the 12th Conference of the European Chapter of the Association for Computational Linguistics, pp. 710–718. Association for Computational Linguistics. Schlangen, D. and G. Skantze (2011). A general, abstract model of incremental dialogue processing. Dialogue & Discourse 2(1), 83–111. Schlesewsky, M. and I. Bornkessel (2004). On incremental interpretation: Degrees of meaning accessed during sentence comprehension. Lingua 114(9–10), 1213–1234. Tian, Y., T. Murayama, and J. Ginzburg (2016). Hesitation markers and self addressed questions. Journal of Psycholinguistic Research. Vallduvı́, E. (2015). Information structure. In M. Aloni and P. Dekker (Eds.), The Cambridge Handbook of Semantics. Cambridge: Cambridge University Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 480 Control, logophorocity, and harmonic modality in Gengbe desire reports1 Thomas GRANO — Indiana University Samson LOTVEN — Indiana University Abstract. With a special focus on jussive clauses, we present and account for a puzzling interaction between mood choice, embedding verb choice, and antecedent choice for logophoric subjects in attitude reports in Gengbe (a Niger-Congo language closely related to Ewe, spoken in southern Togo and Benin). The account draws on the property theory of control (Chierchia, 1984; Dowty, 1985), the property theory of imperatives (Portner, 2004), and the view that logophors abstract to yield derived properties (Pearson, 2015). Insofar as Gengbe jussive clauses are similar in distribution and function to Romance subjunctive clauses, a primary theoretical contribution of the paper is in showing that Portner’s property analysis of imperatives can be fruitfully extended to subjunctive clauses, thereby achieving a theoretical unification of sentence mood and verbal mood. We also a sketch a variant of the account couched in Kratzer’s (2013) decompositional approach to embedding, whereby jussive clauses in Gengbe desire reports instantiate harmonic modality. Keywords: attitude reports, control, jussives, logophors, modality, mood 1. Introduction The grammatical category MOOD is typically taken to subsume at least two subtypes. Following Portner’s (2009) terminology, SENTENCE MOOD has to do with clause type oppositions like those illustrated in (1), and VERBAL MOOD prototypically has to do with selected verbal forms such as the well studied Romance indicative/subjunctive opposition illustrated with the Spanish data in (2). (1) SENTENCE MOOD a. John left. b. Did John leave? c. Leave! (2) DECLARATIVE INTERROGATIVE IMPERATIVE VERBAL MOOD a. Juan cree que Pedro es feliz. ‘Juan believes that Pedro is.IND happy.’ b. Juan quiere que Pedro sea feliz. Lit.: ‘Juan wants that Pedro be.SBJV happy.’ INDICATIVE SUBJUNCTIVE The context for this paper is set by the theory of sentence mood advanced by Portner (2004) and further elaborated by Portner (2007); Zanuttini et al. (2012). Following the widely influential tradition of Stalnaker (1978), Portner takes the position that declarative clauses denote propo1 We would like to thank our linguistic consultant Gabriel Mawusi for his tireless efforts in producing and commenting on the Gengbe sentences reported here and Samuel Obeng for supporting this research. We would also like to thank audiences at Indiana University as well as at SuB 21 for their helpful feedback on the content of the paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 481 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports sitions and that making an assertion amounts to adding a proposition to the Common Ground, which can be modeled as a set of propositions. In a similar vein, Portner follows Hamblin (1973); Karttunen (1977) in analyzing interrogative clauses as denoting sets of propositions, and follows Ginzburg (1995); Roberts (1996) in modeling question speech acts as adding a set of propositions to the Question Set, which can be modeled as a set of sets of propositions. Finally, Portner’s main contribution is in building on a proposal due to Hausser (1980) and analyzing imperative clauses as denoting properties of individuals. For Portner, directive force involves adding a property to the addressee’s To-Do List, which is a set of properties that the participants in the conversation mutually assume that the addressee will try to make true of herself. In this context, the narrow goal of this paper is to argue that JUSSIVE clauses in Gengbe2 are also fruitfully analyzed as denoting properties of individuals, as evidenced primarily by how they interact with antecedent choice for logophoric pronouns in embedded contexts. We define ´ a marker which we jussive clauses in Gengbe as clauses that contain the preverbal marker nẼ, correspondingly call the jussive marker and gloss as JUSS.3 Some representative examples illustrating the distribution and interpretation of jussive clauses in Gengbe are given in the bracketed constituents in (3)–(6). (3) ´ [Kòfı́ n´Ẽ ãù nũ]. Kofi JUSS eat thing ‘Kofi should eat.’ / ‘I want Kofi to eat.’ (4) ´ ´Ẽ`Ẽ Àkú [bé n´Ẽ ãù nũ]. ´ Kòfı́ dóòũs Kofi encourage Aku COMP JUSS eat thing ‘Kofi encouraged Aku to eat.’ (5) ´ Ám´ã dZı́ [bé Àkú n´Ẽ ãù nũ]. Ama want COMP Aku JUSS eat thing ‘Ama wants Aku to eat.’ (6) ´ Ám´ã k´ããóédZı́ [bé Àkú n´Ẽ ãù nũ]. Ama believe COMP Aku JUSS eat thing ‘Ama believes that Aku should eat.’ Assuming for the sake of argument that we are right in analyzing jussive clauses as propertydenoting, what is the theoretical significance of this conclusion? If jussive clauses distributed and functioned just like imperative clauses, then our conclusion would simply count as further supporting evidence for Portner’s theory of clause types, but not a novel theoretical proposal. 2 Gengbe (also known as Gen or Mina) is a Niger-Congo language closely related to Ewe and spoken in southern Togo and Benin. According to Ethnologue, it has 278,900 speakers worldwide. All of the data reported here were collected at Indiana University by the authors in consultation with Gabriel Mawusi, a middle-aged male native Gengbe speaker from Batonou, Togo. 3 A full list of the abbreviations we use in glosses is as follows: ACC = accusative, COMP = complementizer, EXH = exhortative, INDIC = indicative, JUSS = jussive, IMP = imperative, LOG = logophor, PL = plural, POT = potential, PRM = promissive, SBJV = subjunctive, 1/3SG = 1st/3rd-person singular Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 482 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports But in fact, jussive clauses do not function like imperative clauses: of the examples in (3)–(6), the only one we are aware of that could be translated using an imperative clause is (4), and even this is possible only in languages like Korean that allow embedded imperatives (see e.g. Zanuttini et al. 2012). Instead, jussive clauses behave more like Romance subjunctive clauses, useable to express optative-like meaning in unembedded contexts (3), and found in complements to directive (4) and desiderative (5) predicates. The only non-subjunctive-like behavior is witnessed in (6), where the jussive marker is embedded under ‘believe’ and expresses a deontic semantics; in Romance, by contrast, mood choice under ‘believe’ is subject to inter- and intra-linguistic variation, but the subjunctive in this environment in those cases where it is possible is not associated with a deontic semantics. (See e.g. Giorgi and Pianesi 1997 for a survey of mood choice in Romance.) Given that the distribution and interpretation of Gengbe jussive clauses is not absolutely identical to the distribution and interpretation of Romance subjunctive clauses, we do not mean to suggest that they should have identical analyses. But we do take our property analysis of Gengbe jussive clauses to be highly suggestive of the more general utility of taking Portner’s type-theoretic approach to sentence mood and extending it to verbal mood as well, thereby contributing to a theoretical unification of the two major mood subtypes. Making this case constitutes a broader theoretical aim of this paper, and in the course of carrying out this broader aim, we will suggest below that Romance subjunctive clauses are also fruitfully analyzed as property-denoting. The organization of the rest of this paper is as follows. In section 2, we lay out our core data and puzzles. In section 3, we show that the data can be accounted for via three key proposals: (1) logophors are obligatorily bound by an attitude predicate (following Pearson 2015), (2) jussive clauses denote properties, and (3) Gengbe ‘want’ selects for a property whereas Gengbe ‘believe’ is flexible in being able to select for either a property or a proposition. In section 4, we unpack these proposals, grounding them in ideas found in previous literature and advancing independent Gengbe-internal and cross-linguistic support for them. In section 5 we compare two analytical strategies for implementing the property analysis of jussive clauses, one whereby the jussive marker is an individual abstractor à la Zanuttini et al. (2012) and one whereby the jussive marker is an individual-relative priority modal that harmonizes with the embedding predicate in embedded contexts à la Kratzer (2013). Finally, section 6 concludes. 2. Core data and puzzles The first observation we make is that Gengbe has a logophoric pronoun jè which at first glance seems to behave like an ordinary logophor in the sense of Clements (1975): it must be embedded under a speech or attitude predicate, and it is obligatorily co-referential with the subject of that predicate. In (7), multiple embedding gives rise to the expected ambiguity whereby jè can be co-referential either with Ámã´ (the subject of the immediately higher clause) or with Kòfı́ (the matrix subject). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 483 T. Grano & S. Lotven (7) Control, logophoricity, and harmonic modality in Gengbe desire reports ´ Kòfı́1 bé Ám´ã2 k´ããóédZı́ [bé jè1/2/∗3 ãù nũ]. eat thing Kofi say Ama believe COMP LOG ‘Kofi said Ama believes that he/she (= Kofi/Ama) ate.’ With this in mind, the core puzzle we want to solve is the observation that when jè is embedded under dZı́ ‘want’, the availability of different antecedents interacts with mood choice. As seen in (8), when dZı́ embeds the mood marker lá (which we analyze as a potential marker, following Essegbey’s 2008 treatment of Ewe a), the logophor obligatorily co-refers with the subject of the immediately higher clause (the hallmark of obligatory control in the sense of Landau 2000), but ´ the logophor is obviative with respect to as seen in (9), when dZı́ embeds the jussive marker nẼ, the subject of the immediately higher clause and instead obligatorily co-refers with the subject of a higher embedding clause.4 (8) (9) ´ (Àkú1 bé Kòfı́2 bé) Ám´ã3 dZı́ [bé jè(∗1/∗2/)3/∗4 lá ãù nũ]. POT eat thing Aku say Kofi say Ama want COMP LOG ‘(Aku said that Kofi said that) Ama wants to eat.’ ´ (Àkú1 bé) Kòfı́2 bé Ám´ã3 dZı́ [bé jè(1/)2/∗3/∗4 n´Ẽ ãù nũ]. Aku say Kofi say Ama want COMP LOG JUSS eat thing ‘(Aku said that) Kofi said that Ama wants him ( = (Aku/)Kofi) to eat.’ (control) (obviation) The pattern in (8)–(9) is not unique to dZı́ ‘want’ but is found also with other attitude predicates expressing desiderative, intentional or promissive meaning such as wÒsúsú ‘intend’, ` dZèàgbàgbá ‘try’, lÕ` ‘agree’, and fjẼdZÒgbè ‘pledge’. While we take the mood–coreference interaction in (8)–(9) to be the core explanandum of this paper, there are two subsidiary puzzles that we take to be important clues in understanding (8)– (9), and we want to make sure that our analysis accounts for these subsidiary puzzles as well. The first subsidiary puzzle has to do with what happens when the complement to dZı́ ‘want’ has a non-logophoric, full-NP subject. In this situation, what we see is that the mood marker lá is simply unacceptable (10) and nẼ´ has to be used instead (11). (10) ´ *Kòfı́ bé Ám´ã dZı́ [bé Àkú lá ãù nũ]. Kofi say Ama want COMP Aku POT eat thing Intended: ‘Kofi said Ama wants Aku to eat.’ 4 Further strengthening the analytical connection to control and obviation phenomena, it bears noting that logophoric objects behave differently, admitting free choice of antecedent in the context of jussive marking (and potential marking would be ungrammatical here because of the full-NP subject; cf. (10)): (i) Kòfı́1 bé Ám´ã2 dZı́ [bé Àkú3 n´Ẽ kpÓ jè1/2/∗3 ]. Kofi say Ama want COMP Ama JUSS see LOG ‘Kofi said Ama wants Aku to see him/her (= Kofi/Ama).’ This subject/object asymmetry is likely connected to the fact that control is a subject-oriented phenomenon: generally only subject positions can be controlled. Unfortunately, though, this subject/object asymmetry is not something that we will be able to account for in this paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 484 T. Grano & S. Lotven (11) Control, logophoricity, and harmonic modality in Gengbe desire reports ´ Kòfı́ bé Ám´ã dZı́ [bé Àkú n´Ẽ ãù nũ]. Kofi say Ama want COMP Aku JUSS eat thing ‘Kofi said Ama wants Aku to eat.’ The second subsidiary puzzle has to do with what happens when dZı́ ‘want’ is replaced with ´ ´ kããóédZı́ ‘believe’. As we already saw in (7) above, kããóédZı́ ‘believe’ can combine with complements that are not overtly marked for mood. But overt mood marking is also possible. Considering first full-NP subjects in the complement clause, we see that both lá and nẼ´ are acceptable and give rise to a difference in meaning suggested by the supplied free translations: lá gives rise to a future-oriented meaning (12) whereas nẼ´ gives rise to a deontic meaning (13). (12) ´ Kòfı́ bé Ám´ã k´ããóédZı́ [bé Àkú lá ãù nũ]. Kofi say Ama believe COMP Aku POT eat thing ‘Kofi said Ama believes that Aku will eat.’ (13) ´ Kòfı́ bé Ám´ã k´ããóédZı́ [bé Àkú n´Ẽ ãù nũ]. Kofi say Ama believe COMP Aku JUSS eat thing ‘Kofi said Ama believes that Aku should eat.’ Finally, when the full-NPs in (12)–(13) are replaced by the logophor, yet another interesting pattern emerges: when the mood marker lá is used, the logophor can take either of the higher subjects as its antecedent, just as in (7) where there is no overt mood marking. This is illustrated in (14). But when the mood marker nẼ´ is used, we see the return of the dZı́ ‘want’-like behavior witnessed in (9) above: only the more distant subject is available as an antecedent. This is illustrated in (15). (14) ´ Kòfı́1 bé Ám´ã2 k´ããóédZı́ [bé jè1/2 lá ãù nũ]. Kofi say Ama believe COMP LOG POT eat thing ‘Kofi said Ama believes that he/she (= Kofi/Ama) will eat.’ (15) ´ Kòfı́1 bé Ám´ã2 k´ããóédZı́ [bé jè1/∗2 n´Ẽ ãù nũ]. Kofi say Ama believe COMP LOG JUSS eat thing ‘Kofi said Ama believes that he (= Kofi) should eat.’ ´ The behavior seen in (12)–(15) is not unique to kããóédZı́ ‘believe’; it is also borne out for other predicates including ñã´ ‘know’, gblÕ` ‘say’, and kúùdR`ı̃´ı̃ ‘dream’. 3. The proposed solution in three stipulations The goal of this section is to show that all of the puzzles associated with the data from the previous section can be accounted for with just three rather mundane stipulations. (We call them stipulations for now so as to focus on how they account for the data rather than on how they might be independently justified; the task of independently justifying the stipulations is taken up in section 4.) We will first describe the three stipulations, and then show how they make sense of the data. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 485 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports The perspective from which we approach the puzzles begins with the recognition that these puzzles reduce to three kinds of asymmetries: logophoric subjects pattern unlike full-NP subjects, the jussive marker patterns unlike the potential marker, and ‘want’ patterns unlike ‘believe’. One way or another, then, the grammar of Gengbe will need to draw a distinction in each of these three areas. Each of the three stipulations we advance targets one of these asymmetries, putting the bulk of the explanatory burden on the semantic type system. Portner (2004) establishes the utility of exploiting the type system in understanding mood contrasts, which we take to provide a kind of a priori justification for going down this path. The first stipulation identifies a contrast between logophors and ordinary full-NPs or pronouns: namely, what is special about a logophor is that it has to be bound by an attitude predicate (following Pearson 2015, who builds on Heim 2002; von Stechow 2002, 2003). So, if a structure contains a logophoric pronoun, that pronoun can be bound by an attitude predicate in the immediately higher clause, as in (16a), or by an attitude predicate in some higher clause, as in (16b), but if it is not bound by any attitude predicate at all, as in (16c), then the structure is ungrammatical. (16) Stipulation #1: A logophor has to be bound by an attitude predicate: a. Kofi say [ Ama believe [ λ x. [ LOGx eat ] ] ] OK b. Kofi say [ λ x. [ Ama believe [ LOGx eat ] ] ] OK c. Kofi say [ Ama believe [ LOGx eat ] ] ungrammatical The second stipulation identifies a contrast between jussive and potential marking: in particular, the Gengbe jussive marker nẼ´ contributes an individual argument whereas the potential marker lá does not. Assuming for concreteness that a Gengbe clause with no mood marking has a type hsti denotation, this means that a jussive-marked clause will be type he, sti, as in (17a). By contrast, the potential marker has no interesting type-theoretic effect, as in (17b). (17) Stipulation #2: nẼ´ ‘JUSS’ contributes an individual argument but lá ‘POT’ does not: a. [Kofi eat]hsti → [λ x . Kofi JUSS eat]he,sti b. [Kofi eat]hsti → [Kofi POT eat]hsti ´ Finally, the third stipulation identifies a contrast between between dZı́ ‘want’ and kããóédZı́ ‘believe’: dZı́ ‘want’ is type-theoretically rigid in only being able to combine with a property´ denoting complement, whereas kããóédZı́ ‘believe’ is type-theoretically flexible in being able to combine either with a property-denoting complement or a proposition-denoting complement. This is schematized in (18). (18) ´ Stipulation #3: dZı́ ‘want’ can only combine with a property whereas kããóédZı́ ‘believe’ can combine with either a proposition or a property: a. [ dZı́]] = λ Phe,sti λ xλ w.∀w0 ∈ BESTdesire (DOX(x,w)): P(x)(w0 ) hhe, sti, he, stii 0 0 hst, he, stii b. [ k´ããóédZı́]] = λ phsti λ xλ w.∀w ∈ DOX(x,w): p(w ) 0 0 b . [ k´ããóédZı́ ] = λ Phe,sti λ xλ w.[[k´ããóédZı́]] (P(x))(x)(w) hhe, sti, he, stii = λ Phe,sti λ xλ w.∀w0 ∈ DOX(x,w): P(x)(w0 ) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 486 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports The fine-grained semantics of desire predicates will not be relevant for anything that follows but we assume for concreteness as in (18a) that ‘want’ involves a bouletic (BESTdesire -based) ordering source over the attitude holder’s doxastic alternatives, essentially following von Fintel (1999) (though cf. also Heim 1992; Giannakidou 1999 and many others for variations on this theme). Von Fintel’s semantics for ‘want’ is modified here so that the first argument of ‘want’ is a property whose unsaturated individual argument gets identified with the attitude holder (see Chierchia 1984, 1990; Dowty 1985, and more recently Stephenson 2010; Pearson 2016 for more sophisticated variants of this basic idea). As for ‘believe’, we adopt for concreteness the standard Hintikkan view that it effects universal quantification over the attitude holder’s doxastic alternatives; crucially for us, it comes in both a hst, he, stii variant, as in (18b), as well as a hhe, sti, he, stii variant, as in (18b0 ), the latter of which can be derived from the former as a type shift. Just like we did for ‘want’ in (18a), the type-shifted variant of ‘believe’ in (18b0 ) is set up in such a way that the unsaturated position associated with the property argument gets identified with the attitude holder. With these three stipulations in place, all of the puzzling asymmetries laid out in the previous section immediately follow. Consider first what we called the core puzzle, i.e., the interaction seen in desire reports between mood marker choice and antecedent choice for logophors, repeated schematically in (19)–(20). (19) Kofi1 say [Ama2 want [LOG∗1/2 POT eat] ] (20) Kofi1 say [Ama2 want [LOG1/∗2 JUSS eat] ] want+LOG+POT → CTRL want+LOG+JUSS → OBV. The unavailability of a long-distance antecedent construal for the logophor in (19) follows from the fact that only the local antecedent construal results in ‘want’ combining with a type he, sti complement, which is the only kind of complement it accepts. As schematized in (21), local binding of the logophor by ‘want’ renders the relevant complement a type he, sti expression (21a), whereas long-distance binding of the logophor by ‘say’ preserves the type hsti status of the complement to ‘want’ and therefore results in type-mismatch-induced uninterpretability (21b). (21) want+LOG+POT induces control: a. Kofi say Ama [wanthhe,sti,he,stii [λ x. LOGx POT eat]he,sti ] b. Kofi say [λ x.Ama wanthhe,sti,he,stii [LOGx POT eat]hsti ] ← OK ←* In (20), by contrast, when a jussive-marked clause is used, the opposite holds. Local binding of the logophor by ‘want’ conspires with individual-argument-introducing JUSS to yield a type he, he, stii complement for ‘want’, and this yields a type mismatch. But long-distance binding of the logophor by ‘say’ ensures that the complement to ‘want’ is type he, sti (achieved via the JUSS -induced individual argument added onto an underlyingly type hsti clause), so the structure is interpretable. (We assume here and in what follows that ‘say’ is like ‘believe’ in being able to accept both hsti and he, sti complements.) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 487 T. Grano & S. Lotven (22) Control, logophoricity, and harmonic modality in Gengbe desire reports want+LOG+JUSS induces obviation: a. Kofi say Ama [wanthhe,sti,he,stii [λ xλ y. LOGx JUSS eat]he,he,stii ] b. Kofi say [λ x.Ama wanthhe,sti,he,stii [λ y. LOGx JUSS eat]he,sti ] ←* ← OK The two subsidiary puzzles also fall into place. The first of the two subsidiary puzzles was that when ‘want’ embeds a full-NP subject, the embedded clause cannot be potential-marked and instead must be jussive-marked, as repeated schematically in (23)–(24). (23) (24) *Kofi say [Ama want [Aku POT eat] ] want+full-NP+POT → * Kofi say [Ama want [Aku JUSS eat] ] want+full-NP+JUSS → OK The facts in (23)–(24) now similarly follow from type-theoretic principles, as schematized in (25). With no logophoric binding at stake, the potential marker results in a type hsti denotation, which ‘want’ cannot handle, whereas the jussive marker yields a type he, sti complement, appropriate for ‘want’. (25) a. Kofi say [Ama wanthhe,sti,he,stii [Aku POT eat]hsti ] b. Kofi say [Ama wanthhe,sti,he,stii [λ x.Aku JUSS eat]he,sti ] ←* ← OK Finally, the second of the two subsidiary puzzles was the observation that when ‘want’ is replaced by ‘believe’, all of the restrictions go away, except that a logophor in a jussive-marked clause still resists local binding just like it does for ‘want’. This is repeated schematically in (26)–(29). (26) Kofi say [Ama believe [Aku POT eat] ] believe+full-NP+POT → OK (27) Kofi say [Ama believe [Aku JUSS eat] ] believe+full-NP+JUSS → OK (28) Kofi1 say [Ama2 believe [LOG1/2 (29) Kofi1 say [Ama2 believe [LOG1/∗2 POT eat] ] JUSS eat] ] believe+LOG+POT → AMBIG . believe+LOG+JUSS → OBV. Turning first to (26)–(27), type-theoretic flexibility for ‘believe’ ensures that both kinds of mood markers will be acceptable when no logophors are present. As schematized in (30), potentialmarking yields a type hsti complement and jussive-marking yields a type he, sti complement. (30) Type flexibility for ‘believe’ renders believe+full-NP+POT / believe+full-NP+JUSS both OK: a. Kofi say [Ama believehhsti,he,stii [Aku POT eat]hsti ] ← OK b. Kofi say [Ama believehhe,sti,he,stii [λ x. Aku JUSS eat]he,sti ] ← OK Turning next to (28), here again type-theoretic flexibility for ‘believe’ ensures the availability of both binding options: as schematized in (31), long-distance binding yields a type hsti complement and local binding yields a type he, sti complement. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 488 T. Grano & S. Lotven (31) Control, logophoricity, and harmonic modality in Gengbe desire reports Type flexibility also enables both binding options for believe+LOG+POT: a. Kofi say [λ x. Ama believehhsti,he,stii [LOGx POT eat]hsti ] b. Kofi say [Ama believehhe,sti,he,stii [λ x. LOGx POT eat]he,sti ] ← OK ← OK Finally, we turn to (29): why does a jussive-marked clause force long-distance binding of the logophor? The answer is that local binding conspires with jussive marking to yield a type he, he, stii complement, which ‘believe’ (just like ‘want’) cannot tolerate. This is schematized in (32). (32) But even with type flexibility, believe+LOG+JUSS induces obviation: a. Kofi say [Ama believehhsti,he,stii/hhe,sti,he,stii [λ xλ y. LOGx JUSS eat]he,he,stii ] b. Kofi say [λ x. Ama believehhe,sti,he,stii [λ y. LOGx JUSS eat]he,sti ] ←* ← OK In short, we have now seen that all of the data in section 2 follow from the three stipulations in (16)–(18) about the expressions involved in the relevant structures. The task now before us is to independently justify these stipulations. 4. Revisiting the three stipulations 4.1. A logophor has to be bound by an attitude predicate The first of our three stipulations, namely that a logophor has to be bound by an attitude, is not new to us and so we will not dwell on it extensively here. Pearson (2015) defends this view, attributing it to earlier work by Heim (2002); von Stechow (2002, 2003). It is a rather straightforward way of deriving the generalization that logophors can appear only in attitudinal contexts. Insofar as these authors were concerned with facts quite different from those at issue here, we take their work as providing independent justification for this proposal. We are not committed to any particular way of encoding this proposal into the grammar, but for concreteness, we can adopt Pearson’s (2015) approach, following Heim (2002); von Stechow (2002, 2003), in hypothesizing that logophors enter the derivation with an uninterpretable feature [log]. This feature must be checked via binding by an operator that also bears the [log] feature. Attitude predicates bear the [log] feature, and an attitude predicate can pass this feature to an individual abstractor in the left periphery of its CP complement. Returning to our three crucial cases in (33), (33a–b) are both grammatical because the [log] feature on the logophor is checked by its binder, whereas (33c) crashes because the [log] feature on the logophor is not checked. (33) a. Kofi say [ Ama believe[log] [ λ x[log] . [ LOGx[log] eat ] ] ] b. Kofi say[log] [ λ x[log] . [ Ama believe [ LOGx[log] eat ] ] ] c. Kofi say [ Ama believe [ LOGx[log] eat ] ] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde OK OK ungrammatical 489 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports 4.2. NẼ´ ‘JUSS’ contributes an individual argument whereas lá ‘POT’ does not We turn our attention now to the proposal that the jussive marker nẼ´ contributes an individual argument whereas the potential marker lá ‘POT’ does not. The first thing to note is that in unembedded contexts, lá is typically used to express future possibility (34) (cf. Essegbey 2008), ´ as already seen in the introduction, is used to indicate a speaker-oriented desire or whereas nẼ, priority (35). (34) ´ Kòfı́ lá ãù nũ. Kofi POT eat thing ‘Kofi will/might eat.’ (35) ´ Kòfı́ n´Ẽ ãù nũ. Kofi JUSS eat thing ‘Kofi should eat.’ / ‘I want Kofi to eat.’ We also note that Ameka (2008), investigating the cognate Ewe jussive particle né, provides some examples suggesting that this marker sometimes has an optative flavor, and we have confirmed that the same is true for Gengbe, as in (36). (36) gbÒgbÒ v´Õ-wó n´Ẽ dògó. spirit bad-PL JUSS exit ‘Let evil spirits come out.’ (Gengbe version of Ameka’s 2008:152 Ewe example) We take this priority-oriented, optative-like status to be highly suggestive that nẼ´ is in the same family of morphemes identified by Zanuttini et al. (2012) as jussives, which for them include imperatives (37), promissives (38), exhortatives (39), and (possibly) optatives (40) — though their focus is on the former three and they do not commit to a particular analysis of optatives. The data in (37)–(40) are all taken from their paper. (37) (38) (39) (40) Cemsim-ul sa-la. lunch-ACC buy-IMP ‘Buy lunch!’ (Korean imperative, Zanuttini et al. 2012:1234) Cemsim-ul sa-ma. lunch-ACC buy-PRM ‘I will buy lunch.’ (Korean promissive, Zanuttini et al. 2012:1234) Cemsim-ul sa-ca lunch-ACC buy-EXH ‘Let’s buy lunch.’ (Korean exhortative, Zanuttini et al. 2012:1234) kh a:y eat-IMP.3SG ‘Let him eat.’ (Bhojpuri optative, Zanuttini et al. 2012:1252) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 490 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports Zanuttini et al. (2012) propose that jussives are individual abstractors that, when standing in a sufficiently local syntactic configuration with the subject, bind that subject and impose a person restriction on it, as schematized in (41). What distinguishes different kinds of jussives is the value of the person restriction: second-person for imperatives, first-person (exclusive) for promissives, and first-person (inclusive) for exhortatives. The person value also determines whose To-Do List the property gets added to when the utterance is successful in its illocutionary aim: the addressee’s for imperatives, the speaker’s for promissives, and both the speaker’s and the addressee’s for exhortatives. (41) For any phrase XP, [ JUSS[person: v]k XP]] g,c = [λ x : x = [ [person: v]k ] g,c . [ XP]] g[k→x],c ] (Zanuttini et al. 2012:1265) In a footnote (p. 1252, note 30), Zanuttini et al. mention a suggestion by Patrick Grosz for fitting optatives into this setup, namely by ‘relaxing the restriction that it should be possible for the addressee to bring about the situation described’, so that the property associated with the optative is added to the addressee’s To-Do List and ‘the addressee is committed to the judgment that a world in which [the content associated with the optative holds] is preferable to one in which [it] doesn’t, even though we know that the addressee cannot bring the world to this preferable state’. While conceivable, this suggestion seems to us to fit awkwardly with the fact that on this view, imperatives, promissives and exhortatives all receive an analysis whereby the person restriction they impose matches the participant associated with the targeted To-Do List, whereas optatives target the addressee’s To-Do List despite generally being compatible with subjects of any person value. In light of this, what we would like to suggest as an alternative is that optatives induce individual abstraction without any person restriction. The status of the utterance as a property has the discourse-theoretic effect of endowing it with a ‘world-to-word’ direction of fit (in the sense of Searle 1969), but the lack of person restriction has the consequence that it is not directed at any particular individual’s To-Do List. This has the pragmatic effect of expressing a wish without imposing on anyone an obligation for its fulfillment. Applied to the Gengbe jussive marker ´ this analysis amounts to (42).5 (Cf. Sæbø 2009 for a strikingly similar approach to English nẼ, have, though we will resist the urge to speculate here on whether an analytical connection between jussives/optatives and have is a good thing or not.) (42) [ n´Ẽ]] = λ pλ x.p In short, (42) helps make sense of otherwise puzzling asymmetries in how logophors behave in Gengbe attitude reports, and the suggestion made here now is that (42) is independently motivated by the broader distribution and function of the jussive marker in Gengbe paired with Zanuttini et al.’s (2012) property-theoretic approach to jussives. Despite these virtues, one might be reluctant to assign such a near-vacuous denotation to the jussive marker. In section 5 5 Actually, it is an oversimplification to say that nẼ´ comes with no person restriction: it disallows first-person subjects, both in matrix and in embedded contexts. The significance of this fact is unfortunately something that will have to be left for future research. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 491 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports below, we entertain the alternative view that the jussive marker, in addition to contributing an individual argument, also has a modal semantics. First, though, we need to unpack our third proposal concerning the type-theoretic status of ‘want’ and ‘believe’. ´ 4.3. DZı́ ‘want’ can only combine with a property whereas kããóédZı́ ‘believe’ can combine with either a proposition or a property The third and final proposal that we need to substantiate is the idea that dZı́ ‘want’ can only ´ combine with a property whereas kããóédZı́ ‘believe’ is type-theoretically flexible in being able to combine either with a proposition or with a property. This proposal goes against the recent grain in the formal semantics literature of treating all clauses in a type-theoretically uniform way, whether that be as propositions (as explored by Stephenson 2010) or as properties (as explored by Pearson 2013), regardless of whether the clause is embedded or not, controlled or not, or interpreted de se or not. But it is not a new idea either: Dowty (1985) proposes that non-control complements are proposition-denoting whereas control complements are propertydenoting, which, as Dowty discusses, has as a consequence that some embedding verbs (those that disallow control) are type hst, . . .i, others (those that only accept control complements) are type hhe, sti, . . .i, and still others (those that admit both control and non-control complements) are hst, . . .i/hhe, sti, . . .i-flexible. Here we would like to entertain a variant of Dowty’s (1985) proposal whereby what determines whether the complement is proposition- or property-denoting is not whether it is controlled but rather what kind of mood marking it has. By way of independent motivation, consider the observation that English want admits nonfinite complements but not finite complements (43) whereas believe is flexible in admitting both kinds of complements (44). (43) a. John wants [Bill to be happy]. b. *John wants [that Bill is happy]. (44) a. John believes [Bill to be happy]. b. John believes [that Bill is happy]. This situation bears a striking resemblance to that of Romance: ‘want’ is rigid in only accepting subjunctive complements to the exclusion of indicative complements, as seen in the Spanish and Italian examples in (45) and (46), respectively, whereas ‘believe’ gives rise to variability: it ordinarily takes an indicative complement in Spanish (47) and an subjunctive complement in Italian (48). (45) (46) Juan quiere [que Pedro {sea/*es} feliz]. ‘Juan wants that Pedro be.SBJV/INDIC happy.’ Gianni vuole [che Pietro {sia/*è} felice]. ‘Gianni wants that Pietro be.SBJV/INDIC happy.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde Spanish Italian 492 T. Grano & S. Lotven (47) (48) Control, logophoricity, and harmonic modality in Gengbe desire reports Juan cree [que Pedro es feliz]. ‘Juan believes that Pedro is.INDIC happy.’ Gianni crede [che Pietro sia felice]. ‘Gianni believes that Pietro be.SBJV happy.’ Spanish Italian We can encode these subcategorization facts via a cross-linguistic extension of the same typetheoretic machinery that supports our analysis of the Gengbe facts. In particular, suppose that cross-linguistically, ‘want’ rigidly selects for a property (49) whereas ‘believe’ flexibly selects for either a proposition or a property (50). (49) [ want]] = λ Phe,sti λ xλ w.∀w0 ∈ BESTdesire (DOX(x,w)): P(x)(w0 ) hhe, sti, he, stii (50) a. [ believe]] = λ phsti λ xλ w.∀w0 ∈ DOX(x,w): p(w0 ) b. [ believe0 ] = λ Phe,sti λ xλ w.∀w0 ∈ DOX(x,w): P(x)(w0 ) hst, he, stii hhe, sti, he, stii Then the subcategorization facts follow, as long as Romance subjunctive clauses and English nonfinite clauses (regardless of whether they are controlled or not) are property-denoting just like Gengbe jussive-marked clauses (51), whereas finite indicative clauses are propositiondenoting (52). (51) (52) Infinitives/subjunctive clauses a. [ PRO to be happy]] = [λ xλ w . x is happy in w] b. [ Bill to be happy]] = [λ xλ w . Bill is happy in w] c. [ Pedro sea feliz]] = [λ xλ w . Pedro is happy in w] Finite indicative clauses a. [ Bill is happy]] = [λ w . Bill is happy in w] b. [ Pedro es feliz]] = [λ w . Pedro is happy in w] he, sti he, sti he, sti hsti hsti To be sure, there is a rich set of empirical facts and a rich literature surrounding the question of what grammatical factors conspire to determine what kind of finiteness or mood marking a clause will have in a given environment. (See e.g. Portner and Rubinstein 2013 for a recent assessment.) Our type-theoretic proposal is intended not as a replacement for existing proposals about what semantic properties characterize indicative- vs. subjunctive-selecting verbs but rather as an implementation of any such proposal. It does not say anything interesting about why verbs have the type signature they do and hence ultimately needs to be embedded into a theory that does. 5. Harmonic modality? It is crucial to our account of the data that the jussive marker nẼ´ contributes an individual argument, and in section 4.2 above, we proposed that this is all the jussive marker does. But our analysis is also consistent with the view that nẼ´ does more than just this. And given that this marker occurs in contexts associated with a priority semantics, we would like to entertain the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 493 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports possibility that nẼ´ is a priority modal in the sense of Portner (2007, 2009). The individual argument it contributes could then be understood naturally as an argument that helps determine the set of worlds that the modal quantifies over, as in (53) (the basic shape of (53), discounting the individual argument, is inspired by the approach to modals found in Kratzer 2013). According to (53), nẼ´ combines with a situation description p and returns a relation between individuals and situations. This relation is true of an individual x and a situation s iff all those worlds compatible with x’s priorities in s are worlds that contain a situation verified by p. (Actually, this is a simplification: technically, we need a circumstantial modal base and a priority-oriented ordering source: see Portner 2009:135. We suppress this detail here for ease of presentation.) (53) [ n´Ẽ]] = λ phsti λ xλ s.∀w0 ∈ PRIORITY(x,s): ∃s0 [s0 ≤ w0 ∧ p(s0 )] where PRIORITY(x,s) = {∀w | w is compatible with x’s priorities in s} This approach then has consequences for the compositional semantics of desire reports like (54). (54) ´ Ám´ã dZı́ [bé Àkú n´Ẽ ãù nũ]. Ama want COMP Aku JUSS eat thing ‘Ama wants Aku to eat.’ With modal meaning built into the jussive marker, we need to correspondingly shift the modality out of the desire predicate. In particular, we can adopt the semantics for dZı́ ‘want’ in (55), thereby arriving at a meaning like (56) for the desire report in (54). (55) [ dZı́]] = λ Phe,sti λ xλ s.want(s) ∧ EXPERIENCER(s) = x ∧ P(x)(s) (56) [ Ama want COMP Aku JUSS eat thing]] = ∃s [want(s) ∧ EXPERIENCER(s)=Ama ∧ ∀w0 ∈PRIORITY(Ama,s): ∃s0 [s0 ≤ w0 ∧ Aku eats in s0 ]] ‘There is a situation s, s is a wanting whose experiencer is Ama, and all those worlds compatible with Ama’s priorities in s are worlds in which there is a situation in which Aku eats.’ This approach reflects a Kratzer 2013-style decompositional ‘neo-Davidsonian’ approach to clausal embedding (cf. also Moulton 2009; Bogal-Allbritten 2016; Grano 2016).6 On this analysis, dZı́ . . . nẼ´ (‘want . . . JUSS’) instantiates the same kind of harmonic modality that Kratzer (2013) points to in motivating her approach to clausal embedding, such as the examples in (57)–(58). (57) It seems to us entirely desirable that there ought to be a constitutional amendment. (Kratzer 2013:slide 17) 6 One notable way in which we depart from these previous approaches, though, is that the previous approaches treat the attitude predicate as composing with its clausal complement via Predicate Modification (or Restrict), whereas we treat it as composing with its complement via Functional Application. This is needed on our account in order for the attitude predicate to be able to regulate the type of its complement (‘want’ needing a property but ‘believe’ being compatible with either a property or a proposition). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 494 T. Grano & S. Lotven (58) Control, logophoricity, and harmonic modality in Gengbe desire reports The urgency of the situation requires that the dig must continue regardless of the weather and comfort. (Kratzer 2013:slide 18) In examples like (57)–(58), the bolded modals in the embedded clause seem to be redundant with the bolded embedding predicates. On Kratzer’s decompositional approach to embedding, this redundancy is readily made sense of, because the modality is located solely on the modals and the embedding predicates merely serve to help fix the modal base(/ordering source) by supplying a situation variable. A potential source of cross-linguistic support for the harmonic modality approach to (54) comes from the Yiddish and Yiddish English want. . . should locution, exemplified in (59)–(60). (59) (60) Ikh vil er zol geyn. 1SG want 3SG should go ‘I want him to go.’ (Yiddish, Sadock 2012) You want I should help you? (see discussion at http://languagelog.ldc.upenn.edu/nll/?p=11847) Here we see a striking parallel between Yiddish/Yiddish English and Gengbe in the sense that in both languages, ‘want’ routinely embeds a marker that, in matrix contexts, can be used to express priority semantics. If Yiddish (and Yiddish English) ‘should’ and Gengbe nẼ´ are to have the same analysis, this means either that ‘should’ does not have a modal semantics but is rather merely an individual abstractor, or that Gengbe nẼ´ does have a modal semantics, along the lines suggested here. To recap, there are two ways of cashing out the proposal that nẼ´ has the type-theoretic consequence of introducing an individual argument. On this first approach we entertained, it is a pure individual abstractor with no other content. On the second approach we entertained, it is a priority modal that introduces an individual argument which in turn helps determine the worlds that the modal quantifies over. Notably, the individual argument plays very different roles depending on which approach is taken: on the first approach, it corresponds to the hypothetical individual on whose To-Do List the relevant property is placed and who consequently bears an obligation to make the property true of herself. On the second approach, by contrast, it corresponds to the individual whose desires or goals make the content associated with the property a priority. It will be beyond the scope of this paper to adjudicate between these two approaches, but a couple of issues at stake can be mentioned. One potential advantage of the modal approach is that it more readily makes sense of the fact that nẼ´ can be embedded into a belief report in such a way that it has a transparent priority-oriented semantics, as in (61). On the individual abstractor approach, it is unclear why the mere status of the embedded clause as a property would give it a priority flavor. (It also bears noting that in examples like this, the modal approach commits us to positing an appropriate modal in the left-periphery of the embedded clause, just as Kratzer 2013 does for belief reports that do not contain an overt modal.) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 495 T. Grano & S. Lotven (61) Control, logophoricity, and harmonic modality in Gengbe desire reports ´ Ám´ã k´ããóédZı́ [bé Àkú n´Ẽ ãù nũ]. Ama believe COMP Aku JUSS eat thing ‘Ama believes that Aku should eat.’ The two approaches also have different consequences for the illocutionary force of examples like (62). On the individual abstractor approach, (62) has a special illocutionary force in virtue of being property-denoting and the priority flavor is a consequence of this. But on the modal approach, (62) is just an assertion (proposition-denoting, the individual argument of the modal being, by hypothesis, speaker-bound in matrix contexts) and its priority flavor is a consequence of its modality. More research will be needed to determine what kind of illocutionary force (62) in fact has. (62) ´ Kòfı́ n´Ẽ ãù nũ. Kofi JUSS eat thing ‘Kofi should eat.’ / ‘I want Kofi to eat.’ 6. Conclusions The central narrow conclusion of this paper is that a property analysis of Gengbe jussive clauses helps make sense of an otherwise puzzling interaction between embedding verb choice, mood choice, and antecedent choice for logophors. Of broader significance is the prospect of extending this property analysis to subjunctive and infinitival clauses on a cross-linguistic scale, thereby enabling a theoretical unification across superficially disparate but underlyingly related mood categories. In this connection, an important question that still needs to be addressed is: if we are correct in extending the property analysis of jussive clauses to subjunctive clauses and infinitives cross-linguistically, why do the specific puzzles we see in Gengbe not show up in more familiarly studied languages? We think that it is because Gengbe has two properties that are not typical among better studied languages. First, it has logophoric pronouns, which are crucial to the central puzzle. Second it has ‘full’ (in the sense of being ‘finite’ or ‘nontruncated’) clauses as complements to verbs like ‘want’; if this were not the case, we might not expect to see overt logophors or overt mood markers in these complements and hence the puzzles would not arise. So the suggestion is that it is only when these two properties co-occur in a language that they conspire with the possibly universal type-theoretic principles entertained in this paper to give rise to the set of puzzling facts that we saw in section 2. There is one final theoretical point to be made: we think that it is also in light of the two aforementioned properties of Gengbe that we see in Gengbe the recruitment of logophoricity to achieve syntactic control. In (63), repeated from (8) above, the subject of the bracketed clause is obligatorily identified with an argument of the immediately higher clause, which is precisely the hallmark of obligatory control in the sense of Landau (2000). (63) ´ (Àkú1 bé Kòfı́2 bé) Ám´ã3 dZı́ [bé jè(∗1/∗2/)3/∗4 lá ãù nũ]. Aku say Kofi say Ama want COMP LOG POT eat thing ‘(Aku said that Kofi said that) Ama wants to eat.’ This is significant for two reasons. First, it possibly constitutes evidence against Landau’s Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 496 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports (2015:38) claim, following Culy (1994), that logophors never occur in obligatory control complements. If ‘obligatory control complement’ is to be defined in a non-circular way, it seems to us difficult to escape the conclusion that (63) instantiates a logophor in an obligatory control complement. Second, speaking more broadly, our analysis of (63) is consonant with the recent trend in control theory of not viewing controlled subjects as instantiations of a dedicated inaudible pronoun PRO but instead as a species of expression that enjoys wider grammatical currency such as minimal pronouns (Kratzer, 2009; Landau, 2015) or DP copies left behind by movement (Hornstein, 1999). Both the minimal pronoun approach and the movement approach give rise to the expectation that controlled subjects should be phonologically overt under some conditions (as overt pronouns or as pronounced copies, respectively). And also on both approaches, control is not a theoretically primitive notion but is rather an emergent consequence of the lexical items in the sentence and how they interact with each other, which is precisely how our theory treats Gengbe sentences like (63). References Ameka, F. K. (2008). Aspect and modality in Ewe: a survey. In F. K. Ameka and M. E. Kropp Dakubu (Eds.), Aspect and Modality in Kwa Languages, pp. 135–194. Amsterdam: Benjamins. Bogal-Allbritten, E. (2016). Building Meaning in Navajo. Ph. D. thesis, University of Massachusetts. Chierchia, G. (1984). Topics in the Syntax and Semantics of Infinitives and Gerunds. Ph. D. thesis, University of Massachusetts. Chierchia, G. (1990). Anaphora and attitudes de se. In R. Bartsch, J. van Benthem, and P. van Emde Boas (Eds.), Semantics and Contextual Expression, pp. 1–32. Dordrecht: Foris. Clements, G. N. (1975). The logophoric pronoun in Ewe: Its role in discourse. Journal of West African Languages 10, 141–177. Culy, C. (1994). Aspects of logophoric marking. Linguistics 32, 1055–1094. Dowty, D. R. (1985). On recent analyses of the semantics of control. Linguistics and Philosophy 8, 291–331. Essegbey, J. (2008). The potential morpheme in Ewe. In F. K. Ameka and M. E. Kropp Dakubu (Eds.), Aspect and modality in Kwa languages, pp. 195–214. Amsterdam: Benjamins. Giannakidou, A. (1999). Affective dependencies. Linguistics and Philosophy 22, 367–421. Ginzburg, J. (1995). Resolving questions. Linguistics and Philosophy 18, 459–527, 567–609. Giorgi, A. and F. Pianesi (1997). Tense and Aspect. New York: Oxford University Press. Grano, T. (2016). Semantic consequences of syntactic subject licensing: Aspectual predicates and concealed modality. In N. Bade, P. Berezovskaya, and A. Schöller (Eds.), Proceedings of Sinn und Bedeutung 20, pp. 306–322. Hamblin, C. L. (1973). Questions in Montague English. Foundations of Language 10, 41–53. Hausser, R. R. (1980). Surface compositionality and the semantics of mood. In F. Kiefer and J. Searle (Eds.), Speech Act Theory and Pragmatics, pp. 71–95. Dordrecht: Reidel. Heim, I. (1992). Presupposition projection and the semantics of attitude verbs. Journal of Semantics 9, 183–221. Heim, I. (2002). Features of pronouns in semantics and morphology. Handout of talk given at USC. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 497 T. Grano & S. Lotven Control, logophoricity, and harmonic modality in Gengbe desire reports Hornstein, N. (1999). Movement and control. Linguistic Inquiry 30, 69–96. Karttunen, L. (1977). Syntax and semantics of questions. Linguistics and Philosophy 1, 3–44. Kratzer, A. (2009). Making a pronoun: Fake indexicals as windows into the properties of pronouns. Linguistic Inquiry 40, 187–237. Kratzer, A. (2013). Modality and the semantics of embedding. Presentation at Amsterdam Colloquium, December 20, 2013. Landau, I. (2000). Elements of Control: Structure and Meaning in Infinitival Constructions. Dordrecht: Kluwer. Landau, I. (2015). A Two-Tiered Theory of Control. Cambridge: MIT Press. Moulton, K. (2009). Natural Selection and the Syntax of Clausal Complementation. Ph. D. thesis, University of Massachusetts. Pearson, H. (2013). The Sense of Self: Topics in the Semantics of de se Expressions. Ph. D. thesis, Harvard University. Pearson, H. (2015). The interpretation of the logophoric pronoun in Ewe. Natural Language Semantics 23, 77–118. Pearson, H. (2016). The semantics of partial control. Natural Language & Linguistic Theory 34, 691–738. Portner, P. (2004). The semantics of imperatives within a theory of clause types. In R. B. Young (Ed.), Proceedings of SALT 14, pp. 235–252. Ithaca, NY: Cornell University. Portner, P. (2007). Imperatives and modals. Natural Language Semantics 15, 351–383. Portner, P. (2009). Modality. New York: Oxford University Press. Portner, P. and A. Rubinstein (2013). Mood and contextual commitment. In A. Chereches (Ed.), The proceedings of SALT 22, pp. 461–487. Ithaca, NY: CLC Publications. Roberts, C. (1996). Information structure in discourse: Toward an integrated formal theory of pragmatics. In J.-H. Yoon and A. Kathol (Eds.), Papers in Semantics, OSU Working Papers in Linguistics 49. Columbus, OH: The Ohio State University. Sadock, J. (2012). Modular Yiddish 3. ‘Structure of Yiddish’ course notes, University of Chicago, spring 2012. Sæbø, K. J. (2009). Possession and pertinence: The meaning of have. Natural Language Semantics 17, 369–397. Searle, J. R. (1969). Speech Acts: An Essay in the Philosophy of Language. Cambridge: Cambridge University Press. Stalnaker, R. C. (1978). Assertion. In P. Cole (Ed.), Syntax and Semantics 9, pp. 315–332. New York: Academic Press. Stephenson, T. (2010). Control in centred worlds. Journal of Semantics 27, 409–436. von Fintel, K. (1999). NPI-licensing, Strawson-entailment, and context-dependency. Journal of Semantics 16, 97–148. von Stechow, A. (2002). Binding by verbs: Tense, person and mood under attitudes. ms., University of Tübingen. von Stechow, A. (2003). Feature deletion under semantic binding. In M. Kadowaki and S. Kawahara (Eds.), Proceedings of NELS 33, pp. 133–157. Amherst, MA: GLSA Publications. Zanuttini, R., M. Pak, and P. Portner (2012). A syntactic analysis of interpretive restrictions on imperative, promissive, and exhortative subjects. Natural Language & Linguistic Theory 30, 1231–1274. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 498 Operating over (internal) ‘covert-based’ alternatives with scalar focussensitive particles: Evidence from Modern Hebrew1 Yael GREENBERG — Bar Ilan University Abstract. This paper examines a range of readings found with the Hebrew focus sensitive particle bixlal and its accented version BIXLAL observed in Migron 2003, and in a series of works by Greenberg and Khrizman. Following ideas in these works the paper argues that bixlal is a member of the typology of even-like operators in Hebrew, along the unmarked particle afilu, and that the range of readings found with BIXLAL results from the fact that the same even-like operation is done over ‘covert-based’, and in particular degree-based and domain-based, alternatives. This parameter of variation is shown to be relevant for other scalar particles, both even-like and only-like, cross linguistically. The paper is finished by briefly examining another non-standard type of alternatives operated over by some scalar particles, namely speech act alternatives. The general conclusion is that ‘type of alternatives’ is a relevant parameter for scalar focus particles in natural language. Keywords: even, only, scales, alternatives, focus, degrees, domains, gradable adjectives, multidimensional adjectives, NPIs, speech acts, typologies. 1. Introduction: Classical parameters of variations in typologies of even-like particles and the new parameter examined in this paper The lexical entry of even is usually taken to be some version or other of (1) (cf. Horn 1969, Karttunen and Peters 1979, Rooth 1985, 1992, Herburger 2000, Guerzoni 2003, Chierchia 2013, etc.). In prose, (1) says that even (C)(p)(w) presupposes that p is stronger on a contextually given scale (e.g. it is less likely / more noteworthy) than all its distinct focus alternatives in C, and asserts that p is true: (1) ||even||g,c = lC.lp.lw: "qÎC q¹p ® p > C q. p(w) =1 Where C Í ||p||F Ù ||p||O Î C Ù $q q¹ p Ù qÎ C This entry has been very prominent in the literature on scalarity and polarity sensitivity, but it also raised discussions and debates. A significant contribution to these debates comes from typological research of languages where more than one even-like operator exists. Such research identified a number of parameters along which even-like operators may vary, concerning, e.g. the high vs. low position of prejacent in the scale in the scalar presupposition and the logical properties of the licensing environment for the even-like particle, the scopal properties of the particle, the nature of the scale, the presence of an existential presupposition in addition to the scalar one, etc. (See, e.g. Rullmann 1997, Giannakidou 2007, Gast and van der Auwera 2011, Crnič 2011 for reviews and suggestions). 1 For helpful comments thanks to Elitzur Bar-Asher-Siegal, Gennaro Chierchia, Luka Crnič, Micky Daniels, Edit Doron, Danny Fox, Nirit Kadmon, Lena Miashkur, Dina Orenstein, Moria Ronen, Susan Rothstein, Galit Sassoon, Aldo Sevi, Malte Zimmermann, and especially Keren Khrizman. This research was supported by ISF grant 1655/16. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 499 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles The main goal of the present paper is to argue for the existence of yet another relevant parameter of variation, not discussed so far in the literature on overt even-like typologies, namely the ability / inability of the particle to operate over what we will call ‘covert-based’ alternatives. The main empirical support for the linguistic relevance of this parameter is a range of differences between two members of the even-like typology in Hebrew: the default even-like particle, afilu, and the particle bixlal. We will concentrate on a number of readings found with the accented version of bixlal, BIXLAL, observed in Migron 2003, Greenberg and Khrizman 2012a,b, Greenberg 2014, 2016b, which can be paraphrased as very, in general, at all, etc. Inspired by ideas in these works we claim that these readings can be derived by assuming that BIXLAL still denotes the same even-like operation as bixlal, but that instead of operating over standard focus alternatives, it operates over ‘covert-based’, and more specifically, over domain-based and degree-based alternatives to its prejacent.2 This kind of operation will be shown to be relevant also for some only-like particles. More generally, then, the (in)ability to operate over ‘covert-based’ alternatives seems to be a relevant parameter of variation for scalar focus particles cross linguistically. The paper is structured as follows: Section 2 presents the basic data to be accounted for, namely the membership of bixlal in the typology of even-like particles in Hebrew (along with the unmarked form, afilu), and the challenge posed by the special readings of BIXLAL. Section 3 proposes that these special readings should be derived by assuming that BIXLAL is an even-like operator over degree-based and domain-based alternatives, and illustrates the advantages of this proposal in sentences with one-dimensional and multidimensional adjectives. Section 4 briefly considers, and rejects, an alternative, intensifier-based analysis of BIXLAL. Section 5 takes a wider perspective and looks at other overt and covert even-like as well as only-like operators over degree and / or domain-based alternatives. In section 6 we briefly examine the existence of apparently non-scalar readings of bixlal, which we propose to analyze as even-like operations over speech acts alternatives. Section 7 concludes and summarizes more generally potential specifications of the ‘type of alternatives’ parameter for some scalar focus particles. 2. The data 2.1. Bixlal is a member of the family of even-like particles in Hebrew The standard, default even-like particle in Hebrew is afilu. We propose, however, that like many other languages (see e.g. Giannakidou 2007, Crnič 2011, Gast and van der Auwera 2011), Hebrew has more than one member in this typology. In particular, following Greenberg 2014, Greenberg and Orenstein 2016, we propose that besides afilu Hebrew has at least three more members in this family, namely the high register particle af, the ‘NPI’ ve-lu (similar to the English so much as), and the particle bixlal, which will be the main focus of this paper. The claim that bixlal is an even-like operator is not trivial, though, as it is never mentioned in dictionaries or traditional Hebrew grammars as a translation of even, along afilu. The reason seems to be that the most prominent uses of this particle are found in its accented version, BIXLAL, which, as discussed below, is not translated as even but as very, in general, at all, 2 In Greenberg 2014 such alternatives are called ‘internal’, rather than ‘covert-based’. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 500 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles etc.3 Nonetheless, as originally observed in Migron 2003, bixlal CAN be translated as even, and substituted by afilu. An example is (2): (2) Context: Discussing Danny’s and Yosi’s great success in the competition: Dani zaxa be-medalyat kesef, ve-yosi afilu / bixlal zaxa be-[zahav]F / # [bronza]F Danny won in-medal silver and-Yosi afilu / bixlal won in-gold bronze “Danny won a silver medal, and Yosi even won [gold]F / # [bronze]F” In such sentences bixlal behaves like afilu and even in indicating that p is stronger than its alternative (Yosi won gold >c Yosi won silver). Moreover, like even and afilu, bixlal is infelicitous when p is weaker than its alternative (Yosi won bronze <c Yosi won silver). Another property that bixlal shares with afilu is its scopal behavior with respect to surface negation: unlike English even, and just like Hebrew afilu, bixlal can scope either above a negated predicate, or below such a predicate, but not between negation and the predicate:4 (3) A: dani lo rakad ba-mesiba. ve-ma im yosi? Danny not danced in-the-party and-what with Yosi “Danny didn’t dance in the party. And what about Yosi?” B: a. hu afilu/bixlal lo shar b. hu lo shar afilu/bixlal c. hu lo # afilu/#bixlal shar he afilu/bixlal not sang he not sang afilu/bixlal he not afilu/bixlal sang “He even didn’t sing” “He didn’t sing even” “He didn’t even sing” (intended) Finally, there are cases where the only way to translate English even to Hebrew is by using bixlal (not afilu). Such cases are found when the particle associates with whole questions, as in Iatridou and Tetevosov’s (2016) examples of ‘our even’ in (4) and (5): (4) A: Let’s meet at Oleana’s for dinner. B: What do they even serve / serve even? (5) A: Did Olivia get the Fields Medal? B: Is Olivia even a mathematician? Iatridou and Tetevosov propose that in such cases even does not associate with any focused constituent inside the prejacent (e.g. with the accented mathematician in (5)). Rather, it associates with the entire question, and indicates that the prejacent question (e.g. What do they serve in the restaurant? / Is she a mathematician) is the least likely to be ignorant about, or to be asked. Moreover, they propose that in languages like Russian and German the choice between ‘garden variety even’ and ‘our even’ over questions is lexically encoded, so that some even-like particles (Russian daže and German sogar) can only function as ‘garden variety’ even, whereas others (voobšče and überhaupt, respectively) operate over questions.5 Now crucially, in Hebrew only bixlal, not afilu can be used as ‘our even’ over questions: 3 In addition, bixlal has another, apparently non-scalar reading, translated as actually by Migron 2003. We briefly discuss this reading in section 6 below. 4 For space reasons, we do not attempt to explain this pattern here. 5 Iatridou and Tetevosov’s (2016) analysis of überhaupt as an even-based operator thus differs from e.g. Anderssen’s (2006) analysis of this particle as a general domain widener and Rohas-Esponda’s (2014) analysis as marking a move to a higher QUD. We adopt their analysis for bixlal as well. See also section 6 for a brief discussion of voobšče and überhaupt. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 501 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles (6) A: Let’s meet at Oleana’s for dinner B: ma hem bixlal / # afilu magishim? what they bixlal / afilu serve “What do they even serve?” (7) A: “Did Olivia get the Fields Medal? B: Olivia bixlal / # afilu matematikait? Olivia bixlal / afilu mathematician “Is Olivia even a mathematician?” Given this data, then, afilu is similar to German sogar and Russian daže, in being able to function only as ‘garden variety’ even. In contrast, bixlal seems more flexible, as it can denote both an even-like operation over whole questions, like German überhaupt and Russian voobšče, as well as function as ‘garden variety’ even (as in (2)). The conclusion at this stage, then, is that bixlal is indeed a member of the Hebrew even-like family, alongside the default particle, afilu, and it shares with afilu and even the same lexical entry, namely (1) above. 2.2. The challenge: a variety of readings with BIXLAL A challenge to the even-like analysis of bixlal is the fact that when it is accented (as BIXLAL) it induces a variety of readings which make it different from both even and afilu. As originally observed by Migron 2003, the most prominent of these readings is found when BIXLAL combines with negated predicates, and is paraphrased as at all, as in (8). Migron emphasizes, however, that BIXLAL is different from English at all in that it is not an NPI, since it can appear in matrix sentences or in Upward Entailing contexts, as in (9), where it is paraphrased as in general. Greenberg and Khrizman 2012a,b observe that in such contexts BIXLAL can be also be paraphrased as very (10), or completely (11): (8) A: dani lo gavoha. ve-yosi? B: hu BIXLAL lo gavoha / hu lo gavoha BIXLAL Danny not tall and-Yosi he BIXLAL not tall / he not tall BIXLAL “Danny is not tall. And Yosi?” “He is not tall at all” (9) A: dani xaxam be-xeshbon. ve-yosi? B: hu BIXLAL xaxam. Danny smart at-math and-Yosi he BIXLAL smart “Danny is smart at math. And Yosi?” “He is very smart / smart in general” (10) A: dani gavoha. ve-yosi? B: hu BIXLAL gavoha. Danny tall and-Yosi he BIXLAL tall “Danny is tall And Yosi?” “He is very tall” (11) A: le-dani ein shum maxala. ve-yosi? to-Danny there is no disease and-Yosi “Danny has no disease. And Yosi?” B: hu BIXLAL bari. he BIXLAL healthy “He is completely healthy” Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 502 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles How should such readings be analyzed? It is possible, of course, to suggest that BIXLAL is many-way ambiguous, and that its semantics when accented is completely distinct from the even-like semantics we suggested that its unaccented version has. In the next section, however, we take another route. Based on preliminary suggestions in Migron 2003, Greenberg and Khrizman 2012a,b and Greenberg 2014, 2016b, we propose a more unified analysis of bixlal and BIXLAL where it denotes the same even-like operator in all its uses just like even and afilu, but varies in the type of alternatives it can operate over. 3. The proposal: An even-like operator over degree-based and domain-based alternatives 3.1. The core proposal We suggest that even, afilu and bixlal / BIXLAL all have the semantics in (1) above, presupposing that their prejacent, p, is stronger on the relevant scale than all its contextually supplied focus alternatives, q, in C, and asserting that p is true. However, whereas given the data above, even and afilu can only operate over standard, ‘Roothian’ focus alternatives, BIXLAL can operate over ‘covert-based’, and in particular degree- and domain-based alternatives when it is accented.6 Operating over ‘Roothian’ alternatives is done in the standard manner: the alternatives to p are identical to it, besides an overt, focused element (which is usually accented), which is substituted by another overt element of the same semantic type. For example, in (2) above, where p is Yosi won [gold]F, the alternatives are derived by substituting the overt focused element ‘gold’ with other overt elements of the same semantic type, yielding e.g. Yosi won silver, Yosi won bronze, etc. In contrast, ‘covert-based’ alternatives are derived by letting the operator associate with a covert element in p. In such cases the alternatives to p differ from it by the identity of this covert element, while crucially, all overt material in p stays fixed in q. This leads to a situation where the alternatives to p differ from it only in their interpretation, though on the surface, i.e. in terms of their overt material, they seem identical to it. 3.2. Illustrations with one-dimensional adjectives To illustrate the proposal, consider first the way BIXLAL is interpreted in (10), with the onedimensional adjective tall. We suggest that in this case both the prejacent of BIXLAL, p and the contextually salient alternative, q, are of the form: Yosi is POS tall, which, following, e.g. Kennedy and McNally 2005 has the interpretation in (12), saying that the degree to which Yosi is tall is at least as high as the standard of tallness: 6 An obvious question is why the operation over covert-based alternatives is found only with the accented version of the particle, BIXLAL. Based on ideas in Egg and Zimmermann 2011, and in Greenberg and Khrizman 2012a,b, Greenberg 2014, Greenberg 2016b suggests an information-structure based explanation for this pattern. But describing this explanation is beyond the scope of this paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 503 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles (12) p = $d [d ³ standtall Ù tall(Yosi,d)] q = $d [d ³ standtall Ù tall(Yosi,d)] This, of course, raises an immediate question: If p and q are identical, how can the scalar presupposition (p >c q) of the even-like operator BIXLAL be met? The answer, we suggest, is that the covert stand variables in p and q are assigned two different values.7 In q we get standdefault – constructed based on the value to the standard variable in the preceding sentence Danny is POS tall. In contrast, in p we assign stand a higher value, standhigh, such that standhigh > standdefault. This allows p to end up being stronger than q, as required in the scalar presupposition, and as seen in (13). The effect is intuitively paraphrased in (14): (13) $d [d ³ standhigh,tall Ù tall(Yosi,d)] >c $d[d ³ standdefault,tall Ù tall(Yosi,d)] (14) A: Danny is tall relative to the contextually default standard, standdefault, and what about Yosi? B: He is even tall relative to the higher standard, standhigh, (10), as well as its intuitive paraphrase in (14) lead to the inferences that Yosi is very tall, and that he is taller than Danny. To derive these inferences we suggest that, since in the salient sentence (Danny is POS tall) the relevant standard being used is the lower one, standdefault, and since, a higher standard, standhigh is made salient in the prejacent of even, the proposition $d[d ³ standdefault,tall Ù tall(Danny,d)] raises the scalar implicature that the stronger alternative, $d[d ³ standhigh,tall Ù tall(Danny,d)], is false. We end up then, with the understanding that Danny is tall relative to the default standard, but not relative to a higher standard. Hence, Yosi, who is taken to be tall relative to the higher standard (due to the scalar presupposition of BIXLAL), is understood to be taller than Danny, as well as ‘very tall’. Turning now to the at all reading of BIXLAL in (8), found with a negated predicate, in this case we take both p and q to be of the form in (15), asserting that it is not the case that the degree to which Yosi is tall is at least as high as the standard of tallness. Then, to satisfy the scalar presupposition of BIXLAL (p >c q), we assign the standard variable in p a LOWER value, standlow, than the salient standard in q, standdefault. We thus end up with the presupposition in (16), and with the intuitive paraphrase of (8) in (17): (15) p = ¬$d [d ³ standtall Ù tall(Yosi,d)] q = ¬$d [d ³ standtall Ù tall(Yosi,d)] (16) ¬$d [d ³ standlow,tall Ù tall(Yosi,d)] >c ¬$d [d ³ standdefault,tall Ù tall(Yosi,d)] (17) Danny does not reach the contextually salient standard of tallness, standdefault, Yosi does not even reach a lower standard, standlow., i.e. he is not tall at all. 7 See Greenberg (to appear) for a more detailed analysis, where BIXLAL associates with the covert comparison class argument of POS. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 504 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles 3.3. Illustrations with multidimensional adjectives We would now like to derive the readings found when BIXLAL appears in sentences with multidimensional adjectives, e.g. with smart and healthy, as in (9) and (11) above. To do that we start by following Sassoon 2013, 2016 in assuming that multidimensional adjectives (healthy, ill, smart, etc.) involve cardinality measurement of ‘respects’ or ‘dimensions’ (e.g. healthy / ill w.r.t. blood pressure / sugar level, John is smart w.r.t. math / humanities, etc.). Each of the dimensions is itself a gradable property, introducing its own scale and standard degree, similarly to the standard degree used for one-dimensional adjectives like tall. We will henceforth call this standard degree standd, to distinguish it from another standard operative with multidimensional adjectives, namely standn. This latter standard is taken by Sassoon to be the standard number of dimensions required to be satisfied with each multidimensional adjective. This standard number, standn, is sometimes lexically determined: for example, Sassoon argues that by default, to be healthy is to reach the standard degree of health in ALL relevant dimensions, e.g. blood pressure and sugar level and heart condition etc. In contrast, to be ill is to reach the standard degree of illness is at least SOME dimension. Healthy and ill, then, can be classified as ‘universal’ and ‘existential’ multidimensional adjectives, respectively. In other cases, the standard number of dimensions is contextually determined. For example, to be smart is to be smart relative to a contextually determined number of dimensions (e.g. math, history, linguistics, etc.). Given these ideas, then, we can assume that in the ‘positive form’ of a sentence like Yosi is A (where A is a multidimensional adjective) there is a covert POS, as in (18), and that such a sentence is interpreted as in (19): (18) Yosi is POS A (where A is a multidimensional adjective) (19) $n [n ³ standn,A Ù |lG.G Î DimA Ù G Î D Ù $d [d ³ standd,G Ù G(Yosi,d)]| ≥ n ] In words, such a sentence is true iff there is a number, n, of gradable dimensions G which are relevant dimensions of A (i.e. members of the domain D) for which Bill’s degree exceeds the standard degree, namely standd. And this number n exceeds the standard number of dimensions, namely standn, in the domain of relevant dimensions for A. The important point for us now is that (19) has three contextual covert variables, namely the underlined standd, standn and D. Since we take BIXLAL to be an even-like operator over covert-based alternatives, we predict that when it is present each of these three covert variables can be in principle exploited to create such ‘covert-based’ alternatives. The prediction is indeed borne out. To illustrate that consider first (9) above. Here we can exploit the variability of either standd or standn. This gives us (at least) three possibilities. First, the alternatives can vary w.r.t. the value of standd, assigning a higher value to this variable in p than in q. The resulting interpretation is that Danny is smart-w.r.t.-math relative to the contextually salient standard, and Yosi is even smart-w.r.t.-math relative to a higher standard. Hence Yosi is considered very smart (w.r.t.-math), e.g. his grades at math are higher. This reading can be intuitively paraphrased as in (20): Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 505 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles (20) A: Danny is smart (at math). He always gets an A in the math exams. B: And Yosi is even VERY smart (at math). He always gets an A+ in these exams. The alternatives can also vary w.r.t. the value of standn, – assigning a higher value to this variable in p than in q. This can be achieved in two ways, and lead to two readings: first, Yosi can end up being smart with respect to an additional dimension (besides math), so the resulting interpretation is that Danny is smart-w.r.t.-one-dimension (i.e. smart-w.r.t.-math) and Yosi is even smart with respect to two dimensions, e.g. with respect to both math and history. Alternatively, Yosi can end up being smart w.r.t. all (relevant) dimensions, leading to the interpretation that Danny is smart-w.r.t.-one-dimension (i.e. smart-w.r.t.-math) and Yosi is even smart with respect to ALL (relevant) dimensions (math, history, art, linguistics, …). This option is what leads to the ‘in general’ use of BIXLAL. The two options can be now more intuitively paraphrased as in B’s two answers in (21): (21) (Context: Students in this college study math, biology, physics, history, philosophy and linguistics) A: Danny is smart. He has great grades at math. B1: And Yosi is even VERY smart. He is also great in history. B2: And Yosi is even VERY smart. He is great in all fields, i.e. smart in general. The third variable that can be exploited to yield covert-based alternatives with BIXLAL is the domain restriction variable, D. Consider for example (11) above, with the ‘universal’ multidimensional adjective healthy, in the following context: we are organizing a challenging trip, and in order to join this trip, all candidates should be healthy, i.e. should have normal values along important medical parameters, namely blood pressure, sugar level and heart functioning. In this case we take p, the prejacent of BIXLAL (Yosi is POS healthy), to be stronger than its apparently identical alternative q (which is again Yosi is POS healthy), similarly to what we did with the other cases in (8)-(11). Here, though, we cannot take p to be stronger than q due to a higher value assigned to standd, since there is no specific dimension of health where Yosi’s degree is claimed to be higher. Nor do we assign standn a higher value, since the value for this standard in A’s utterance is already maximal, due to the default specification of this standard with adjectives like healthy: i.e. Danny is already considered healthy with respect to all relevant dimensions (blood pressure, sugar level and heart functioning). Instead, to make p stronger than q in this case we can assign the domain variable, D, two distinct values: Ddefault in q, Dwide in p, where Ddefault Ì Dwide. Given this suggestion, then, the intuitive paraphrase of (11) is as in (22): (22) Danny is healthy with respect to all dimensions of health relevant for the trip, i.e. all dimensions in Ddefault, and Yosi is even healthy w.r.t. additional, less relevant dimensions, i.e. all dimensions in the wider domain, Dwide. To support this proposal, we can remind ourselves what is independently known about domain widening in other constructions. Following e.g. Kadmon and Landman 1993 ideas on any (as in I don’t have any potatoes), we take domain restriction to be used in order to exclude ‘irrelevant’ entities (e.g. small or rotten potatoes). Domain widening thus typically indicates that such entities can be now considered relevant. This seems to be exactly what happens in (11) as well. This sentence can be very naturally be continued with “He doesn’t even Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 506 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles have a mild cold”. In contrast, continuing (11) with “He doesn’t even have cancer” will sound very odd, as predicted. We can now also predict that with ‘existential’ multidimensional adjectives (like ill), BIXLAL will not yield domain widening. This is because such an operation will not make p stronger than its alternative (cf. e.g. discussions of Kadmon and Landman 1993, Krifka 1995, Chierchia 2013 on any). Indeed, unlike (11) with healthy, (23) with ill can be naturally continued with “He even has cancer”, but continuing it with “he even has a mild cold” sounds very odd: (23) A: dani xole, ve-yosi? B: hu BIXLAL xole. Danny ill and-Yosi? he BIXLAL ill “Danny is ill. And Yosi?” “He is very ill” Notice also that BIXLAL can induce domain widening in the Hebrew correlate of the Kadmon and Landman’s 1993 example in (24) with a negated predicate, yielding again an at all reading. In this case, too, we suggest that BIXLAL denotes an even-like operation over the covert domain variable, ending up with the intuitive paraphrase in (25): (24) ein li tapuxey adama BIXLAL not-have to-me potatoes BIXLAL “I don’t have potatoes at all” (25) I don’t have potatoes in Ddefault, and I don’t even have less relevant potatoes in Dwide. To summarize so far, we argued that BIXLAL is an even-like operator, similar to English even, and Hebrew afilu, and that the range of readings found with it can be derived by assuming that it operates over a special kind of alternatives, namely ‘degree-based’ and ‘domainbased’ alternatives. What all these cases have in common is an abstract / structural property: the ability to apply the even-like operation over ‘covert-based alternatives’ (cf. Erlewine 2014 on association with covert variables). Thus, wherever its prejacent contains a covert contextual variable, BIXLAL can exploit it by assigning this variable a distinct value which will make p stronger than q, as required by the scalar presupposition. 4. Rejecting an intensifier-based analysis of BIXLAL Since many of the readings found with BIXLAL seem to lead to some sort of intensification, one might wonder whether, instead of claiming that this particle is a special even-like operator over special, covert-based alternatives, we can come out with a simpler analysis, namely that BIXLAL is a flexible intensifier. There are two reasons, however, why such an analysis cannot work, both have to do with properties that BIXLAL shares with even / afilu which set it apart from intensifiers. These are the scopal interaction of BIXLAL with negation and its sensitivity to standards of comparison. Above we have already noted that the unaccented particle bixlal behaves like afilu with respect to surface negation. In particular, we saw in example (3) above, that both particles can precede surface negation, and can appear after the neg+predicate combination, but cannot ap- Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 507 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles pear between negation and the main predicate. As can be seen now in (26), BIXLAL behaves in exactly the same way. In contrast, the scopal behavior of Hebrew intensifiers with respect to surface negation is much more flexible. This can be seen, for example, in the behavior of me’od (‘very’) in (27):8 (26) A: dani lo gavoha, ve-yosi? Danny not tall and-Yosi “Danny is not tall. And what about Yosi?” B: a. hu BIXLAL lo gavoha b. hu lo gavoha BIXLAL c. # hu lo BIXLAL gavoha he BIXLAL not tall he not tall BIXLAL he not BIXLAL tall “He is not tall at all” (27) A: dani lo gavoha, ve-yosi? Danny not tall and-Yosi “Danny is not tall. And what about Yosi?” B: a. hu ME’OD lo gavoha b. hu lo gavoha ME’OD c. hu lo ME’OD gavoha he very not tall he not tall very he not very tall “He is very not tall” “He is not very tall” “He is not very tall” In addition, BIXLAL shares with afilu, as well as with English even, another interesting property which sets it apart from intensifiers. In (10) above, for example, (‘Danny is tall, and Yosi is BIXLAL (“very”) tall’), the presence of BIXLAL in B’s utterance immediately leads to the inference that Danny, mentioned in A’s utterance is tall as well. Crucially, this inference is present not only when Danny’s tallness is explicitly asserted, as in (10), but also in (28), which immediately entails that being 1.75m tall is considered tall. This is indicated by the infelicity of the continuation “He is not that tall” in A’s utterance. Indeed, when BIXLAL is absent this inference completely disappears, and the first sentence can be naturally continued with “He is not that tall”: (28) A: dani hu 1.75 (# hu lo gavoha), ve-yosi? B: hu BIXLAL gavoha Danny is 1.75 he not tall and-Yosi he BIXLAL tall “Danny is 1.75m tall (he is not tall), and Yosi?” “He is even VERY tall” This makes BIXLAL different from intensifiers like English very and Hebrew me’od. For example, the mere presence of me’od (‘very’) or mamash (‘really’) in (29) does not lead to any inference that being 1.75m tall is considered ‘tall’, and A’s utterence is perfectly compatible with the continuation “He is not tall’: (29) A: dani hu 1.75. hu lo gavoha, ve-yosi? B: hu MEOD / MAMASH gavoha Danny is 1.75 he not tall and-Yosi he very / really tall “Danny is 1.75m tall (He is not tall), and Yosi?” “He is VERY / REALLY tall” Crucially, the unique inference found with BIXLAL in (28) makes it similar to English even, as observed in Greenberg 2015, 2018. Consider (30) and (31): 8 The behavior of the intensifier me’od (‘very’) in this respect seems typical of Hebrew intensifiers in general, and found also with mamash (‘really’) or le-gamrey (‘completely’) (although the latter is limited to modify Upper closed adjectives, cf. Kennedy and McNally 2005). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 508 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles (30) A: Danny is 1.75m tall. B1: and Yosi is taller. B2: and Yosi is even taller. (31) A: Danny is 1.75m. tall B1: and Yosi is 1.78m. B2: and Yosi is even 1.78m. It is well known that comparatives based on relative adjectives, as in B1’s answer in (30), do not entail the positive form of the adjectives they are based on, for neither the source nor the target of the comparison (e.g. Kennedy and McNally 2005). Indeed, Yosi is taller than Danny does not entail or even imply that Yosi or Danny is tall, and can be naturally continued with … but both are short. The interesting thing happens in B2’s answer, with even: here, Greenberg 2015, 2018 observes, the presence of even leads exactly to these entailments. Indeed, continuing Yosi is even taller with … but both are short leads to infelicity.9 As can be seen in (31) this effect is not limited to comparatives. Here too the presence of even in B’s utterance entails that being 1.75m as well as being 1.78m are considered tall. Hebrew afilu yields exactly the same effects as even in such cases. Based on such data, Greenberg 2015, 2018 proposes that for even p to be felicitous, both p and its alternatives q must intuitively ‘lead to’ a degree of a scale associated with a gradable property G, which is at least as high as the standard for this gradable property. This observation is not accounted for by the traditional semantics for even, according to which p should be only required to be stronger (less likely / more noteworthy) than q. Combining this observation with several other pieces of data which pose challenges for the popular ‘comparative likelihood’ view of even (see, e.g., Greenberg 2016a, 2018 for discussion), Greenberg offers a revised, ‘gradability-based’ semantics for even, which is sensitive to standards of comparison along a contextually supplied scale. Reviewing this proposal in detail is beyond the scope of this paper. The important point at this stage is that in terms of sensitivity to standards, BIXLAL seems to behave exactly like even and afilu, and unlike intensifiers. This, together with its behavior with surface negation, further supports the analysis of BIXLAL as an evenlike particle, as suggested above. 5. Some cross-linguistic / cross-constructional support for the linguistic reality of the operation over ‘covert-based’ alternatives We proposed that BIXLAL is not an intensifier, but an even-like operator, which unlike English even and Hebrew afilu operates over ‘covert-based’, namely degree-based and domainbased alternatives. More generally, we take the data in sections 3 and 4 to indicate that the ability / inability to operate over such ‘covert-based’ alternatives is a relevant parameter for even-like operators in Hebrew. But is Hebrew the only language where operation over such ‘covert-based’ alternatives is possible? Clearly our proposal would be more convincing if we find more manifestations of this parameter. Luckily, the answer seems to be positive. 9 Umbach 2009 notes a similar effect with German noch. We believe, however, that the mechanism involved is different. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 509 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles One type of candidate is the covert even operator argued to be involved in the semantics of some NPIs, as in Krifka 1995 and Chierchia 2013. For example, Chierchia 2013 takes minimizers like give a damn to involve the covert even-like operator E. Give a damn, according to Chierchia’s proposal, expresses the property of caring to the most minimal degree, namely lx$ s care(x,s,dmin), and it obligatorily triggers degree-based alternatives of the form lx$ s care(x,s,d’), where d’ > dmin. Similar considerations apply to expressions with at all,10 which also triggers degree-based alternatives. These obligatorily triggered alternatives must be operated upon (‘exhaustified’), and Chierchia argues that what operates over them is the covert even-like operator E, which requires its associate to be stronger (e.g. less likely) than all alternatives. Chierchia shows how such an operation is only licensed in Downward Entailing contexts, hence the NPI-hood of give a damn and at all.11 In addition to this covert even-like operator over covert degree-based alternatives with at all, Chierchia proposes that some NPIs, e.g. any, involve a covert operator over domain-based alternatives as well, namely the only-like operator O (or exh). For example, a sentence like I don’t have any potatoes has a similar assertion to that of I don’t have potatoes, namely ¬$ x Potato (x) Ù D(x) Ù Have (I, x), but it obligatorily triggers subdomain alternatives of the form ¬$ x Potato (x) Ù D’(x) Ù Have (I, x), where D’ Ì D. These alternatives then must be exhaustified by the covert only-like operator O, which rejects all stronger alternatives. This is only licensed in Downward Entailing contexts, hence the NPI-hood of any. We can see, then, that in Chierchia's 2013 theory the covert only-like and even-like operators are allowed to operate over covert domain-based and degree-based alternatives, namely the type of alternatives Hebrew BIXLAL operates over, given the analysis developed above. In addition to these covert operators we can also find potential candidates for being overt operators over such covert-based alternatives. One such particle is the Hindi bhii. Lahiri 1998 argues that when bhii combines with the numeral ek (‘one’) it yields numeral-based alternatives (e.g. one, two, three), whereas when it combines with the indefinite koi it seems to associate with the ‘contextually weakest predicate’. Chierchia 2013 reinterprets this observation and proposes that in this case bhii expresses an even-like operation over domain-alternatives, similarly to what we proposed above for BIXLAL. The Russian voobšče is another potential candidate for being an overt even-like operator over covert-based alternatives. Above we already saw Iatridou and Tetevosov’s 2016 claim that voobšče expresses an even-like operation over questions. But Iatridou and Tetevosov 2016 mention in a footnote that it can yields an at all reading with negated predicates, as in (32). Moreover, voobšče seems to also yield a very / -er than reading in UE contexts (cf. Miashkur 2017a,b), as in (33): 10 According to Chierchia 2013, though, at all involves ‘scale reversal’ as well. Our analysis of BIXLAL above thus makes two contributions to this analysis of at all: on the one hand, it supports the general line of an even-based analysis of at all: in particular, since BIXLAL, which is independently analyzed above as an even-like operator, is the only way to express at all in Hebrew, we have overt evidence that the semantics of at all indeed involves an even-like semantics. On the other hand, our analysis of BIXLAL seems to show that there are maybe two strategies for deriving at all readings cross linguistically: in contrast to Chierchia’s 2013 analysis of English at all, Hebrew BIXLAL as at all is NOT taken as the alternative-triggering expression which then necessitates a covert even-like operator to operate over these alternatives. Instead, the Hebrew at all, i.e. BIXLAL, is the (overt) even-like operator itself. 11 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 510 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles (32) Lev voobšče ne čital “Devida Kopperfil’da” Lev voobšče NEG read.PST David Copperfield “Lev did not read ‘David Copperfield’ at all” (Iatridou and Tetevosov 2016) (33) A: Džon 1.85m. A Bill? / Čto nasčet Billa? John 1.85m but Bill / what on account of Bill “John is 1.85m. And what about Bill?” B: On voobšče vysokij. he voobšče tall “He is even very tall / taller” These readings are not available with the standard even-like operator in Russian daže, and they can be analyzed in a similar fashion to the operation over degree-based alternatives with BIXLAL proposed above. Notice also that German überhaupt, which was analyzed as ‘our even’ over questions in Iatridou and Tetevosov 2016, has been reported to yield at all and in general readings too (cf. Anderssen 2006, Rojas Esponda 2014). Given our analysis of BIXLAL above we propose to analyze these uses of überhaupt too as involving an even-like operation over covert-based alternatives.12 Finally, there seem to also be attested overt only-like operators over ‘covert-based’ alternatives, for example, the Hebrew exclusive particles be-sax ha-kol and STAM, discussed in Orenstein and Greenberg 2014, Orenstein 2016, and Greenberg and Orenstein 2016. We will concentrate here on be-sax ha-kol, which can express both a regular exclusive reading, similar to the default only-like operator, rak, as well as an ‘approximative’ reading, similar to that found with more or less. Compare, for example, rak and be-sax ha-kol in (34a,b): (34) Context: John and Mary booked a room in a hotel and asked that the room will be clean, large, with view to the sea. After John checks the room he tells his wife: a. ha-xeder rak naki the-room rak clean “The room is only clean” b. ha-xeder be-sax ha-kol naki the-room be-sax ha-kol clean “The room is only / more or less clean” In (34a), with rak we get a regular scalar reading of exclusives, rejecting standard, ‘Roothian’ focus alternatives which are stronger than the prejacent, similarly to what we get with English only or just (cf. Coppock and Beaver 2014). This yields the intuitive paraphrase in (35a). In contrast, with be-sax ha-kol we can also get a new ‘approximative’ reading, intuitively paraphrased in (35b). Orenstein and Greenberg 2012, 2014, Orenstein 2016, Greenberg and Orenstein 2016 argue that under this approximative reading be-sax ha-kol is still an exclusive operator, but that what is rejected is a degree-based alternative. In particular, the proposal is that both the prejacent of be-sax ha-kol, p, and the alternative q are of the same form: The room is POS clean, namely, $d[d ³ stand(clean,C) Ù clean(the room,d)], but the standard variable in 12 Notice, though, that the range of interpretations überhaupt induces is more limited than with both bixlal and voobšče. A full analysis of these particles is beyond the scope of this paper (but see Miashkur 2017a,b for a fuller picture of voobšče vs. daze). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 511 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles p is assigned a lower value than the default value in q, which is the maximal degree of cleanness. The resulting interpretation is that the room is not clean relative to the maximal standard, but clean relative to a lower standard, similarly to more or less clean. (35) a. The room is only clean and not more than that: not clean and large, not clean with view to the sea, etc. b. The room is only more or less clean, and not more than that: it is not maximally clean. The operation over ‘covert-based’ alternatives, then, can be added to the list of parameters along which only-like particles vary (cf. Tomaszewicz 2012, Coppock and Beaver 2014, Orenstein and Greenberg 2014, Orenstein 2016, Greenberg and Orenstein 2016). More generally, the analysis of Hebrew BIXLAL as an even-like operator over covert-based alternatives, can be positioned in a wider cross linguistic and cross constructional context. The emerging picture is that the (in)ability of scalar operators to operate over ‘covert-based’ alternatives should be taken as a relevant parameter of variation in this wider typology. 6. A direction for further research: Scalar operators over a range of speech acts alternatives A challenge to our even-like analysis of bixlal and BIXLAL is the existence of some uses of bixlal, originally pointed out by Migron 2003, which on the surface do not seem scalar at all. Consider, for example, (36): (36) A: Rina carfatiya? Rina French “Is Rina French?” B: lo. Hi bixlal britit no she bixlal British “No way. She is actually British.” (cf. Migron 2003) In (36) bixlal is not translated as even. Moreover, the prajacent of bixlal, She is British, does not stand in any scalar relation to the salient alternative, She is French. In particular, (36) does not seem to indicate that being British is ‘stronger’, e.g. less likely or more noteworthy, than being French. Indeed, Migron takes this use of bixlal to be translated as actually, and to merely indicate the shift from one alternative to the other in an unordered set of alternatives. Given this data one can take bixlal to be simply ambiguous between a scalar and a non-scalar reading (cf. also Kadmon and Sevi 2014 for a suggestion). But perhaps we can still analyze this use of bixlal under the even-like semantics proposed above. The crucial observation we would like to make in this connection, following Greenberg and Khrizman 2012b, Greenberg 2014, 2016b, Greenberg and Orenstein 2016, is that the presence of bixlal in (36) indicates a correction speech act, which crucially involves strong / significance denial. Intuitively, in (36) we take the proposition that Rina is British to correct and as part of this correction to strongly deny the proposition that Rina is French. This effect makes this ‘corrective’ use of bixlal different from that of actually (which indeed seems to merely indicate a shift of one proposition in the discourse to an alternative one). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 512 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles As a support of this observation, notice that if the denial is explicitly marked as being minor, the use of bixlal is infelicitous. For example, in (37) bixlal is only felicitous if the speaker takes having turquoise eyes as being significantly different from having blue eyes: (37) A: le-dani yesh einaym kxulot to-dani there-is eye blue “Danny has blue eyes” B: # lo be-diyuk / mamaS lo. yesh lo bixlal eiynam be-ceva TURKIZ not precisely really not there-is to-him bixlal eyes in-color turquoise # Not precisely / Absolutely not. He actually has TURQUOISE eyes” As a preliminary proposal, then, we suggest that bixlal in (36) and (37) is another manifestation of discursive-even, similar to ‘our even’, voobšče, überhaupt, and bixlal over questions, discussed in Iatridou and Tetevosov 2016 and in section 2 above. The difference is that instead of operating over questions alternatives, in the cases discussed here we get an even-like operation over denials, indicating that the denial is ‘stronger’ on the relevant scale than alternative denials. Thus, (36)-(397) can be paraphrased as (38)-(39), respectively: (38) Not only is Mary not French, she is even British! (39) Not only does John not have blue eyes, he even has turquoise eyes! Interestingly, we find parallel behavior of Russian voobšče, expressing an even-like operation over denials as well, as in (40) (K. Khrizman, and O. Miashkoor p.c.): (40) A: ty kak istinnyj gruzin dolzhen ocenit' eto vino you as real Georgian must appreciate this wine “Being a genuine Georgian, you should be able to appreciate this wine” B: ty chto??? kakoj ja gruzin… ya voobšče tatarin you what what I Georgian I voobšče a Tatar “What’s wrong with you? I am not Georgian, I am a Tatar.” Moreover, in addition to these even-like operators over speech acts, it seems that there are also only-like particles which can operate over speech act alternatives. First, similarly to ‘our even’ the exclusive only seems to be able to operate over questions, as in (41), where it indicates that the question “When will he arrive?” is the only (relevant) thing the speaker is ignorant about. In addition, Greenberg and Orenstein 2016 point out that exclusives like only / just seem to be able to operate over denial speech acts, as in (42), indicating that the only thing to deny in the statement that Mary is a great teacher is that she speaks very quietly. In both cases the exclusive gives a similar effect to the adversative particle but. Finally, Wiagand 2016 discusses an ‘unexplanatory’ use of just, as in (43), indicating that the speaker does not know the reason or cause for the fact that the lamp broke (beyond a minimal reason or cause), and analyzes it as operating over speech act alternatives as well: (41) When John is here we will go to the movies. Only when will he exactly arrive? (42) Mary is a great teacher. She just speaks so quietly. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 513 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles (43) I was sitting here and the lamp just broke (Wiagand 2016) An important task, then, is to find ways to capture the data concerning both the only-like and the even-like operations over the full range of speech acts alternatives in a precise and systematic way. For space reasons we leave this task for further research (cf. Iatridou and Tetevosov 2016, Wiagand 2016 and Daniels 2018 for suggestions). 7. Summary The starting point of this paper was a range of readings found with the Hebrew particle bixlal and its accented version BIXLAL, originally observed and discussed in Migron 2003 and in a number of works by Greenberg and Khrizman. Inspired by the intuitions in these works, we argued that (a) the unaccented bixlal is a member of the typology of even-like operators in Hebrew, along the unmarked particle afilu, and that (b) the range of readings found with BIXLAL results from the same even-like operation done over ‘covert-based’, namely degreebased and domain-based alternatives. We supported this analysis of bixlal and BIXLAL, and rejected an intensifier-based analysis, by pointing out the similar scopal behavior of these particles to afilu relative to surface negation, and the unique sensitivity of BIXLAL to standards of comparison, independently observed also for English even (Greenberg 2015, 2018). The behavior of bixlal and BIXLAL was then located in a wider set of observed facts concerning other overt and covert even-like and only-like particles which can be taken to operate over covert-based alternatives. We also discussed another non-standard type of alternatives operated over by some scalar particles, namely speech act alternatives.13 The emerging picture, then, points to the existence of a general parameter of variation for scalar, even-like and only-like particles, namely the type of alternatives that the particle can operate over (cf. Orenstein 2016, Greenberg and Orenstein 2016). A description of the different specifications of this parameter, and the manifestation of some of the scalar particles discussed above along these specifications, are schematically given in the following table: The ‘Type of alternatives’ parameter for scalar (even-like and only-like) operators14 Even-like particles Only-like particles Can operate over standard ‘Roothian’ even, afilu, bixlal, only, just, merely, focus alternatives: sogar, daze, covrak, be-sax ha-kol, ert E covert O (exh) Can operate over ‘covert-based’ (e.g. bhii, BIXLAL, be-sax ha-kol, degree-based and domain-based) voobšče, überSTAM, covert O alternatives: haupt, covert E (exh) Can operate over ‘Speech act’ alternatives even, überhaupt, just, only, rak (e.g. questions, denials, explanations) bixlal, voobšče 13 Cf. Wiagand 2016, who takes the operation over speech act alternatives to be a special case of operation over ‘covert-based’ alternatives (which, following the terminology of Greenberg 2014, she calls ‘internal’ alternatives). 14 Cf. Liu 2016, who considers a ‘type of alternatives’ parameter as well, for Chinese even-like and only-like particles. Liu’s parameter, however, seems to me more similar to the ‘type of scale’ parameter, discussed in Coppock and Beaver 2014, Orenstein and Greenberg, 2014, Orenstein 2016, Greenberg and Orenstein 2016. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 514 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles We hope that future research will contribute to the understanding of this picture, by examining the variation of additional scalar particles along this ‘type of alternative’, parameter both within and across languages, by refining the theoretical tools used to capture this parameter, and by examining the interaction of this parameter with other more well studied parameters along which even-like and only-like operators can vary. References Anderssen, J. (2006). Generalized domain widening überhaupt. In D. Baumer, D. Montero and M. Scanlon (Eds.), Proceedings of the 25th West Coast Conference on Formal Linguistics, pp. 58–66. Cascadilla Proceedings Project. Chierchia, G. (2013). Logic in Grammar: Polarity, Free Choice, and Intervention. Oxford: Oxford University Press. Coppock, E. and D. Beaver (2014). Principles of the exclusive muddle. Journal of Semantics 31, 371–432. Crnič, L. (2011). Getting Even. Ph. D. thesis, MIT. Daniels, M. (2018). Focus over a speech act operator: A revised semantics for ‘Our even’. Paper presented at NELS49. Egg, M. and M. Zimmermann (2011). Stressed out! Accented discourse particles — the case of doch. In A. Aguilar, A. Chernilovskaya, and R. Nouwen (Eds.), Proceedings of Sinn und Bedeutung 16, pp. 225–238. Erlewine, M. (2014). Movement out of Focus. Ph. D. thesis, MIT. Gast, V. and J. van der Auwera (2011). Scalar additive operators in the languages of Europe. Language 87(1), 2–54. Giannakidou, A. (2007). The landscape of EVEN. Natural Language and Linguistic Theory 25, 39–81. Greenberg, Y. (2014). External and internal alternative-sensitive operators. Workshop on Focus Sensitive Expressions from a Cross Linguistic Perspective, Bar Ilan University Greenberg, Y. (2015). Even, comparative likelihood and gradability. In T. Brochhagen, F. Roelofsen and N. Theiler (Eds.), Amsterdam Colloquium 20, pp. 147–156. Greenberg, Y. (2016a). A novel problem for the likelihood-based semantics of even. Semantics and Pragmatics 9, 1–28. http://dx.doi.org/10.3765/sp.9.2. Greenberg, Y. (2016b), Accentuation, givenness and operation over ‘covert-based’ alternatives with some focus sensitive particles. Word Order Variations at the Interfaces workshop, Ben Gurion University. Greenberg, Y. (2018). A revised, gradability semantics for even. Natural Language Semantics 26: 51–83. Greenberg, Y. (to appear). An overt even operator over covert-based focus alternatives. Journal of Semantics. Greenberg, Y. and K. Khrizman (2012a). The Hebrew bixlal: A general strengthening operator. Proceedings of IATL 27, pp. 139–162. MIT Working Papers in Linguistics. Greenberg, Y. and K. Khrizman (2012b). Strengthening across domains: The case of the Hebrew focus and polarity sensitive bixlal. Talk presented at the 2012 Summer Workshop, Jerusalem / Tel Aviv Reading Group, Tel Aviv university. Greenberg, Y. and D. Orenstein (2016). Typologies for even-like and only-like particles: Evidence from Modern Hebrew. Talk presented at ESSLLI 28 workshop on particles. Guerzoni, E. (2003). Why Even Ask? On the Pragmatics of Questions and the Semantics of Answers. Ph. D. thesis, MIT. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 515 Y. Greenberg Operating over (internal) ‘covert-based’ alternatives with scalar focus-sensitive particles Herburger, E. (2000). What Counts: Focus and Quantification. Cambridge, MA: MIT Press. Horn, L. (1969). A presuppositional analysis of only and even. In The 5th Annual Meeting of the Chicago Linguistic Society, pp. 97–108. Iatridou, S. and A. Tetevosov (2016) Our even. Linguistics and Philosophy 39, 295–331. Kadmon, N. and F. Landman (1993). Any. Linguistics and Philosophy 16, 353–442. Kadmon, N. and A. Sevi (2014). Nuclear accent and lexical meaning: The case of bixlal. Workshop on Focus Sensitive Expressions from a Cross Linguistic Perspective, Bar Ilan University. Karttunen, L. and S. Peters (1979). Conventional implicature. In Ch.-K. Oh and D. A. Dinneen (Eds.), Syntax and Semantics Volume 11: Presupposition. New York: Academic Press. Kennedy, C. and L. McNally (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language 81(2), 345–381. Krifka, M. (1995). The semantics and pragmatics of polarity items. Linguistic Analysis 25, 1– 49. Lahiri, U. (1998). Focus and negative polarity in Hindi. Natural Language Semantics 6, 57– 123. Liu, M. (2016), Varieties of alternatives: Mandarin focus particles. Linguistics and Philosophy 40, 61–95. doi:10.1007/s10988-016-9199-y. Migron, H. (2003). Ma kore po Bixlal? Ms., Hebrew University. Miashkur, O. (2017a). A parametric comparison of two scalar particles in Russian. Paper presented at IATL33. Miashkur, O. (2017b). A parametric comparison of Russian scalar particles daze and voobšče. MA thesis, Bar Ilan University. Orenstein, D. and Y. Greenberg (2012). A flexible exclusive particle: The case of the Hebrew be-sax ha-kol (“all in all”). In Proceedings of SuB 17. Orenstein D. and Y. Greenberg (2014). Exclusives in Hebrew: A core meaning and varying parameters. In Proceedings of IATL 29. Orenstein, D. (2016). The Semantics, Pragmatics and Focus Sensitivity of Exclusive Particles in Modern Hebrew. Ph. D. thesis, Bar Ilan University. Rojas-Esponda, T. (2014). A discourse model for überhaupt. Semantics and Pragmatics 7, 1– 45. Rooth, M. (1985). Association with Focus. Ph. D. thesis. University of Massachusetts, Amherst. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1, 75–116. Rullmann, H. (1997). Even, polarity, and scope. In M. Gibson, G. Wiebe and G. Libben (Eds.), Papers in Experimental and Theoretical Linguistics 4, pp. 40–64. Sassoon, G. (2013). A typology of multidimensional adjectives. Journal of Semantics 30, 335–380. Sassoon, G. (2016). A degree-approach account of multidimensional gradability. Ms. Bar Ilan University. Tomaszewicz, B. (2012). A family of exclusives in Polish. Paper presented at GLOW 35, Association with Focus Workshop. University of Potsdam. Umbach, C. (2009). Another additive particle under stress: German additive noch. In LOLA 10, pp. 149–156. Wiagand, M. (2016). Just and its meanings: Exclusivity and scales in Alternative Semantics and in speech act theory. Ms. Cornell University. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 516 Two strategies of reopening QUDs — evidence from German auch & noch1 Mira GRUBIC — University of Potsdam Abstract. This paper argues for a domain restriction account for wh-words in questions using resource situations, in parallel with the domain restriction of quantifiers proposed in Kratzer (2011). It is argued that under a situation semantic account assuming resource situations, the different behaviour of additive particles can be explained: Under a question under discussion account, additive particles like too and also are used when a (possibly covert) question is ‘reopened’ in order to add a further true answer (Beaver and Clark 2008, i.a.). This paper suggests that there are two ways in which a question can be re-addressed: it can either be reopened with (i) a different resource situation or (ii) with a different topic situation. This can explain the different behaviour of the additive particles auch and noch in German. Keywords: situation semantics, questions, additive particles 1. Introduction The domain of wh-elements is contextually restricted, just like the domain of quantifiers: While in (2), there may have been many people at the party, but nobody relevant to the speaker/hearer, the question in (1) also only asks for party-goers relevant to the person posing the question. (1) Who came to the party? (2) Nobody came to the party. Kratzer (2011) presents a situation-semantic account of quantifier restriction according to which a subsituation of the topic situation (= the situation that the utterance is about) is responsible for the restriction. This paper proposes that the same is the case for wh-questions like (1): the restriction of alternatives inherent in these questions is argued to come about via resource situations. The situation semantic background for this paper will be provided in section 2. It is also argued that under a QUD account of additive particles, the behaviour of the German particles auch (= “also, too”) and noch (= “still”, “in addition”) provides evidence for such a treatment of wh-questions: First, noch is most felicitous with an overt topic situation shifter (e.g. dann ‘then’) in declarative utterances. Second, noch is the preferred additive particle in questions, whereas auch seems to indicate that the speaker knows the answer to the question (Umbach, 2012). Third, in contrast to auch, which requires the focus of the host sentence to be distinct from that of the antecedent, noch imposes no such distinctness requirement. It is argued here that these differences can be accounted for under an analysis that assumes that both auch and noch indicate that a previous question is reopened, but whereas auch indicates reopening of the question with respect to a new resource situation, noch indicates reopening of the question with respect to a new topic situation. The background assumptions concerning additive particles, the German data, the analysis and a comparison with earlier analyses are presented in section 3. 1I would like to thank the audiences at Sinn und Bedeutung and at the ESSLLI 2016 workshop “Formal, Probabilistic and Typological Approaches to Discourse Particles and Modal Adverbs” (where I presented a partly overlapping talk on the typology of additive particles) for their feedback. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 517 M. Grubic Two strategies of reopening QUDs 2. Situations 2.1. The topic situation In a situation semantic account, propositions are functions from situations (i.e. parts of worlds) to truth values. This means that the truth of a declarative utterance is evaluated with respect to the situation that it is about, its topic situation (Kratzer, 2011). Kratzer illustrates this using the example in (3) (from Barwise and Etchemendy, 1987: 122): Here, ‘Claire has the three of clubs’ is intuitively false, even though it is true in the evaluation world that Claire has the three of clubs. This intuition can be captured by assuming that this sentence is evaluated with respect to a subsituation of the evaluation world, a subsituation which is part of Game 1. (3) (Emily is playing a card game (Game 1), and somewhere else, Claire is playing cards (Game 2). Both have the three of clubs.) Someone, watching game 1, mistakes Emily for Claire & says: # Claire has the three of clubs. The topic time (Klein, 1994), the interval about which the utterance makes a claim, temporally delimits the topic situation (Kratzer, 2011: §3). Temporal or locative adverbials provide further information about the topic situation (Klein, 2008: 289). According to Kratzer (2011), the topic situation of a sentence can be derived from its question under discussion (QUD) (Roberts, 1998, 2012). In a QUD account, every declarative utterance is assumed to be an answer to an (often implicit) assumed hearer-question, the current question under discussion. In the absence of an explicit QUD, the focus/background division of the utterance indicates which implicit QUD the speaker attributes to the addressee at this moment in discourse. For example, an utterance with so-called broad focus, in which the whole sentence is in focus, is assumed to answer a very general question, e.g. What happened? (4),2 while an utterance with narrow focus, in which a subconstituent of the sentence is in focus, is assumed to answer a question which asks for the constituent in focus, e.g. (5). The topic situation of the answer is the same as that of its question, e.g. (a subsituation of) a specific party in (4) or (5). (4) (What happened?) Amy and Ben danced. (5) (Who danced?) A MY AND B EN danced. The idea of implicit QUDs is used to model the idea each declarative utterance is believed, by the speaker, to address the currently most relevant lack of information that the hearer has. The QUD account also accounts for discourse coherence, by proposing a hierarchy of questions (Roberts, 2012). Here, the notational convention used in Büring (2003) to display this hierarchy as a discourse tree is adopted, e.g. (6). The dominating nodes are superquestions, the daughter nodes subquestions, and sister nodes are in temporal order, such that questions further to the right are asked later. The current question under discussion is lowest in the tree. 2 In the examples, SMALL CAPS are used to indicate stress (where relevant), bold font and italics are used for highlighting the important parts of the example. # is used for infelicity, ?? and ? for marginal felicity. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 518 M. Grubic (6) Two strategies of reopening QUDs Q1: What is the way things are? ... Q2: What is the way things were since we last met? ... Q3: What happened at the dinner last Sunday? ... CQ: What did Yvonne eat? A: Yvonne ate pizza The topmost question “What is the way things are” is about the actual world w0 , to completely answer it would mean to know everything about our actual world, i.e. to be able to identify which world in context set is the actual world (Roberts, 2012: 5). Since this is impossible to answer in one sentence (if at all), this question is recursively split up into subquestions. Any superquestion entails its subquestions in the sense of Groenendijk and Stokhof (1984: 16): every complete answer to the superquestion also answers the subquestions (Roberts, 2012: 7). For example, a full answer to Q3 in (6), listing all that happened at the dinner, would also answer the current question What did Yvonne eat?. According to Schwarz (2009: 166), there is also a relation between the topic situations of the questions in the QUD hierarchy: each subquestion is about part of the situation asked about in its superquestion. For example, the situation of Yvonne eating something asked about in the current question is a subsituation of the dinner-last-Saturday-situation asked about in its superquestion Q3. Following Schwarz (2009: 93–94), the topic situation is represented as a free situation pronoun (7), which is an argument to a topic operator (8). Applying this topic operator to a proposition and a topic situation yields the set of all counterparts (‘≈’ is the counterpart relation) of the topic situation in which the proposition is true, see (9) for an example. Thereby, counterparts of the topic situation are situations in other worlds which in all relevant respects are exactly like the topic situation. (7) s2 topic Yvonne ate pizza (8) [[topic]] = λ p.λ s’.λ s. s ≈ s’ & p(s) (9) [[s2 topic Yvonne ate pizza]]g = λ s. s ≈ g(2) & Yvonne ate pizza in s Since the topic situation pronoun is free, it receives a value from the context, namely the situation that its immediate QUD is about. This situation is salient since the QUD is salient. 2.2. The resource situation As discussed in Kratzer (2011), there is evidence that for quantifier restriction, another situation is needed, the resource situation. For example, as shown in (10) (from Soames, 1986: 357), there are cases of restriction to a subset of the individuals present in the topic situation. The topic situation here contains the test persons in a sleep lab, as well as the research assistants. The quantifier everyone, however, is implicitly restricted to the test persons. This is seen as Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 519 M. Grubic Two strategies of reopening QUDs evidence that the restriction of quantifiers is not provided by the topic situation, but, in this case, by a subsituation of the topic situation. (10) Everyone is asleep and being monitored by a research assistant. (Soames 1986) Similarly, examples involving so-called incomplete definite descriptions such as (11) (from McCawley, 1979: 378) can be used to argue for the necessity of resource situations. Definite descriptions like the dog require the referent to be the unique salient dog. In the topic situation of (11), however, there are two dogs. The felicity of such examples can be explained under the assumption that the referent is presupposed to be the unique salient individual of this kind in the resource situation (Schwarz, 2009), which in this case might involve members of the household. (11) (Context: the family dog got into a fight) I’ll have to see to it that the dog doesn’t get near that dog again. One main proposal of this paper is that wh-phrases are also restricted via resource situations. The individuals that can potentially replace the wh-phrase in the answer are said to be restricted, too. For example, in (12), in the same sleep lab situation, the possible answers can plausibly be argued to be restricted to those that involve test persons. (12) Who is asleep and being monitored by a research assistant? Additionally, in a question-answer sequence like (13), where the wh-phrase is replaced by a quantifier in the answer, the resource situation of the wh-element and the quantifier are arguably the same, again involving only the test persons. (13) Q: Who is asleep and being monitored by a research assistant? A: Everyone! A question, in the QUD approach, denotes the set of its possible answers (14) (following Hamblin 1973). For example, the denotation of the question in (14) is a set of possible answers in which the wh-element is replaced by a relevant individual.3 Thereby, the wh-phrase denotes a set of individuals. In (14), who the set of human individuals in the resource situation. The resource situation is represented as a situation pronoun, which is the first argument of who, cf. (15b), where the value for the free situation pronoun is provided by the assignment function g. (14) [[who was asleep]] = {Amy was asleep, Ben was asleep, Cem was asleep, Dana was asleep ...} (15) a. b. [[who]]= λ s.λ x. x is a human in s [[who s1]]g = λ x. x is a human in g(1) The wh-phrase is combined with the predicate via pointwise functional application (e.g. Rooth 3 It is debated whether plural individuals are possible alternatives for singular individuals, cf. Beaver and Clark (2008) for discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 520 M. Grubic Two strategies of reopening QUDs 1992, 1996). This is a process of combining two sets, by which every member of the first set is combined with every member of the second set by standard functional application. Thus (14) is derived as shown in (16), or more generally in (17). (16) {Amy is asleep in g(2), Ben is asleep in g(2), Cem ...} who was asleep in s2 {Amy, Ben, Cem, ...} {λ x. x is asleep in g(2)} (17) [[who s1 was asleep in s2]] = [[was asleep in s2]] ([[who s1]]) = {λ s. s≈g(2) & x was asleep in s | x is a human in g(1)} To sum up, statements are made about a topic situation, and evaluated for truth or falsity with respect to this topic situation. The topic situation can be identified with the help of overt cues, e.g. tense, temporal or locative adverbials, but usually it is identified because it is inherited from the sentence’s QUD, the (usually implicit) hearer-question that the sentence answers. Evidence from the restriction of quantifiers and definite determiners shows that in addition, a resource situation must be assumed. The following section will present evidence from the German additive particles auch and noch that both topic and resource situations play a role for additive particles. 3. Additive particles Additive particles like English also/too do not contribute to the truth-conditional meaning of the sentence, they merely introduce a presupposition. They are focus-sensitive: the presupposition changes when the placement of the focus changes. (18) John also introduced B ILL to Sue. PRESUPP : John introduced somebody else to Sue. (19) John also introduced Bill to S UE. PRESUPP : John introduced Bill to somebody else. The presupposition of additive particles is different from those of many other presupposition triggers (e.g. stop) in that it needs to be salient, i.e. on the minds of the speaker and the addressee, rather than merely mutually known. For example, the utterance in (20), Mary stopped smoking, is possible without the information that Mary used to smoke being recently mentioned or otherwise salient. For the additive particle in (21), Bill smokes, too, to be felicitous, the information that somebody else smokes (e.g. Mary smokes) must be recently mentioned, or in the immediate non-linguistic context (e.g. the addressee might be smoking at the time of utterance). If it is merely mutually known that somebody else smokes, but not salient at this time in discourse, this is not enough to license the use of too. For this reason, the additive presupposition has been classified as anaphoric (Kripke 2009; Beaver and Zeevat 2007; Tonhauser et al. 2013, i.a.) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 521 M. Grubic Two strategies of reopening QUDs (20) Mary stopped smoking. PRESUPP : Mary used to smoke (doesn’t have to be salient) (21) Bill smokes, too. PRESUPP : Somebody (e.g. Mary) smokes (has to be salient!) There are several different ways to model the anaphoricity of additive particles (e.g. Heim 1992; Geurts and van der Sandt 2004, cf. Ruys 2015 for a discussion). The approach adopted here is a QUD account of additive particles. Under this account, additive particles are anaphoric because they indicate that the current QUD is already partially answered in the recent context (Beaver and Clark, 2008; Jasinskaja and Zeevat, 2009). For example, in the case of (21), the relevant part of the QUD hierarchy would look like (22): the same question has been asked and answered before, and is reopened, thereby indicating that the previous answer (Mary smokes) was a partial answer, and providing a further partial answer (Bill smokes). ... (22) Who smokes? Who smokes? M ARY smokes B ILL smokes, too The complete answer (Mary and Bill smoke) must be stronger than either of the partial answers alone. For this reason, examples like (23), where one of the answers entails the other, are infelicitous (Kripke, 2009; Beaver and Clark, 2008). (23) #Bill smokes, and Bill and Mary smoke, too. This section introduced the general QUD account adopted in this paper. The following sections discuss the additive particles auch and noch in German. It will be argued that while both indicate that a QUD is reopened, auch indicates reopening with respect to the same topic situation (but a different resource situation), whereas noch indicates reopening with respect to a different topic situation. 3.1. German additive particles In German, auch (=‘also’, ‘too’) is the standard additive particle. Unstressed auch associates with focus (cf. e.g. Jacobs, 1983; König, 1991; Krifka, 1998: i.a.). Like other German focussensitive particles, auch prefers to be as close to the focus as possible (see Büring and Hartmann 2001’s Closeness Principle), as shown in (24)–(25). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 522 M. Grubic Two strategies of reopening QUDs (24) Gestern hat Johann auch B ILL Susi vorgestellt. yesterday has Johann PRT Bill Susi introduced. “Yesterday, Johann also introduced B ILL to Susi.” PRESUPP : Johann introduced somebody else to Susi. (25) Gestern hat Johann Bill auch S USI vorgestellt. yesterday has Johann Bill PRT Susi introduced. “Yesterday, Johann also introduced Bill to S USI.” PRESUPP : Johann introduced Bill to somebody else. There is also a stressed variant of auch, which associates with preceding out-of-focus constituents (Krifka, 1998). For example, Krifka shows that AUCH can associate with the unstressable pronoun es (= ‘it’), in contrast to nur (= ‘only’) and unstressed auch. (26) Es gehört AUCH Peter. it belongs.to also Peter “It belongs to Peter, too.” (27) ?? Nur/?? auch es gehört Peter. only also it belongs.to Peter “Only/Also it belongs to Peter.” The corresponding examples with the stressable pronoun das (=‘that’), in contrast, are fine. (28) Das gehört AUCH Peter. that belongs.to also Peter “That belongs to Peter, too.” (29) Nur/auch das gehört Peter. only/also that belongs.to Peter “Only/Also that belongs to Peter.” According to Krifka, AUCH associates with contrastive topics, i.e. topics marked with a certain accent (a “B accent”, cf. Jackendoff 1972), indicating a QUD hierarchy in which sister questions about alternatives to the contrastive topic play a role (Büring, 2003: 520). For example, if Fred ate the beans is pronounced with a contrastive topic accent on Fred and a focus on beans, it indicates a QUD hierarchy such as (30), indicating a following sister question which also addresses the question who ate what. (30) Who ate what? What did Fred eat? What did Mary eat? Fred ate the beans Mary ate the eggplant When AUCH associates with a contrastive topic, it indicates a QUD strategy like (31), in which a preceding sister question was answered in the same way. (31) What belongs to who? Who does the bag belong to? Who does the phone belong to? The bag belongs to Peter The phone belongs to Peter The German particle noch (“still”) also has an additive use (Umbach, 2012; Eckardt, 2007; Nederstigt, 2006), cf. (32) (from Umbach 2012: 1844). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 523 M. Grubic (32) Two strategies of reopening QUDs Otto hat auch/noch einen S CHNAPS getrunken. Otto has PRT a Schnaps drunk. “Otto also drank a S CHNAPS.” (P RESUPP : Otto drank something else (e.g. a beer)) It however differs from better-studied additive particles like also/too (E.)/auch (G.) in interesting ways. The following section will describe some of these differences. The main claim will be that both additive particles indicate that a QUD is reopened. Noch indicates that it is reopened with respect to a new topic situation, whereas auch indicates that new alternatives are taken into consideration, i.e. that the resource situation is changed. 3.2. Differences between ‘auch’ and ‘noch’ This section describes three important differences between auch and the additive use of noch: First, that noch is most felicitous with overt topic situation shifters, second, that it is the ‘neutral’ additive particle in questions, whereas auch leads to ‘showmaster questions’ and third, that it allows for the reopened QUD to be answered in the same way. Overt topic situation shifters In contrast to auch, additive noch is not entirely felicitous in standard additive contexts, where the antecedent (e.g. Otto had a beer) is immediately followed by a parallel utterance ‘He also had a schnaps’, cf. (33). (33) Otto had a beer. Er hat auch/?? noch einen S CHNAPS getrunken he has PRT a schnaps drunk (intended:) “He also had a schnaps.” Instead, noch is most felicitous if there is an overt indication of a shift in topic situation (e.g. with dann (‘then’), ansonsten/sonst (‘otherwise’)), see (34). (34) Otto had a beer. Dann hat er noch einen S CHNAPS getrunken. then has he PRT a schnaps drunk “And he also drank a schnaps.” This is also discussed in Umbach (2012: 1851), who proposes that in such sentences, “dann indicates that the two answer events combined by dann do not overlap”, and provides example (35) as evidence. Here, according to Umbach, the thunderstorm (without rain) and the rain count as two separate, non-overlapping, events. (35) There was a thunderstorm Dann hat es noch GEREGNET. then has it PRT rained “It rained in addition.” Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 524 M. Grubic Two strategies of reopening QUDs The reverse, i.e. that auch is most felicitous if there is no shift in topic situation, can be observed in cases of accommodation. For example, in (36)–(37), there is an overt indication of a new topic situation (the next year) in the host sentence of the additive particle, making it an utterance about a different topic situation than the overtly presented antecedent. In the case of noch in (36), this is not problematic: noch links these two utterances without any need for accommodation. (36) In 2014, Max visited his parents for Christmas. Das Jahr danach hat er noch die Eltern seiner F REUNDIN besucht the year after has he PRT the parents of.his girlfriend visited “In addition, the next year, he visited the parents of his girlfriend.” → He visited his parents in 2014 & his girlfriend’s parents in 2015 In the case of auch in (37), however, the prominent reading is that Max visited his and his girlfriend’s parents the next year, i.e. an antecedent about the same topic situation (the next year) is accommodated.4 (37) In 2014, Max visited his parents for Christmas. Das Jahr danach hat er auch die Eltern seiner F REUNDIN besucht. the year after has he PRT the parents of.his girlfriend visited “The next year, he visited the parents of his girlfriend too.” → He visited his parents in 2014 & his and his girlfriend’s parents in 2015 Example (38) is a similar example: this is a variation of Umbach’s example (35), replacing noch by auch. Again, as in (37), the new topic situation — introduced by dann — is understood to involve a thunderstorm in addition to rain. (38) There was a thunderstorm Dann hat es auch GEREGNET. then has it PRT rained “Then it rained, too.” Questions In questions, noch is most felicitous, whereas auch indicates that the questioner knows that a further answer is true, i.e. the auch-question is a kind of ‘showmaster question’, according to Umbach (2012). For example, Umbach notes that in a context like (39), only Lisa’s aunt, who knows everything that happened at the zoo, can ask the auch-question in (39a). Lisa’s mother, who didn’t accompany them to the zoo and doesn’t know what happened there, can only ask the noch-question in (39b). The auch question is thus asked by a person who already has a particular answer in mind, hence Umbach’s term ‘showmaster question’. (39) 4 This (Little Lisa tells her mother what happened when she visited the zoo with Auntie.) A: Und was ist im Zoo AUCH passiert? and what is in.the zoo PRT happened “What happened at the zoo, too?” difference between noch and auch is very subtle, and is currently being experimentally tested. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 525 M. Grubic Two strategies of reopening QUDs M: Und was ist im Zoo NOCH passiert? and what is in.the zoo PRT happened “What else happened at the zoo?” This is accounted for by the current approach as follows: in the showmaster question in (40a), Lisa’s aunt reopens the same QUD with respect to a different resource situation, i.e. she indicates that in her first answer, Lisa has not taken all relevant alternatives into account. Reopening the QUD with respect to the same topic situation but a different resource situation, as in the case of auch, indicates that relevant alternatives were forgotten or ignored, whereas reopening the QUD with respect to a new topic situation, as in the case of noch, merely slightly shifts the topic of conversation, and is thus the ‘neutral’ variant in overt questions. Stressed ‘noch’ When a QUD is reopened using noch, the same answer is available again. According to Umbach (2012), noch in (40) associates with a deaccented focused constituent, namely ‘Schnaps’. (40) Otto had a schnaps. And you won’t believe it: Er hat NOCH einen Schnaps getrunken. he has PRT a schnaps drunk “He had another schnaps.” / “# He had a schnaps, too” Example (41), in contrast, is odd, independent of the accenting pattern. (41) Otto had a schnaps. And you won’t believe it: #Er hat auch einen Schnaps getrunken. he has PRT a schnaps drunk “# He had a schnaps, too” This can be explained by the fact that, since the QUD (What did Otto drink?) is reopened with respect to a new topic situation in (40), the same answer (Otto drank a schnaps) will still be informative. In (41), in contrast, the QUD is reopened with respect to the same topic situation, thus only a different answer (e.g. Otto drank a beer) would be felicitous.5 To sum up, auch and noch differ first with respect to their occurrence with overt topic situation shifters, which is most felicitous with noch. Second, in questions, noch is the standard additive particle, while auch seems to indicate that the speaker knows the answer to the question. This was attributed to the resource situation-shifting nature of auch. Third, a noch-answer can be the same as its antecedent answer, while an auch-answer has to differ. This is due to the topic shift inherent with noch: it allows for the same alternatives to become available again. 5 There seems to be a connection between stressed noch and additive or incremental more (Greenberg, 2010, 2012), which Greenberg analyses as indicating further development of a previous eventuality. (i) Otto had one more schnaps. This is an interesting account, which would also complement nicely an account of noch along the lines of Ippolito (2007), but since the noch and more data differ in some respects, a discussion of this is left for future work. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 526 M. Grubic Two strategies of reopening QUDs 3.3. Analysis of ‘auch’ and ‘noch’ Unstressed auch indicates that there is a previous answer to the same QUD, but with a more restricted set of alternatives. The current QUD extends this set to include previously neglected relevant alternatives. For example, the answerer in (42) might have thought of the alternatives {a schnaps, a glass of wine, a glass of cider} in the first answer, but forgotten the beer. By uttering an auch-sentence, she thus repairs this by considering a new domain of alternatives which now includes the beer. The question is thus reopened with respect to a new resource situation, as represented in the discourse tree in (42). (42) What in sr1 did Otto drink in st ? What in sr2 did Otto drink in st ? Otto drank a schnapsF in st Otto drank ‘auch’ a beerF in st This is essentially the analysis given in Umbach (2012: 1860–1861) for unstressed auch, who proposes the term extension question for questions with shifted resource situations, cf. Umbach’s definitions in (43)–(44). (43) unstressed auch in answers addresses an extension question; unstressed auch in questions indicates that the question is an extension question. (44) A question Q=hB, Di is an extension question with respect to a preceding question Q’=hB’, D’i iff (i) B=B’, (ii) D∩D’ = 0, / (iii) D∪D’ is a superordinate domain. In contrast, noch indicates that there is a previous answer to a parallel QUD about a different topic situation in the discourse context, cf. (45). (45) What did Otto drink in st1 ? What did Otto drink in st2 ? Otto drank a schnapsF in st1 Otto drank ‘noch’ a schnapsF in st2 This requirement that the preceding QUD be about a different topic situation can be represented as in (46)–(47). Thereby, noch does not indicate anything about the domain of alternatives, i.e. it does not require the domain to be different or the same in the two questions. (46) noch in answers addresses a shifted question ; noch in questions indicates that the question is shifted. (47) A question Q=hB, Di about S is a shifted question with respect to a preceding question Q’=hB’, D’i about S’ iff (i) B=B’, (ii) S6=S’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 527 M. Grubic Two strategies of reopening QUDs 3.3.1. Combining ‘auch’ and ‘noch’ Since it is possible to combine auch and noch, the account for auch does not require the topic situation to remain the same, and the account for noch does not require the resource situation to remain the same. The prediction thus is that both situations would be different from those of the antecedent, cf. (48), leading to a few predictions, briefly discussed below. (48) What in sr1 did Otto drink in st1 ? What in sr2 did Otto drink in st2 ? Otto drank a schnapsF in st1 Otto drank ‘auch’ a beerF in st2 Prediction I: auch noch should allow for a topic situation shift (without accommodation) (49), like noch. (49) In 2014, Max visited his parents for Christmas. Das Jahr danach hat er auch noch die Eltern seiner F REUNDIN besucht. the year after has he PRT PRT the parents of.his girlfriend visited “The next year, in addition, he visited the parents of his girlfriend.” → He visited his parents in 2014 & his girlfriend’s parents in 2015 Prediction II: auch noch should indicate a shift of resource situation, and thus lead to showmaster questions (like auch), which seems to be the case: the question in (50) is much more natural when it is posed by the aunt than when it is posed by the mother. (50) (Little Lisa tells her mother what happened when she visited the zoo with Auntie.) Auntie: Und was ist im Zoo auch noch passiert? and what is in.the zoo PRT PRT happened “What else happened at the zoo, too?” Prediction III: auch noch should indicate a shift of resource situation, and thus disallow giving the same answer again (like auch). This is in fact the case: (51) is infelicitous, unless auch is understood to associate with the full VP in its scope, leading to the presupposition that he did something else apart from drinking another schnaps. This is the reading obtained when noch is accented, and there is a slight pause between auch and noch. (51) Otto had a schnaps. And you won’t believe it: #Er hat auch noch einen Schnaps getrunken. he has PRT PRT a schnaps drunk (intended:) “He had another schnaps.” Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 528 M. Grubic Two strategies of reopening QUDs 3.3.2. Comparison with other approaches Dimroth 2002 The proposal presented here for noch is reminiscent of a proposal in Dimroth (2002) for stressed NOCH as in (52). Dimroth proposes that stressed NOCH associates with the topic time, just like stressed AUCH associates with a (contrastive) topic. (52) Otto had a schnaps. And you won’t believe it: Er hat NOCH einen Schnaps getrunken. he has PRT a schnaps drunk “He had another schnaps.” A problem with this, which has already been voiced in Nederstigt (2006), is that if noch could associate with something topical and thus out-of-focus, it should be able to stand alone, as stressed AUCH can, cf. (53). (53) At 10p.m., Otto had a schnaps. And at 11 p.m.? AUCH./#N OCH. The other accounts known to me (e.g. Nederstigt, 2006; Eckardt, 2007; Umbach, 2012) all assume that noch/NOCH associates with focus in all examples. Eckardt 2007: Eckardt (2007) proposes that (unstressed) noch can be used to reopen a QUD if the previous answers are positive. According to her, the QUD is reopened as a sub-QUD, involving a subset of its super-QUD’s domain, i.e. the discourse tree would look as in (54). Noch can also be used in such a reopened QUD, if it is overt. (54) Who (of A,B and C) can swim? Ali can swim Who (of B and C) can swim? Ben can swim This is used to explain the observation that noch is often used for the last element in a list of positive answers, cf. (A) in (55). (55) Q: Who (of A, B and C) can swim? A: A LI kann schwimmen, und B EN kann noch schwimmen, aber C EM kann nicht schwimmen. “A LI can swim, and B EN can swim, but C EM can’t swim” This account would predict that the answer in (56) is bad, a prediction that I don’t share.6 6 Note however that judgments on these particles are notoriously difficult. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 529 M. Grubic (56) Two strategies of reopening QUDs Q: Who (of A, B and C) can swim? A: (#) A LI kann schwimmen, B EN kann nicht schwimmen, aber C EM kann noch schwimmen. “A LI can swim, B EN can’t swim, but C EM can swim” Umbach (2012), in her discussion of this account, notes that it is problematic because it cannot account for all of the differences between noch and auch. For example in noch-questions, the domain of alternatives is clearly extended. Umbach 2012 According to Umbach’s own proposal, noch and unstressed auch both reopen a QUD with an extended domain (57). (57) Who (of {A,B}) can swim? Who (of {C,D}) can swim? Ali can swim Cem can swim The main difference between the two is that the alternatives in the case of noch are in a temporal order, an order of (expected) time of mentioning. This temporal order allows to distinguish string-identical alternatives (schnaps1 , schnaps2 ) in the case of stressed NOCH, which can not be distinguished in the case of auch. For stressed AUCH, Umbach (2012) proposes that it reopens a QUD with a subset of the original domain, as Eckard had proposed for noch, cf. (58). (58) Who (of {A,B,C}) can swim? Who (of {B,C}) can swim? Ali can swim Ben can swim She analyses auch in wh-questions as an instance of stressed AUCH, with the wh-element as a topic. This accounts for ‘showmaster questions’: (59) Wer kann AUCH schwimmen? “Who can swim, too?” The current account rejects the idea that the exact same QUD (about the same topic situation) can be reopened with respect to a subset of the same domain (as proposed by Eckardt for noch and Umbach for AUCH). Implicit QUDs essentially reflect speaker assumptions about the alternatives relevant for the hearer. Thus to remind the speaker that she forgot a relevant alternative means to extend the domain of alternatives. In addition, an ordering of alternatives by order of mentioning is not adopted in the current account, since additive particles, being anaphoric, always involve another answer being mentioned earlier than the current one. It is therefore hard to imagine a context in which auch would be Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 530 M. Grubic Two strategies of reopening QUDs licensed but noch wouldn’t under this account. A final difference between the current account and Umbach’s is that the wh-element in AUCH-questions is not assumed to be a topic. 4. Summary and outlook The behaviour of the German additive particles auch and noch provides evidence for resource situations in wh-questions: auch indicates that a QUD about the same topic situation is reopened, with a different resource situation, i.e. considering further alternatives, whereas noch indicates reopening of a question, but about a different topic situation. There are several questions remaining for future discussion. First, many examples involving noch are very subtle. It is thus of vital importance to test the phenomena discussed in these papers with a large group of native speakers. This will be done in future work. Second, it is not entirely clear how the account for additive noch discussed in this paper relates to the other uses of noch as still, e.g. the temporal use in (60), the related locative use in (61), the marginality use in (62), and the comparative use in (63), i.a. (e.g. König, 1977; Löbner, 1989; Krifka, 2000; Umbach, 2009). (60) T EMPORAL /A SPECTUAL Es regnet noch. It rains still “It is still raining.” PRESUPPOSITION : It was raining earlier CONVERSATIONAL IMPLICATURE : It will stop raining soon (61) L OCATIVE /M ARGINALITY Osnabrück liegt noch in Niedersachsen. Osnabrück lies still in Niedersachsen “Osnabrück is still in Lower Saxony.” (62) M ARGINALITY Paul ist noch gemässigt. (Peter ist schon radikal) Paul is still moderate Peter is already radical “Paul is still moderate. (Peter is already radical)” (63) C OMPARATIVE Berta ist noch größer als Adam. Berta is still taller than Adam “Berta is even taller than Adam.” While the topic situation in (60) (e.g. “now”) is certainly different from that of the earlier event, the current analysis neither captures the presupposition that the two events are of the same kind (“rain”) nor the implicature that later, there will be no event of this kind. The analysis presented here can thus not easily be applied to cases like (60) and other, e.g. non-temporal, noch examples. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 531 M. Grubic Two strategies of reopening QUDs In contrast, it is a great advantage of the accounts of Eckardt (2007) and Umbach (2012) that they do intuitively relate to previous accounts of the temporal reading in (60). For example, Eckardt’s proposal that noch adds a positive answer to a QUD after a preceding stretch of discourse containing positive answers to this QUD is related to Löbner (1989)’s analysis of temporal noch, which assumes that (60) adds a current period of rain, after a presupposed preceding period of rain. Umbach, in contrast, relates her proposal to Krifka (2000)’s account, in which noch imposes an order on focus alternatives (e.g. it is raining, it isn’t raining in (60)) on a temporal scale, such that the alternative it is raining precedes the alternative it isn’t raining. Umbach assumes that the different alternatives, i.e. the current utterance and its antecedent, are also ordered on a temporal scale, but not concerning the event time of the mentioned events but concerning the time of mention in discourse: the noch-sentence presupposes an ordering such that there is an alternative that is lower on the scale, i.e. was mentioned earlier. Therefore, an important aspect of future work on this particle will be to find a unified account for the additive use described here and temporal and other uses of noch. References van der Auwera, J. (1993). Already and still: Beyond duality. Linguistics and Philosophy 16, 613–653. Barwise, J. and J. Etchemendy (1987). The Liar. 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Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 533 M. Grubic Two strategies of reopening QUDs Ruys, E. G. (2015). On the anaphoricity of too. Linguistic Inquiry 46(2), 343–361. Schwarz, F. (2009). Two Types of Definites in Natural Language. Ph. D. thesis, University of Massachusetts, Amherst. Soames, S. (1986). Incomplete definite descriptions. Notre Dame Journal of Formal Logic 27, 349–75. Tonhauser, J., D. Beaver, C. Roberts, and M. Simons (2013). Towards a taxonomy of projective content. Language 89, 66–109. Tovena, L. M. and M. Donazzan (2008). On ways of repeating. Recherches Linguistiques de Vincennes 37, 85–112. Umbach, C. (2009). Comparatives combined with additive particles: The case of German noch. In Proceedings of Sinn & Bedeutung 13. Stuttgart. Umbach, C. (2012). Strategies of additivity: German additive noch compared to auch. Lingua 122(15), 1843–1863. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 534 Internal and external readings of same: Evidence for a uniform account1 Daniel HARDT — Copenhagen Business School Abstract. Same is an anaphoric element that performs a comparison, which can either be external or internal to a sentence. Hardt and Mikkelsen (2015) show that same, unlike other anaphoric expressions, imposes a parallelism constraint, and they present three types of examples showing that same is infelicitous in the absence of parallelism. Hardt and Mikkelsen propose an account that applies uniformly to internal and external readings; however, the evidence they present largely targets external readings – they don’t offer empirical evidence that clearly supports the uniform approach. Furthermore, Barker (2007) argues that internal readings must be treated differently than external readings. In this paper, I show that the parallelism effects observed by Hardt and Mikkelsen in fact apply to internal readings as well. This provides support for a uniform treatment of internal and external readings of same. It also suggests that discourse relations, which typically apply to separate overt predications, also apply to the implicit predications that arise in distributional structures. Keywords: same, anaphora, parallelism 1. Introduction Same performs a comparison, which can either be external, as in (1), or internal, as in (2). (1) John read War and Peace. Tom read the same book. (2) Every boy read the same book. In (1), the definite the same book must be identified with the antecedent NP, War and Peace. It would appear to impose a semantic identity condition on an antecedent expression in surrounding discourse. In this way same is like pronouns, definites, and ellipsis, all of which require identity with an antecedent. In (2), the internal reading is licensed, or controlled, by a quantified NP, every boy. Since Carlson (1987), it has been recognized that the controller need not be a NP, but can be a variety of syntactic categories. Barker (2007) captures this diversity of controllers with an account that only applies to internal readings. Hardt and Mikkelsen (2015), on the other hand, argue for treating internal and external readings in a uniform way, and they argue furthermore that same gives rise to a discourse parallelism requirement. They give three types of observations in support of this theory. But all three of these observations concern external readings, and not internal readings. Thus they don’t provide concrete empirical support for their proposal that internal and external readings receive the same treatment. In this paper, I present new arguments in favor of a uniform account of external and internal readings of same: I show that all three of Hardt and Mikkelsen’s observations, distinct antecedent, parallel antecedent, and negated antecedent, apply to internal readings as well as external readings. 1 Thanks to Line Mikkelsen for useful input. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 535 D. Hardt Internal and external readings of same: Evidence for a uniform account 2. Background 2.1. Internal readings As pointed out by Carlson (1987), same can give rise to internal readings. He points out that this requires a distributive element, a quantifier or coordination. We term this element the controller (shown in bold). So in (3), the controller is the QP Every boy, while in (4) it is the conjoined NP John and Sam. As (5) and (6) illustrate, the controller need not be a nominal category – here we observe a conjoined V and a conjoined PP. (3) Every boy read the same book. (4) John and Sam read the same book. (5) Sam praised and criticized the same book. (6) Sam assigned the same book in March and in April As Carlson puts it, in the internal reading, the sentence “provides its own context” for the interpretation of same. Any conjoined constituent can function as controller, it would appear, as long as it is interpreted distributively. Heim (1985) also acknowledges the diversity of potential controllers. This is dealt with explicitly by Barker (2007)[p. 25], who introduces a structural postulate which makes it possible to λ abstract over any distinguished element. In what follows, I will simply assume that a controller can be any syntactic object that can participate in coordination. 2.2. External readings While internal readings “provide their own context”, one can observe analogous readings for same where surrounding discourse provides the context, as in (7), which is directly analogous to (4) above. (7) John read War and Peace. Sam read the same book. We can think of John and Sam as controllers in (7). Note that, just like internal readings, external readings exhibit a diversity of controllers – verbs in (8) and prepositional phrases in (9). (8) John praised War and Peace. Then he criticized the same book. (9) John assigned War and Peace in March. He assigned the same book in April. Much previous literature (Brasoveanu (2011); Heim (1985)) emphasizes the evident analogy between internal and external readings. But Barker (2007) argues that his proposed account Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 536 D. Hardt Internal and external readings of same: Evidence for a uniform account should only apply to internal readings, and while Hardt and Mikkelsen (2015) follow most previous literature in seeking a uniform account, their empirical arguments, based on parallelism, don’t seem to naturally apply to internal readings. Thus, the question of a uniform treatment of internal and external readings is left rather open. In what follows, I will show that Hardt and Mikkelsen’s parallelism arguments can also be made with respect to internal readings. The key to doing this is to look at examples where the controllers are verbal rather than nominal categories. 3. Hardt and Mikkelsen’s proposal Hardt and Mikkelsen take as their starting point a double indexing approach for same, as proposed by Brasoveanu (2011). This is a natural reflection of the fact that same compares two expressions: a local containing expression and its antecedent. 3.1. Brasoveanu’s account I illustrate the account of Brasoveanu (2011) with respect to (10). (10) Everyu0 boy read theu1 same2u1 book. Intuitively, the interpretation is this: (11) for every pair of boys b1 and b2 and pair of books k1 and k2 such that b1 read k1 and b2 read k2 , k1 = k2 To capture this, Brasoveanu defines a distribution operator that distributes over pairs of individuals, and then gives same and different the ability to access such pairs. Brasoveanu gives the following meaning for same: (12) samem un λ Pet .λ ve .P(v); ∗(P(un+m ); [identical{un+m , un }]) On Brasoveanu’s account same compares a containing NP with an antecedent NP. The challenge for internal readings is that there is no explicit antecedent for same. To address this, Brasoveanu posits a distribution operator which allows comparison of individuals within the domain of quantification. To understand how this works, consider the drs for (10): (13) maxu0 ([atoms-only{u0 }, boy{u0 }]); distu0 ([u1 |atoms-only{u1 }], singleton{u1 }, book{u1 }; ∗((book(u1+2 ); [identical{u1+2 , u1 }]); [read{u0 , u1 }])) The contribution of every boy is the maximal set of boys, while the dist operator tests each element of that set to see that it satisfies the nuclear scope. In doing this dist in fact examines Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 537 D. Hardt Internal and external readings of same: Evidence for a uniform account all pairs of elements, call them boy1 and boy2 , and checks each element to see that it satisfies the nuclear scope, which itself involves an update, namely a book associated with each boy – these boy-book pairs are termed stacks. In this example each stack has length 2; in general they can be of any length. Thus dist checks every pair of stacks, s1 and s2 , to ensure that both s1 and s2 satisfy the nuclear scope. These expressions make use of the stack-concatenation operator, ∗, which examines its two input stacks, and concatenates them. The concatenated stack can then be used to compare two analogous individuals, using the offset, which is the length of the input stacks. u0 u1 boy1 book1 * u0 u1 boy2 book2 = u0 u1 u2 u3 boy1 book1 boy2 book2 The resulting stack makes available two discourse referents, u1 and u3 ; in the drs above, the identical condition is placed on these two discourse references, as desired. The distribution operator ensures that all possible pairs of stacks will be compared, which in this case means that all pairs of boys read the identical book. Hardt and Mikkelsen take issue with Brasoveanu, in that they claim that same is different, in that it indexes eventualities, unlike different and other anaphoric expressions. 3.2. Parallelism The main claim of Hardt and Mikkelsen (2015) is that same requires parallelism. More specifically, the clause containing same and the antecedent clause must be related by Parallel, as defined here, folllowing Kehler (2002): (14) Parallel: Infer P(a1 , a2 , . . .) from the assertion of S1 and P(b1 , b2 , . . .) from the assertion of S2, for a (non-trivial) common P and similar ai and bi . Parallel requires a common relation P that subsumes the relation of both S1 and S2, as well as similar parallel elements. To satisfy Parallel, two eventualities must contain similar predicates applied to similar arguments. Two predicates count as similar if they both entail a non-trivial common relation. The arguments are similar to the extent that similar predicates apply to them. An intuitive way of computing this can be found in accounts such as Asher (1993) and Prüst et al. (1994), where parallelism is thought of as a kind of most specific unifier, which captures the semantic commonality between the two eventualities. 3.3. Semantic representation Hardt and Mikkelsen (2015) follow Brasoveanu in giving a uniform treatment of same in this way, whether it appears with internal or external readings. However, recall that Hardt and Mikkelsen define same somewhat differently, so that, on their account, a Parallel condition is placed on the containing and antecedent eventualities. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 538 D. Hardt Internal and external readings of same: Evidence for a uniform account The meaning for same for Hardt and Mikkelsen builds on that given in Brasoveanu (2011), with two key modifications: first, same compares eventualities rather than individuals. Second, the comparison is the discourse condition Parallel, rather than a simple identity. This is the meaning for same proposed by Hardt and Mikkelsen (2015): samem en λ Pet .λ ve .P(v); ∗[parallel{en+m , en }] The subscript en indexes same to the containing eventuality, and the antecedent eventuality is determined by adding the offset m to n. The discourse condition Parallel is applied to these two eventualities. We return now to (10), which receives the following representation: (15) [Everyu0 boy read theu1 same3e2 book.]e2 With this indexing, the subscript for same, e2 , indexes the containing S, rather than the containing NP as in Brasoveanu’s system. Other than that, the analysis proceeds in exactly the same way; the superscript on same is the offset, which is the size of the stack. Then, by using the stack concatenation operator ∗ below, the drs allows same to impose Parallel on two instantiations of the eventuality, [read{u0 , u1 }]. (16) maxu0 ([atoms-only{u0 }, boy{u0 }]); distu0 ([u1 , e2 |atoms-only{u1 }], singleton{u1 }, book{u1 }), e2 : read{u0 , u1 }; ∗[parallel{e2+3 , e2 }]) u0 u1 e2 boy1 book1 read(boy1, book1) = * u0 u1 boy2 book2 e2 read(boy2, book2) u0 u1 e2 u3 u4 e5 boy1 book1 read(boy1, book1) boy2 book2 read(boy2, book2) Hardt and Mikkelsen’s meaning for same can be applied for internal readings just as it is applied for external readings. However, the imposition of Parallel for internal readings would appear to be vacuous – as Hardt and Mikkelsen, say, for internal readings “it is somewhat difficult to discern the interpretive effect of same” (p 25). And indeed it is unusual to impose a discourse condition on the implicit predications that arise from distributive structure in this way. However, as we will see, there are in fact clear effects of parallelism on these internal readings. 4. Hardt and Mikkelsen’s observations – external readings Hardt and Mikkelsen (2015) present a series of contrasts that distinguish same from different, as well as other anaphoric forms. In each case same is ruled out where different and other Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 539 D. Hardt Internal and external readings of same: Evidence for a uniform account anaphoric forms are allowed. Distinct antecedent The following example is originally due to Hardt et al. (2012), who observe that it is most naturally read as describing a single fish-catching event, and on that reading, same is infelicitous, while other forms are acceptable. (17) a. b. John caught a big fish, and he caught it/*the same fish without any fishing equipment. Hardt et al. (2012) observe that same requires that the antecedent and containing clause must be distinct events. Hardt and Mikkelsen (2015) argue that this is a consequence of their parallelism constraint: Parallel is not satisfied because the containing clause, (17b), has a manner modifier, without any fishing equipment, which lacks a corresponding parallel element in the antecedent clause, (17a). Moreover, no such parallel element can be inferred, without losing the singleevent reading. (18) [Johnu1 caught au2 big fish]e3 , a. and [heu1 caught itu2 without any fishing equipment]e4 . e5 b. *and [heu1 caught theu4 same−1 e5 fish without any fishing equipment] . The following is the drs for the antecedent clause in (18): (19) [u1 , u2 , e3 |u1 = John, f ish(u2 ), big(u2 ), e3 : caught{u1 , u2 }] The following is the drs for the continuation in (18a), which is acceptable: (20) [e5 |e5 : caught{u1 , u2 , without-equipment}] (21) gives the drs for the infelicitous continuation with same: (21) [u4 , e5 | f ish(u4 ), u4 = u2 , e5 : caught{u1 , u4 , without-equipment}]; ∗[parallel{e5 , e4 }] Here we can see that Parallel fails. We can see that e5 is caught(u1 , u4 , without-equipment), and e4 is caught(u1 , u4 ). Thus Parallel fails because there are not similar parallel elements. Negated antecedent (22) John didn’t read War and Peace. a. He read a different book. b. *Susan read the same book. c. Susan read it. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 540 D. Hardt Internal and external readings of same: Evidence for a uniform account According to Hardt and Mikkelsen (2015), a negated antecedent is ruled out for same, because the antecedent eventuality must be accessible, as defined in DRT (Kamp and Reyle (1993)). They argue that this shows that the effect is a consequence of the fact that same imposes the Parallel condition on the containing and the antecedent eventuality; if the antecedent eventuality is not accessible, the drs would be ill-formed. Hardt and Mikkelsen provide the following indexing for (22): (23) [not [Johnu1 read War and Peaceu2 ]e3 ]. e5 a. [Heu1 read au4 different−2 u4 book] . e6 b. *[Susanu4 read theu5 same−3 e6 book] . u e c. [Susan 4 read itu2 ] 5 . The following is the drs for the antecedent clause, (23). (24) [u1 , u2 |u1 = John, u2 = war-and-peace, not[e3 |e3 : read{u1 , u2 }]] The drefs u1 and u2 are introduced at the top level drs, because they represent names. However, the eventuality dref e3 is introduced in the drs that is embedded under not. Because of this, e3 is not accessible to subsequent discourse. (25) shows the drs for the continuation in (23a). (25) [u4 , e5 |book{u4 }, e5 : read{u1 , u4 }]; ∗(book(u4−2 ); [disjoint{u4 , u2 }]) Here, different simply compares the drefs u4 and u2 . There is no accessibility problem, since u2 is introduced by the name War and Peace and is therefore accessible at the top level drs. The drs for (23b) is as follows: (26) [u4 , u5 , e6 |u4 = Susan, book{u5 }, u5 = u2 , e6 : read{u4 , u5 }]; ∗[parallel{e6 , e3 }] The problem here is that same must compare two eventualities, e6 and e3 , but since e3 is embedded under negation, it is not accessible. Finally, the drs for the continuation with a pronoun in (23c) is as follows: (27) [u4 , e5 |u4 = Susan, e5 : read{u4 , u2 }] It is clear that this is acceptable: the pronoun is simply co-indexed with the accessible antecedent, u2 . Notice that on Brasoveanu’s analysis, same would not be ruled out, since, like different, it merely requires an accessible NP antecedent, in this case War and Peace. Of course, it might appear that War and Peace is also inaccessible, since it is embedded within the negation. However, it is standard in DRT to treat proper names differently; they are normally accessible at the top level drs. See Kamp and Reyle (1993) for details. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 541 D. Hardt Internal and external readings of same: Evidence for a uniform account Parallel antecedent (28) John praised War and Peace. a. And Bill read it/*the same book. b. But Bill criticized the same book. According to Hardt and Mikkelsen (2015) same is ruled out in (28a), because Parallel is not satisfied by the antecedent clause John praised War and Peace, because it is not possible to infer a common non-trivial P that subsumes read and praised. Compare (28a) to the felicitous (28b): here Parallel is satisfied because one can infer from the verbs criticize and praise a common non-trivial P, namely evaluate, with similar parallel elements <John, Bill> and <War and Peace, the book>. This is illustrated here for one version of (28): (29) [Johnu1 praised War and Peaceu2 ]e3 . e6 a. * And [Billu4 read theu5 same−3 e6 book] e6 b. But [Billu4 criticized theu5 same−3 e6 book] Here we translate (29a) into the following drs’s: [u1 , u2 , e3 |u1 = John, u2 = war-and-peace, e3 : praise{u1 , u2 }] [u4 , u5 , e6 |u4 = Bill, book{u5 }, u5 = u2 , e6 : read{u4 , u5 }]; ∗[parallel{e6 , e3 }] Observe that Parallel is imposed on eventualities e6 (read(Bill, War and Peace)) and e3 (praise(John, War and Peace)). As discussed above, Parallel fails here because the predicates praise and read do not entail a non-trivial common property. 5. New observations – internal readings In this section, we show that all the observations offered by Hardt and Mikkelsen (2015) with respect to external readings in fact apply in a similar way to internal readings. Distinct antecedent The following example is due to Barker (2007): (30) a. b. David hit and killed Goliath. David hit and killed the same man. As Barker observes, with Goliath, there is an ambiguity – there could be two events, a hitting event and a killing event, or there could be one event in which the hitting of Goliath was the killing of Goliath. With same, this ambiguity goes away – the hitting and killing must be Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 542 D. Hardt Internal and external readings of same: Evidence for a uniform account distinct events. This is in fact observed by Hardt and Mikkelsen (2015), who point out that their Parallel constraint requires that the two events it relates are distinct. This is in fact completely analogous to the distinct antecedent claim given above with respect to external readings. Following Hardt and Mikkelsen, we assume that (30a) receives the following drs representation: S [v0 , v1 , v2 |v0 = hit, v1 = killed, v2 = v0 v1 ]; distv2 ([u3 , u4 , e5 | john{u3 }, man{u4 }, e5 : v2 {u3 , u4 }; ∗[parallel{e5+4 , e5 }]) (31) v2 u3 hit john = v2 hit u4 e5 man1 hit(john, man1) * v2 u3 u4 e5 killed john man2 killed(john, man2) u3 u4 e5 v6 u7 u8 e9 john man1 hit(john, man1) killed john man2 killed(john, man2) The condition parallel is applied to the two eventualities, e5 and e9 . As discussed above, Hardt and Mikkelsen argue that the Parallel condition quite generally includes a requirement that the two eventualities are distinct. Since it is same that introduces the parallelism requirement, this explains the fact that (30a) allows the same-event reading, while (30b) does not. Negated antecedent Above we saw that Hardt and Mikkelsen (2015) claimed that negated antecedents for same were ruled out because of the parallelism constraint. In particular, since same required parallelism between the containing and antecedent clauses, a negated antecedent clause rendered it inaccessible, resulting in an ill-formed drs. In (32) we show an analogous effect with an internal reading, where there is a negated antecedent, and we see that same is ruled out, although an ordinary definite description (without same) is acceptable. (32) John didn’t read, but did skim the book/*the same book. As observed by Carlson (1987), a controller can be a coordinated element that is interpreted distributively. Here, we have two coordinated verbal elements. Crucially, the coordination includes a negative polarity in the first conjunct and positive polarity in the second. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 543 D. Hardt Internal and external readings of same: Evidence for a uniform account S [v0 , v1 , v2 |v0 = did not read, v1 = did skim, v2 = v0 v1 ]; distv2 ([u3 , u4 , e5 | john{u3 }, book{u4 }, e5 : v2 {u3 , u4 }; ∗[parallel{e5+4 , e5 }]) v2 u3 u4 e5 did not read john book1 not(read(john, book1)) v2 u3 u4 e5 skimmed john book2 skimmed(john, book2) = v2 u3 did not read j * u4 e5 v6 u7 b1 not(read(j, b1)) skimmed j u8 e9 b2 skimmed(j, b2) Here, we see that Parallel is applied to events e5 and e9 – it fails, because e5 is negated. Parallel antecedent It was observed by Hardt and Mikkelsen (2015) that Parallel gives rise to a preference for predicates that are semantically related. For example, praise and criticize both entail a common property, evaluate. On the other hand, investigate and reject are not related in a parallel way; rather, reject in this case is a consequence of investigate. Here we see this effect with internal readings. (33) a. b. John investigated and rejected the theory * John investigated and rejected the same theory. (34) John praised and criticized the same theory. Below we show how this contrast is captured. We begin with the representation of the acceptable (34): S [v0 , v1 , v2 |v0 = praised, v1 = criticized, v2 = v0 v1 ]; distv2 ([u3 , u4 , e5 | john{u3 },theory{u4 }, e5 : v2 {u3 , u4 }; ∗[parallel{e5+4 , e5 }]) v2 u3 u4 e5 * praised john theory1 praised(john, theory1) v2 u3 u4 e5 criticized john theory2 criticized(john, theory2) = v2 u3 praise j u4 t1 e5 v6 u7 praise(j, t1) criticized j u8 t2 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde e9 criticized(j, t2) 544 D. Hardt Internal and external readings of same: Evidence for a uniform account We observe that Parallel is imposed on eventualities e5 (praise(john, theory1)) and e9 (criticized(john, theory2)). Because of the semantic relationship between praise and criticize, Parallel is satisified. We turn now to the unacceptable (33b): S [v0 , v1 , v2 |v0 = investigated, v1 = rejected, v2 = v0 v1 ]; distv2 ([u3 , u4 , e5 | john{u3 },theory{u4 }, e5 : v2 {u3 , u4 }; ∗[parallel{e5+4 , e5 }]) v2 u3 u4 e5 investigated john theory1 investigated(john, theory1) v2 u3 u4 e5 rejected john theory2 rejected(john, theory2) * = v2 u3 investigated j u4 t1 e5 v6 u7 investigated(j, t1) rejected j u8 t2 e9 rejected(j, t2) Here, Parallel is imposed on eventualities e5 (investigated(john, theory1)) and e9 (rejected(john, theory2)). The predicates investigate and reject don’t have a non-trivial entailed property, and thus Parallel is not satisified. 6. Conclusions Hardt and Mikkelsen (2015) show that same differs from other, related expressions, in that it gives rise to a parallelism requirement that must hold between the containing clause and an antecedent clause. They show this by presenting three types of parallelism effects: distinct antecedent, negated antecedent, and parallel antecedent. These effects were all shown to hold for external readings – cases where the antecedent clause and the containing clause appear in separate, overt predications. Although Hardt and Mikkelsen’s account is formulated to apply in the same way for internal readings, they do not show that parallelism has clear effects in the case of internal readings. In this paper, I have shown that all these parallelism effects, distinct antecedent, negated antecedent, and parallel antecedent, apply to internal readings just as they do for external readings. This is perhaps surprising – discourse constraints such as parallelism typically are applied to separate overt predications, rather than the implicitly distinct predications that arise in distributional structures. I think these parallelism effects have not previously been observed for internal readings, because the typical internal readings have involved quantificational NP controllers, such as (2). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 545 D. Hardt Internal and external readings of same: Evidence for a uniform account In such cases, it is difficult to see how to construct examples that potentially violate parallelism. In this paper we have seen that they are readily constructed in examples involving controllers that are coordinated verbal categories. These examples can give rise to implicit predications that are not necessarily parallel, since the coordinated elements can differ in polarity, event structure or the semantic content of the predication, all of which are crucial in satisfying parallelism. While it is well-established that anaphoric elements are sensitive to parallelism, the observations in this paper, like those of Hardt and Mikkelsen (2015), do not merely show that parallelism is relevant to the interpration of same. Rather, the claim is that same is unacceptable in the absence of parallelism, and this is captured quite directly, by making the parallelism constraint part of the lexical meaning of same. The observations in this paper provide additional support for this view. References Asher, N. (1993). Reference to Abstract Objects in Discourse. Dordrecht: Kluwer. Barker, C. (2007). Parasitic scope. Linguistics and Philosophy 30(4), 407–444. Brasoveanu, A. (2011). Sentence-internal different as quantifier-internal anaphora. Linguistics and Philosophy 34(2), 93–168. Carlson, G. (1987). Same and different: Consequences for syntax and semantics. Linguistics and Philosophy 10(4), 531–565. Hardt, D. and L. Mikkelsen (2015). Same but different. Linguistics and Philosophy 38(4), 289–314. Hardt, D., L. Mikkelsen, and B. Ørsnes (2012). Sameness, ellipsis and anaphora. In M. Aloni and F. Veltman (Eds.), Proceedings of the Eighteenth Amsterdam Colloquium, Amsterdam, pp. 341–350. Foris. Heim, I. (1985). Notes on comparatives and related matters. Unpublished ms., University of Texas, Austin. Kamp, H. and U. Reyle (1993). From Discourse to Logic. Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory. Dordrect: Kluwer. Kehler, A. (2002). Coherence, Reference, and the Theory of Grammar. Stanford, CA: CSLI Publications. Prüst, H., R. Scha, and M. van den Berg (1994). A discourse perspective on verb phrase anaphora. Linguistics and Philosophy 17(3), 261–327. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 546 Presupposition projection from disjunction in online processing1 Aron HIRSCH — Massachusetts Institute of Technology Jérémy ZEHR — University of Pennsylvania Florian SCHWARZ — University of Pennsylvania Abstract. Stalnaker (1973, 1974) suggested that presuppositions are evaluated dynamically in a way that crucially takes into account the ‘left-to-right’ unfolding of linguistic expressions. Recently, even more explicit considerations of the timing of online processing have been invoked to account for patterns of presupposition projection (e.g. Schlenker, 2008, 2009; Chemla and Schlenker, 2012; Hirsch and Hackl, 2014). However, relatively little is known about the actual time course of presupposition interpretation, in particular in environments that involve projection. In this paper, we take disjunction as our testing ground, and use visual world eye tracking data to shed light on the unfolding of presupposition projection in real time. Our key generalization is that presuppositions are evaluated immediately when the interpreter encounters the trigger in the left-to-right parse, bearing out a key assumption in the relevant theoretical literature, namely that presupposition projection can be related to incremental processing. Keywords: presupposition, presupposition projection, disjunction, eye-tracking, visual world paradigm, experimental pragmatics 1. Introduction A central issue in presupposition theory is the problem of presupposition projection: how are the presuppositions of a complex sentence determined from those of its atomic parts? As shown in (1), presuppositions interact with certain embedding expressions differently from entailments: (1) a. The bathroom is in a funny place. b. The bathroom is not in a funny place. The entailed contribution of the predicate is in a funny place is affirmed in (1a), but denied in (1b). Yet, the inference that there is a bathroom, introduced by the definite description the bathroom is conveyed by both sentences: the existence presupposition of the definite description projects from the scope of negation in (1b). In this paper, we study the interaction between presupposition projection and online processing, focusing on co-ordinate constructions, which exhibit a complex pattern of projection effects. In the general case, presuppositions project from both the first and second co-ordinate: both of the sentence variants in (2) presuppose that there is a bathroom. 1 We thank the audiences at SuB 21 (Edinburgh), the Schwarz Lab meeting at UPenn, and the Experimental Syntax and Semantics Lab meeting at MIT for useful comments and discussion. We also thank Kendra Carson and Claire Huang for their assistance in preparing auditory stimuli and collecting data, and Dorothy Ahn for the visual stimuli. This project has been supported by NSF-grant BCS-1349009 to Florian Schwarz. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 547 A. Hirsch, J. Zehr, & F. Schwarz (2) Presupposition projection from disjunction in online processing a. The rooms have odd shapes, and the bathroom is in a funny place. b. The bathroom is in a funny place, and the rooms have odd shapes. However, it has long been observed that presupposition projection from conjunction can depend on the linear order of the conjuncts, in particular in cases where the conjunct not containing the presupposition trigger entails the presupposition: (3) a. There is a bathroom, and the bathroom is in a funny place. b. #The bathroom is in a funny place, and there is a bathroom. The effect of the first conjunct entailing the presupposition of the second conjunct in (3a) is that the sentence as a whole has no presupposition at all. In contrast, the reverse conjunct order in (3b) seems to be infelicitous. Intuitively, this is due to a clash between the requirement introduced by the presupposition in the first conjunct that it be taken for granted that there is a bathroom, and the presentation of that very notion as new information in the second, i.e., the redundancy of the second conjunct seems to induce infelicity here. The simple example above suggests that linear order interacts with presupposition projection. Most early accounts of projection effectively stipulated this type of effect as a lexical property of sentential connectives (Karttunen, 1973; Heim, 1983). Recent approaches, though, have sought a more explanatory perspective by linking projection to online processing: asymmetric projection in conjunction emerges from the left-to-right nature of processing (Schlenker, 2009: cf. Schlenker 2008; Fox 2008; Chemla and Schlenker 2012; Hirsch and Hackl 2014). While this move towards greater explanatory adequacy is conceptually appealing, these approaches crucially rely on assumptions about online processing that have not been empirically tested, in particular with regards to how projection is evaluated in real time. Our goal is to directly test one key assumption in this regard, namely (4), which we take to be an implicit or explicit feature of all accounts linking projection behavior to online processing: (4) Rapid Incremental Presupposition Evaluation (‘RIPE’) The interpreter decides whether or not a presupposition projects immediately when they encounter the trigger in the left-to-right parse. Although (4) seems intuitive given general evidence for rapid incremental interpretation, it is not obviously borne out in all cases. An apparent corollary of (4) would seem to be that only material which precedes a given presupposition trigger should be able to influence whether or not the presupposition projects. However, there are cases where material following the trigger is relevant. Consider the contrast in (5), involving disjunction. (5b) is a well-known example due to Barbara Partee (Partee, 2005), and (5a) is a minimal variant thereof. (5) a. Either the bathroom is in a funny place, or Mary is lost. b. Either the bathroom is in a funny place, or there is no bathroom. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 548 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing In both cases, the presupposition trigger (the bathroom) is in the first disjunct, while the second disjunct is varied, with an impact on projection: in (5a), the presupposition projects, but it does not in (5b), i.e. only (5a) gives rise to an inference that there is a bathroom. Indeed, the point of (5b) is to communicate agnosticism about whether there is a bathroom. The pattern in (5) looks inconsistent with RIPE: if projection is evaluated in online processing as soon as the trigger is encountered, then downstream material should not play a role. Given this apparent evidence against RIPE, we take disjunction as our empirical object of study. To foreshadow, we argue that, despite initial appearances, disjunction is in fact compatible with RIPE, following Hirsch and Hackl (2014). Our main contribution here is to provide novel empirical evidence from visual world eye-tracking that directly supports RIPE in disjunction. 2. RIPE: motivation and puzzles We begin by illustrating how asymmetric projection in conjunction can be derived from effects of real time processing (§2.1-2.3). The account we sketch follows Schlenker (2009) — and relies on RIPE. This motivates our choice to pursue RIPE. In the last part of the section, we make explicit the puzzle for RIPE posed by disjunction (§2.4-2.5). 2.1. Background: asymmetric projection in dynamic semantics Stalnaker (1973) developed a seminal analysis of presupposition, by which presuppositions impose requirements on the discourse context. The context is modeled as the set of possible worlds in which all propositions mutually agreed upon by the conversational participants are true (the ‘context set’, c). A presupposition constrains c such that if a sentence S globally presupposes a proposition p, then S can only be felicitously uttered in contexts where p is true at every world in c. c is assumed to evolve as the discourse unfolds, and the felicity requirement applies to the context set that takes all previous parts of the discourse into account. Heim (1983) extended Stalnaker’s approach to a more general model of context update where the context relative to which a presupposition is evaluated is not necessarily c itself. To illustrate, consider conjunction. Heim models the denotation of lexical items not in terms of truth-conditions, but rather in terms of the impact they have on the context set (their ‘context change potential’). Conjunction is defined to sequentially update c with the propositions expressed by the two conjuncts (‘+’ corresponds to intersection applied to the sets of possible worlds that c, φ1 , and φ2 stand for): (6) a. ‘S1 and S2 ’ uttered in context c b. (c + φ1 ) + φ2 The key consequence of this sequential update is that S1 and S2 are interpreted relative to different contexts: S1 is directly evaluated relative to c, while S2 is interpreted relative to a context c0 resulting from updating c with the proposition expressed by S1 (c0 = c + φ1 ). In turn, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 549 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing presuppositions triggered in the two conjuncts are evaluated differently: a presupposition of S1 must be true at all worlds in c, while a presupposition of S2 must be true at all worlds in c0 . Heim’s system is well suited to capture asymmetric projection in conjunction. Concretely, recall (7), where the presupposition trigger the bathroom occurs in the first conjunct: (7) #The bathroom is in a funny place, and there is a bathroom. The presupposition is evaluated relative to c and imposes the requirement that the make-up of c conform to (8). By constraining the initial context, the presupposition is felt to project.2 (8) c ⊆ {w : there is a bathroom in w} The situation is different when the order of the conjuncts is permuted in (9). In this case, the presupposition is evaluated relative to the context c0 output by updating c with the first conjunct (There is a bathroom), as in (10a). The presupposition of the bathroom then places the constraint on c0 in (10b). (9) (10) There is a bathroom, and the bathroom is in a funny place. a. c’ = c ∩ {w : there is a bathroom in w} b. c’ ⊆ {w : there is a bathroom in w} Because c0 only contains those worlds in c at which there is a bathroom, the condition in (10b) is necessarily met, independent of the original make-up of c. Thus, the presupposition does not place any constraint on the initial context and is not felt to project. 2.2. From lexical stipulation to online processing While Heim’s approach offers an elegant analysis for the projection properties of conjunction (and other connectives), it does not achieve full explanatory adequacy. Heim relies on a specific lexical entry for conjunction, which is not formally motivated on independent grounds. In particular, nothing in the framework rules out an alternative entry for conjunction where the conjuncts update the initial context in the reverse order (Rooth p.c. to Heim, Soames 1989, Heim 1990): (11) a. ‘S1 and S2 ’ uttered in context c b. (c + φ2 ) + φ1 cf. (6b) 2 Note that not only is the presupposition felt to project in (7), but the conjunction as a whole is also felt to be degraded. This is easily explained by the fact that the second conjunct winds up as contextually trivial, as it does not add anything new to c. Stalnaker (1973) already argued this to be a violation of a constraint against redundancy. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 550 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing With this entry, S2 is interpreted relative to c, and S1 is interpreted relative to c+φ2 . Thus, presuppositions would always project from the second conjunct, but variably from the first conjunct, depending on the content of the second. It does not seem to be a lexical idiosyncracy that update proceeds as in (6), and not as in (11). In (6), update proceeds left-to-right, as c is updated with the first conjunct and then the second. In (11), update proceeds right-to-left. The correlation between update order and the left-to-right linear order of the conjuncts can be explained in a principled way if update is directly linked to online processing. This is the direction pursued in recent work, and we outline one illustrative approach here: Schlenker’s (2009) theory of local contexts. Departing from Heim, Schlenker returns to a classical semantic framework, where sentence meanings are modeled as truth-conditions. When interpreting a sentence S in a context c, the interpreter must determine whether the proposition S expresses (φS ) is true or false at each world in c. Worlds at which φS is true should be kept in c and worlds at which φS is false should be eliminated. Schlenker proposes that, when the interpreter parses a sub-constituent E of S, they simplify their task as much as possible by disregarding those worlds in c at which they can be sure that the interpretation of E does not affect the overall truth-value of S. The set of worlds under consideration when E is processed is the local context for E. Local contexts are computed online, so only information preceding E can be taken into account when determining its local context. Let us consider how Schenker’s approach applies to conjunction. Two stages of the left-to-right parse for a schematic conjunction are flagged in (12): (12) [0] S1 and [1] S2 At stage [0], the interpreter starts by considering all worlds in c, and c itself is thus the local context for S1 . After parsing S1 , the interpreter can identify worlds in c at which φ1 is true and false. Because φ1 ∧ φ2 is necessarily false if φ1 is false, φ2 only affects the truth-value for the conjunction at worlds where φ1 is true; at those worlds, the conjunction is true if φ2 is true and false otherwise. Accordingly, when they parse S2 , the interpreter only considers worlds at which φ1 is true: the local context for S2 is c + φ1 . With the local contexts for S1 and S2 being c and c + φ1 , the dynamics of context update closely mirror Heim’s entry in (6). Since context update is integrated with online processing, the only way for presupposition projection behavior to be linked to context update is for it too to be integrated with online processing – and, in this way, we arrive at the need for RIPE (which is implicit in Schlenker’s discussion). For concreteness, consider the parse of (7) above with the stages shown in (13): (13) [0] The bathroom [1] is in a funny place and [2] there is a bathroom. At stage [0], parsing of the first disjunct begins and the local context is c. With RIPE, the presupposition is evaluated immediately on encounter of the bathroom at stage [1]. At this Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 551 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing point, the local context remains c, so the presupposition is evaluated relative to c and projects.3 Permuting the conjunct order results in the presupposition being evaluated in a different local context, exactly as in Heim’s system: (14) [0] There is a bathroom and [1] the bathroom [2] is in a funny place. At stage [1], the local context for the second conjunct, c0 , is determined by updating c with the proposition that there is a bathroom. Then, at stage [2], the presupposition of the bathroom is evaluated relative to c0 . Just as for Heim, the presupposition is guaranteed to be satisfied in c0 regardless of the make-up of c, so fails to project. In sum, by integrating context update and presupposition evaluation with online processing, Schlenker achieves the same predictions as Heim did, but without lexical stipulation. RIPE plays a key role in the account, as it ensures that a presupposition is evaluated relative to the local context for the conjunct in which that presupposition is triggered. 2.3. Previous evidence for RIPE Given conceptual rationale for RIPE, we ask: what empirical evidence can be used to directly test RIPE? While psycholinguistic work on the online processing of presupposition is still in a nascent state, early results seem to accord with RIPE. Several self-paced reading studies have shown fairly immediate effects of contextual manipulations bearing on the status of presuppositions, with increased reading times when the context was inconsistent with the presupposition (Schwarz, 2007; Tiemann et al., 2011). This is in line with presuppositions being evaluated right away when the trigger (and other material in the sentence required to flesh out the content of the presupposition) is encountered. Schwarz and Tiemann (2016) further corroborate this with temporally more fine-grained reading time measures from eye-tracking during reading, and Schwarz (2014, 2015); Romoli et al. (2015) provide parallel evidence from visual world eye tracking. There is, however, a limitation to the previous results: the bulk of evidence for RIPE comes from studies looking at presupposition triggers in simple, unembedded contexts, so no issues of projection arise.4 This is potentially problematic insofar as the predictions of RIPE could be descriptively adequate for unembedded occurrences of presupposition triggers, but not extend to embedded contexts where projection is an issue. By studying co-ordination, our experiments 3 As we discussed earlier (cf. (3b)), the presupposition marks its content as information taken for granted in the global context, and continuing the sentence by asserting it results in redundancy. (Note that the presupposition equally affects the local context for the second conjunct, since it is a subset of the global context.) 4 The key exception to this is Schwarz and Tiemann (2016), who look at the presupposition of again under negation and in conditionals, with results that they argue show that evaluating projection presuppositions relative to the global context takes longer than in the case of unembedded ones; we return to the relation between our results and theirs in the general discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 552 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing directly assess whether RIPE makes adequate predictions when projection is involved. We focus on disjunction which seems to pose a particular challenge for RIPE. 2.4. The disjunction puzzle Schlenker’s incremental system makes a key prediction for disjunction: when a presupposition trigger occurs in the first disjunct, the presupposition should project, just as presuppositions project from a first conjunct. Consider the disjunction data seen earlier: (5) a. [0] Either the bathroom [1] is in a funny place, or [2] Mary is lost. b. [0] Either the bathroom [1] is in a funny place, or [2] there is no bathroom. Regardless of the connective, the local context at the outset of the parse is c. Given RIPE, the presupposition is evaluated at stage [1], relative to c. Thus, the presupposition should constrain c and be felt to project. The prediction is borne out in (5a) – but fails in (5b). Whether or not the presupposition projects, then, depends on the second disjunct. When the second disjunct is independent of the presupposition, it projects, as in (5a). But, at least when the second disjunct expresses the negation of the presupposition, it does not project, as in (5b). This effect of the second disjunct looks at odds with RIPE, since the second disjunct is not encountered until stage [2], after the presupposition is evaluated at stage [1]. Given RIPE, it looks as though the second disjunct comes too late to influence projection. One reaction to this puzzle may be to abandon RIPE so that the interpreter delays all projection decisions until the end of the sentence. In that case, we would expect that projection could be affected both by information that precedes and follows the presupposition trigger. In fact, this option is explicitly considered by Schlenker, who suggests that the asymmetries that can ultimately be attributed to RIPE merely have the status of a processing preference, and can in principle be overriden by a symmetric evaluation of presuppositions. In doing so, however, we lose a straightforward account of asymmetric projection in conjunction5 and must regress to lexical stipulation to account for the contrast in (a)symmetry between the two types of coordination.6 Here, we pursue the possibility that the disjunction data can be reconciled with RIPE. 2.5. Reconciling Disjunction with RIPE Hirsch and Hackl (2014) suggest a way to reconcile the disjunction pattern with RIPE. In their 5 But note that the empirical picture for conjunction is less clear than it may seem at first. For an attempt at settling this experimentally, see Mandelkern et al. (2017), who do not find any evidence for symmetric projection in conjunction. 6 In principle, one could also consider a processor that waits to assess projection until the end of the sentence but then bases its computations on linear order, but this would effectively bring us back to stipulating an effect of order, rather than deriving it independently, so we will leave this possibility aside in what follows. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 553 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing view, the interpreter always makes a decision about whether or not to project a presupposition immediately on encounter of the trigger, but that decision can be revised later in the parse. RIPE is correct, but commitments made at intermediate stages of parsing can be altered. We start with the first part of the disjunction which is shared by (5a-b), and focus on two stages of the incremental parse, as annotated below. (5a-b) [0] Either the bathroom [1] is in a funny place, . . . Parsing of the first disjunct begins at stage [0], at which point the local context is the initial context set. At stage [1], the bathroom is encountered and, by RIPE, the interpreter evaluates the presupposition. The presupposition places the constraint on c in (8), so projects globally. (8) c ⊆ {w : there is a bathroom in w} This result accords with intuitions for (5a), but not (5b). Hirsch and Hackl’s account for (5b) relies on a later stage of parsing, subsequent to stage [1]. Consider the full parse, including the second disjunct: (5b) [0] Either the bathroom [1] is in a funny place, or there is no bathroom [2]. The core idea is that (5b) involves a pragmatic garden path, where the interpreter commits to projection immediately on encounter of the trigger at stage [1] – as expected based on RIPE – and then revises that commitment later at stage [2], after the second disjunct is encountered. The donwstream revision is motivated by independent principles of discourse interpretation. In particular, Hirsch and Hackl note that a disjunction p or q is subject to the felicity constraint in (15), motivated by general Gricean principles (see also Schlenker 2008): (15) Non-opinionatedness (NO) To felicitously use a disjunction p or q, the speaker must not believe p, ¬p. q, or ¬q. If the condition in (8) holds, then the notion that the building in fact has a bathroom has to become part of the common ground prior to evaluation of the disjunction in (5b). This means that the speaker must believe (or is at least acting as if they believed) that the building has a bathroom, which in turn commits the speaker to believing that the second disjunct in (5b) is false. In other words, because the second disjunct is equivalent to the negation of the presupposition, projecting the presupposition leads to a violation of Non-Opinionatedness. Having committed to projection at stage [1], the interpreter inevitably runs into an NO violation when they parse the second disjunct at stage [2]. This, Hirsch and Hackl propose, leads to the interpreter back-tracking on their earlier commitment so as to respect NO. This can be done by appealing to some version of a local accommodation operator (Heim, 1983), which effectively results in presupposed content being treated on par with regular entailed content (also see the A-operator of Beaver and Krahmer, 2001). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 554 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing Note that NO is a principle that applies specifically to disjunctions. As a result, the situation in conjunctions is not parallel, and it does not come as a surprise under this view that one does not seem to observe the same right-to-left filtering in the case of conjunctions (also see footnote 5). This proposal therefore offers an explanatory account of the contrast in incrementality between conjunctions and disjunctions, and thus escapes the stipulative aspect of an alternative approach à la Heim where the two connectors are lexically defined to meet the projection observations. 2.6. Section summary We have seen that RIPE is a central assumption of an account linking asymmetric projection in conjunction to online processing – an account achieving significant explanatory depth. Though disjunction seems to provide counter-evidence, Hirsch and Hackl suggest that disjunction could be compatible with RIPE after all. The goal now is to directly test whether RIPE holds in disjunction. We use visual world eye-tracking experiments to assess the time course of presupposition projection, and in particular to test whether commitments to projected presuppositions are reflected in eye movements prior to the second disjunct having fully unfolded. 3. Experiment 1: trigger in first disjunct Exp. 1 investigated disjunctions with a presupposition trigger in the first disjunct. Consistent with RIPE, our results support Hirsch and Hackl’s idea that the interpreter rapidly assumes that the presupposition projects upon encountering the trigger, before the second disjunct unfolds. 3.1. Design & Methods The experimental stimuli included disjunctions like (16), with the presupposition trigger stop in the first disjunct. In (16), stop triggers the presupposition that Henry went to the aquarium prior to Wednesday (in shorthand: Aquarium<Wd). The assertion in the first disjunct is that Henry did not go to the aquarium from Wednesday on (¬Aquarium>Wd). (16) Either Henry stopped going to the aquarium on Wednesday, or he waited until Saturday to go to the movies. Participants heard recordings of sentences like (16) while their gaze was tracked relative to a visual display. The visual display consisted of three pictures, each containing a character and a calendar strip with iconically represented activities (Schwarz, 2014), as in Figure 1. Participants’ task was to choose the character they took the sentence to be about. The crucial picture is the target picture, which came in three variants, corresponding to three experimental conditions, illustrated in Fig. 1A-C. In addition, there was a distractor picture and a ‘covered box’ (adapted from Huang et al., 2013), where crucial information on what happened on relevant days in the calendar strip is blacked out. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 555 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing A (PsTrue-EntFalse) B (PsFalse-DiffAct) Covered Box C (PsFalse-SameAct) Figure 1: Illustration of Target variants and Covered Box for Exp. 1 The logic of the design was to manipulate whether or not the presupposition of stop was met in the target picture, and assess whether the presupposition being met increased the likelihood of participants fixating on the target as the sentence unfolded. In Condition A, the presupposition is met: for the sample item above, Henry went to the aquarium before Wednesday in A. In Conditions B-C, the presupposition fails, since other activities took place prior to Wednesday (Condition B), or no activities did (Condition C). In the item above, the character went to the library prior to Wednesday in Condition B. We refer to B as the DiffActivity (PsFalse) condition and C as the SameActivity (PsFalse) condition. While B constitutes a minimal control condition for A in that they share the same day structure, C was included to control for any independent effect of the presence of slots featuring the mentioned stopped activity. While the target varies in whether or not the presupposition is satisfied, the distractor picture (not shown) is incompatible with the presupposition in all cases. In the covered box, activities prior to Wednesday are obscured, so the presupposition could be satisfied, but is not necessarily so: in the sample item, the character may or may not have gone to the aquarium on Monday and Tuesday. In this way, the covered box is always compatible with the presupposition. Factoring in the assertion now, neither target variant ultimately verifies both the presupposition and the assertion. In Condition A, where the pesupposition is verified, the assertion fails, since the character continued to go to aquarium after Wednesday, and went to the beach, not the movies, on Saturday. In Conditions B and C, the presupposition fails, as discussed, and the assertion fails as well. The covered box is ultimately, then, the only picture participants can select: in the covered box, the character does go to the movies on Saturday, verifying the nonpresupposing disjunct. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 556 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing Since we are interested in the online looking pattern, however, more important for our purposes is the status of the assertion prior to the end of the sentence. We focus on the critical region underlined in (16). Prior to encounter of movies at the end of the sentence, all pictures are still potentially compatible with the assertion, since all have an activity on Saturday. In this way, we can isolate effects of presupposition at this point. Predictions The critical measure is the relative proportion of fixations on the target relative to the covered box in the online data. If participants rapidly compute the presupposition of stop and assume projection, per RIPE, an effect of condition should emerge in the critical region: participants should be more likely to fixate on the target image in Condition A (PsTrue) than in either Conditions B or C (PsFalse). In those conditions, their gaze should be drawn to the covered box comparatively more strongly, since the covered box is the only potential presupposition match. On the other hand, if presuppositions are not rapidly evaluated on account of the trigger, but rather are deferred until the full disjunction is fully processed, no effect of condition is predicted. For the behavioral measure, participants are expected to select the covered box as the best overall picture match in all cases, as discussed. While RIPE predicts an effect of condition during the critical region, an alternative lexicalist approach which stipulates that disjunctions project a conditional presupposition symmetrically for triggers in either disjunct does not. If the semantics of disjunctions is such that the second disjunct can affect whether or not a presupposition introduced in the first disjunct has to be met globally (cf. (11b)), then the evaluation of this presupposition most plausibly would be deferred until the second disjunct is processed. In that case, no effect of condition should emerge in the critical region. Participants and Procedure 24 items were created with the properties described above, with 4 versions each (a fourth control condition, not discussed here for reasons of space, had a target where both the presupposition and the entailed content of the first disjunct were true). In addition, there were 30 fillers, all of which involved disjunctions, with varying properties (such as truth of 1st vs. 2nd disjunct, presence of presupposition trigger, etc.) to counterbalance a number of different factors across the experiment. 35 students at the University of Pennsylvania participated for course credit. The experiment was implemented in the Experiment Builder software by SR Research, and data was collected on an EyeLink 1000 eye tracker. 3.2. Results Data Analysis Eye movement data were analyzed beginning at the onset of the disjunction marker or, in order to measure proportions of looks to the target after the first disjunct had been fully heard but before the second disjunct had been completed. Since the key alternative candidate for matching the disjunction was the covered box (which was compatible with a global interpretation of the presupposition), we computed a target advantage score where looks to the covered box were subtracted from looks to the target. For purposes of analysis, proportions were transformed to Elogits, and the analysis for individual time-windows used mixed effect models with subjects and items as random effects, as well as a slope for condition to the extent Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 557 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing TargCB Adv % 0.3 0.2 condition 0.1 PsTrue-EntFalse 0.0 PsFalse-EntFalse-DiffActivity PsFalse-EntFalse-SameActivity -0.1 -0.2 0 500 1000 1500 2000 2500 Disj Onset Figure 2: Looks to Target-Looks to Covered Box by Condition relative to onset of ‘or’ that these models converged. Significance of individual effects was assessed through model comparisons with minimally varied models where the condition-factor had been removed. The graph in Fig. 2 illustrates Target Advantage scores over time for the second disjunct (the black line indicates the mean disambiguation point, corresponding to the onset of movies in (16)). There is a clear effect of presupposition: during the second disjunct, participants are significantly more likely to fixate on the target in Condition A (PsTrue) than in Conditions B-C. The contrast with condition B (DiffActivity) is present early on (0-500ms; β = 2.14, SE = 0.61, t = 3.52, χ 2 = 10.06, p < 0.01), but does not last throughout. The contrast with condition C (SameActivity) emerges first in the 500-1000ms time window (β = 1.48, SE = 0.60, t = 2.47, χ 2 = 6.08, p < 0.5), and lasts through the remainder of the ambiguous period. Discussion The contrast in the proportion of looks in the second disjunct indicates that the manipulation of whether or not the presupposition is met in the target picture has an effect. This is consistent with the idea that the interpreter assumes projection online, i.e. when the trigger is in the first disjunct, they immediately compute the presupposition and assume projection. This is in line with the prediction of RIPE, but not with an alternative possibility where the potential relevance of the second disjunct for projection is taken into consideration before any consideration of the presupposition is undertaken. 4. Experiment 2: trigger in second disjunct In Experiment 2, we extend the data set by testing whether RIPE is supported when the presupposition is triggered in the second disjunct, rather than the first. Again, our results support the idea that the presupposition is rapidly computed and assumed to project online. 4.1. Extending to trigger-second order As a first step, let us consider what the incremental system we sketched based on Schlenker (2009) predicts for a disjunction with a presupposition trigger in the second disjunct. The disjunction in (17) offers an illustration: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 558 A. Hirsch, J. Zehr, & F. Schwarz (17) Presupposition projection from disjunction in online processing Either [0] Mary’s lost, or [1] the bathroom [2] is in a funny place. As with any parse, the local context at stage [0] is simply the entire context set, c. At stage [1], the local context for the second disjunct, c0 , is determined. A disjunction S1 or S2 is true at any world where one or both of φS1 and φS2 is true. The content of S2 , therefore, affects the truth-value of φS1 ∨ φS2 only at worlds which φS1 is false. As such, c0 in (17) is that subset of c containing only worlds at which Mary is not lost: (18) c0 = c∩{w : Mary is not lost at w} At stage [2], the bathroom is encountered and the presupposition is evaluated relative to c0 . For it to be satisfied, the building must have a bathroom at every world in c0 , as in (19a). The predicted overall presupposition, then, can be paraphrased as the conditional in (19b). (19) a. c0 ⊆ {w : the building has a bathroom at w } b. If Mary isn’t lost, the building has a bathroom. In predicting a conditional presupposition, Schlenker’s approach converges with proposals in dynamic semantics which stipulate an entry for or by which a presupposition triggered in the second disjunct projects as conditional (Beaver, 2001: contra Geurts 1999). Yet, this prediction is problematic. Intuitively, (17) does not presuppose (19b), but rather something stronger: the presupposition is simply that the building has a bathroom, independent of whether or not Mary is lost. Observing a non-conditional presupposition where a conditional is predicted is known as the proviso problem. Though the proviso problem may seem to argue against an account like Schlenker’s altogether, the situation is more complex, as there are examples where a conditional presupposition is observed. A well-known case is (20) (adapted from Geurts, 1996: p. 271), where the intuited presupposition is that if John is a diver, he has a wetsuit. (20) Either John isn’t a diver, or he brought his wetsuit on the trip. To explain the non-conditional presupposition of (17), many authors accept the prediction of a conditional presupposition, but augment the account with a pragmatic mechanism which strengthens the conditional to a non-conditional. In (17), (19b) is strengthened to (21): (19b) (21) If Mary isn’t lost, the building has a bathroom. The building has a bathroom. Different accounts of strengthening have been advanced (van der Sandt, 1992; Geurts, 1999; Beaver, 2001; Singh, 2007; Schlenker, 2011; Lassiter, 2012). While we cannot go into great detail for reasons of space, the last two in particular lend themselves to an integration with the present discussion. Briefly, they assume that conditional presuppositions get strengthened if the material featuring in the antecedent is taken to be irrelevant for whether or not the presupposition holds. For Schlenker (2011), in particular, this is introduced as a process that makes reference to left-to-right order in processing, parallel to the motivation for RIPE above: preceding material can be considered for presupposition evaluation, but also can be deemed irrelevant Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 559 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing in this regard if it contextually fails to bear on whether or not the presupposition holds. For our purposes, this suggests that resolving the proviso problem is a process that takes place equally rapidly as presupposition projection in general, so that strengthened presuppositions should be detectable in online processing measures. Experiment 2, then, directly extends the approach from Experiment 1 by looking at the effect of presupposition triggers in the second disjunct. 4.2. The paradigm The test sentences in Experiment 2 consisted of disjunctions such as (22), where the aspectual verb continue occurs in the second disjunct and triggers the presupposition that Henry went to the movies prior to Wednesday (movies<Wd). (22) On Wednesday, Henry either went to the aquarium, or he continued going to the movies. As in Experiment 1, each test sentence was paired with a visual display made up of three pictures: a target, a distractor, and a covered box. The target picture was varied between two experimental conditions, as in Fig. 3.7 In both, the first disjunct (that Henry went to the aquarium) is true. In Condition A, the presupposition of continue is met as well, as Henry went to the movies on Sunday, Monday, and Tuesday. In Condition B, Henry did not go to the movies before Wednesday (but only after Wednesday), so the presupposition is false. Thus, the target image in both conditions is compatible with the asserted content of the disjunction as a whole (given that it matches the first disjunct), but differs minimally between conditions in whether the presupposition is verified (version A; hence, PsTrue) or not (version B; PsFalse). In the covered box, Henry’s activities on Monday, Tuesday, and Wednesday were obscured, as in (3), leaving it open whether or not the presupposition (or the disjunction as a whole) is matched in this picture. The distractor (not show here) was neither compatible with the presupposition nor the assertion, as it had a different activity prior to Wednesday. Predictions The crucial data are again provided by the online eye-tracking measure. In this case, we define the critical region as extending from the onset of continue to the onset of the last word of the sentence, as in (22). Note that, unlike in Experiment 1, the presupposition trigger itself is part of this critical region. While the full second disjunct is needed to flesh out the content of the presupposition (that Henry went to movies before Wednesday), the encounter of continue alone already suffices to draw the inference that the character in question had some sequence of activities preceding Wednesday. As a result, already at the beginning of the critical region, we may see an effect of condition. A greater proportion of looks to the target is expected in Condition A (some activity on Monday-Wednesday) than in Condition B (no activity on these days). As the noun movies is encountered, this asymmetry should remain since the target in A satisfies the full presupposition (that Henry went to the movies prior to Wednesday). But, crucially, an effect prior to movies can give clear evidence that the presupposition is considered rapidly, prior to the end of the clause (even before the full content of the presupposition has been provided). 7 In addition, there were two further conditions where the first disjunct was false in the target picture for counterbalancing purposes; we do not discuss these here in detail for reasons of space. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 560 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing Target A (PsTrue) Covered Box Target B (PsFalse) Figure 3: Illustration of Target variants and Covered Box for Exp. 2 To re-iterate, any effect of condition in Experiment 2 would implicate two rapid online processes relating to presupposition interpretation. First, the presupposition of continue has to be considered rapidly for any effect to arise. Secondly, the relationship of this presupposition to the preceding linguistic context has to be determined immediately as well, to determine that having gone to the aquarium on Wednesday (the content of the first disjunct) is not likely to bear on the question of going to the movies prior to Wednesday, leading to strengthening of the presupposition to a non-conditional one (assuming, as before, a conditional presupposition, in line with a RIPE-based account of projection, to begin with). The secondary measure of picture selection is also informative in Experiment 2, as it allows us to assess whether participants adopt a strengthened non-conditional presupposition in the final interpretation. In Condition A, the target matches the strengthened presupposition and assertion, so is the expected response regardless. In Condition B, however, the strengthened presupposition is not met, so participants must select the covered box if they adopt that interpretation. Otherwise, if they compute a conditional presupposition or locally accommodate a strengthened presupposition, they can select the overt picture. In addition to the selection itself, we collected reaction time data from the offset of the sentence to the time of picture selection. Participants & Procedure The experimental stimuli consisted of 24 items structured as in the sample item above. In addition, there were 30 filler items, again varying crucial properties, such as presence of a trigger and truth or falsity of the disjunction as a whole, for purposes of counterbalancing to avoid potential experiment-level strategic effect and to mask the experimental manipulations. 48 undergraduate students at the University of Pennsylvania participated in the experiment for course credit. As in Exp. 1, the experiment was implemented in Experiment Builder, and data was collected on an EyeLink1000 eye tracker. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 561 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing presupposition False Target % 0.7 True 0.6 0.5 0.4 0 500 1000 1500 2000 PsOnset time Figure 4: Proportion of looks to Target by condition in Exp. 2, relative to the onset of continue. Black line marks mean disambiguation point (corresponding to movies in (22)) 4.3. Results Eye movement data The graph in Fig. 4 shows the proportion of looks to the target by condition relative to the onset of the presupposition trigger continue, with the black line again indicating the mean onset of the disambiguating word (movies in illustrations above). A difference between the conditions with A (PsTrue) and B (PsFalse) versions of the Target emerges already before 1000ms after the onset of continue. This is reflected in a significant effect during the time-window starting with the onset of continue and ending with the onset of the disambiguating noun (the correlate of movies) as confirmed by mixed-effect model analyses on Elogit-transformed proportions of looks to target and subsequent model comparison (β = 0.77, SE = 0.35, t = 2.18, χ 2 = 4.61, p < 0.5), suggesting that the presupposition of continue, that some activity must have been going on prior to Wednesday, is already having an effect on the interpretation prior to the full second disjunct unfolding. This is consistent with the prediction of RIPE. Right after participants encountered continue, they are more likely to fixate on the target if the presupposition is verified than if the presupposition fails. Behavioral data Beginning with response pattern by condition, participants were more likely to select the target picture in Condition A (96%), where the presupposition was met, than in Condition B (75%), where is was not, but where the covered box offered a viable alternative choice where the presupposition could be met. A logistic mixed-effect model analysis revealed this difference to be statistically significant (β = 3.45, SE = 0.52, z = 6.59, p < 0.001). While Condition A and Condition B differ, it is notable that participants still do select the target with high frequency in Condition B (75%). This suggests that participants often do not have a strengthened presupposition projected in the final interpretation. This looks initially at odds with the online data which provide evidence for an effect of presupposition in the critical region. We suggest that those target choices obtained after participants strengthened the conditional presupposition, but then revised this strengthening. This explanation is further consistent with the reaction time data. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 562 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing Reaction times by condition and response choice also reveal a telling pattern. Fairly unsurprisingly, covered box choices when the presupposition was not met in the target picture (Condition B) were slower than target choices (8061 vs. 6874 ms respectively). However, target choices were furthermore significantly faster when the presupposition was met (6297ms, version A), as confirmed by mixed effect model analyses and model comparison (β = −653, SE = 281, t = −2.33, χ 2 = 4.97, p < 0.5). This suggests that even though the target picture was the majority choice overall in the B version, this choice was not as straightforward as in the A version, presumably due to the difference in the presupposition being met. Importantly, such a delay would not be expected if target choices in Condition A and B equally obtained with a satisfied conditional presupposition. 5. Discussion Our starting point in this paper was the observation of an asymmetry in presupposition projection in conjunctions. We argued that recent explanatory accounts for this asymmetry based on left-to-right processing share an implicit assumption, which we made explicit in the form of RIPE. We then reviewed cases that are not as clearly asymmetric, in particular disjunction. Facing this contrast between conjunctions and disjunctions, we were left with two alternatives: either give up the general asymmetric model based on RIPE and stipulate an asymmetric lexical entry for conjunctions and a symmetric entry for disjunctions, or maintain RIPE and explain apparent symmetry in disjunctions as resulting from a more complex process involving an initial commitment to projection, which is then rescinded in cases where this conflicts with independent pragmatic principles, in particular NO. The goal of our experiments was to show that empirical evidence on processing is indeed consistent with RIPE, in that it reflects early commitments to projected presuppositions. We focused on disjunctions, where RIPE makes a crucial prediction: while RIPE predicts early commitment to presupposition projection, approaches that posit a symmetric entry for disjunctions would naturally account for speakers not committing to projection before encountering the entire second disjunct. We saw that the results are consistent with RIPE, in that our eye-tracking data from Experiment 1 suggest early commitment to presupposition projection, contrary to what is expected according to lexicalist approaches. We furthermore saw that a strengthening mechanism endorsed by most recent authors takes place rapidly when the presupposition trigger appears in the second member of a disjunction, which is again in line with a rapid processing and integration of presuppositions. Taking the results at face value, especially those from Experiment 2, one might consider a third possibility, namely that presuppositions are initially taken to project unconditionally from the first and second disjuncts as well. That is, one might interpret the results of the second experiment not as showing that there is rapid strengthening of an underlying conditional presupposition (as we concluded), but rather as showing that processing presuppositions does not take preceding information into consideration at first. Such an interpretation would be reminiscent of some early accounts of presupposition projection, endorsing what is known as the cumulative hypothesis (Langendoen and Savin, 1971). The presupposition-suspension mechanism (e.g. local accommodation) involved in Hirsch and Hackl’s back-tracking mechanism, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 563 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing which is used to account for the optionality of projection from the first member of a disjunction, could then be held responsible for the optionality of projection from the second member despite the posited initial commitment in projection. While this view would be compatible with our results taken in isolation, we argue that it is not tenable in the more general landscape of presupposition projection. First, as illustrated with the sentence in (20), presuppositions sometimes project conditionally out of disjunctions. This observation is at odds with a parser that would unconditionally project presuppositions as soon as it encounters a trigger. Moreover, while a process such as local accommodation possibly taking place both in the first and second member of a disjunction is well in line with the apparent symmetry of disjunctions, it is hard to see how the mere availability of local accommodation could account for the asymmetry of conjunctions. By contrast, note that RIPE does not suffer the same criticism, since resorting to local accommodation in disjunctions is motivated by an independent pragmatic principle, NonOpinionatedness, which does not apply to conjunctions: the lack of presupposition projection in conjunctions where a trigger appears in the second conjunct results from the conditional nature of the presupposition induced by incremental-processing , and not from local accommodation. More generally, our results provide new insights into the online processing of presuppositions and therefore further constrain theories of presupposition projection. Insofar as decisions about presupposition projection are made right away, the range of options for lexically encoded projection properties, should there be the need for any, is substantially reduced. An important task to carry out in more detail in future work is to relate the present results to previous findings, such as those by Schwarz and Tiemann (2016), who conclude based on evidence from eye-tracking during reading that projection takes time. While that conclusion may at first sight seem at odds with the interpretation of our data offered here – that projection decisions are made rapidly –, this need not be the case, as the steps the processor engages in to determine whether a presupposition project could well start out right away when the trigger is encountered, and yet take time to complete. Furthermore, it is worth noting that the time-windows of our effects are only immediate in the broader sense that they show up prior to relevant further information having been introduced, which is again perfectly consistent with the notion that the overall process of presupposition projection does take a certain amount of time to complete. Finally, yet another important direction for future work is to extend the present methodology to other connectives, and in particular to settle the question of whether or not conjunctions display any genuinely symmetric projection effects. References Beaver, D. (2001). Presupposition and Assertion in Dynamic Semantics. Stanford, CA: CSLI Publications. Beaver, D. and E. Krahmer (2001). Presupposition and partiality: Back to the future. Journal of Logic, Language and Information 10(2), 147–182. Chemla, E. and P. Schlenker (2012). Incremental vs. symmetric accounts of presupposition projection: An experimental approach. Natural Language Semantics 20(2), 177–226. Fox, D. (2008). Two short notes on Schlenker’s theory of presupposition projection. Theoretical Linguistics 34(3), 237–252. Geurts, B. (1996). Local satisfaction guaranteed: A presupposition theory and its problems. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 564 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing Linguistics and Philosophy 19(3), 259–294. Geurts, B. (1999). Presuppositions and Pronouns. Amsterdam; New York: Elsevier. Heim, I. (1983). On the projection problem for presuppositions. In M. Barlow, D. Flickinger, and N. Wiegand (Eds.), Proceedings of WCCFL 2, pp. 114–125. Stanford University. Heim, I. (1990). Presupposition projection. In R. van der Sandt (Ed.), Reader for the Nijmegen Workshop on Presupposition, Lexical Meaning, and Discourse Processes. University of Nijmegen. Hirsch, A. and M. Hackl (2014). Incremental presupposition evaluation in disjunction. In J. Iyer and L. Kusmer (Eds.), Procedings of NELS 44, Volume 1, Amherst, MA, pp. 177– 190. GLSA. Huang, Y., E. Spelke, and J. Snedeker (2013). What exactly do number words mean? Language Learning and Development 9(2), 105–129. Karttunen, L. (1973). Presuppositions of compound sentences. Linguistic Inquiry 4(2), 169– 193. Langendoen, D. T. and H. Savin (1971). The projection problem for presuppositions. In C. Fillmore and D. T. Langendoen (Eds.), Studies in Linguistic Semantics, pp. 373–388. New York: Holt, Reinhardt and Winston. Lassiter, D. (2012). Presuppositions, provisos, and probability. Semantics and Pragmatics 5(2), 1–37. Mandelkern, M., J. Zehr, J. Romoli, and F. Schwarz (2017). Asymmetry in presupposition projection: The case of conjunction. Talk to be presented at SALT 27. Partee, B. (2005). Reflections of a Formal Semanticist as of Feb 2005. Unpublished Manuscript. Romoli, J., M. Khan, J. Snedeker, and Y. Sudo (2015). Resolving temporary referential ambiguity using presupposed content. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 67–88. Cham: Springer International Publishing. Schlenker, P. (2008). Be articulate: A pragmatic theory of presupposition projection. Theoretical Linguistics 34(3), 157–212. Schlenker, P. (2009). Local contexts. Semantics and Pragmatics 2, 1–78. Schlenker, P. (2011). The Proviso Problem: A note. Natural Language Semantics 19(4), 395– 422. Schwarz, F. (2007). Processing presupposed content. Journal of Semantics 24(4), 373–416. Schwarz, F. (2014). Presuppositions are fast, whether hard or soft: Evidence from the visual world paradigm. In T. Snider, S. D’Antonio, and M. Weigand (Eds.), Semantics and Linguistic Theory (SALT), Volume 24, pp. 1–22. LSA and CLC Publications. Schwarz, F. (2015). Presuppositions vs. asserted content in online processing. In F. Schwarz (Ed.), Experimental Perspectives on Presuppositions, pp. 89–108. Cham: Springer International Publishing. Schwarz, F. and S. Tiemann (2016). Presupposition projection in online processing. Journal of Semantics Advance Access, 1–46. Singh, R. (2007). Formal Alternatives as a Solution to the Proviso Problem. Semantics and Linguistic Theory 17, 264–281. Soames, S. (1989). Presupposition. In D. Gabbay and F. Guenther (Eds.), Handbook of Philosophical Logic, Volume IV, pp. 553–616. Dordrecht: Reidel Publishing Company. Stalnaker, R. (1973). Presuppositions. Journal of Philosophical Logic 2(4), 447–457. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 565 A. Hirsch, J. Zehr, & F. Schwarz Presupposition projection from disjunction in online processing Stalnaker, R. (1974). Pragmatic presuppositions. In M. K. Munitz and P. K. Unger (Eds.), Semantics and Philosophy, pp. 197–213. New York: New York University Press. Tiemann, S., M. Schmid, N. Bade, B. Rolke, I. Hertrich, H. Ackermann, J. Knapp, and S. Beck (2011). Psycholinguistic evidence for presuppositions: On-line and off-line data. In I. Reich, E. Horch, and D. Pauly (Eds.), Proceedings of Sinn und Bedeutung 15, Münster, pp. 581– 597. Monsenstein. van der Sandt, R. (1992). Presupposition projection as anaphora resolution. Journal of Semantics 9, 333–377. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 566 On the role of classifiers in licensing Mandarin existential wh-phrases1 Hsin-Lun HUANG — University of Massachusetts Amherst Abstract. As in many languages in the world, wh-phrases in Mandarin can be interpreted as more than interrogative, depending on where they appear. This paper focuses on one of the noninterrogative readings of Mandarin wh-phrases, the existential reading, and presents an account of the licensing conditions for this particular reading by examining its distribution. Moreover, this paper aims to tackle the issue concerning the required co-occurrence of existential whphrases and classifiers in certain environments, a puzzle that has received much notice (Li, 1992; Lin, 1998; Liao, 2011) but is not yet resolved. This paper argues that Mandarin whphrases require two ingredients to be existential, non-veridicality (Xie, 2007; Lin et al., 2014) and existential closure (∃) (Kratzer and Shimoyama, 2002). And classifiers play the role of providing existential force to the wh-phrase when ∃ is unavailable. The (un-)availability of ∃ is conditioned by the application site of ∃ and the syntactic heights of non-veridical operators, whose scope constitutes the licensing domain for the wh-phrase: ∃ is unavailable when it falls outside the scope of the non-veridical operators, given a licensing condition proposed in this paper that limits the application of ∃ to wh-phrases to being within a non-veridical domain. In that case, a classifier is required for the existential interpretation of the wh-phrase. Keywords: Mandarin, classifiers, wh-phrases, non-veridicality, existential closure 1. Introduction The interpretation of Mandarin wh-phrases can vary, depending on the environments they appear in. Besides the interrogative reading, (1a),2 Mandarin wh-phrases can have other noninterrogative readings, one of them being existential, (1b) (Huang, 1982; Cheng, 1991, 1994, 1995; Li, 1992; Lin, 1996, 1998, 2004, 2014; a.o.): (1) a. Zhangsan xihuan shenme? Zhangsan like what ‘What does Zhangsan like?’ b. Zhangsan bu xihuan shenme Zhangsan not like what ‘What doesn’t Zhangsan like?’ ‘Zhangsan doesn’t like anything.’ However, the existential reading is not readily available in all situations: A wh-indefinite is not grammatical in most positive episodic sentences (Li, 1992; Lin, 1998). The following sentence can only obtain an interrogative interpretation: 1I would like to thank my two main advisors of this project, Seth Cable and Vincent Homer, for enlightening me and leading me along the way. I would also like to thank Kyle Johnson, Rajesh Bhatt, and the audience at the UMass Semantics Workshop fall 2015 for their valuable comments and suggestions. Yangsook Park and Jon Ander Mendia have my biggest gratitude for helping me with some of the semantic issues in the project. Finally, I would like to thank Rong Yin for many of the judgements on the scope readings of the wh-phrases. Of course, any errors that remain would be my own. 2 Unlike English, Mandarin is a wh-in-situ language. In other words, there is no overt movement of the whphrase to Spec.CP to take scope, as in the case of English. To obtain the reading where the wh-phrase takes scope over the matrix clause, it is generally assumed that wh-phrases are inherently quantificational and undergo LF movement to take scope. Please see Huang (1982) for a more detailed account of Mandarin wh-interrogatives. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 567 H.-L. Huang (2) On the role of classifiers in licensing Mandarin existential wh-phrases Zhangsan kandao-le shenme Zhangsan see-ASP3 what ‘What did Zhangsan see?’/*‘Zhangsan saw something.’ Various licensing conditions have been proposed for Mandarin existential wh-phrases. Yet one fact that has been noted in the literature but not accounted for is the required co-occurrence of these wh-phrases and classifiers in certain environments (Li, 1992; Lin, 1998; Liao, 2011): (3) a. b. Zhangsan haoxiang mai-le-(ge) shenme Zhangsan seem buy-ASP-CL what ‘It seems that Zhangsan bought something.’ Zhangsan bixu mai-*(ge) shenme Zhangsan must buy-CL what ‘Zhangsan must buy something.’ Being in the scope of epistemic and deontic modals (i.e. haoxiang (‘seem’) in (3a) and bixu (‘must’) in (3b)) is reported to be one of the licensing conditions for existential wh-phrases. But clearly, the obligatory presence of the classifier in the deontically modalized environment suggests that we need to take into account the role classifiers play in licensing existential whphrases that distinguishes between the licensing environments as those in (3). In fact, the deontic environment is not the only environment that requires a classifier for existential wh-phrases. In the remainder of this paper, we will scrutinize the distributions of existential wh-phrases and classifiers. The goal is to develop an analysis that implements classifiers into the licensing conditions for the wh-phrases, capturing their distribution correlation. 1.1. Distribution of existential wh-phrases The following are the reported environments where existential wh-phrases are licensed: — Under negation, in polar questions, and in conditionals: (Huang, 1982; Cheng, 1994; Li, 1992; Lin, 1996, 1998, 2004, 2014) (4) Zhangsan mei chi shenme Zhangsan not eat what ‘Zhangsan didn’t eat anything.’ (6) Yaoshi Zhangsan chi-le shenme, qing gaosu wo if Zhangsan eat-ASP what please tell me ‘If Zhangsan eats anything, please tell me.’ (5) Zhangsan chi-le shenme ma? Zhangsan eat-ASP what Q ‘Did Zhangsan eat anything?’ 3 A SP stands for aspect. Le, in this case, is a perfective aspect in Mandarin. For following glosses, C L = classifier; Q = question particle; D E = modification marker; PAR = particle. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 568 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases — Under epistemic modality: (e.g. epistemic adverbs (7), non-factive epistemic verbs (8), and the inference le (9))4 (7) Keneng/xiangbi shei you qifu ta le possibly/probably who again bully him ASP ‘Possibly/most probably, somebody bullied him again.’ (Lin, 1998) (8) Zhangsan yiwei/renwei wo mai-le shenme, keshi wo genben mei mai renhe dongxi Zhangsan think/think I buy-ASP what but I at-all not buy any thing ‘Zhangsan thinks that I bought something, but I didn’t buy anything at all.’ (Li, 1992) (9) Ta kandao-(le) shenme le he see-ASPperfective what ASPinchoative ‘(It seems that) he saw something.’ (Li, 1992) — In B EFORE-clauses: (10) Zai dui yuangong zuo shenme zhiqian, duo kaolu kaolu at to employee do what before more think think ‘You (should) think twice before doing something to the employees.’ (Xie, 2007) — Under imperfective/progressive aspect: (11) Wo jinqu de shihou, ta zhengzai he shenme I enter DE time he ASPprogressive drink what ‘When I went in, he was drinking something.’ (Xie, 2007) — In disjunction: (12) Yaome shei lai-guo, yaome wo wangji guan chuanghu le either who come-ASP either I forget close window ASP ‘Either somebody came (broke in), or I forgot to close the window.’ (Xie, 2007) — Under deontic modality: (13) Zhangsan bixu mai-*(ge) shenme Zhangsan must buy-CL what ‘Zhangsan must buy something.’ 4 According to Li (1992), a way of indicating circumstantial inferences in Mandarin is through the sentencefinal le, which is different from the perefective aspect le that attaches to verbs. The sentence-final le is often seen as an inchoative le that signals a change of state has occurred (Li and Thompson, 1981), and this property correlates with the fact that the inchoative le is often used in people’s inferential statements. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 569 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases — In “future” environments: (e.g. modal verbs (14), imperatives (15), and verb complements (16)) (14) Wo mingtian hui qu mai-*(ge) shenme dongxi song ta I tomorrow will go buy-CL what thing give him ‘I will go to buy something for him tomorrow.’ (15) Guo-lai chi-*(dian) shenme ba! come eat-CL what PAR ‘Come over to eat something.’ (16) Wo xiawu dasuan5 qu mai-*(ben) shenme shu lai kan go buy-CL what book come read I this-afternoon plan ‘I plan to buy some book to read this afternoon.’ (Lin, 1998) For convenience, the following table summarizes the overall licensing environments for existential wh-phrases shown above, and a divide is made between the environments based on the obligatory presence of classifiers: (17) Distributions of existential wh-phrases and classifiers: No classifiers required: classifiers required: – Negation – – Polar questions – Conditionals – Epistemic modality: ⋄ Epistemic adverbs Future environment: ⋄ Deontic modality ⋄ Imperatives ⋄ Verbs with future-event-denoting complements ⋄ Non-factive epistemic verbs – ⋄ Inference le B EFORE-clauses – Imperfective/Progressive – Disjunction 2. The classifier puzzles Given the distribution of classifiers in the licensing environments of existential wh-phrases, we can roughly frame our first classifier puzzle as follows: (18) 5 The Classifier puzzle #1: Why does an existential wh-phrase require a classifier only in certain environments? complement of verbs like dasuan (‘plan’) typically refer to actions in the future (Lin, 1998). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 570 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases Another classifier puzzle concerns an observation made by Liao (2011), where the requirement of classifiers in the deontic environment can be lifted when the environment is embedded under an epistemic one: (19) Zhangsan haoxiang bixu mai-(ge) shenme Zhangsan seem must buy-CL what ‘It seems that Zhangsan must buy something.’ (Liao, 2011) Thus, we may ask: (20) Classifier puzzle #2: Why is the classifier no longer needed in the above situation? The next section is dedicated to developing an analysis that aims to tackle these puzzles by implementing classifiers into the licensing mechanism for Mandarin existential wh-phrases. 3. Analysis Contra Huang (1982), this paper adopts the point of view that wh-phrases are inherently nonquantificational and acquire their quantificational force externally (Cheng, 1991; Tsai, 1999, 2003, 2010). They are analyzed as denoting sets of alternatives under Hamblin (1973) style semantics, following Kratzer and Shimoyama’s (2002) treatment of Japanese indeterminate pronouns, as well as Li and Law’s (2014) treatment of Mandarin wh-phrases:6 (21) a. b. Jshenme (‘what’)Kw, g Jshei (‘who’)Kw, g = {xe : thingw (x)} = {ye : personw (y)} ∈ Dhei/t 7 ∈ Dhei/t If the denotations of wh-phrases percolate up to the CP level via Pointwise Function Application (Yatsushiro, 2009), we will get the denotations of wh-questions, where each wh-question denotes a set of propositions. In order for a wh-phrase to be interpreted as existential, the set of propositions has to be captured by a sentential ∃, existentially closing the set (Kratzer and Shimoyama, 2002; pg. 7): (22) For Jα Kw, g ⊆ Dhsti : J∃α Kw, g = {λ w’ . ∃p [p ∈ Jα Kw, g & p(w’) = 1]} Classifiers are hypothesized to be serving the role of ∃ within the domain of vP. Reasons for this hypothesis will be made clear later, but it is important to note that the existential closure of wh-phrases (either by the covert ∃ or by a classifier) is not without conditions. We simply cannot close the sets denoted by wh-phrases anywhere, given the following sentence: 6 The motivation for Li and Law’s (2014) treatment of Mandarin wh-phrases as sets of alternatives comes from the intervention effects when a focus operator like zhiyou (‘only’) enters certain hierarchical configurations with the wh-phrase. 7 The type hei/t is the type of sets of alternatives defined in Yatsushiro (2009). The semantic composition of wh-phrases in this paper follows Yatsushiro’s (2009) system, where wh-phrases compose via Pointwise Function Application and end up generating sets of propositions, i.e. the denotation of wh-questions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 571 H.-L. Huang (23) On the role of classifiers in licensing Mandarin existential wh-phrases Zhangsan zuotian chi-le-(ge) shenme Zhangsan yesterday eat-ASP-CL what ‘What did Zhangsan eat yesterday?’ / *‘Zhangsan ate something yesterday.’ Even in the presence of a classifier, the wh-phrase in (23) can only be interpreted as an interrogative rather than an existential. Therefore, we also need to factor in all and only the environments where the existential reading is found. Given the nature of the licensing environments in the introduction, Xie (2007) and Lin et al. (2014) propose non-veridicality in the sense of Zwarts (1995) as the licensing condition for Mandarin existential wh-phrases: (24) (Non-)veridicality for propositional operators: A propositional operator F is veridical iff Fp entails p: Fp  p; otherwise, F is nonveridical. (Lin, Weerman, and Zeijlstra, 2014) All of the boldfaced items (other than the wh-phrases) in (4) to (16) can be viewed as a nonveridical operator under the definition above,8leaving aside the case of imperatives, which has no overt operators though non-veridical in nature. Taking the environmental factor into account, I propose the following licensing conditions for Mandarin existential wh-phrases that connect ∃ and non-veridicality: (25) 8 General licensing conditions for existential wh-phrases: a. Non-veridicality: A wh-phrase can only be grammatical under an existential reading when closed by ∃ in a non-veridical environment (i.e. in the scope of a non-veridical operator). b. Existential closure: (i) ∃ applies higher than vP with the following semantics: J∃Kw, g = λ αhsti/t λ w’ . ∃p [p ∈ α ∧ p(w’) = 1] (hsti/t being the type of sets of propositions) (ii) A classifier can close the set denoted by its argument wh-phrase:9 JC L∃ Kw, g = λ αhei/t λ Phe, esti/t λ yλ w’ . ∃z [z ∈ α ∧ Pw’ (z)(y) = 1] One might wonder why the imperfective/progressive aspect is viewed as non-veridical. According to Xie (2007), who follows Giannakidou (2002) in defining non-veridicality over temporal relations denoted by aspectual operators, an aspectual operator is veridical iff the topic time strictly follows the time of the resultant state of an eventuality the aspectual operator is predicated of. Otherwise, the aspectual operator is non-veridical. Since under the imperfective/progressive aspect the topic time is included in the event time of an eventuality (of which the time of resultant state is a part), the imperfective/progressive aspect is therefore non-veridical. 9 This application assumes the structure proposed in Cheng and Sybesma (1999, 2005) for Mandarin nominals, where the classifier is a functional head C L ( ASSIFIER ) that forms a constituent with the wh-phrase following it: (i) CLP CL NP wh-phrase Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 572 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases Although rather stipulative, we need the condition of non-veridicality in (25a) to rule out sentences like (23), where the wh-phrase could potentially be existentially closed by ∃ or a classifier. Moreover, once we factor in the positions of the non-veridical operators, the condition in (25a) and the hypothesis that ∃ applies higher than vP (25b) can help us account for the environment-dependent co-occurrence of the wh-phrase and classifiers, which will be the focus of the next section. This analysis also makes predictions about the scope of the wh-phrase, depending on where it is existentially closed. It will be shown that the predictions are borne out after establishing the syntactic positions of the non-veridical operators and their interactions with ∃. 3.1. Application of ∃ The account for the classifier requirement in existential wh-phrase licensing will resort to the interaction between the non-veridical operators and the application site of ∃. The licensing reasoning goes as follows: (i) A wh-phrase has to be existentially closed within a non-veridical domain, (25a). (ii) ∃ applies higher than vP, (25b), contrary to the common assumption that it applies low at VP (Diesing, 1990, 1992). (iii) If the non-veridical operator is no higher than vP, existentially closing the wh-phrase would be ungrammatical, i.e. a violation of (25a). (iv) In that case, a classifier comes in as a replacement for ∃ (hence the hypothesis that classifiers serve as ∃ within the domain of vP). Given this reasoning, we are in other words saying that the environments where classifiers are required are environments where the non-veridical operators scope lower than ∃. This statement can be corroborated by the clausal structure in Tsai (2010), where different types of modals assume different syntactic heights:10 10 Tsai (2010) reaches this structure after investigating the syntactic and scope interactions between the different types of modals (i.e. epistemic, deontic, and dynamic modals). His argument is not presented here due to reasons of space. For a detailed argument for this structure, I refer the readers to Tsai (2010). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 573 H.-L. Huang (26) On the role of classifiers in licensing Mandarin existential wh-phrases MPEpi Epi. Adv. M’ Epi. Aux. TP S UBJ T’ T MPDeo Deo. Adv. M’ Deo. Aux. vP v’ v MPDyn Dyn. Aux. VP Given the positional difference between the epistemic and deontic modals, whose scopes constitute the licensing domains for existential wh-phrases, we can now explain the contrast between the epistemic and deontic environments in terms of the classifier requirement: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 574 H.-L. Huang (27) On the role of classifiers in licensing Mandarin existential wh-phrases Haoxiang shei qifu-le Zhangsan seem who bully-ASP Zhangsan ‘It seems that somebody bullied Zhangsan.’ [TP3 haoxiang [TP2 ∃ [TP1 sheii [vP ti [VP qifu-le Zhangsan ]]]]] MPEpi haoxiang TP ∃11 TP DP shei T’ T vP VP V qifu DP Zhangsan J(27)Kw, g (28) = ∃w” ∈ M(w, epistemic) . ∃p [p ∈ {λ w’ . bullyw’ (y, ZS) | personw (y)} ∧ p(w”) = 1]12 Zhangsan haoxiang chi-le shenme Zhangsan seem eat-ASP what ‘It seems that Zhangsan ate something.’ [TP3 haoxiang [TP2 ∃ [TP1 Zhangsani [vP ti [VP chi-le shenme ]]]]] MPEpi haoxiang TP TP ∃ DP Zhangsan T T’ vP VP V chi J(28)Kw, g DP shenme = ∃w” ∈ M(w, epistemic) . ∃p [p ∈ {λ w’ . eatw’ (ZS, x) | thingw (x)} ∧ p(w”) = 1] 11 The covert existential closure ∃ is put in Spec.TP in the structure of (27). This is a position where it can compose with the TP of type hsti/t given its semantics. However, it is not limited to being in this position. It can be in any position where its argument’s type allows it to compose, as long as that position is higher than vP. 12 For a thorough derivation of the semantics of the current and following examples, please see the appendix. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 575 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases The epistemic modal is a sentential operator whose non-veridical licensing domain for the whphrase encompasses the application site of ∃. Therefore, the wh-phrase can be closed by ∃ and interpreted as an existential, following the condition in (25a). On the other hand, the deontic modal scopes low (at vP) and ∃ falls outside of its non-veridical domain. As a result, the wh-phrase, be it a subject or an object, cannot be closed by ∃ and obtain the existential reading: (29) Shei yinggai xi matong who should wash toilet *‘Somebody should wash the toilet.’ / ‘Who should wash the toilet?’ *[TP2 ∃ [TP1 sheii [vP2 yinggai [vP1 ti [VP xi matong ]]]]] *TP TP ∃ DP shei T’ MPDeo T yinggai vP VP V xi DP matong (30) Zhangsan yinggai chi shenme Zhangsan should eat what *‘Zhangsan should eat something.’ / ‘What should Zhangsan eat?’ *[TP2 ∃ [TP1 Zhangsani [vP2 yinggai [vP1 ti [VP chi shenme ]]]]] *TP TP ∃ DP Zhangsan T’ T MPDeo yinggai vP VP V chi DP shenme Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 576 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases Due to the unavailability of ∃, the set of alternatives denoted by the wh-phrase cannot be existentially closed but has to percolate up, leading to the obligatory interrogative reading, i.e. the reading of a wh-question. 3.2. Classifiers as ∃ The only way for the wh-phrase to be existential in this case of low-scoping non-veridical operators is for the classifier to take over the job of ∃ and close the set denoted by the whphrase with the semantics proposed in (25bii), repeated here as (31a): (31) a. b. JC L∃ Kw, g = λ αhei/t λ Phe, esti λ yλ w’ . ∃z [z ∈ α ∧ Pw’ (z)(y) = 1]13 Zhangsan yinggai/bixu mai-dian shenme Zhangsan should/must buy-CL what ‘Zhangsan should/must buy something.’ [TP Zhangsani [vP2 yinggai/bixu [vP1 ti [VP mai-dian∃ shenme ]]]] TP DP2 T’ Zhangsan MPDeo T yinggai / bixu vP VP V mai 13 The DP1 dian∃ shenme JshenmeKw, g = {xe : thingw (x)} JDP1 Kw, g = λ Phe, esti λ yλ w’ . ∃z [z ∈ {xe : thingw (x)} ∧ Pw’ (z)(y) = 1] J(31b)Kw, g = ∀w” ∈ M(w, deontic) . ∃z [z ∈ {xe : thingw (x)} ∧ buyw” (ZS, z) = 1] denotation proposed for classifiers as ∃ may seem too restrictive since its second argument position assumes a predicate of type he, esti, i.e. the type of transitive verbs. However, we can allow for slight variation of the denotation between those in (ii), assuming the verbal structure proposed by Huang, Li, and Li (2009) in (i): vP (i) S UBJ . v’ v VP IO V’ V Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde DO 577 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases However, if what we have in the case of low-scoping deontic modals is a wh-subject as in (29), inserting a classifier before the wh-subject would not help for two reasons: (i) the whsubject falls outside of the non-veridical licensing domain (i.e. outside of the scope of the deontic modals), and (ii) Mandarin classifiers are clitic-like items that usually need to attach to numerals, demonstratives, or verbs, and cannot stand alone sentence-initially: (32) *Ge ren xihuan Zhangsan CL person like Zhangsan ‘Somebody likes Zhangsan.’ The clitic need of classifiers thus makes sentences with a [C L + Wh] subject ungrammatical, even under an interrogative reading: (33) *Ge shei yinggai xi matong CL who should wash toilet *‘Somebody should wash the toilet.’ / *‘Who should wash the toilet?’ *[TP [DP ge/ge∃ shei]i [vP2 yinggai [vP1 ti [VP xi matong ]]]] *TP DP14 ge/ge∃ shei T’ T MPDeo yinggai vP VP V xi DP matong If we try to generalize the contrast between the epistemic and deontic modals under discussion to other licensing environments, we can see that generally speaking, the requirement of classi(ii) For [C L + Wh] direct objects (DOs), JC L∃ Kw, g = λ αhei/t λ Phe,he, estii λ xλ yλ w’ . ∃z [z ∈ α ∧ Pw’ (z)(x)(y) = 1] For [C L + Wh] indirect objects (IOs), JC L∃ Kw, g = λ αhei/t λ Phe, esti λ yλ w’ . ∃z [z ∈ α ∧ Pw’ (z)(y) = 1] = (31a) Please note that when C L∃ shows up with a wh-phrase as the indirect object, the denotation for C L∃ remains the same as in the case of transitive verbs, because the first argument position in the denotation of the di-transitive verb will have been saturated by the direct object before the verb composes with the [C L∃ + Wh] IO. 14 As will be clear in later sections, Mandarin classifiers assume two types of functions, that of regular classifiers (i.e. those that go with regular NPs) and that of ∃ (as in the case of existential wh-phrases). The two types are differentiated by the ∃ subscript on the classifier: C L∃ closes the set of alternatives denoted by the wh-phrase and renders it existential while C L is transparent to the set denotations of wh-phrases and the DP [C L + Wh] remains a wh-interrogative. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 578 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases fiers can be seen as a reflection of high vs. low non-veridical operators. All of the non-veridical operators that do not require a classifier in their scope to license an existential wh-phrase are sentential (or not sentential but higher than vP as in the case of the imperfective/progressive aspect), or can embed structures bigger than a vP (e.g. non-factive epistemic verbs). Classifiers are needed elsewhere; that is, under the operators that are not higher than a vP (e.g. deontic modals) or cannot embed structures larger than a vP (e.g. the future verbs, which cannot embed a full finite TP). Our first puzzle concerning the environment-dependent requirement of classifiers is thus solved. 4. Classifier distribution Having established the licensing mechanism for Mandarin existential wh-phrases, we can now also explain our second classifier puzzle, where the classifier that was once required under a deontic modal is no longer needed when the deontic modal is further embedded under an epistemic modal: (34) Zhangsan haoxiang bixu mai-(ge) shenme Zhangsan seem must buy-CL what ‘It seems that Zhangsan must buy something.’ [TP3 haoxiang [TP2 ∃ [TP1 Zhangsani [vP2 bixu [vP1 ti [VP mai-(ge∃ ) shenme ]]]]]] As shown by the LF above, the epistemic modal expands the licensing domain of the wh-phrase from the vP to the sentential level to include the high ∃, providing another option of existential closure for the wh-phrase. As a result, the classifier is no longer necessary for the existential reading. The second classifier puzzle is also solved. Given the way the current account is set up, it makes a prediction that if we expand the licensing domain of the wh-phrase by embedding a classifier-requiring environment under a nonclassifier-requiring one, we can remove the need of a classifier for licensing the wh-phrase. The following examples show that this prediction is indeed borne out:15 (35) Zhangsan hui qu mai-(xie) shenme dongxi song ta ma? Zhangsan will go buy-CL what thing give him Q ‘Will Zhangsan go to buy something for him?’ [CP [TP2 ∃ [TP1 Zhangsan hui qu mai-(xie∃ ) shenme dongxi song ta ]] ma]? 15 The existential interpretation of the wh-subject in the case of low non-veridical operators (e.g. deontic modals) that was non-rescuable by the insertion of a classifier can now be rescued under embedding, as predicted, given the availability of ∃ made by domain expansion. Example (29) embedded under the polar question particle ma is shown here for illustration: (i) Shei yinggai xi matong ma? who should wash toilet Q ‘Should somebody wash the toilet?’ [CP [TP2 ∃ [TP1 Sheii [vP2 yinggai [vP1 ti [VP xi matong ]]]]] ma ]? Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 579 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases (36) Yaoshi Zhangsan bixu chi-(dian) shenme, qing gaosu wo if Zhangsan must eat-CL what please tell me ‘If Zhangsan must eat something, please tell me.’ [TP2 yaoshi ∃ [TP1 Zhangsan bixu chi-(dian∃ ) shenme, ...]] (37) Wo yiwei Zhangsan dasuan zhao-(ge) shei lai bangang I think Zhangsan plan find-CL who come help ‘I thought Zhangsan planned to find somebody to help.’ [TP3 Wo yiwei [CP [TP2 ∃ [TP1 Zhangsan dasuan zhao-(ge∃ ) shei ... ]]]] Above are three instances of non-veridical operators that require a classifier in their scope (a modal verb hui (‘will’) in (35), a deontic modal bixu (‘must’) in (36), and a future verb dasuan (‘plan’) in (37)) being embedded under operators that do not (the polar question particle ma in (35), a conditional morpheme yaoshi (‘if’) in (36), and a non-factive epistemic verb yiwei (‘think’) in (37)). And the classifiers are now optional in all of the instances. 5. Scope of wh-phrases The issue about what options of existential closure are available to the wh-phrase makes another prediction about the scope interpretation of the wh-phrase. In the examples shown above, we should have scope ambiguity of the wh-phrase, depending on what it is closed by in its licensing domain. And we do indeed find scope ambiguity in cases like those: (38) Zhangsan haoxiang bixu chi-dian shenme Zhangsan seem must eat-CL what ‘It seems that Zhangsan must eat something.’ (seem > must > C L∃ ) ‘It seems that there is something such that Zhangsan must eat it.’ (seem > ∃ > must) CP TP C ma TP ∃ DP shei T’ T MPdeo yinggai vP VP V xi DP matong Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 580 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases The scope ambiguity exists under the assumption that classifiers only serve as ∃ in the case of existential wh-phrase licensing when needed. In other words, they do not necessarily close the set denoted by the wh-phrase if the higher covert ∃ is also available. Consequently, the wh-phrase has two options of existential closure given the domain expansion by the epistemic modal, leading to the scenario where the two options of existential closure fall on either side of the low non-veridical operator (i.e. the deontic modal). Hence, the wide and narrow scope reading of the wh-phrase with respect to the low non-veridical operator are both accessible. Given the presence of the classifier in (38) and the possibility of obtaining a wide scope reading of the wh-phrase, we are in a way saying that classifiers are ambiguous between ∃ and regular classifiers so that the set denotation of the wh-phrase can percolate up the structure and be closed by the higher ∃ in the latter case.16 This is a necessary hypothesis to make, given how the licensing mechanism is constructed: Existentially closing the wh-phrase in environments other than non-veridical would result in ungrammaticality. However, the following sentence is grammatical, but only with an interrogative reading of the wh-phrase: (39) Zhangsan tingdao-le-xie shenme Zhangsan hear-ASP-CL what *‘Zhangsan heard something.’ / ‘What did Zhangsan hear?’ Furthermore, in the absence of a classifier in environments like (38), the wh-phrase is predicted to be non-ambiguous and have only wide scope with respect to the low non-veridical operator, which is attested by the following example: (40) Zhangsan haoxiang bixu chi shenme Zhangsan seem must eat what *‘It seems that Zhangsan must eat something.’ (*seem > must > C L∃ ) ‘It seems that there is something such that Zhangsan must eat it.’ (seem > ∃ > must) It is the higher covert ∃ that is existentially closing the wh-phrase in this case under the licensing domain of the high non-veridical operator. Given the application site of ∃, i.e. higher than vP, the wh-phrase necessarily has wide scope with respect to the low non-veridical operator. 16 According to Cheng and Sybesma (1999, 2005), from whom I adopt the structure of Mandarin nominals, the function of the C L head is the ι operator that renders the definite reading of the NP it composes with. Apparently, our analysis of wh-phrases as denoting sets of alternatives would not be able to compose with a regular classifier if we follow Cheng and Sybesma’s analysis. Therefore, we need to propose another denotation for the classifier so that it can compose with a wh-phrase and pass up the wh-phrase’s set denotation: (i) JC Lwh Kw, g = λ fhei/t . f The classifier in this case is treated as denoting an identity function whose first argument is a set of alternatives. This denotation guarantees the exclusive relationship between this type of regular classifiers and wh-phrases (as opposed to the ι -classifier with regular NPs), as well as the derivation of the interrogative reading of a wh-question as in (39). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 581 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases 6. Conclusion To conclude, the analysis of licensing Mandarin existential wh-phrases presented in this paper builds on two major factors that make necessary conditions for the existential interpretation of wh-phrases: Non-veridicality and existential closure (∃). By attributing the role classifiers play in the licensing mechanism to fulfilling the function of ∃ when ∃ is unavailable, we are able to account for the distribution of classifiers that is environment-dependent. The (un-) availability of ∃ is conditioned by two other factors: The application site of ∃, i.e. above vP, and the syntactic heights of non-veridical operators that license the wh-phrase. Given our hypothesis that a wh-phrase can only be grammatically closed by ∃ in a non-veridical domain, classifiers are required to take over the job of ∃ when the licensor of the wh-phrase is a low non-veridical operator, outside of whose scope ∃ falls. Thus, the distribution of classifiers in the case of existential wh-phrases is licensor-related, i.e. their environment-dependent nature, and their obligatory presence can be made optional under the expansion of the non-veridical licensing domain by embedding a low licensor below a high licensor to include the covert ∃ that was once out of reach. And the availability of both means of existential closure in this case renders the wh-phrase scope ambiguous, which is also proven true in this paper. References Cheng, L. L.-S. (1991). On the Typology of Wh-Questions. Ph. D. thesis, Massachusetts Institute of Technology, Cambridge, MA. Cheng, L. L.-S. (1994). Wh-words as polarity items. In P. J.-K. Li, C.-R. Huang, and C.-C. J. Tang (Eds.), Chinese Languages and Linguistics 2, pp. 615–640. Academia Sinica, Taiwan: Institute of History and Philosophy. Cheng, L. L.-S. (1995). On dou-quantification. Journal of East Asian Linguistics 4, 197–234. Cheng, L. L.-S. and R. Sybesma (1999). Bare and not-so-bare nouns and the structure of NP. Linguistic Inquiry 30, 509–542. Cheng, L. L.-S. and R. Sybesma (2005). Classifiers in four varieties of Chinese. In G. Cinque and R. S. Kayne (Eds.), Handbook of Comparative Syntax, pp. 259–292. Oxford University Press. Diesing, M. (1990). The Syntactic Roots of Semantic Partition. Ph. D. thesis, University of Massachusetts at Amherst. Diesing, M. (1992). Indefinites. Cambridge, MA: MIT Press. Giannakidou, A. (2002). Licensing and sensitivity in polarity items: From downward entailment to (non)veridicality. In M. Andronis, E. Debenport, A. Pycha, and K. Yoshimura (Eds.), Proceedings from the Annual Meeting of the Chicago Linguistics Society 38, pp. 29–54. Hamblin, C. (1973). Questions in Montague English. Foundations of Language 10, 41–53. Huang, J. C.-T. (1982). Logical Relations in Chinese and the Theory of Grammar. Ph. D. thesis, Massachusetts Institute of Technology, Cambridge, MA. Huang, J. C.-T., A. Li, and Y. Li (2009). The Syntax of Chinese. Cambridge: Cambridge University Press. Kratzer, A. and J. Shimoyama (2002). Indeterminate pronouns: The view from Japanese. In Y. Otsu (Ed.), Proceedings of the Third Tokyo Conference on Psychoinguistics, pp. 1–25. Hituzi Syobo. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 582 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases Li, C. N. and S. A. Thompson (1981). Mandarin Chinese: A Functional Reference Grammar. Berkeley: University of California Press. Li, H. and J. Law (2014). Focus intervention: A quantificational domain approach. In J. Iyer and L. Kusmer (Eds.), Proceedings of NELS 44, Amherst, MA, pp. 273–287. GLSA. Li, Y.-H. A. (1992). Indefinite wh in Mandarin Chinese. Journal of East Asian Linguistics 1, 125–155. Liao, H.-C. (2011). Alternatives and Exhaustification: Non-interrogative uses of Chinese whwords. Ph. D. thesis, Harvard University, Cambridge, MA. Lin, J., F. P. Weerman, and H. H. Zeijlstra (2014). Mandarin shenme as a superweak NPI. In J. Hoeksema and D. Gilbers (Eds.), Black Book: A Festschrift in Honor of Frans Zwarts, pp. 229–251. Groningen: University of Groningen. Lin, J.-W. (1996). Polarity Licensing and Wh-phrases Quantification in Chinese. Ph. D. thesis, University of Massachusetts at Amherst. Lin, J.-W. (1998). On existential polarity wh-phrases in Chinese. Journal of East Asian Linguistics 7, 219–255. Lin, J.-W. (2004). Choice functions and scope of existential polarity wh-phrases. Linguistics and Philosophy 27, 451–491. Lin, J.-W. (2014). Wh-expressions in Mandarin Chinese. In A. Simpson, J. C.-T. Huang, and A. Y.-H. Li (Eds.), Handbook of Chinese Linguistics. Wiley Blackwell. Tsai, W.-T. D. (1999). On lexical courtesy. Journal of East Asian Linguistics 8, 39–73. Tsai, W.-T. D. (2003). Lexical courtesy revisited: Evidence from Tsou and Seediq whconstructions. Gengo Kenkyu 123, 331–361. Tsai, W.-T. D. (2010). Tan Hanyu motaici de fenbu yu quanshi zhi duiying quango [On the syntax-semantics correspondences of Chinese modals]. Zhongguo Yuwen [Studies of the Chinese Language] 3, 208–221. Xie, Z. (2007). Non-veridicality and existential polarity wh-phrases in Mandarin. In Proceedings from the Annual Meeting of the Chicago Linguistic Society 43, 121–135. Yatsushiro, K. (2009). The distribution of quantificational suffixes in Japanese. Natural Language Semantics 17, 141–173. Zwarts, F. (1995). Nonveridical contexts. Linguistic Analysis 25(3-4), 286–312. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 583 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases Appendix. Semantic derivations of existential wh-phrases The proposed denotations for Mandarin wh-phrases: (i) Jshenme (‘what’)Kw, g (ii) Jshei (‘who’)Kw, g = = {xe : thingw(x)} {ye : personw (y)} ∈ ∈ Dhei/t Dhei/t Yatsushiro’s (2009) definition of Pointwise Functional Application: (iii) Semantic types of alternative sets (Yatsushiro, 2009; pg. 152) For any type α ; α /t is the type of sets of entities of type α , Dα /t = POW(Dα ) (iv) Pointwise Functional Application (Yatsushiro, 2009; pg. 153): If X is a phrase with two immediate subconstituents Y and Z, then JXKg is defined as follows: .................................................................................... if JYKg is of type α ; JZKg is of type hα , β i, then JXKg = JZKg (JYKg ) ∈ Dβ ; .................................................................................... if JYKg is of type α /t; JZKg is of type hα , β i, then JXKg = {JZKg (y) | y ∈ JYKg } ∈ Dβ /t ; .................................................................................... if JYKg is of type α ; JZKg is of type hα , β i/t, then JXKg = {z(JYKg ) | z ∈ JZKg } ∈ Dβ /t ; .................................................................................... if JYKg is of type α /t; JZKg is of type hα , β i/t, then JXKg = {z(y) | z ∈ JZKg and y ∈ JYKg } ∈ Dβ /t .................................................................................... Semantic derivation of (27): (27) Haoxiang shei qifu-le Zhangsan seem who bully-ASP Zhangsan ‘It seems that somebody bullied Zhangsan.’ [TP3 haoxiang [TP2 ∃ [TP1 sheii [vP ti [VP qifu-le Zhangsan ]]]]] JZhangsanKw, g = Zhangsan ∈ De JqifuKw, g = λ xλ yλ w’ . bullyw’ (y, x) ∈ Dhe,he, stii JvPKw, g = λ yλ w’ . bullyw’ (y, ZS) ∈ Dhe, sti JTP1 Kw, g = {λ w’ . bullyw’ (y, ZS) | personw (y)} ∈ Dhsi/t J∃Kw, g = λ αhsti/t λ w” . ∃p [p ∈ α ∧ p(w”) = 1] JTP2 Kw, g = λ w” . ∃p [p ∈ {λ w’ . bullyw’ (y, ZS) | personw (y)} ∧ p(w”) = 1] ∈ Dhsti JhaoxiangKw, g = λ P . ∃w”’ ∈ M(w, epistemic) . P(w”’) = 1 JTP3 Kw, g = ∃w”’ ∈ M(w, epistemic) . ∃p [p ∈ {λ w’. bullyw’(y, ZS) | personw (y)} ∧ p(w”’) = 1] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 584 H.-L. Huang On the role of classifiers in licensing Mandarin existential wh-phrases Semantic derivation of (28): (28) Zhangsan haoxiang chi-le shenme Zhangsan seem eat-ASP what ‘It seems that Zhangsan ate something.’ [TP3 haoxiang [TP2 ∃ [TP1 Zhangsani [vP ti [VP chi-le shenme ]]]]] JchiKw, g = λ xλ yλ w’ . eatw’ (y, x) ∈ Dhe,he, stii JvPKw, g = {λ yλ w’ . eatw’ (y, x) | thingw (x)} ∈ Dhe, sti/t JTP1 Kw, g = {λ w’ . eatw’ (ZS, x) | thingw (x)} ∈ Dhsti/t J∃Kw, g = λ αhsti/t λ w” . ∃p [p ∈ α ∧ p(w”) = 1] JTP2 Kw, g = λ w” . ∃p [p ∈ {λ w’ . eatw’ (ZS, x) | thingw (x)} ∧ p(w”) = 1] ∈ Dhsti JhaoxiangKw, g = λ P . ∃w”’ ∈ M(w, epistemic) . P(w”’) = 1 JTP3 Kw, g = ∃w”’ ∈ M(w, epistemic) . ∃p [p ∈ {λ w’ . eatw’ (ZS, x) | thingw (x)} ∧ p(w”’) = 1] Semantic derivation of (31b): (31b) Zhangsan bixu mai-dian shenme Zhangsan must buy-CL what ‘Zhangsan must buy something.’ [TP Zhangsan1 1 [vP2 bixu [vP1 t1 [VP mai [DP dian∃ shenme ]]]]] Jdian∃ Kw, g = λ αhei/t λ Phe,he, stii λ yλ w’ . ∃z [z ∈ α ∧ Pw’ (z)(y) = 1] JDPKw, g = λ Phe,he, stii λ yλ w’ . ∃z [z ∈ {x : thingw (x)} ∧ Pw’ (z)(y) = 1] JmaiKw, g = λ xλ yλ w” . buyw” (y, x) ∈ Dhe,he, stii JVPKw, g = λ yλ w’ . ∃z [z ∈ {xe : thingw (x)} ∧ buyw’ (y, z) = 1] ∈ Dhe, sti JvP1 Kw, g = λ w’ . ∃z [z ∈ {xe : thingw (x)} ∧ buyw’ (g(1), z) = 1] ∈ Dhsti JbixuKw, g = λ P . ∀w”’ ∈ M(w, deontic) . P(w”’) = 1 JvP2 Kw, g = ∀w”’ ∈ M(w, deontic) . ∃z [z ∈ {xe : thingw (x)} ∧ buyw”’ (g(1), z) = 1] J1 vP2 Kw, g = λ y . ∀w”’ ∈ M(w, deontic) . ∃z [z ∈ {xe : thingw (x)} ∧ buyw”’ (y, z) = 1] JTPKw, g = ∀w”’ ∈ M(w, deontic) . ∃z [z ∈ {xe : thingw (x)} ∧ buyw”’ (ZS, z) = 1] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 585 586 Composing discourse parenthetical reports1 Julie HUNTER — Universitat Pompeu Fabra, Barcelona and Université Paul Sabatier, Toulouse Nicholas ASHER — IRIT, CNRS, Toulouse Abstract. Hunter (2016) proposed that a speech report with a parenthetical interpretation but non-parenthetical syntax will contribute a modal discourse relation of the form ♦R to discourse logical form. This paper provides a compositional account of the mechanism by which these modal relations are triggered. It then extends Hunter’s proposal to reports involving factive embedding verbs and provides an explanation of why explicit discourse connectives sometimes block parenthetical readings of reports in their scope. Keywords: coercion, discourse connectives, discourse structure, factive verbs, parenthetical reports, speech reports 1. Introduction As observed in Simons (2007) and Urmson (1952) inter alia, sometimes the main point of a speech or attitude report is conveyed by the embedded clause alone. Compare (1) and (2): (1) a. b. Liz is sad. A famous critic said that her new album isn’t worth a dime. (2) a. b. John didn’t come to my party. Jill said that he was out of town. In both (1) and (2), (b) is naturally understood as offering an explanation of the content of (a); the intuitive explanantia are in bold. In (1), it is the fact that the critic said what she did that explains why Liz is upset; in other words, the entire report contributes to the explanation. On the most natural reading of (2), however, the embedded clause of (2b) alone contributes to the explanation; the fact that Jill said what she did plays a backgrounded, evidential role. Urmson (1952) called uses of embedding verbs like that in (2) parenthetical. In these uses, embedding verbs play a secondary role, apparently serving to provide evidence for, or qualification of, the reported content. In this way, they resemble verbs of speech or attitude in the slifted clauses (Ross, 1973) of syntactically parenthetical reports such as (3). (3) He was out of town, Jill said. Despite the similarity between (2b) and (3), we will assume that (2b) has a parenthetical reading (because say has a parenthetical reading) but non-parenthetical syntax. That is, following Simons (2007), we will assume that in (2b), the content expressed by the clause in bold falls in the scope of the embedding verb say, as the surface form of the report suggests. 1 We gratefully acknowledge research support from ERC research grant 269427. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 587 J. Hunter & N. Asher Composing discourse parenthetical reports Hunter (2016) developed a discourse-based account of reports with parenthetical readings but non-parenthetical syntax. In particular, Hunter proposed that the discursive contribution of a parenthetical report is to introduce a modal rhetorical relation between the embedded content of the report and the discourse preceding the report. In this paper, we build on the account of coercion developed in Asher (2011) and Asher and Luo (2012) to provide a compositional analysis of Hunter’s proposal. We then extend the resulting account to model two facts about parenthetical reports not covered in other models: the fact that factive verbs such as found out can also be used parenthetically, as observed in Simons (2007), and the fact that certain discourse connectives seem to block parenthetical readings of reports in their syntactic scope, as discussed in Hunter and Danlos (2014). (4b), for instance, only has a non-parenthetical reading. (4) a. b. John didn’t come to my party because Jill said he was out of town. We begin in Section 2 with a presentation of Hunter (2016)’s proposal. We then present the basics of Asher and Luo’s account and our application of it in Section 3. Section 4 extends the resulting compositional account to parenthetical readings of factive verbs, and Section 5 examines the effects of explicit discourse connectives on the interpretation of reports. 2. The function of discourse parenthetical reports Following Hunter (2016), we will call reports with a parenthetical interpretation but nonparenthetical syntax, such as (2b), discourse parenthetical to indicate that their parenthetical interpretation follows from discursive facts. There are no morphological features, like the evidential markers found in many languages, that force (2b) to receive an evidential reading. Nor should we assume that (2b) has an underlying parenthetical syntax that differs from its surface form. (See Simons, 2007: for arguments against a syntactic account.) There may be semantic differences between a parenthetical reading of a report and a non-parenthetical reading of the same report in the sense that the two interpretations might support different entailments. Normally, an instance of a speech or attitude report with a non-factive embedding verb such as say does not entail any level of commitment to the embedded clause, as illustrated by (1). In the absence of further context, however, the discourse in (2) arguably entails the possibility that John was out of town: if the speaker is not committed to this possibility, the relevance of (2b) to (2a) is unclear. Still, these entailments do not follow from (1b) and (2b) alone; they are discourse-level entailments that result from the interaction of a report and another discourse unit in the preceding discourse. That the interpretation of a discourse parenthetical report results from the way a report is used in a discourse has been observed numerous times in the literature on parenthetical reports in English (Hooper, 1975; Simons, 2007; Urmson, 1952). Formal models of their discursive behavior are harder to come by. What does it mean to say that a parenthetical reading follows from the way that a report is used? How do we define the discourse function of a parenthetical report? Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 588 J. Hunter & N. Asher Composing discourse parenthetical reports Simons (2007) sketched a diagnostic for parenthetical readings using question/answer pairs like (5). (5) a. b. Why wasn’t John at the party? Jill said that he was out of town. In (5), only the embedded clause of (5b) is ‘at-issue’, in Simons’ sense, because only the embedded clause provides an answer to the question posed in (5a). According to Simons’ proposed diagnostic, a parenthetical report is one in which only the embedded clause is atissue. Thus this diagnostic predicts, seemingly correctly in this case, that (5b) is parenthetical. This suggestion is not yet an account, however, because it does not provide a general model of discourse function that could be applied in the absence of explicit question/answer pairs. In the case of (2), we can imagine that (2b) answers a question like Why not?, but short of a predictive account of how one can identify implicit questions, Simons’ question/answer-based diagnostic cannot be used for arbitrary discourses. Moreover, the diagnostic does not yield an analysis of cases in which a speaker explicitly denies the embedded content of a seemingly parenthetical report. Suppose, for example, that the speaker in (2) followed (2b) with (6): (6) But that’s a total lie because I saw him out walking his dog early the next morning. Given (6), we cannot say that the embedded content of (2b) answers the question Why not? or Why didn’t John come to your party?—the speaker explicitly commits herself to the negation of that content. A final concern is how to model reports for which both the embedded clause and the report as a whole are relevant to the discourse but in different ways. To put this in terms of Simons’ diagnostic, how do we handle cases in which both the embedded clause and the report as a whole answer questions that have been posed in the discourse, as in (7)? (7) a. b. Why didn’t John come to your party? Did anyone tell you? Jill said he was out of town. In such examples, it’s hard to say that one part of the report is at-issue while the other isn’t; it’s rather that the embedded clause and the report as a whole are at-issue relative to different discourse units. Of course, in (7), the second question is obviously very relevant to the first, but as emphasized in Hunter (2016), this is not always the case; the two parts of a report can be relevant to separate discourse units whose relevance to one another is much less clear. Hunter (2016) argues that rhetorical theories (Asher, 1993; Asher and Lascarides, 2003; Hobbs, 1985; Mann and Thompson, 1988) can provide a model for the discourse function of parenthetical reports that generalizes Simons’ suggestion and is more suitable for arbitrary discourses.2 2 This suggestion has been made before. See Danlos and Rambow (2011); Dinesh et al. (2005); Hardt (2013); Hunter et al. (2006). Hunter (2016) examines past efforts to model parenthetical reports in rhetorical accounts and details many of the problems faced by these earlier proposals. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 589 J. Hunter & N. Asher Composing discourse parenthetical reports In a theory of rhetorical structure, what it means to have a certain discourse role or function is to enter into a particular rhetorical relation (or set of relations). The heart of Hunter (2016)’s proposal is that a report p is parenthetical just in case the embedded clause of p enters into a rhetorical relation R with a discourse unit that is discourse prior to p—that is, prior to the entire main clause of p—and the attributive predicate does not contribute to this relation. In (2), for example, (2a) is discourse prior to (2b), but the attributive predicate of (2b) does not contribute to the explanatory relation that is proposed to hold between the content in its scope and (2a): (8) Explanation(John didn’t come to my party, he was out of town) This approach bypasses the need for implicit questions3 , allows that both the embedded clause and the report as a whole can play independent rhetorical roles, and generalizes Simons’ diagnostic for parenthetical reports on the assumption that answering a question yields a rhetorical relation between a question and its answer. An important aspect of Hunter’s proposal is that the rhetorical relation that relates the embedded clause of a parenthetical report to the preceding discourse will fall in the scope of a possibility operator. (8) poses a problem as it stands because Explanation is a veridical relation (Asher and Lascarides, 2003). This means that an instance of (8) cannot be true in a context unless both of its arguments are true in the same context. This is intuitively correct for (2): for John’s being out of town to explain his absence at the party, he must have actually been out of town. The logical form in (8) is therefore too strong; as stressed by Simons (2007), reports are often used in situations like (2) precisely to hedge one’s commitment to the embedded content. In some contexts it might be possible to infer full speaker commitment to this content, but a parenthetical use of a report does not in and of itself require such a strong commitment. To weaken the entailments of a parenthetical report, the first step is to exploit the syntactic and semantic features of the report and assume that the attributive predicate takes not only syntactic scope over the embedded clause, but discourse scope over it as well. That is, the embedded clause is related to the attributive predicate via a rhetorical relation of Attribution, and the embedded clause is subordinate to the attribution predicate in the discourse representation. (9) gives the contribution of the Attribution relation to the logical form of the discourse. (9) Attribution(Jill said that, he was out of town) Semantically, this means that the embedded content of a report will not be entailed, at least not in virtue of figuring in an Attribution relation. (10) describes the entailments of the two arguments of an Attribution relation. (10) a. b. Jill said that: |= ∃p.said(Jill,p) he was out of town: specifies the content of p, but 6|= p 3 We leave open here the possibility that discourse relations might be modelled in a question-based model, though see Hunter and Abrusán (2016) for a discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 590 J. Hunter & N. Asher Composing discourse parenthetical reports Of course, the Attribution relation is a general one that will apply to non-parenthetical reports as well. As such, Attribution will not support the stronger entailments that we see with parenthetical reports. Thus we arrive at the following impasse: if in building the representation for a parenthetical report, we ignore the discursive contribution of the Attribution relation, we will predict overly strong entailments. If we add Attribution to correct this, we end up with overly weak entailments. To get around this problem, Hunter (2016) proposed a general rule that any time a discourse unit β figuring in an Attribution relation of the form Attribution(α, β ) is rhetorically related to a unit γ that is textually prior to α, and thus outside of the scope of the Attribution, a relation R that can be inferred to hold between γ and β based on the contents of γ and β alone is weakened to ♦R. This rule is formalized in PA below, where e and e0 are edges in a discourse graph that connect nodes representing discourse units; α, β and γ are labels for discourse units; and l is a labelling function that maps each edge to a label for a discourse relation (e.g., Attribution). PA: (∃e.e(α, β ) ∧ l(e) = Attribution) → (∃γ∃e0 (γ <t α ∧ e0 (γ, β )) → ∃R(l(e0 ) = ♦R)) The effects of PA are illustrated in Figure 1. γ α ♦R Attribution β Figure 1: Relations to units inside Attributions PA is designed to capture the idea that when a speaker uses a report parenthetically, she uses the attributive predicate as a kind of buffer so that the embedded content can be relevant, but she does not have to fully commit to its content. From the perspective of discourse structure, PA reflects the fact that even if an attribution predicate does not seem relevant or ‘at-issue’ with regard to the preceding discourse, it nevertheless plays a crucial function in the overall discourse by affecting the relation inferred between its embedded clause and the preceding discourse. Some consequences of adopting PA are, first, that it respects the constraint of veridicality imposed by many discourse relations, including Explanation, because a modal discourse relation only entails the possibility that its arguments are true: (11) ♦R(α, β ) |= ♦(α ∧ β ) A full commitment to the content of β will be consistent with a formula of the form ♦R(α, β ), but it will not be necessary. At the same time, commitment to ¬β will be inconsistent with a formula of the form ♦R(α, β ), as desired. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 591 J. Hunter & N. Asher Composing discourse parenthetical reports A further desirable consequence is that both α and β can be discourse relevant. Nothing in this proposal hinges on a binary distinction between at-issue and not-at-issue content, which, as argued in Hunter (2016), is untenable when we look at the way reports are actually used in longer stretches of discourse. Hunter’s account, however, leaves some important questions about the nature of PA unanswered. First, what triggers PA and can we derive it compositionally? Also, does ♦R(α, β ) yield the right entailments for α? Are there any examples in which a parenthetical report weakens a speaker’s commitment to the argument α? In the next section, we argue that the transformation described by PA is a type of coercion, as understood in the frameworks of Asher (2011) and Asher and Luo (2012), and explain the entailments of a formula of the form ♦R(α, β ) in more detail. 3. Coercion Coercion is an observed process whereby the meaning of a predicate P combines with the meaning of an expression e in its scope to produce a meaning shift. To illustrate, the predicate is a very fancy and tasty Bordeaux in (12) combines with the noun phrase this bottle, yet the final interpretation does not involve a predication of the bottle, but of the contents of the bottle. (12) This bottle is a very fancy and tasty Bordeaux. The combination of is a very fancy and tasty Bordeaux with the bottle coerces a shift in meaning. Coercion, many have argued, is the result of an adjustment to either the meaning of the predicate, the meaning of the argument, or to the composition that fits their meanings together, so that the argument of the predicate satisfies the predicate’s selectional restrictions, which in “ordinary circumstances” the argument does not. In (12) the predicate has to hold of wine or at least something that is edible or potable, and a mechanism of coercion like that proposed in Asher (2011) reinterprets the predication so that the predicted meaning is something like the content of this bottle is a very fancy and tasty Bordeaux. Our claim is that a relation of the form ♦R that relates the embedded content of a parenthetical report to the preceding discourse is the product of coercion, triggered by a conflict between the demands of the Attribution relation and the demands of R. To unpack this claim, we begin with a brief overview of some relevant aspects of Segmented Discourse Representation Theory (SDRT; Asher and Lascarides, 2003), the formal framework that we will use to develop our coercion account. The language of SDRT contains a countable set of discourse unit labels DU = {π, π1 , π2 , . . .}, and a finite set of discourse relation symbols R = {R, R1 , . . . Rn }, and formulas φ , φ1 , ... from some fixed language L for describing elementary discourse move contents, where L is a language like that of higher order logic used in, for instance, Montague Grammar. SDRT formulas are of the form hπ : φ i, where φ is either: (i) a formula of L; (ii) a relational formula of the form R(π1 , π2 ), which says that π1 stands in relation R, e.g., Explanation or Attribution, to π2 ; Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 592 J. Hunter & N. Asher Composing discourse parenthetical reports (iii) a formula of the form ♦ψ where ψ is an SDRT formula; or (iv) a conjunction of SDRT formulas. To provide an illustration, (2) yields three discourse units, π1 , π2 , and π3 : π1 : John didn’t come to my party. π2 : Jill said that π3 : he was out of town. Each of these units is then associated with a formula of L—φ1 , φ2 and φ3 , respectively—that specifies its content. For φ2 , for example, the formula is ∃p.said(Jill,p); for φ3 , the formula is, Out-of-town(Sel(John, Jill, party), where Sel, a part of the vocabulary of L, is a function picking out an appropriate individual type variable or discourse referent from the logical forms for the discourse so far (the formulas for π1 and π2 ). The combination of π1 − π3 in (2) will also yield two further formulas, Attribution(π2 , π3 ) and ♦ Explanation(π1 , π3 ). How do we derive these formulas? While the Attribution relation between π2 and π3 is syntactically determined and triggered by the embedding verb say, the derivation of ♦ Explanation(π1 , π3 ) involves a more complicated process. SDRT requires that any discourse unit π 0 must, if it is not discourse initial, be rhetorically connected to some other unit π, if it is to make a coherent contribution to the discourse in which it figures; every coherent discourse can be represented as a directed, acyclic and weakly connected graph. This means that at least one part of the report in (2b) must be related to the preceding discourse. In this case, the preceding discourse consists of a single unit, so the task is simplified: either π2 or π3 must be related to π1 .4 Often, the relation to the preceding discourse is not specified via a syntactic connection or an explicit discourse connective such as because. Where the selection of a relation or a discourse constituent is left unspecified, SDRT exploits the Sel function; selR (selΠ {πm , ...}, selΠ {πn , ...}), for instance, says that some relation from the set R of relations must be selected to apply to a selection of constituents from {πm , ...} and from {πn , ...}. In (2), the connection between (2b) and (2a) is not explicitly marked, so the axioms of SDRT only yield a very underspecified contribution: (13) selR (π1 , selΠ {π2 , π3 }). In words this means that some discourse relation selected from the set R of discourse relations must hold between the constituent π1 and one of the constituents introduced in (2b). Which discourse relation and which constituent are ultimately chosen to flesh out an underspecified formula depends on semantic and syntactic constraints and the surrounding discourse context. Combining the discourse units π1 − π3 from (2), their associated contents, (13), and Attribution(π2 ,π3 ), we arrive at the logical form in (14). (14) is given in the SDRT language using a richly typed, dynamic, compositional framework (Asher and Pogodalla, 2011). (14) ∃π1 , π2 , π3 (π1 : ¬come(john, my-party) ∧ π2 : say(jill, π3 ) ∧ π3 : out-of-town(john) ∧ λ xλ y selR (y, x)(π1 )(selΠ {π2 , π3 }) ∧ Attribution(π2 ,π3 )) 4 Were (2) embedded in a larger discourse, both π and π might be related to the preceding discourse. In fact, 2 3 adding discourse connections can increase the unity and coherence of a discourse. This is captured in the principle Maximise Discourse Coherence from Asher and Lascarides (2003). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 593 J. Hunter & N. Asher Composing discourse parenthetical reports Let’s now look at how we would resolve the underspecification in (14) in the context of a coercion story. The contents of π1 and π3 support Explanation(π1 , π3 ), and in fact, this is the most probable connection to π1 in this case. Normally we would infer this relation to resolve the choice of rhetorical relation in (13), but because of the Attribution relation between π2 and π3 , we run into a conflict. To make this conflict precise, we begin by assigning types to the variables π1 , π2 , ... that represent discourse units in SDRT. There are two types for discourse representation variables, UP (U), for uncommitted, and DOWN (D), for determinate. The general idea is that the content associated with a variable of type D will be entailed by the discourse; for a variable of type U, neither its associated content nor the negation of this content will be entailed. Veridical relations, including Explanation, Elaboration, Narration, Contrast, and so on, are of type D → D → D. Non-veridical relations, including Conditional and Disjunction, have the type U → U → D. Attribution is a right-nonveridical relation, meaning that it is non-veridical in its right argument; that is, it has the type D → U → D. The proposed typing for Attribution is designed to reflect the fact that the act of attributing content to an agent should not in itself require speaker commitment to the attributed content. As it stands, however, it does not capture the fact that the content inside of an Attribution’s scope might itself contain relations that are veridical. For instance, consider: (15) [Jill said that]π1 [John went running at 6]π2 [and he went to dinner with Julie at 7.]π3 where π1 , π2 , and π3 label the elementary discourse units.5 The SDRS K for (15) contains a complex discourse unit, π0 , that itself contains a discourse relation. (16) gives its logical form. (16) ∃π0 , π1 , π2 , π3 (Attribution(π1 , π0 ) ∧ π0 : Narration(π2 , π3 )) The formula Attribution(π1 , π0 ) requires π0 to be of type U, but this conflicts with the type D assigned to the veridical relation Narration(π2 , π3 ). A similar problem arises with conditionals: (17) [If John doesn’t have to work this evening]π1 [then he will go running]π2 [or he’ll go play squash.]π3 We get the following logical form: (18) ∃π0 , π1 , π2 , π3 (Conditional(π1 , π0 ) ∧ π0 : Disjunction(π2 , π3 )) The relation Conditional requires π0 to be of type U; Disjunction requires it to be of type D. In the case of both Conditional and Attribution, we need to capture the fact that veridical relations in their scope are only veridical relative to a context introduced by the antecedent of the conditional or the attribution predicate, respectively. To do this, we relativize types to con5 We use square brackets to mark the boundaries of discourse units. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 594 J. Hunter & N. Asher Composing discourse parenthetical reports texts.6 A context will be represented as a segmented discourse representation structure (SDRS) or formula under the scope of an operator; the outermost SDRS K0 is a context, as is any SDRS Ki that is a constituent of K0 and is within the scope of an operator. Note that a formula under the scope of a modal operator also serves as a typing context. If a discourse unit is typed D in a context K, which we will write as π K : D, then its normal entailments are entailed in K; more precisely, if π K : D, the content associated with π must be satisfied at worlds or points of evaluation in which any relations in K involving π are satisfied. If a discourse unit π is such that π K : U, then the content of π is not entailed in K even if it figures in a relation R that is entailed in K. By relativizing types to contexts, we capture the idea that while a speaker may not be committed to the content of a report, when she attributes content to another agent, she commits to the other agent being committed to the report’s content. Note that in an SDRS, an instance of a discourse relation R occurs in one and only one context. The relation between the entailments of a context K and the entailments of a context K0 embedded in K obeys the following retyping rule: where K is a context, π K : u, and where K0 is a 0 constituent of K under the scope of a modal operator or intensional relation, then π K : d is an allowable typing. We also allow type raising from D to U when we shift from a context K0 to a context K in which K0 is embedded: if λ πψ requires a discourse unit of type U as argument in K, but is given an argument π1 of type D from K0 , then a general coercion permits us to rewrite the type of π1 to U; i.e. π1K : U. Finally, for any constituent π in K introduced by an indicative clause not in the scope of an intensional operator or intensional relation in K, π K : D. We say that an SDRS K has a consistent type assignment just in case: K respects the retyping rule; the discourse relations in K have arguments of the type required by the semantics of the relations; and for every context K0 , and for every discourse unit π in K0 , π has a unique type assignment relative to K0 . The SDRS K for (16), for instance, has a consistent type assignment in which π1 : D and, after type raising, π0 : U in K. But π0 is an SDRS in the scope of an intensional relation; it therefore constitutes a typing context of its own and specifies its own assignments to discourse units figuring in discourse relations in π0 . In this context, π0 is of type D—i.e., π0π0 : D; and we also have π1π0 : D and π2π0 : D, which yields a consistent typing of K. We note that examples like (19) do not require any kind of retyping or context shifting. While (19b) and the embedded clause of (19a) have the same propositional content, they contribute different discourse units and can therefore receive different type assignments. (19) a. b. Jill said John was out of town. And (indeed) he was out of town. The types we have assigned to discourse units are distinct from the types assigned to contents, just as the contents associated with discourse units are distinct from the units themselves. The fact that (19b) serves as a correction or amplification of (19a) is because the same content is now linked to a label that commits the speaker to John’s being out of town. 6 For more on typing within contexts, see the notion of coercive sub-typing, e.g. Luo (1999). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 595 J. Hunter & N. Asher Composing discourse parenthetical reports The conflict that induces the coercion observed with the parenthetical report in (2b) is triggered by the fact that the Attribution relation and the Explanation relation in (2) share the same second argument, namely π3 , but Explanation types this argument as D, while Attribution types it as U . More generally, discourse parenthetical reports will always trigger this kind of conflict; as explained in Hunter (2016), we do not find the embedded clauses of discourse parenthetical reports in non-veridical relations such as Disjunction or Conditional. The only available reading of (20), for example, is one in which Linda said takes scope over the entire conditional. (20) If John finishes his housework, then Linda said he’ll come to the party. In this case, the report is not parenthetical. To resolve the conflicting type requirements imposed by a formula of the form Attribution(π, π 0 ) on the one hand and a veridical relation that takes π 0 as an argument on the other, something has to give: either the type assignment for a constituent, the type of the predicates over the constituents (i.e. the discourse relations), or the way these predicates combine with their arguments has to change. Our retyping rule will not solve the conflict: suppose we replace λ xλ yselR (y, x)(π1 )(selΠ {π2 , π3 }) in (14) with Explanation(π1 , π3 ), which requires π3 to have the type D. Raising π3 from D to U will leave Explanation with an argument of type U, which conflicts with its veridical semantics. The retyping rule would only work if the entire Explanation were under the scope of the Attribution. Retyping π3 from U to D in Attribution(π2 , π3 ) will not work either. An important principle of the account of coercion in Asher (2011) is that lexical items or grammatically determined types do not change their type due to coercion, and Asher (2011) adduces considerable evidence for this principle. We believe that this principle is also plausible at the discourse level. Given this assumption and the fact that the Attribution relation is grammatically determined, we cannot change the type requirements of Attribution. It follows that π3 will retain its typing of U in the context of the Attribution, and there is therefore no consistent type assignment for an SDRS that includes those two relations on π3 . Shifting the type of π1 or π2 would also be ineffective, because doing so would only introduce a conflict between these discourse referents and the requirements of Explanation and Attribution, respectively. Shifting the inferred link between π2 and π3 is not allowed because the link is grammatically determined. The only possibility, then, is to shift the inferred link between π3 and π1 . To spell this out formally, we need two things. We need to specify how the predication within a given context changes using a functor that takes a relation R and its two arguments α and β and returns a modified predication of R applied to α and β ; this is easy to do with our types and the availability of a modal operator. The other task is to specify what predicate licenses the introduction of the functor. We begin with the second task. In standard coercion cases, the licensing predicate is typically R itself. For discourse coercions, however, it is the discourse environment that typically licenses the coercion. In particular, it is the presence of the Attribution that licenses the coercion of the environment involving the Explanation relation. Given the contents of π1 , π2 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 596 J. Hunter & N. Asher Composing discourse parenthetical reports and π3 , the discourse model selects the most plausible specification for selR and selΠ in (14): Explanation(π1 ,π3 ). From the discourse model, we then rewrite the logical form in (14) as: (21) ∃π1 , π2 (π : ¬come(john, my-party) ∧ π2 : ∃π3 say(jill, π3 ) ∧ π3 : out-of-town(john) ∧ λ xλ y Explanation(y, x)(π1 )(π3 ) ∧ Attribution(π2 ,π3 )) But now we have a type conflict on π3 , and λ reduction cannot proceed further: the type that Explanation requires of π3 (D) conflicts with the type assigned to it by Attribution (U) in K(21) . This type clash leads to the introduction of a coercion functor that can be specified as follows. • Coercion to ♦R: f: λ β : U. λ α: D. λ R: D → D → D. ♦R(α, β ). The presence of the Attribution entailing the typing π3 : U together with the simple assertion of (2a) entailing π1 : D and the discourse model’s prediction of a veridical relation’s holding of π1 and π3 license a rewriting of (22) λ xλ y Explanation(y, x)(π1 )(π3 ) as (23) f(λ xλ y Explanation(y, x))(π1 )(π3 ) λ -reduction can proceed now that the types all match, yielding: (24) ♦ Explanation(π1 , π3 ) So our final logical form for (2) looks like this: (25) ∃π1 , π2 (π1 : ¬come(john, my-party) ∧ π2 : ∃π3 say(jill, π3 ) ∧ π3 : out-of-town(john) ∧ ♦ Explanation(π1 , π3 ) ∧ Attribution(π2 ,π3 )) Note that f is a conservative functor that maintains consistency with the original requirement of a veridical relation R such that R |= ♦R. Note also, however, that ♦ itself specifies a typing context, so that within the context of ♦ it is consistent to have π1 : D and π3 : D, as would be needed if a veridical relation had fallen in the scope of Jill said in (2b) (cf. (15)). The functor f does not change the type of either α or β ; it rather shifts the relation inferred between them to a relation that is compatible with arguments of either type D or type U. Because the type of the arguments stays constant, the entailment in (11), repeated here as (26), does not reflect the actual entailments of an example like (2). (26) ♦R(α, β ) |= ♦(α ∧ β ) In (2), the content of (2a) is asserted independently of the subsequent discourse, and is therefore Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 597 J. Hunter & N. Asher Composing discourse parenthetical reports of type D; the functor simply renders the relation compatible with the typing of π3 , which is U. We can therefore make the stronger claim for an example like (2): (27) ♦R(α, β ) |= α ∧ ♦β This conforms to the intuition that (2a) is entailed in (2). This entailment requires some unpacking. The formula (25) entails, as described in (27), that the content of π1 is satisfied at the actual world and the content of π3 is satisfied at a world consistent with the speaker’s commitments. Yet to the extent that a causal relation might hold between the eventualities eα and eβ described by α and β , respectively, the Explanation relation as well as eα and eβ must all hold in the same world. This is ensured by a fact about epistemic possibilities: given that π1 is asserted, the speaker is committed to it, and so the content of π1 holds at all worlds consistent with her commitments. What ♦Explanation(π1 , π3 ) adds is the claim that in some of those commitment worlds, π3 is also verified, and furthermore, in at least some of those worlds, π3 describes an eventuality that caused that described by π1 . In other words, under the scope of ♦, π1 and π3 are of both type D, so the constraints on Explanation are satisfied. Interestingly, there is an asymmetry in coercion facts. While (2) seems to have a discourse parenthetical reading of the sort we have derived in (25), an example that inverts the form of (2) does not. (28) a. b. Jill said John is sick. He ate a bad clam. The claim in (28b) is naturally interpreted either as extending the report context introduced by (28a)—thus committing Jill to the content of (28b)—or as providing an explanation not only of why John is sick but also, in effect, of why Jill said what she did. As defined, the functor f only works if the second argument of the coerced relation is U. In (28) it is the first argument of the implicit causal relation that is typed U, so our functor f will not apply to this case. Our account thus predicts that we can never have an instance of a veridical relation whose left argument is the embedded clause of a report and whose right argument is outside of the scope of the report (i.e. we can never coerce the argument of an Attribution to D ). This is surprising and may even seem suspicious. Yet some data, including (28), suggest that we should not countenance a functor g : λ β : D. λ α: U. λ R: D → D → D. ♦R(α, β ). One reason for not stipulating the functor g is that alternative means of producing a modalized relation exist: (29) a. b. Jill said John is sick. Maybe it’s because he ate a bad clam. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 598 J. Hunter & N. Asher Composing discourse parenthetical reports Simple assertions allow for modalisation in a way that reports do not. There is no way to lexically induce the possible explanation reading for (2)—a speaker must either choose a report construction, which carries the extra information of a source, or a simple modal. Combining the two leads to non-parenthetical readings of the reports. So the presence of such alternatives for the inverted ordering might explain the asymmetry between our intuitions about (2) and (28). On the other hand, there are examples, like (30), in which something like coercion of the first argument seems to work. (30) [The school said]π [Isabel is sick.]π1 Maybe [she caught Rose’s flu.]π2 This example implies ♦Explanation(π1 , π2 ). However, note that (30) differs from (2) in that π2 falls within the scope of a modal. We think that (30) manifests a kind of modal subordination involving the intensional context provided by Attribution(π, π1 ) and the modal operator contributed by Maybe. Modal subordination could allow for an attachment between the two discourse units of type U, yielding a formula of the form: (31) ∃π, π1 , π2 (Attribution(π, π1 ) ∧ π : school said ∧ π1 : sick(isabel) ∧♦(Explanation(π1 , π2 ) ∧ π2 : caught(isabel,flu))) Given that ♦ is a normal modality, (31) implies ♦Explanation(π1 , π2 ). (32) provides another case in which a ♦R is arguably inferred from a first argument of type and a second argument of type D: (32) U [Where was John on Tuesday evening?]π [Jill said that]π1 [she and John went running at 6.]π2 [Then/After that, he and I had dinner at 7.]π3 (32) intuitively implies ♦Narration(π2 , π3 ). In this case, however, it is the surrounding discourse structure that indirectly sets up the coercion on Narration. The answer to the question in π includes π2 and π3 . But let’s concentrate first just on relating π, π1 and π2 . The connections between these units will parallel those between the units in (2), yielding ♦QAP(π, π2 ), where QAP stands for Question-Answer-Pair. Now π3 simply extends the answer that is being proposed by π2 to a more complicated answer: perhaps the proposed sequence of events answers the question posed in π. Semantically, this means that in some world w from the set of worlds compatible with the speaker’s commitments, π2 and π3 hold in w and the eventuality described by π3 took place after the eventuality described by π2 in w. In other words, there is an attachment of π3 to π2 forming a Narration under the scope of the modal introduced by the QAP, in a manner similar to the logical form for (16). This gives the following, abbreviated logical form: (33) ∃π, π1 , π2 , π3 , π4 .(Attribution(π1 , π2 ) ∧ ♦QAP(π, π4 ) ∧ π : Where was John? ∧ π1 : Jill said ∧ π2 : running ∧ π3 : dinner ∧ π4 : Narration(π2 , π3 )). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 599 J. Hunter & N. Asher Composing discourse parenthetical reports We note several consequences of (33). First, the Narration relation and its temporal consequences hold only between the events described in π2 and π3 , not the time of Jill’s saying, as intuitions dictate. Second, because of (27), ♦QAP(π, π4 ) entails ♦Narration(π2 , π3 ), as desired, even though this formula is not in the logical form. Third, this is the only possible SDRS given our constraints on consistent typing. We could not put Narration(π2 , π3 ) outside the scope of (33) the ♦QAP relation in (33), because π2 : U and this would conflict with typing demands of Narration as a veridical relation. Example (32) does not provide a genuine motivation for adopting the functor g described above. ♦Narration is indeed entailed, but not because of a direct conflict between Narration and Attribution; it’s epistemic status follows from the fact that π3 develops a context that is already modal. At the same time, given that the speaker asserts π3 , its contents will hold at all worlds consistent with her commitments, including the actual world whether or not it is also a π2 (33) world. Thus we arrive at the following consistent top-level typing for (33): π (33) : D, π1 : D, (33) (33) π2 : U, and π3 : D. Indeed, our typing rules mandate these. Our typing rules also permit π4 π4 π2 : D, π2 : D, and π4π4 : D as part of a consistent typing. Our account right now relies on the potentially controversial assumption that Attribution always types its second argument as U. We now turn to a discussion of this assumption in the context of factive embedding verbs. 4. Factives On our proposal, the type assigned to a rhetorical relation R is entailed by R’s semantics; it is a property of the relation itself. As a result, the type is unaffected by semantic differences between connectives that license R. This means that Attribution, for example, will have the type D → U → D even when triggered by a factive verb, as in (34). (34) a. b. John didn’t come to my party. Jill found out that he’s been working nights at the station. This might at first seem counterintuitive. After all, a factive verb entails the truth of its complement, so shouldn’t its complement have the type D? First of all, it is important to distinguish between the discourse contribution of a report and its interpretation. The discourse contribution determines what relation is added to the logical form for a discourse, but while these relations play a significant role in discourse interpretation, they do not tell the whole story. The content of discourse units certainly effects interpretation, and in the case of reports, world knowledge or opinions about the reliability of sources cited in reports (de Marneffe et al., 2012) can influence what information interpreters ultimately take away. There is therefore no problem with saying that discourse structure contributes certain entailments and that the content of discourse units, including the semantics of the various embedding verbs used in reports, can strengthen these entailments. A typing of U for a clause embedded under a factive verb is consistent with the demands of the verb, but the final discourse level entailments triggered by reports with factive verbs can ultimately be stronger. What we have Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 600 J. Hunter & N. Asher Composing discourse parenthetical reports modeled is the general function of discourse parenthetical reports, and we are take as basic that the attribution predicate of such a report acts as a buffer between the embedded content and the preceding discourse. What’s more, in many cases, the claim that discourse parenthetical reports involving factive embedding verbs trigger relations of the form ♦R is more than consistent with the demands of factive verbs—it is also borne out by the data. Even Attributions triggered by factive verbs allow a speaker to hedge her commitment to the discourse function of the embedded clause. If a speaker A asks, (a) “Why didn’t John come to the party?”, a speaker B can reply, (b) “Jill found out that he has taken on a night job” and thereby hedge her commitment to the Question/Answer relation suggested by the contents of (a) and (b), even while committing to the truth of the embedded clause in (b) in virtue of the factivity of find out. Factivity licenses an inference from the discourse logical form but does not contribute type information to its construction, and thus doesn’t affect the typing relevant to the interaction between attributions and the surrounding discourse context. This formalizes the observation in Simons (2007) that parentheticality and factivity are orthogonal notions. Of course, intonation plays a role in the way that discourse parenthetical reports are ultimately interpreted. A more certain and declarative intonation for (b) above might encourage the interpretation of an Explanation rather than the weaker ♦Explanation relation. Intonation certainly plays an important, if poorly understood, role in discourse interpretation. Nevertheless, even a declarative intonation does not force the stronger interpretation. Speaker B could continue (b) with (c): “That might be why he didn’t come,” thereby making the ♦Explanation explicit. Our point is that the use of a factive verb in a discourse parenthetical report does not in and of itself require a non-modal relation; the systematic discourse contribution of all reports is the weaker ♦R. Strengthening of this relation at the level of discourse interpretation must be explained by independent factors. 5. Connectives As we’ve seen, while the content of (2a) and the embedded content of (2b) together lead the discourse model to predict an Explanation relation, other information from (2) triggers a coercion. This coercion is blocked once we make the causal connection explicit as noted by Hunter and Danlos (2014). The report in (35b) can only receive a non-parenthetical reading. (35) a. b. John didn’t come to my party because Jill said he was out of town. A consequence of our coercion story is that the typing demands of a connective with a grammatically determined scope must be satisfied. We predict this because the semantics of the connector because entails a non-modal commitment to Explanation over its complement clause, and our coercion account cannot change such grammatically given entailments. The contrast between (36) and (37) also illustrates this point, though the data are more subtle. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 601 J. Hunter & N. Asher (36) a. b. Liz’s album got a bad review. John said she’s really upset. (37) a. b. Liz’s album got a bad review, so John said she’s really upset. Composing discourse parenthetical reports In (36b), John’s saying what he did might be completely independent of the review mentioned in (36a); (36b) arguably has a parenthetical reading and licenses ♦Result. In (37b), to the extent that (37) is acceptable, we infer that John himself suspects that the review caused Liz’s distress. The fact that John said what he did is thus a reaction to the review, so the matrix clause of (37b) describes a result of (37a). The matrix clause is of type D, so it satisfies the type demands of Result. At the same time, connecting (37b) to (37a) with Result is only really coherent if the embedded clause of (37b) is also related to (37a) with ♦Result. But our coercion story still appplies to any connection between the embedded clause of the report with (37a). So in fact we predict a graph with both Result and ♦Result for (37). Our prediction does not apply to all explicit connectives. Compare (38) with (35) or (39): (38) [A man died]π1 [after police say/said]π2 [he was hit by a fire truck.]π3 (39) A man died because police said he was hit by a fire truck While no inferred ♦Explanation to the embedded discourse unit is possible in (35) or (39), an inference to ♦Explanation is involved in the interpretation of (38) (Hunter and Danlos, 2014). This has to do with the semantics and discourse function of after, whose semantic scope is not determined by its syntactic position—in (38) the second argument of after is π3 . While it marks a temporal relation or possible temporal relation in this case, a causal relation between π1 and π3 is also inferred, and there our coercion account applies. Finally, we note a possible difference between syntactically embedded markers like because, connectives like after and markers that are marked with a comma, such as after that and afterwards (cf. Danlos, 2013). Consider the following data from (Hunter & Danlos 2014): (40) John is very generous. For example, Jill said that he gave $50 to a homeless man yesterday. (41) John didn’t come to the party. Instead, Jill said that he went to dinner with his brother. Parenthetical readings for (40) and (41) are possible with explicit connectives, but once we embed the connective inside the report, we lose the parenthetical reading of (41): (42) John didn’t come to the party. Jill said instead that he went to dinner with his brother. All of this suggests that while the typing demands imposed by discourse connectives must in Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 602 J. Hunter & N. Asher Composing discourse parenthetical reports general be respected, further work is needed to understand differences between the various types of discourse connectives. 6. Conclusion Our main goal in this paper has been to develop a compositional account of the discourse function of parenthetical reports. Hunter (2016) argued that the role of discourse parenthetical reports is to contribute a modal discourse relation to a discourse structure. The derivation of such relations was, however, left unexplained and the ♦ relations that Hunter posited seemed more like primitive discourse relations. Such an approach does not take into account the fact that discourse parenthetical reports in fact arise from the interaction of an Attribution environment and the surrounding discourse context; the embedded content of a discourse parenthetical report and the discourse unit to which it attaches in the preceding discourse do not on their own support a relation of the form ♦R. In the account developed here, ♦R is derived from R via coercion and a context sensitive notion of typing (Asher and Luo, 2012). The Attribution relation plays a key role in this story by introducing a typing on its second argument that is incompatible with the requirements of the relation R. We have also extended our basic account to discourse parenthetical readings of factive verbs. In our account, all reports with non-parenthetical syntax are modelled with the discourse relation Attribution, and Attribution always has the type D → U → D, regardless of the embedding verb involved. We argued not only that this is consistent with the demands of factives and a reasonable understanding of how discourse structure contributes to discourse interpretation, but also that discourse parenthetical readings of even factive verbs can entail merely modal relations. As pointed out in Simons (2007), factivity and parentheticality are orthogonal notions. Finally, we have shown how our account predicts that the attribution clause of a report in the scope of an explicit discourse connective must be relevant to that connective. Pure discourse parenthetical readings in which the attribution predicate is not related to the preceding discourse, or at least not related to the unit to which the embedded clause is related, are predicted to be blocked by explicit connectives because our coercion operation cannot shift grammatically determined types. We did note, however, that some connectives seem to allow parenthetical readings. A detailed case study of different connectives is needed to complete our account, but we think this account is promising enough to warrant such a study in the future. References Asher, N. (1993). Reference to Abstract Objects in Discourse. Dordrecht: Kluwer. Asher, N. (2011). Lexical Meaning in Context: A Web of Words. Cambridge University Press. Asher, N. and A. Lascarides (2003). Logics of Conversation. Cambridge University Press. Asher, N. and Z. Luo (2012). Formalisation of coercions in lexical semantics. In Proceedings of Sinn und Bedeutung, Volume 17, pp. 63–80. Asher, N. and S. Pogodalla (2011). SDRT and continuation semantics. In T. Onada, D. Bekki, and E. McCready (Eds.), New Frontiers in Artificial Intelligence: JSAI-isAI 2010 Workshops, LENLS, JURISIN, AMBN, ISS, Tokyo, Japan, November 18-19, 2010, Revised Selected PaProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 603 J. Hunter & N. Asher Composing discourse parenthetical reports pers, pp. 3–15. Berlin, Heidelberg: Springer. Danlos, L. (2013). Connecteurs de discours adverbiaux: Problèmes à l’interface syntaxesémantique. Linguisticae Investigationes 36(2), 261–275. Danlos, L. and O. Rambow (2011). Discourse relations and propositional attitudes. In Proceedings of the Constraints in Discourse Workshop (CID 2011), Agay, France. de Marneffe, M.-C., C. D. Manning, and C. Potts (2012). Did it happen? The pragmatic complexity of veridicality assessment. Computational Linguistics 38(2), 301–333. Dinesh, N., A. Lee, E. Miltsakaki, R. Prasad, and A. Joshi (2005). Attribution and the (non-)alignment of syntactic and discourse arguments of connectives. In Proceedings of ACL Workshop on Frontiers in Corpus Annotation, Ann Arbor, MI, USA. Hardt, D. (2013). A uniform syntax and discourse structure: The Copenhagen dependency treebanks. Discourse and Dialogue 4(2), 53–64. Hobbs, J. (1985). On the coherence and structure of discourse. Technical report, Center for the Study of Language and Information, Stanford University. Report CSLI-85-37. Hooper, J. B. (1975). On assertive predicates. In J. Kimball (Ed.), Syntax and Semantics, Volume 4, pp. 91–124. New York: Academic Press. Hunter, J. (2016). Reports in discourse. Dialogue & Discourse 7(4), 1–35. Hunter, J. and M. Abrusán (2016). Rhetorical relations and QUDs. In New Frontiers in Artificial Intelligence: JSAI-isAI Workshops LENLS, JURISIN, KCSD, LLLL Revised Selected Papers. Berlin: Springer. Forthcoming. Hunter, J., N. Asher, B. Reese, and P. Denis (2006). Evidentiality and intensionality: Two uses of reportative constructions in discourse. In Proceedings of the Constraints in Discourse Workshop (CID 2006), Maynooth, Ireland. Hunter, J. and L. Danlos (2014, April). Because we say so. In Proceedings of the EACL 2014 Workshop on Computational Approaches to Causality in Language (CAtoCL), Gothenburg, Sweden, pp. 1–9. Association for Computational Linguistics. Luo, Z. (1999). Coercive subtyping. Journal of Logic and Computation 9(1), 105–130. Mann, W. and S. Thompson (1988). Rhetorical structure theory: Towards a functional theory of text organization. Text 8, 243–281. Ross, J. (1973). Slifting. In M. Gross, M. Halle, and M. Schutzenberger (Eds.), The Formal Analysis of Natural Languages, The Hague, pp. 133–169. Mouton. Simons, M. (2007). Observations on embedding verbs, evidentiality, and presupposition. Lingua 117(6), 1034–1056. Urmson, J. O. (1952). Parenthetical verbs. Mind 61(244), 480–496. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 604 Constraints on the embeddability of epistemic modals1 Michela IPPOLITO — University of Toronto Abstract. In this paper I investigate occurrences of epistemic modals such as must and might embedded under three classes of attitude verbs: (i) doxastic and doxastic-like verbs like believe, (ii) desiderative verbs like want, and (iii) emotive doxastic and dubitative verbs like fear, hope and doubt. The first class allows both necessity and possibility epistemic modals; the second class allows neither necessity nor possibility epistemic modals; and finally, the third class allows possibility but not necessity epistemic modals. We begin our inquiry by reviewing Anand and Hacquard (2013)’s proposal. I present some challenges for the proposal and, in particular, for their proposal for class (iii). I show that the restrictions on embedded epistemic modals are similar to the restrictions on embedded V-to-C in German (Truckenbrodt (2006)) and argue that the two phenomena can be given similar explanations. Keywords: epistemic modals, attitude verbs, embedded V-to-C. 1. Introduction Epistemic modals can be sometimes embedded under propositional attitude verbs. This paper is a study of what constrains their distribution under attitude verbs, starting from the broad observation that there seem to exist three types of attitudes: those that license epistemic modals in their scope, those that do not allow epistemic modals in their scope, and those that allow possibility but disallow necessity modals. Building on Bolinger (1968)’s generalization, and bulding on a corpus study done by Hacquard and Wellwood (2012), Anand and Hacquard (2013) observe that epistemic modals are acceptable in the complement of doxastic verbs such as think, argumentative verbs such as say, and semi-factive verbs like realize. (1) a. b. c. John thinks that Mary must/might be innocent. John said that Mary must/might be innocent. John realized that Mary must/might be innocent. The second type includes verbs that do not allow epistemic modals in their complement. These include desiderative verbs such as want and directives like demand. (2) a. #John wants Mary to have to be the murderer. b. #John demanded that Mary must/might have been the murderer. The third kind includes emotive doxastic attitudes such as fear and dubitative verbs such as doubt: these verbs only allow possibility epistemic modals in their complement. 1I would like to thank the audiences at Sinn und Bedeutung 21, the Linguistics and Philosophy Workshop at the University of Chicago, the SemPrag reading group at the University of Toronto, as well as the linguists and philosophers at the University of Milano-Bicocca. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 605 M. Ippolito Constraints on the embeddability of epistemic modals (3) a. John fears that Mary may/might have known the killer. b. #John fears that Mary must have known the killer. (4) a. John doubts that Mary may/might have known the killer. b. #John doubts that Mary must have known the killer. 2. Anand and Hacquard (2013) To account for the contrast between the attitude verbs that allow embedded epistemic modals and those that do not, Anand and Hacquard propose that (i) only “representational” attitudes can provide an information state and (ii) embedded epistemic modals quantify over an information state determined by the embedding attitude. Let’s begin with point (i). The non-representational nature of a desiderative verb like want derives – they claim – from the fact that want, unlike believe, has a comparative semantics. Following Stalnaker (1984), Asher (1987), Heim (1992), and more explicitly Villalta’s work on desiderative predicates (Villalta (2008)), they provide the semantics in (5). (5) [[want]]c,w,g = λ p.λ x.∀q ∈ g(C)\p : p >DESx,w q where DESx,w is defined as follows: -for any w, w0 , w00 : w0 >DESx,w w00 iff w0 is more desirable to x in w than w00 . -for any p, q ⊆ W : p >DESx,w q iff ∀w00 ∈ q : [∃w0 ∈ p : [w0 >DESx,w w00 ]] and ∃w0 ∈ p : [∀w00 ∈ q : [w00 6>DESx,w w00 ]] Since want – they claim – is non-representational, it fails to provide an information state that will function as the “antecedent” for the embedded modal. As shown in (6), on the other hand, the attitude believe does provide an information state, i.e. the subject’s doxastically accessible worlds, which will then be the set of worlds quantified over by the embedded epistemic modal. (6) [[believe]]w = λ p.λ x.∀w0 ∈ Accdox (w, x) : p(w0 ) = 1 Part (ii) of Anand and Hacquard’s story, i.e. that embedded epistemic modals quantify over an information state determined by the embedding attitude, builds on Yalcin (2010), whose goal was to account for the contrast between (7a) and (7b). (7) a. b. Imagine that [it’s raining but you don’t believe it is]. #Imagine that [it’s raining but it might not be]. Yalcin’s proposal is that the unacceptability of (7b) is due to the fact that the embedded epistemic modal “inherits” its modal base from the quantificational domain of the embedding attitude, generating a contradiction: (7b) asserts that all worlds compatible with the addressee’s imagination are worlds where it is raining and there is a world compatible with the addressee’s imagination where it is not raining. Extending this idea, Anand and Hacquard propose the general rule in (8). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 606 M. Ippolito (8) Constraints on the embeddability of epistemic modals For any attitude att, 0 0 [[att φ ]]c,w,S,g = λ x.∀w0 ∈ S0 [[φ ]]c,w ,S ,g = 1, where S0 is the quantificational domain provided by att. In the majority of cases this creates structures with redundant meanings, equivalent to a modal sentence with the force of the embedded epistemic modal and the flavor of the embedding attitude. (9) a. b. (10) a. b. John believes that Mary must be the killer ≡ for all worlds w compatible with John’s doxastic state in the evaluation world, Mary is the killer in w. ∀w ∈ DOXJ [∀w00 ∈ DOXJ : Mary is the killer in w00 ] ≡ ∀w00 ∈ DOXJ : Mary is the killer in w00 John believes that Mary might be the killer ≡ there is at least a world w compatible with John’s doxastic state in the evaluation world such that Mary is the killer in w0 . ∀w ∈ DOXJ [∃w00 ∈ DOXJ : Mary is the killer in w00 ] ≡ ∃w00 ∈ DOXJ : Mary is the killer in w00 The third type of attitude verbs we will discuss are emotive doxastic verbs like fear and hope and dubitative doubt. Let’s begin with the former. Anand and Hacquard propose the semantics in (11): a hopes that φ presupposes that a’s doxastic state is compatible with both φ and ¬φ and it asserts that φ is compatible with a’s doxastic state and that φ is preferable to ¬φ . (11) [[a hope that φ ]]c,w,S,g a. defined iff φ −verifiers in S0 6= 0/ ∧ φ −falsifiers in S0 6= 0; / (uncertainty condition) if defined, =1 iff 0 b. ∃w0 ∈ S0 : [[φ ]]c,w,S ,g = 1∧ (doxastic assertion) c. ∧φ −verifiers >DESa,w φ −falsifiers (preference assertion) When the complement is modalized, then we have (12). (12) [[a hope that Mod p]]c,w,S,g a. defined iff Mod p−verifiers in S0 6= 0/ ∧ Mod p−falsifiers in S0 6= 0; / (uncertainty condition) if defined, =1 iff 0 b. ∃w0 ∈ S0 : [[Mod p]]c,w,S ,g = 1∧ (doxastic assertion) c. ∧Mod p−verifiers >DESa,w Mod p−falsifiers (preference assertion) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 607 M. Ippolito Constraints on the embeddability of epistemic modals Since Modp verifiers are the same as p verfiers (see Anand and Hacquard (2013) for a discussion of this point), a sentence such as John hopes that it might be raining carries an uncertainty presupposition (that there is a non-trivial subset of John’s belief worlds where it is raining and a non-trivial subset where it is not raining); it makes a doxastic assertion (that there is at least some world compatible with John’s beliefs where it is raining); and, finally, it also makes a preference assertion (that rain is more desirable to John than no rain). Crucially, the incompatibility between hope and must is explained away as a contradiction: #John hopes that it must be raining is ruled out as a contradiction between the doxastic assertion (that in all of John’s doxastic worlds it is raining) and the uncertainty presupposition requiring John’s doxastic state to be compatible with no rain. Dubitative doubt receives a very similar semantics. (13) [[a doubts that φ ]]c,w,S,g a. defined iff φ −verifiers in S0 6= 0/ ∧ φ −falsifiers in S0 6= 0; / (uncertainty condition) if defined, =1 iff 0 b. ∃w0 ∈ S0 : [[φ ]]c,w,S ,g = 1∧ (doxastic assertion) c. ∧φ −falsifiers >PROBa,w φ −verifiers (preference assertion) Just like in the case of hope and fear, embedding necessity modals under doubt, as in #John doubts that it must be raining, generates a contradiction between the uncertainty presupposition (requiring that John’s doxastic state be compatible with rain and no rain) and the doxastic assertion (that John’s doxastic state entails that it must be raining). In the next section, I will discuss some challanges for Anand & Hacquard’s proposal. 3. Challenges There are two challenges that one might raise to challenge the type of proposal defended by Anand and Hacquard. The first problem concerns the analysis of attitude verbs that show a mixed behavior with respect to the embeddability of epistemic modals, i.e. emotive doxastic and dubitative attitudes. In particular, this problem challanges the uncertainty presupposition that is essential in Anand and Hacquard’s story to derive the unacceptability of embedded necessity modals. The second problem is a more general worry about Yalcin’s “copying” analysis of the embedded epistemic modals when applied to the cases introduced above. Let us begin with the uncertainty presupposition problem. 3.1. The uncertainty presupposition problem There is an immediate prediction that the uncertainty presupposition story makes, i.e. that a negated sentence with doubt should also carry the uncertainty presupposition. However, this prediction is not fulfilled, as (14) clearly shows. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 608 M. Ippolito (14) Constraints on the embeddability of epistemic modals John doesn’t doubt that Mary will win the race. He is certain that she will. Similarly for fear: a negated sentence with this attitude should still carry the presupposition that the subject’s doxastic state is compatible with both the prejacent and its negation. However, (15) shows that this is not the case. (15) The police no longer fear that John’s death was a homicide; they are certain that it was an accident. One could argue that with negation, the uncertainty presupposition is locally accomodated to avoid inconsistency, along the lines of (16). (16) NOT(John is uncertain about whether Mary will win the race) John doubts that Mary will win the race. The problem with this story is that we think of local accomodation as a “rescuing” mechanism, a mechanism that is called upon to avoid a contradiction. What is troubling about the (alleged) uncertainty presupposition is that it is always incompatible with the meaning of negated doubt, regardless of any explicit sentence contradicting it. Compare (14) to (17). (17) John doesn’t doubt that Mary will win the race. What (17) shows is that, if there is a contradiction, it is not caused by the continuation in (14) but by the meaning of negated doubt itself. Anand and Hacquard’s uncertainty presupposition is anomalous in that it is never consistent with a negative assertion, a logical environment that we standardly take to be transparent to presuppositions. Nor can such a presupposition be detected in the other two environments we typically resort to to identify presuppositions. (18) a. A: Does John doubt that Mary will win the race? B: Not at all, he’s certain that she will. (19) a. John might know that it is raining outside. But if he (still) doubts that it is, then he will open the window. The conclusion is that the crucial piece of Anand and Hacquard’s account of the distribution of necessity epistemic modals embedded under emotive doxastics and doubitatives is problematic and, as such, it undermines the whole proposal. 3.2. Epistemic flavor Suppose Mary’s colleagues have just returned from a walk outside and they tell her that there is a snowstorm outside. Since it’s July, Mary doesn’t believe them and insists that it can’t be true. They tell her to go to the nearest window and look outside. Mary does and sees the snowstorm. Her colleagues can report Mary’s belief with (20b) but not with (20a). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 609 M. Ippolito (20) Constraints on the embeddability of epistemic modals a. #Mary finally believes that there must be a snowstorm outside. b. Mary finally believes that there is a snowstorm outside. Anand and Hacquard’s story assumes a standard semantics for the epistemic modal, where the modal is treated as a quantifier over possible worlds restricted by an epistemic accessibility function (called “conversational background” in Kratzer’s system) as shown in (21). (21) [[must]]w, f = λ p<st> .∀w0 ∈ T T f (w) : [p(w0 ) = 1] The modal base of the modal is f (w), where f is the epistemic accessibility function. Combining this semantics with Yalcin’s proposal that, when embedded, the modal base of an epistemic modal is inherited from the modal base of the higher attitude, it follows that, when embedded under an attitude verb, an epistemic modal loses its modal base and, therefore, its epistemic flavor as well. However, the contrast between (20a) and (20b) shows that this is inaccurate: the epistemic flavor of the modal is retained. It looks like we have a choice to make: either we abandon Yalcin’s idea (as applied to the problem we are concerned about in this paper) or we abandon the standard semantics for the modal. In what follows I am going to explore the latter option. The tentative conclusion will be that this is not an unproblematic solution after all. An obvious alternative to the standard semantics for epistemic must is the proposal in von Fintel and Gillies (2010), according to which must has a strong semantics (quantifies over all worlds in which the speaker’s direct evidence is true) but carries an “unsettledness” presupposition, according to which the speaker’s direct evidence does not settle the truth of the prejacent. (22) Strong must + Evidentiality. Fix a c-relevant kernel K: a. [[must φ ]]c,w is defined only if K does not directly settle [[φ ]]c b. [[must φ ]]c,w = 1 if BK ⊆ [[φ ]]c T where BK = K and K whatever direct information is available to the speaker. However, we are faced again with the challenge of presuppositions disappearing all too easily, as shown in (23) and (24b). (23) A: Do the police believe that the murderer might be a woman? B: #Hey, wait a minute! The police don’t believe that their evidence doesn’t settle whether the murderer is a woman. B0 : No, they have ruled that out. (24) a. b. John doesn’t believe that the keys might be in the car. von Fintel & Gillies: >> John believes that KJ does not directly settle whether the keys are in the car. John doesn’t believe that the keys might be in the car since he saw them on the kitchen table just now. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 610 M. Ippolito Constraints on the embeddability of epistemic modals One might hold that (24b), just like the cases we discussed above, is acceptable because the unsettledness presupposition is locally accomodated in the scope of negation. However, consider the question below. (25) A: Does the detective believe that the murderer might be a woman? a. B: Not at all. He is certain that the murderer is a man. b. B: Yes. In fact, he is certain that the murderer is a woman. Both answers are fine. A defender of the unsettledness presupposition could explain the possibility of the negative answer in (25a) as the result of local accommodation. But explaining the positive answer in (25b) is harder. Locally accomodating the presupposition in the scope of the question operator would generate the question in (26). (26) Is it the case that (the detective believes that his evidence does not directly settle whether the murderer is a woman and it is consistent with his doxastic state that the murderer is woman) However, positively answering (26) entails “endorsing” the presupposition and as such it should be in contradiction with the continuation in (25b). The conclusion is that (i) if we adopt a Kratzerian semantics for epistemic modals combined with the Yalcin/Anand & Hacquard semantics in (8) we cannot explain the contrast in (20) and (ii) if we adopt the semantics in (8) combined with a presuppositional story like the one proposed by von Fintel & Gillies, we run into the projection problems just described. The source of these difficulties is, I claim, the semantics in (8). 4. Constraints on embedded V-to-C movement in German This section is about embedded V-to-C sentences in German, an apparently unrelated phenomenon that shows restrictions very similar to the restrictions on embedding epistemic modals. The V-to-C data discussed in this paper are from Truckenbrodt (2006). The V-to-C phenomenon has some of the properties of what Dayal and Grimshaw call “quasi-subordination” clauses which show properties of both main and subordinate clauses (Dayal and Grimshaw (2009)). V-to-C clauses have also been said to have assertive illocutionary force (e.g. Gärtner (2002)). In what follows, we will look at V-to-C sentences embedded under four kinds of attitudes and operators. Following the classification established in the V-to-C literature, these four groups are: (i) doxastic and speech act verbs, (ii) desiderative verbs, (iii) negation and inherently negative verbs such as doubt, and (iv) emotive doxastic verbs such as hope. By looking at these two phenomena in parallel, we will see that embedded German V-to-C clauses pattern like epistemic modals with respect to groups (i) and (ii) but show a split behavior with respect to groups (iii) and (iv): embedded V-to-C patterns like possibility epistemic modals with respect to emotive doxastics but like necessity epistemic modals with respect to negative or negated attitudes. The first observation is that V-to-C clauses in German can be embedded under doxastic verbs, speech act verbs, and so-called verbs of cognition. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 611 M. Ippolito (27) Constraints on the embeddability of epistemic modals a. b. c. Maria glaubt, Peter geht nach Hause. Maria believes, Peter goes to house Maria believes that Peter is going home. Maria behauptet, Peter geht nach Hause. Maria claims, Peter goes to house Maria claims that Peter is going home. Maria träumt, Peter geht nach Hause. Maria dreams, Peter goes to house Maria dreams that Peter is going home. V-to-C sentences cannot be embedded under desiderative verbs. (28) *Maria will, sie ist in diesem Fall in Berlin. Maria wants, she is in this case in Berlin Maria wants to be in Berlin in that case. V-to-C can occur embedded under an emotive doxastic predicate like hoffen, “to hope”. However, V-to-C cannot occur embedded under an inherently negative verb like zweifeln, “to doubt”, or under a negated attitude verb as in (30b). (29) Maria hofft, sie ist in diesem Fall in Berlin. Maria hopes, she is in that case in Berlin Maria hopes that she is in Berlin in that case. (30) a. *Hans bezweifelt, Peter geht nach Hause. Hans doubts, Peter goes to house Hans doubts that Peter is going home. b. *Hans glaubt nicht, Peter geht nach Hause. Hans believes not, Peter goes to house Hans doesn’t believe that Peter is going home. In the remaining part of this section, I will summarize Truckenbrodt (2006)’s proposal for embedded V-to-C in German. With the German facts and his apparatus in place, I will then return to the topic of embedded epistemic modals and lay down my proposal in the next section. Truckenbrodt proposes that embedding a V-to-C clause in German requires that the embedding predicate make salient a set of worlds Bw (x) that represents x’s doxastic (or doxastic-like) state in w, where x is the subject of the attitude. It also requires that the proposition p expressed by the embedded CP be entailed by Bw (x). Following Gärtner (2002), Truckenbrodt also proposes an “absorption” requirement. (31) Absorption: The meaning of attitude + CP must entail Bw (x) ⊆ p. To see how the proposal works, we will look at a case of grammatical embedding of a V-to-C sentence and a case of an ungrammatical embedding. The grammatical one is illustrated in (32). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 612 M. Ippolito (32) Constraints on the embeddability of epistemic modals Maria glaubt, Peter geht nach Hause. Maria believes, Peter goes to house Maria believes that Peter is going home. The two requirements introduced above are satisfied: (i) the predicate makes salient a set of doxastic-like words, i.e. DOXw (Maria) (see (33a)); (ii) DOXw (Maria) entails the proposition expressed by the embedded clause, i.e. that Peter is going home as shown in (33b). (33) a. b. Bw (x) = DOXw (Maria) DOXw (Maria) ⊆ (λ w0 . Peter is going home in w0 ) Since (32) asserts that Maria’s doxastic state entails that Peter is going home (DOXw (Maria) ⊆ (λ w0 . Peter is going home in w0 )), the assertion entails (33b) and Absorption is satisfied. A violation of Absorption is the cause of the unacceptability of V-to-C under an inherently negative verb like bezweifeln, “to doubt”. To doubt (and the same applies to bezweifeln) is a “weak” predicate: according to Truckenbrodt, saying that a doubts p only requires a’s doxastic state to be compatible with p, something that we can represent as: DOXw (Hans) ∩ (λ w0 . Peter is going home in w0 ) 6= 0. / Hence, the assertion is weaker that what V-to-C requires, i.e. that Hans’s doxastic state entails that Peter is going home. To sum up, embedded V-to-C requires that the proposition expressed by the complement clause be entailed by the doxastic state of the subject of the embedding attitude verb and this requirement cannot be weaker that what the whole sentence (matrix clause + embedded clause) asserts. In the next section we will go back to the restrictions on embedded epistemic modals and, building on the strong similarities with the restrictions on embedded V-to-C in German and on some of the insights of Truckenbrodt’s proposal, we will defend a proposal that accounts for the constraints on embedded epistemic modals. 5. Back to embedded epistemic modals I assume a standardly weak semantics for epistemic modals, along the lines of Kratzer (1981), Kratzer (1991), and following Stephenson (2007), I treat epistemic modals as being judge dependent, where the judge parameter is manipulated by an embedding attitude verb. Epistemic modals (both necessity and possibility modals) carry a doxastic presupposition requiring that the judge be in a certain (to be specified) doxastic relation to the modal statement. When embedded under an attitude verb, the latter will bind the judge parameter of the embedded epistemic modal. As a result, the doxastic presupposition will require that the subject of the attitude verb (now identified with the lower judge) be in a certain doxastic relation to the epistemic complement.2 The meaning for both epistemic must φ and might φ are given in (34) and (35): the necessity modal presupposes that the subject believe the modal proposition, whereas the possibility modal presupposes that the subject’s doxastic state is compatible with the modal statement. Similarly to the Kratzerian entries above, EPI is the epistemic conversational back2 It is possible to maintain that even “unembedded” occurrences of an epistemic modal are actually embedded under a covert ASSERT operator, along the lines defended in Alonso-Ovalle and Menéndez-Benito (2010), among others. In this case, the embedded judge parameter would end up coinciding with the speaker. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 613 M. Ippolito Constraints on the embeddability of epistemic modals ground and ST is the stereotypical ordering source ranking the accessible worlds according to how close they are to a set of stereotypes holding in the actual world.3 (34) [[must φ ]]c,w,t, j is defined just in case DOX j (w) ⊆ (λ w0 . must j (w0 )(φ )); if defined, [[must φ ]]c,w,t, j = 1 iff ∀w00 ∈ STw (EPI j (w)) : p(w00 ) = 1 (35) [[might φ ]]c,w,t, j is defined just in case DOX j (w) ∩ (λ w0 . might j (w0 )(φ )); if defined, [[might φ ]]c,w,t, j = 1 iff ∃w00 ∈ STw (EPI j (w)) : p(w00 ) = 1 To illustrate this part of the proposal, take the case of the attitude verb believe, as in John believes that it must be raining. The structure shows that the judge parameter for the epistemic modal is abstracted over so that it can be manipulated by believe. As a result of this operation, the judge parameter of the modal is bound by the subject of the doxastic attitude. (36) ((((hhhhhh hh (((( John <st> ` believes<<e<st>><e<st>>> ``` `` ` <e<st>> XX XX   X λ j0 <st> PPP P  must<st<st>> <st> !aa !! a it be raining Following Gärtner’s and Truckenbrodt’s proposal, I will adopt a variant of their Absorption principle. As shown in (37), this principle requires that the meaning of the attitude + CP be at least as strong as the doxastic presupposition of the epistemic modal. This principle rules out cases where the doxastic condition is stronger than (asymmetrically entails) the assertoric meaning of the complex sentence.4 (37) Absorption Principle The doxastic presupposition must not be stronger that the meaning of attitude + CP. When the meaning of attitude + CP and the doxastic presupposition are inconsistent, the sentence can be rescued if it is possible to locally accommodate the presupposition. In what follows, we will go through the three types of embedding predicates we discussed above: doxastic-like predicates, desiderative predicates; emotive doxastic and dubitative verbs. 3 The proposal sketched in this section of the paper shares some features with the proposal in Crnič (2014). The two proposals were developed independently. 4 I assume that cases where the presupposition and the assertion are inconsistent are ruled out on independent grounds. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 614 M. Ippolito Constraints on the embeddability of epistemic modals 5.1. Embedding epistemic modals under different types of attitude verbs The doxastic type is unproblematic: recall the observation that both necessity and possibility modals can be embedded under this kind of predicate. Here is an example discussed above. (38) John believes that the keys must be in the car. The doxastic presupposition is that DOXJ (w) ⊆ (λ w0 . the keys must be in the car in w0 ) and, since the assertion is the same, Absorption is satisfied and the doxastic condition is “absorbed”. Note that in this proposal, (38) both presupposes and asserts that John believes that the keys must be in the car. This is not unprecedented, though: for example, consider the following sentences. (39) a. b. The king of France exists. God exists. (40) If John believes that the king of France exists, . . . In (39a), assuming a presuppositional analysis of the definite article, the presupposition of the definite description is that there exists a King of France, and the assertion is that he exists. Assuming the view according to which proper names presuppose the existence of their reference, (39b) presupposes that God exists and it asserts just that. (40) is a different case. Here, the presupposition triggered again by the definite article is that a King of France exists and, since it is embedded under the attitude believe, it is John’s doxastic state that is required to entail that there exists a King of France: someone uttering the conditional antecedent in (40) would seem to be presupposing exactly the content of the antecedent itself. Since whether John’s doxastic state entails that a King of France exists is precisely the content of the conditional supposition, the presupposition has been argued to be is suspended or locally accommodated. We leave the exact nature of this process aside. What we are interested here is merely pointing out that the identity of presupposition and assertion is not unique to (38). The emotive doxastic and dubitative predicates are more challenging: they allow possibility but not necessity modals. Let’s begin with the former type. (41) a. John fears that Mary may/might have known the killer. b. #John fears that Mary must have known the killer. I assume here that to fear has a doxastic assertoric component according to which a fears that p asserts that p ∩ DOXα (w) 6= 0. / To fear also has a (un)desirability component (that p is less desirable than ¬p to the attitude’s holder) but since this component is not doxastic, I am leaving the issue of its precise status aside in the present discussion.5 Now, let’s begin with the unacceptability of embedded must. As we can see in (42), the assertion (in (42a)) is weaker than the doxastic presupposition (in (42b)). Therefore, Absorption fails. 5 One possibility is that the (un)desirability component of fear is presupposed. A question like (i) is interpreted as a question about the possibility of a certain eventuality (as in (a)) and not as a question about its desirability (as in (b)): Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 615 M. Ippolito (42) Constraints on the embeddability of epistemic modals a. b. DOXJ (w) ∩ (λ w0 . mustJ (w0 )(λ w00 .the keys are in the car in w00 )) 6= 0/ DOXJ (w) ⊆ (λ w0 . mustJ (w0 )(λ w00 .the keys are in the car in w00 )) Not with might, however. The doxastic presupposition (in (43b)) requires that John’s doxastic state be compatible with the embedded clause; hence, it is not stronger than the assertoric content of fear + CP. In other words, the doxastic presupposition only requires that there be some doxastic worlds where the relevant evidence/knowledge is true and the keys are in the car. Embedding might under to fear satisfies Absorption because the presupposition is identical to the assertion in (43a). (43) a. b. DOXJ (w) ∩ (λ w0 . mightJ (w0 )(λ w00 .the keys are in the car in w00 )) 6= 0/ DOXJ (w) ∩ (λ w0 . mightJ (w0 )(λ w00 .the keys are in the car in w00 )) 6= 0/ Dubitative verbs such as to doubt show the same restrictions as emotive doxastic attitude verbs, i.e. they are compatible with possibility but not necessity epistemic modals.6 The relevant examples are repeated below. (44) a. John doubts that Mary may/might have known the killer. b. #John doubts that Mary must have known the killer. I will assume that the doxastic assertoric content in a sentence like a doubts that p is that a’s doxastic state does not entail p: ¬(DOXα (w) ⊆ φ ) (≡ ¬φ ∩ DOXα (w) 6= 0). / 7 Let’s begin with embedded must: as we can see in (45), Absorption fails because the assertion in (45a) and the doxastic presupposition in (45b) are inconsistent. (45) a. b. (i) DOXJ (w) ∩ (λ w0 .¬mustJ (w0 )(λ w00 .the keys are in the car in w00 )) 6= 0/ (it’s doxastically possible that it is not epistemically necessary that the keys are in the car; i.e. it’s possible that it is consistent with J’s knowledge that the keys are not in the car) DOXJ (w) ⊆ (λ w0 .mustJ (w0 )(λ w00 .the keys are in the car in w00 )) (it is doxastically possible that it is epistemically necessary that the keys are in the car) Do you fear that the Raptors will lose? a. Do you think it’s possible that the Raptors will lose? b. Do you find it undesirable that the Raptors will lose? The semantics for fear might then look like this: (ii) [[α fears that φ ]] is defined only if φ <DES,α ¬φ ; if defined, = 1 if ∃w0 ∈ DOXα (w) : φ (w0 ) = 1 This would also explain the judgment in (15). 6 It might be that fear and be afraid have slightly different semantics, but for reasons of space I cannot explore this possibility here. 7 This seems a fairly weak semantics for doubt since intuitively an utterance of a doubts that p conveys that a believes p to be somewhat unlikely. Whether this “unlikelihood” meaning should be part of the assertoric content of the sentence, is not clear. The verb to doubt seems to have an evidential component, which might be responsible for this stronger interpretation. A more detailed investigation of the meaning of this predicate is needed. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 616 M. Ippolito Constraints on the embeddability of epistemic modals When the embedded modal is a weak modal (might or may), Absorption succeeds because the weakness of the modal weakens the whole doxastic condition, as shown in (46b). (46) a. b. DOXJ (w) ∩ (λ w0 .¬(mightJ (w0 )(λ w00 .the keys are in the car in w00 )) 6= 0/ DOXJ (w) ∩ (λ w0 .(mightJ (w0 )(λ w00 .the keys are in the car in w00 )) 6= 0/ The doxastic presupposition in (46b) requires that John’s doxastic state be compatible with it being epistemically possible that the keys are in the car, while the assertion in (46a) is that it is doxastically possible that the evidence/knowledge is incompatible with the keys being in the car. Since these two components are consistent and the doxastic presupposition in (43b) is not stronger than the assertion, Absorption is satisfied. This correctly predicts that when to doubt is negated, embedding must is possible: the assertion is that John believes that it is epistemically necessary that the keys are in the car, and this is exactly what the doxastic condition requires. A similar situation arises with embedded might. 5.2. Back to embedded V-to-C Recall that embedded V-to-C patterns like embedded epistemic modals with respect to doxastic verbs and desiderative verbs but shows a split with respect to the other categories. This is summarized again in (47). (47) a. b. V-to-C patterns like possibility epistemic modals when embedded under emotive doxastic verbs. V-to-C patterns like necessity epistemic modals when embedded under inherently negative or negated attitude verbs. One might try to capture the difference between German embedded V-to-C and embedded epistemic modals by proposing that embedded V-to-C in German requires Absorption to be weaker than what we proposed for epistemic modals. (48) a. b. Strong Absorption (epistemic modals): the doxastic presupposition cannot be stronger than the assertion. Weak Absorption (V-to-C): doxastic presupposition and assertion must be merely compatible. I have repeated the relevant examples in (49a) and (49b). Recall that in German, a V-to-C clause can be embedded under hoffen, “to hope”, but not under bezweifeln, “to doubt”. (49) a. Maria hofft, sie ist in diesem Fall in Berlin. Maria hopes, she is in that case in Berlin Maria hopes that she is in Berlin in that case. b. *Hans bezweifelt, Peter geht nach Hause. Hans doubts, Peter goes to house Hans doubts that Peter is going home. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 617 M. Ippolito Constraints on the embeddability of epistemic modals Let us begin with (49b). If you doubt that p, the assertion is that ¬p is (doxastically) possible, while the doxastic presupposition that comes with the V-to-C configuration is that the subject believes that p. Assertion and doxastic condition are incompatible and Weak Absorption is not satisfied. Things are different with hoffen, “to hope”: if you hope that p, the assertion is that p is (doxastically) possible. Since this is compatible with the V-to-C doxastic presupposition that the attitude’s subject believes that p, Weak Absorption is satisfied. 5.3. Negated attitude verbs Our next task is to look into the (un)acceptability of V-to-C in negated sentences and relate this discussion to the behavior of epistemic modals embedded under negated attitude verbs. The following German sentence with negation is judged unacceptable in Truckenbrodt (2006). (50) *Hans glaubt nicht, Peter geht nach Hause. Hans believes not, Peter goes to house Hans doesn’t believe that Peter is going home. However, other sentences with negation are judged fine by the same author. In (51) we have a periphrastic negative form.8 (51) Es ist nicht der Fall dass Hans glaubt Peter geht nach Hause. it is not the case that Hans believes Peter is going home It is not the case that Hans believes that Peter is going home. As for English, epistemic modals embedded under negated believe seems acceptable in most contexts.9 (52) After reviewing the evidence, the police no longer believe that it must/might be a homicide. This is especially interesting when one compares the acceptability of (52) with the (relative) unacceptability of doubt + must. The puzzle is the following. We have argued that embedding a necessity epistemic modal under doubt violates (Strong) Absorption because the doxastic condition is inconsistent with the assertion. Therefore, embedding must under negated believe 8 Judgments improve also if negation is in the quantifier niemand as in the following response to the question Who believes that Peter is going home?: (i) NIEMAND glaubt, Peter geht nach Hause. nobody believes Peter is going home NOBODY believes that Peter is going home 9 There odd: (i) (ii) is variability in the judgments with negation. For example, some speakers accept (i) but find (ii) rather I believe that it must have been hard to write on epistemic modals. I don’t believe that it must have been hard to write on epistemic modals. Hopefully, the accommodation story that we will tell can help towards explaining this variability. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 618 M. Ippolito Constraints on the embeddability of epistemic modals should also fail Absorption since the assertion (that the subject does not believe p) is inconsistent with the doxastic condition (that the subject believes p). One way to resolve this tension is to propose that, when Absorption is not met, the last resort is to locally accommodate the presupposition, if possible. In the cases we are considering here, what rescues embedding must under a negated believe is the possibility of locally accommodating the doxastic presupposition in the scope of negation. However, this possibility does not seem available to inherently negative verbs like doubt, as the following contrast shows: (53) a. Mary doesn’t believe that John quit smoking because she knows that he is not a smoker. b. ??Mary doubts that John quit smoking because she knows that he is not a smoker. The last example suggests that, unlike negation, the inherent negative component of the verb doubt cannot be targeted for local accommodation. The contrast between (50) and (51) in German could be construed as also stemming from the possibility of locally accommodating the doxastic condition with the periphrastic form es ist nicht der Fall dass but not with postverbal nicht. However, more research on this is needed. 5.4. Desiderative attitude verbs As noted by many already, neither necessity nor possibility epistemic modals can be embedded under desiderative verbs like want and directive verbs like demand. (54) a. John wants the keys to have to be in the car. (*epistemic) b. #John demanded that Mary must have been the murderer. As we saw above, this contrasts with emotive doxastic to hope which can embed possibility epistemic modal might (but not necessity must; cf. (3) and (4)). Anand and Hacquard attribute the impossibility of embedding epistemic modals under want to the non-representational nature of this attitude verb, which they claim only has a desiderative (ranking) semantics, as shown in the entry below from Anand and Hacquard (2013). (55) [[want]]c,w,g = λ p.λ x.∀q ∈ g(C)\p : p >desx,w q This move is problematic, though, since we know that it is possible, and in fact even advisable, to provide a semantics for want which includes a doxastic component (Stalnaker (1984), Asher (1987), Heim (1992)). Below is a possible entry for want, modeled after Heim (1992). There is no reason to believe that the subject’s doxastic state would not be made salient by (56). (56) [[want]]c,w,g = λ p.λ x.(DOXx (w) ∩ p) <DESx,w (DOXx (w) ∩ ¬p) There is, however, an interesting difference between to hope and to want which might be relevant in explaining their different behavior with respect to the embeddability of epistemic Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 619 M. Ippolito Constraints on the embeddability of epistemic modals modals. Consider the following examples. (57) a. b. c. d. John wants Mary to win the game. John wants Mary to have won the game. (somewhat strange) John hopes that Mary will win the game. John hopes that Mary won the game. Want, but not hope, is typically future-oriented (and more agentive), and if (57b) is acceptable at all, the verb want seems to be interpreted as synonymous to hope (with no agentivity and no futurity). Note that the majority of verbs that do not allow embedded epistemic modals have a future orientation: desiderative verbs (want, wish); directive verbs like commands (command, order), permissions (allow, permit), and prohibitions (forbid, ban); “future” verbs like promise. Note as well that if a “future” verb can take a non-future complement, then it does allow an epistemic modal (expect, guess).10 Thus, what would explain the incompatibility of want and epistemic modals is not the lack of a representational component but its future orientation, which is somehow incompatible with epistemic modal verbs.11 6. Open questions and conclusion One phenomenon that seems to share some features with embedded epistemic modals is slifting (Ross (1975), Grimshaw (2011), Reis (1996), Wagner (2004)) illustrated in the following example from Grimshaw (2011). (58) Mary, they say / I’m sure / it’s clear / the teacher explained to me, is a talented singer. The phenomenon of slifting has been already connected to embedded V-to-C by Scheffler (2009): V2 embedding and slifting are possible with verbs of saying, belief, and verbs like hope and fear; neither one is possible with factive verbs, downward epistemic verbs, desiderative verbs like want, and negative verbs like doubt. One of the contributions of the present paper is to highlight that the constraints on embedded V-to-C (and slifting) show striking similarities to the constraints on the embeddability of epistemic modals. One open question is whether the proposal defended here can be extended to the slifting cases. A second issue that one might explore in the future is the issue of cross-linguistic differences. Anand and Hacquard’s paper offered some cross-linguistic experimental data but there is more variability than is conceded by the generalizations the authors take their data to support. The strongest variability I found is in the area of emotive doxastic and dubitative verbs. In addition to finding that a not marginal number of English speakers accept necessity epistemic modals under hope, fear, and doubt, I have encountered varieties of languages that accept necessity epistemic modals under fear and doubt. Below are some examples from Russian and Bengali. The acceptability contrast between (59a) and (59b) in Russian correlates with the different modal expression in the em10 One might follow Abusch (2004) and her treatment of futurate predicates in assuming that the LF representation in (ia) for the complement of future oriented attitudes contains a future shifting operator as in (ib). (i) a. b. 11 See want: [CP λ n [IP n [FUT [CP λ n [IP n VP]]]]] [[FUT]] = λ P.λt.P((t, ∞))] Homer (2010) for more on the relation between epistemic modals and tense operators. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 620 M. Ippolito Constraints on the embeddability of epistemic modals bedded clause: in (59b) an adverbial form is used. Note, also, that the modal expression used in Bengali is also adverbial.12,13 (59) Russian a. ??Ivan somnevaetsja chto Masha dolzhna byt’ doma Ivan doubts-refl that Masha must-F-sg to-be home John doubts that Mary must be home b. Ivan somnevaetsja chto Masha dolzhno byt’ doma Ivan doubts-refl that Masha must-Adv(N-sg) to-be home John doubts that Mary must be home. (60) Bengali a. Johner bhoe 0/ je niscoi norohotto hoeche John-gen fear COP COMP certainly homicide happen-Pfv-3.pres John is afraid that a homicide must have occurred. To conclude, I have shown that the restrictions on which attitude verbs can embed epistemic modals bear a strong resemblance to the restrictions on embedded V-to-C movement in German, and that these two phenomena can be given similar explanations. I have proposed that epistemic modals presuppose that their judge (the owner of the epistemic state we quantify over) believes the modal claim. When embedded under attitude verbs, the judge parameter of the epistemic modal is bound by the attitude’s subject and, as a result, it is the attitude’s subject that is required to believe the embedded modal statement. I argued that the semantics proposed by Anand and Hacquard (2013) for emotive doxastic and dubitative verbs to explain the impossibility of embedding necessity epistemic modals is problematic. Instead, I have argued that Absorption can explain these restrictions once a minimal semantics for these attitude verbs is assumed. A weaker Absorption principle explains the restrictions on embedded V-to-C in German. Open questions remain, in particular about the incompatibility between future operators and epistemic modals (as discussed in the section on desiderative verbs), the relation between embedded epistemic modals/V-to-C and slifting, the behavior of factive predicates (which we haven’t talked about in this paper), as well as the nature of Absorption itself. References Abusch, D. (2004). On the temporal composition of infinitives. In J. Guéron and J. Lecarme (Eds.), The Syntax of Time. MIT Press. Alonso-Ovalle, L. and P. Menéndez-Benito (2010). Modal indefinites. Natural Language Semantics 18(1), 1–31. Anand, P. and V. Hacquard (2013). Epistemics and attitudes. Semantics and Pragmatics 6.8, 1–59. Asher, N. (1987). A typology for attitude verbs and their anaphoric properties. Linguistics and Philosophy 10, 125–198. 12 For some Italian speakers these embedding are also acceptable, even though on a scale of acceptability, a bit degraded compared with the corresponding weaker modal cases. Note also that Italian uses regular modal verbs. 13 Thanks to Julie Goncharov and Neil Banerjee for their Russian and Bengali judgments respectively. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 621 M. Ippolito Constraints on the embeddability of epistemic modals Bolinger, D. (1968). Post-posed main phrases: An English rule for the Romance subjunctive. Canadian Journal of Linguistics 14, 3–30. Crnič, L. (2014). Pragmatics of epistemics in attitudes: A reply to Anand & Hacquard (2013). Hebrew University of Jerusalem, manuscript. Dayal, V. and J. Grimshaw (2009). Subordination at the interface: A quasi-subordination hypothesis. Rutgers University, manuscript. Gärtner, H.-M. (2002). On the force of V2 declaratives. Theoretical Linguistics 28, 33–42. Grimshaw, J. (2011). The place of slifting in the English complement system. Handout, FGIST 3. Hacquard, V. and A. Wellwood (2012). Embedding epistemic modals in English: A corpusbased study. Semantics and Pragmatics 5(4), 1–29. Heim, I. (1992). Presupposition projection and the semantics of attitude verbs. Journal of Semantics 9, 183–221. Homer, V. (2010). Epistemic modals: High ma non troppo. In S. Kan, C. Moore-Cantwell, and R. Staubs (Eds.), Proceedings of NELS 40. GSLA. Kratzer, A. (1981). The notional category of modality. In H.-J. Eikmeyer and H. Rieser (Eds.), Words, Worlds, and Contexts, pp. 38–73. Berlin: de Gruyter. Kratzer, A. (1991). Modality. In A. von Stechow and D. Wunderlich (Eds.), Semantics. An International Handbook of Contemporary Research, pp. 639–650. Berlin: De Gruyter. Reis, M. (1996). Extractions from verb-second clauses in German? In U. Lutz and J. Pafel (Eds.), On Extraction and Extraposition in German, pp. 45–48. John Benjamins. Ross, J. R. (1975). Slifting. In M. Gross and M. Halle (Eds.), The Formal Analysis of Natural Language, pp. 133–169. Mouton. Scheffler, T. (2009). Evidentiality and German attitude verbs. In Proceedings of the 32nd Annual Penn Linguistics Colloquium. Penn Libraries, retrieved at http://repository.upenn.edu/pwpl/vol15/iss1/21/. Stalnaker, R. (1984). Inquiry. Cambridge, MA: MIT Press. Stephenson, T. (2007). Judge dependence, epistemic modals, and predicates of personal taste. Linguistics and Philosophy 30(4), 487–525. Truckenbrodt, H. (2006). On the semantic motivation of syntactic verb movement to C in German. Theoretical Linguistics 32, 257–306. Villalta, E. (2008). Mood and gradability: An investigation of the subjunctive mood in Spanish. Linguistics and Philosophy 31(4), 467–522. von Fintel, K. and A. S. Gillies (2010). Must ... stay ... strong! Natural Language Semantics 18, 351–383. Wagner, M. (2004). Asymmetries in the syntax and prosody of verb-initial interpolated clauses in German. In S. Blaho, L. Vicente, and M. de Vos (Eds.), Proceedings of Console XII. Yalcin, S. (2010). Probability operators. Philosophy Compass 5(11), 916–936. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 622 The temporal presuppositions of Somali definite determiners1 Rudmila-Rodica IVAN — University of Massachusetts, Amherst Deniz ÖZYILDIZ — University of Massachusetts, Amherst Abstract. Nominal temporal markers (NTMs) locate the time at which the property or relation denoted by a nominal holds of an entity (Enç, 1981). What distinguishes Somali from other languages with overt NTMs is that these markers are also definite determiners. We follow up on the observation that there is a contrast in the interpretation of definite determiners - KA and - KII, and propose that this contrast is a difference in the scalar implicatures triggered by each determiner. This difference is linked to an interaction between the temporal presuppositions of - KA and - KII and the lexical semantics of their NP complement. Our analysis captures the fact that these determiners do not obey common diagnostics of “nominal tense” (Tonhauser, 2007), while accounting for the data in Lecarme (1996) as well as the more recent proposal (Lecarme, 2008, 2012) that - KII and - KA track the (in)visibility of the entity denoted by the DP. Keywords: Somali, determiners, definiteness, nominal TAM, presupposition 1. Introduction The aim of this paper is to explain the contrast between what has been described in the literature as the “regular” definite determiner - KA (Green et al., 2015) and the “remote,” “tensed” or “evidential” definite determiner - KII (Lecarme, 1996, 2008, 2012) in Somali. A comparison between Somali - KII and Guaranı́ -kue, as discussed in Tonhauser (2007), illustrates that the current take on nominal temporal markers (NTMs) cannot fully account for the Somali data. We propose that a scalar implicature based account, in line with the work of Thomas (2014) for Mbyá Guaranı́, and Altshuler and Schwarzschild (2013) on cessation implicatures in English, can capture the semantic contribution of Somali - KII. Our account relies on novel data involving contexts where this contrast obtains, and ones where it does not. The choice between - KA or - KII for Somali nominals can give rise to temporal interpretations, as well as to (in)visibility readings, by which we mean that the denotation of the DP is judged to be visible or invisible to the discourse participants. We claim that the these contrasts are due to a competition between - KA and - KII. Assuming that Somali NTMs behave like a regular tense system, similarly to Mbyá Guaranı́ (Thomas, 2014), we propose that - KA requires the NP predication to be true of an individual at topic time, while - KII requires it to be true at some salient time preceding topic time. Based on the Open Interval Hypothesis proposed by Altshuler and Schwarzschild (2013) (see also Cable 2017), whereby a present stative sentence asymmetrically entails its past tense variant, we assume that a sentence with a - KA marked nominal asymmetrically entails a sentence with its - KII marked counterpart. Thus, the use of - KII generates the implicature that the - KA alternative is false, resulting in the aforementioned 1 We would like to thank our very patient informants, the audiences at the UMAss Funny Languages Afternoon (02/19/2016), the UMass Semantics Workshop (03/08/2016), the Definiteness Across Languages workshop (Mexico City, June 24–26 2016), Triple A 3 (Tübingen, July 4–6 2016) and Sinn und Bedeutung 21 (Edinburgh, September 4–6 2016), and, naturally, Rajesh Bhatt, Seth Cable, Veneeta Dayal, Vincent Homer, Florian Schwarz, and Kristine Yu for their comments, helpful discussion and feedback, and for sparking our interest in this project. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 623 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners interpretative contrasts. We speculate that contexts where the contrasts are not observed are ones where the relevant implicatures are not generated. The paper is structured as follows. Section 2 provides background information regarding the elicitation, novel data confirming that both - KA and - KII pattern like definite determiners, and the core data regarding the relevant semantic contrasts between the two determiners. Section 3 focuses on nominal tense as discussed in the literature and on the key properties of nominal temporal markers identified by Tonhauser (2007) for Guaranı́, namely precedence, change of state and existence. Section 4 discusses novel data which illustrate that two of three properties of Guaranı́ -kue, change of state and existence, do not hold of Somali - KII. In section 5, we present the core generalization and argue in favor of a competition based account for the two Somali definite determiners. Section 6 concludes. 2. Background Information 2.1. Elicitation The data discussed in this paper was mainly collected from a primary consultant, who self reports as a native speaker of Standard Somali. The elicitations took place at the East African Cultural Center (EACC) in Springfield, Massachusetts, between September 2015 and May 2016. Four other occasional attendees of the EACC contributed on site, and a linguistically trained native speaker from Minnesota contributed by e-mail. 2.2. The definiteness of - KA and - KII Somali has two noun classes, referred to in the literature as the masculine and the feminine (Saeed, 1993, 1999; Green et al., 2015). Masculine nouns are suffixed with morphemes whose initial segment is /k/ (phonologically realized as [k], [g] or [h] and noted K) as shown in (1a). As illustrated in (1b), for feminine nouns the initial segment of the suffix is /t/ (phonologically realized as [d], [dh], [sh] and noted T). All of the instances of the allomorphs in (1) are referred to as - KA and - KII throughout the paper. (1) a. aqal-ka, aqal-kii, telefoon-ga, telefoon-gii house- KA house- KII telephone- KA telephone- KII the house, the telephone (masculine) b. shimbir-ta, shimbir-tii, qorrax-da, qorrax-dii bird- KA bird- KII sun- KA sun- KII the bird, the sun (feminine) As previously mentioned, both - KA and - KII are claimed to be definite in the literature (Saeed, 1993; Lecarme, 1996; Green et al., 2015). Our data confirms that - KA and - KII marked nominals pattern like definites; consequently, for the purposes of this paper, they will be refered to as definite determiners. For a different take on definiteness in Somali and for arguments in favor Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 624 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners of the existence of a null definite determiner which is taken to be responsible for the definite interpretation of the nominals suffixed with - KA and - KII, see Özyıldız and Ivan (2017). According to Heim (1983) and Matthewson (1998), definite noun phrases refer to familiar, previously introduced discourse referents. This holds true of both - KA and - KII marked NPs, as shown in example (2). Both definite determiners allow anaphoric reference to the boy introduced in the preceding piece of discourse. (2) A NAPHORIC REFERENCE Context: A boy and a girl came. The boy laughed. a. Wiil iyo gabadh baa yimid. Wiil-kii baa qoslay. boy and girl FOC came. boy- KII FOC laughed b. Wiil iyo gabadh baa yimid. Wiil-ka ayaa qoslay. boy and girl FOC came. boy- KA FOC laughed ‘A boy and a girl came. The boy laughed.’2 [03/19/2016] Furthermore, both - KA and - KII can refer to unique NPs in both immediate and larger situations. In (3), where the sun is a unique entity, the use of either determiner is grammatical. (3) R EFERENCE TO UNIQUE NP S Context: Axmed was working home all day. He decides to go out and sees the sun. Marku baxay wux-uu arkay qorrax{-ka/-kii}. when went out FOC =3 S saw sun- KA /- KII ‘When he went out, he saw the sun.’ [03/07/2016] According to Schwarz (2009, 2013), in languages with multiple definite determiners, these determiners can be either weak or strong.3 Weak definite determiners cannot be used anaphorically, only being able to refer to NPs that are unique in the context, while strong definite determiners can also have anaphoric uses as in (2). The fact that both - KA and - KII are grammatical in example (2), which tests for anaphoricity, and (3), which tests for non-anaphoric reference, suggests that the strong/weak determiner distinction is not at play in regulating the distribution of Somali definite determiners. The difference between the two seems to lie elsewhere. 2.3. Core data Work by Lecarme (1996, 2004, 2012) argues that -kii is a “tensed” determiner denoting the past tense (for arguments against this analysis, see Tonhauser (2006: pp. 325–333)). The temporal analysis of - KII is motivated by data like (4) (Lecarme, 1996: ex. (10), p. 161), where - KA is ungrammatical when referencing a past year. Lecarme argues that sannad-kii receives a temporal past interpretation, thus rendering it ungrammatical with future-oriented adverbials. 2 It should be noted that different focus markers are used in the two subexamples. We speculate that this difference is due to the fact that the counterpart of (2a) with - KA, wiilka baa, is morphologically ill-formed. 3 This is not the weak/strong determiner distinction from Barwise and Cooper (1988). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 625 R. Ivan & D. Özyıldız (4) a. sannad-ka dambe year-KA next ‘next year’ The temporal presuppositions of Somali definite determiners b. sannad-kii/*-ka hore year-KII/*-KA before ‘last year’ Lecarme (1996, 2012) notes that - KII can also have temporal interpretations on nouns denoting a set of individuals, such as ‘student.’ We replicated this effect with the NP ‘president.’ In a context where Barack Obama is the current president, like in (5), the DP madaxweynaha, which bears - KA, may only refer to Obama, and not to Bush—who was the salient former president in the context. On the other hand, madaxweynihii, with - KII, may only refer to Bush, and not to Obama. Both sentences in (5) were judged true with this reference scheme. They were judged false when - KII was used in (5a) and - KA, in (5b). (5) T EMPORAL CONTRAST between - KA and - KII Context: The year is 2016 and Barack Obama is the president of the United States. a. Madaxweynaha wux-uu ku nool yahay guriga cad. president-KA FOC =3 S at lives house white ‘The president lives in the White House.’ ≈ Barack Obama b. Madaxweynihii wux-uu ku nool yahay Texas. president-KII FOC =3 S at lives Texas ‘The president lives in Texas’. ≈ George Bush [01/30/2016] Lecarme (2012) also identifies a “modal” or “evidential” contrast between - KA and - KII, whereby visible entities are marked with the former and invisible entities with the latter. This effect was replicated in our elicitations. In the context of a solar eclipse, the use of - KA on the NP ‘sun’ implies that the sun is in plain sight, whereas the use of - KII implies that the sun is eclipsed. (6) V ISIBILITY CONTRAST between - KA and - KII Context: During a solar eclipse. Answer to “What are you doing?” Wax-aan fiirinayaa cadceed-da/-dii. FOC =1 S watching sun- KA /- KII I’m watching the sun. a. Inference with - KA: The sun is visible. b. Inference with - KII: The sun is eclipsed. c. - KII is odd if the sun is visible; - KA is odd if the sun is eclipsed. [01/30/2016] The use of - KII on an NP corresponding to a temporary state, like ‘rain,’ gives rise to the same effect. If the rain is ongoing and visible, then only - KA is felicitous. (7) Context: It’s raining and I’m outside. Roob{-ka/#-kii} baan eegayaa rain-KA /-# KII FOC =1 S watching I’m watching the rain. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde [05/11/2016] 626 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners We argue that a unified account can generate both the temporal and the invisibility readings presented in the examples above. Our proposal is laid out in Section 5. The next two sections give an overview of the properties of NTMs and argue that Tonhauser (2007)’s seminal account of Guaranı́ NTMs cannot be extended to Somali - KII. 3. Properties of nominal tense The current section introduces the notion of NTMs and outlines the three properties identified by Tonhauser (2007) based on the future (-rã) and past (-kue) nominal markers of Guaranı́. These three properties are precedence, change of state and existence. 3.1. Nominal Tense An important first observation is that both NPs and VPs can locate the time at which a property is true of an individual. For instance, in (8), the past tense ‘watched Harry Potter’ indicates that the activity is true of x, at some interval of time, t, which is a subpart of yesterday. On the other hand, ‘linguistics grad student’ is true of x, at some time, t 0 , which includes yesterday, the property of being a linguistics grad student generally spanning from 2 to 5 years. (8) Yesterday, a linguistics grad student watched Harry Potter. In (8) there is an overlap between the time interval at which x is a linguistics grad student and the time interval during which x watches Harry Potter. However, NPs and VPs within the same sentence need not hold true at the same time. Consider (9) where, in a context where all of the contextually relevant individuals stop being students, the property of being a ‘student’ was true of the individuals in every’s restrictor before utterance time, and it is false at utterance time. (9) Every student is now a UMass graduate. The observation that verbal tense does not affect the temporal interpretation of noun phrases was first made by Enç (1981). She proposed that this can be captured by means of nominal tense. One morphological realization of nominal tense and aspect is represented by the morphemes in (10) which restrict the time interval at which the nominal they attach to is true. (10) ex-soldier, former friend, future president, wife-to-be Although subtly distinct from the phenomenon illustrated in (9), the affixes and adjectives in (10) point to the core intuition: the time at which the property (soldier, friend, president, wife) holds true of the individual is either before (ex-, former), or after (future, -to-be) topic time. According to Wiltschko (2003), semantic nominal tense is universal; the crosslinguistic difference lies in whether nominal tense is syntactically marked. In fact, overt nominal TAM (tense and aspect morphology) is rare. Nordlinger and Sadler (2004) list twelve different languages which exhibit NTMs (Lake Miwok, Halkomelem, a.o.). Somali (Lecarme, 1996), Guaranı́ (Tonhauser, 2007) and Tsou (Chang, 2015) are ones that have been discussed more extensively. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 627 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners 3.2. Guaranı́ nominal TAM Tonhauser’s (2006; 2007) seminal account of nominal temporal markers in Guaranı́ discusses the morphemes -kue and -rã. Tonhauser argues that they are nominal aspectual markers and identifies three properties which NTMs might be expected to display cross-linguistically. The example below illustrates that Guaranı́ makes use both of a future nominal temporal marker, -rã, and of a past one, -kue. It should be noted that the example, glosses and translation below are taken from Tonhauser (2007), and that the two NTMs are not equivalent to the English adjectives future and former, the Guaranı́ nominal temporal markers having a wider use than their English counterparts. (11) Juan ha’e pa’i-kue/-rã. Juan 3.PRON priest- KUE /- RA ‘Juan is a former/future priest.’ (Tonhauser (2007), ex. (8), page 836) To capture the different properties of Guaranı́ NTMs, Tonhauser (2007) distinguishes between two main intervals: the NP time, tNP , and the nominal time, tnom (or possessive time, tposs ). The NP time represents the evaluation time of the entire NP, the time at which the phrase is interpreted. This generally picks out topic time. The other relevant interval tnom (or tposs ) is the time at which the property (or relation) expressed by the noun phrase is true of the individual(s) in the relevant domain (or, in the case where the NP is relational, is true of the members of the relation). As previously mentioned, Tonhauser (2007) argues that nominal temporal (or aspectual) markers have three properties: precedence, change of state and existence, which are described in terms of the relations between tnom and tNP . These properties are outlined in the following subsections. 3.2.1. The precedence meaning property Perhaps the most salient meaning property of NTMs in general and of -kue and -rã is that they encode a precedence relation: respectively a past-time oriented relation and a future-time oriented one. In (12), the use of -kue conveys that the time at which the property of being a priest holds true of the individual precedes tNP , while the use of -rã conveys that the predicate holds true of the individual after tNP , and, consequently, after topic time. (12) P RECEDENCE R ELATIONS a. priest-KUE ≈ past priest b. priest-R Ã≈ future priest Precedence relations: tnom < tNP tnom > tNP before TT after TT In the case of possessives, the precedence relation can apply either to the possessive or to the nominal itself. In (13), for instance, which is adapted from Tonhauser (2007), both the Guaranı́ che-róga-kue and the English my former house are ambiguous between two possible readings. One interpretation is that the possessive time is located at tNP (in this case, utterance time) and the nominal time, tnom , precedes tNP ; in this instance, the speaker is looking at the ruins of their house. The second reading is one where tnom overlaps with tNP , but tposs is located prior to the noun phrase time; here, the speaker is looking at a building which was once their house. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 628 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners (13) Ko’agã a-hecha che-róga-kue. now SG-see SG-house-KUE ‘I am seeing my former house.’ (Tonhauser, 2007: ex. (12), p. 838) All of the occurences of -kue discussed in this section are parallelled by similar examples with future-oriented NTM, -rã. However, we will henceforth only refer to examples with -kue, as Somali does not have a future oriented nominal temporal marker. 3.2.2. The change of state meaning property Much like the English former, Guaranı́ -kue also encodes a change of state meaning, namely, the NP predication (or relation) ceases to hold true of an individual x before tNP (or topic time). (14) a. *Albus is a former teacher and he is still a teacher b. Albus is a former teacher and now he’s a teacher again The examples in (14) (which can also be replicated for Guaranı́ -kue, see Tonhauser (2007: exx. (13/14), p. 838)) illustrate that the nominal predication, teacher, is true prior to tNP and that it ceases to be true prior to tNP . Furthermore, (14b) shows that neither the English former nor the Guaranı́ -kue encode that the property is not true at tNP , but merely that it had stopped being true sometime before noun-phrase time. Albus can be a former teacher and a current teacher, the predication need not be false at tNP . Tonhauser (2007) points out that although both -kue, former and English past tense have the precedence meaning property, only the first two have the change of state property. The first utterance in (15) merely implicates that Hermione is no longer in the Hospital Wing at the time of utterance. The fact that still is felicitous in the second utterance illustrates that English past tense, unlike former or Guaranı́ kue does not semantically encode a change of state. (15) Hermione was in the Hospital Wing last week. She is still there today. The observation that Guaranı́ -kue is not like English past tense in this instance serves as an argument for Tonhauser (2007) in favor of the view that -kue and -rã are aspectual nominal markers, and not tensed. We will return to this fact in section 4, where we compare Guaranı́ nominal TAM to Somali - KII. 3.2.3. The existence meaning property The third property of NTMs identified by Tonhauser (2007) is that of existence, which assumes that both tnom and tnp should fall within the time of existence of the individuals denoted by the noun phrase. This would account for the infelicity of -kue in the context below. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 629 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners (16) Context: The town of San Isidro once had a priest called Jose. This man died as a priest. # pe pa’i-kue Jose that priest-KUE Jose ‘that ex-priest Jose’ (Tonhauser, 2007: ex. (21), p. 842) It should be noted that English former is also not felicitous in (16). The intuition is that the property of being a former priest was never true of Jose while he was alive. The only context in which ‘priest’-kue would be felicitous is one where Jose stopped being a priest while alive.4 3.2.4. Summary: -kue properties To reiterate, Tonhauser (2007) proposes that there are three distinct properties which are true of Guaranı́ nominal temporal markers. These properties are summarized below. (17) NTM properties 1. P RECEDENCE: tnom / tposs precedes tNP (topic time) 2. C HANGE OF S TATE: the property or relation ceased to be true before tNP 3. E XISTENCE: the time of the existence of x includes tnom and tNP According to Tonhauser (2007), these three properties are individually encoded in the lexical entry of -kue. The lexical entry for -kue as applied to property NPs is given below.5 The formal semantic analysis below, applied to the denotation of predicates, establishes that for all properties P and entities x, the property KUE(P) is true of an individual, x, at the noun-phrase time, tNP , in a world w if and only if there is a time t that precedes the noun phrase time and t is the situation time of P(x) in world w and the noun phrase time is included in the lifetime of x. (18) ∀P ∀x [ KUE(P)(x) = 1 at tNP in w iff ∃tnom [ tnom < tNP & τ(P(x)) = tnom in w & tNP ⊆ τ(x) ] ] Before moving on to the next section, it should be noted that both existence and change of state are hardwired into the lexical entry of -kue. For the intents and purposes of this paper, -kue behaves like English ‘former,’ but, as Tonhauser (2007) points out, this is a simplification. 4. Somali - KII vs. Guaranı́ -kue: - KII is not ‘former’ This section tests whether the properties identified by Tonhauser (2007) for Guaranı́ -kue hold of Somali - KII. The data illustrate that although - KII has the precedence meaning property, it does not semantically encode the change of state or the existence properties. In this sense, - KII is different from -kue and English ‘former.’ Furthermore, we show that, unlike -kue, Somali - KII does behave like tense and it can give rise to temporal and invisibility implicatures. 4 On the other hand, -kue would be felictious in the context in (16) if it applied to a possessive relation: ‘our priest’-kue would denote a possession relation which ceased to be true. 5 The definition of -kue for possessive relations is similar. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 630 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners 4.1. Lack of the existence property The existence property refers to the fact that Guaranı́ -kue is not felicitous in contexts like the one in (16), where the property of being a priest held true of an individual right up to the moment of their death. We attempted to replicate this finding with our Somali consultants. The expectation was that if - KII had the existence property, a sentence like (19) would be infelicitous in the context given, with - KII on the subject NP. (19) Context: Uttered right after the current president’s death. . . madaxweyni-hii/madaxweyna#-ha wuu dhintay president-KII/president- KA FOC =3 S . M died ‘The president died.’ [01/30/2016] The example above illustrates that in a context where the individual picked out by the current ‘president’ dies as a president - KII is, in fact, felicitous. This is unexpected if - KII were to have the same meaning as Guaranı́ -kue and had the existence property. Furthermore, it seems that - KA is infelicitous in (19), presumably because there is no president in the context.6 Nevertheless, the data shows that Somali - KII, unlike Guaranı́, does not have the existence property. 4.2. Lack of the change of state property As shown in Section 3.2.2, the property of the NP that -kue attaches to ceased to be true of the individual picked out by the nominal prior to the noun phrase time. In contrast, the examples in this section suggest that -kii does not obligatorily trigger a change of state inference.7 The context and item in (20) are replicated from Tonhauser (2007: ex. (44)). (20) Context: Yesterday I went to a bike shop and out of all of the bikes they had I chose one for my sister. I didn’t have enough money yesterday. Tomorrow I’ll go back to the shop and buy the bike I chose. Baskiil-ka / Baskiil-kii bari baan gadanaya bike-KA / bike-KII tomorrow FOC .1 S buy.FUT ‘I will buy the bike tomorrow.’ [11/04/2015] According to Tonhauser (2007), in Guaranı́ the change of state interpretation in the context in (20) is necessary. For her consultants, ‘bike’-kue may only refer to a broken bike (which renders the target sentence odd in the scenario above). In Somali, both baskiil-ka and baskiil-kii are perfectly felicitous and refer to a bike which had been previously introduced in the discourse. No change of state inference is drawn in this context. Further attempts to favor Guaranı́-type change of state meanings on object denoting NPs were unsuccessful. 6 Our primary informant comments: “If he died, you cannot say [k]a.” is a subtle difference between “change of state” (predication ceased to be true before but may be true again at topic time) and “cessation” (predication ceased to be true and is still not true at topic time) inferences (Altshuler and Schwarzchild 2012, Thomas 2014). 7 There Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 631 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners (21) Context: Shards of a broken jar are set on the table. Dhala-day-dii *(jajabkee-dii) miiska ayuu saaran yahay jar-POSS .1 S - KII *(shards-KII) table-KA FOC on is ‘The shards of my jar are on the table.’ Intended: ‘My (broken/former) jar is on the table.’ [01/30/2016] The aim of the scenario above was to get our informants to express that an object was broken solely through the use of - KII. For the purposes of this elicitation task, a broken jar was brought into the elicitation session and set in plain view, on the table between the authors and the informant. It was found that the possessive construction dhaladaydii, ‘my jar-KII’ may only refer to an intact jar. As illustrated in (21), an overt genitive construction, “the shards of the jar,”8 must be used in order to express the broken state of the object. The change of state inference cannot be expressed by means of - KII alone. Somali seems to express the equivalent of the English ‘former NP’ by using the adjective hore in combination with a - KII marked NP. (22) Context: We are talking about several students. Maxamed is the one who dropped out of college / graduated. Maxamed waa arday-dii hore. Maxamed DECL students-KII . PL ‘former’ ‘Maxamed is one of the former students.’ [11/04/2015] It is unlikely, however, that the combination of - KII and hore is equivalent to the semantics of ‘former NP,’ given that our informant accepts a continuation like in (23) to the sentence in (22). (23) Out of the blue Maxamed waa arday-dii hore ee wali ardayga ah Maxamed DECL students-KII . PL hore which still student-KA is ‘Maxamed is one of the previous9 students who is still a student.’ [11/04/2015] If anything in the semantics of - KII or of hore were uniformly equivalent to that of ‘former,’ the sentence should sound odd. This oddness is what we observe with Guaranı́ kue and English ‘former.’ We take this as evidence that Somali - KII does not obligatorily have the change of state property. In example (23), the behavior of Somali -KII parallels that of the English past tense in a stative sentence like (15), where a cessation inference (that Hermione is no longer in the Hospital Wing or that Maxamed is no longer a student) is triggered but is cancellable. (15) Hermione was in the Hospital Wing last week. She is still there today. 8 Similar examples obtain for possession, where “my jar-kii” or “my phone-kii” alone cannot denote a jar/phone that used to be mine. Transfer of possession, in these cases, can be expressed with a relative clause. Our proposal predicts that change of state inferences should not obtain with permanent properties like ‘being a jar.’ 9 The word hore is translated in Qoorsheel (1978) as ‘ahead,’ ‘before,’ and ‘former,’ among other meanings. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 632 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners The data explored in this section so far point to the fact that Somali - KII does not behave like English ‘former’ or like Guaranı́ -kue: - KII does not encode the properties of existence and change of state identified by Tonhauser (2007). While Somali - KII may be different from Guaranı́ NTMs, it does encode the precedence property. The following subsection further motivates the analysis of - KII as a nominal tense marker. 4.3. The temporal contrast of Somali definite determiners The previous subsection illustrated that - KII does not obligatorily generate a change of state inference. Nevertheless, this inference does arise in certain contexts. Example (5) is repeated below. Recall that in context, president- KA may only refer to the current president, Barack Obama, and the use of - KA in (5b) would lead to infelicity. Similarly, president- KII would not be felicitous in (5a), necessarily referring to George Bush, the salient past president, in (5b). (5) Context: The year is 2016 and Barack Obama is the president of the United States. a. Madaxweynaha wux-uu ku nool yahay guriga cad. president-KA FOC =3 S at lives house white ‘The president lives in the White House.’ ≈ Barack Obama b. Madaxweynihii wux-uu ku nool yahay Texas. president-KII FOC =3 S at lives Texas ‘The president lives in Texas’. ≈ George Bush [01/30/2016] Event nouns modified by - KII may also give rise to cessation implicatures. The example in (24) is replicated from Lecarme (2008: ex. (11), p. 204). The two sentences below were elicited during The Big E festival, an annual event in Springfield, MA, that takes place at the end of September. Crucially, (24a) can only be uttered if the exhibition is still running at Utterance Time, exhibition- KII being infelicitous in this scenario. The use of - KII is felicitous in (24b), where it is contextually given that the exhibition is closed at the time of speech; as in the case of (5), - KA is infelicitous if the speaker is aware that the festival ended. (24) a. Context: The Big E is ongoing at the time of speech. Bandhig-ga ma=ad daawatay? exhibition-KA Q=2 S see.2 S . PAST ‘Have you seen the exhibition?’ b. Context: It is mid-October and The Big E recently ended. Bandhig-gii ma=ad daawatay? exhibition-KII Q=2 S see.2 S . PAST ‘Have you seen the exhibition?’ [09/27/2015] In (23), in section 4.2, we observed that student- KII does not entail a change of state, but that it gives rise to a cancellable implicature that the individual denoted by the DP is not a student at UT. However, the ‘optionality’ of this inference is context-dependent: compare (22) with (25), where the change of state inference is obligatorily triggered. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 633 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners (25) Context: Axmed graduated from school and got a job at a company. Arday-gii/#-ga wuxuu ka shaqayay hayad. student- GII/- GA FOC =3 S at working company ‘The (former) student is working at a company.’ [05/11/2016] The choice of - KII over - KA is context dependent and it is sensitive to a temporal contrast between the two, which may give rise to a change of state interpretation of the target sentence. The data indicates that this is a cancellable implicature reminiscent of the use of past tense in stative sentences (see (15)). 4.4. The (in)visibility contrast of Somali definite determiners Lecarme (2008, 2012), based on data like the one in (26), suggests that Somali definite determiners are sensitive to visibility from the perspective of the speaker: if the referent is absent from the immediate visual context, then - KII is used, whereas - KA would be inappropriate. Lecarme (2008) also notes that the contrast is not optional: the use of - KII is not felicitous if the referent is visible. (26) a. Context: The speaker’s pen is in the drawer, invisible to the speaker. Qalin-kay-gii/*-gu meeyey? pen-M . POSS .1 S-KII /*- KA . TOP Q.is.M . S ‘Where is my pen?’ b. Context: There are multiple pens on the desk. Qalin-kay-gu waa kee? pen-M . POSS .1 S - KA . TOP DECL Q. M ‘Which one is my pen?’ (Lecarme, 2008: ex. (20), p.212) This contrast was also replicated in our elicitations: sun- KII in (27b) may only refer to an ‘invisible,’ eclipsed sun, while sun- KA in (27a) necessarily refers to a visible sun. (27) a. Shalay waxa=an firinayay cadceed-da yesterday FOC =1 S look.PAST sun-KA ‘Yesterday I looked at the sun’ ≈ visible b. Shalay waxa=an firinayay cadceed-dii yesterday FOC =1 S look.PAST sun-KII ‘Yesterday I looked at the sun’ ≈ eclipsed [01/30/2016] However, the (in)visibility contrast is not always observed. In the scenario in (28), the sun is in plain sight, yet the use of - KII is licensed. This is unexpected under Lecarme’s (2008; 2012) account. Contrary with the generalization that - KII marked NPs are invisibile entities, our data illustrates that invisibility does not always pattern with the remote definite determiner. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 634 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners (28) Context: We are outside, taking a walk. The sun is shining. Cadce-dii/#-da cirkay joogta sun-KII/#- KA sky be.at.PRES ‘The sun is in the sky.’10 Another case where - KII refers to visible entities was that of (21), where the object in question, the jar, was in the immediate context of the informant (on the table, in front of the speaker). It seems that although invisibility readings do arise with - KII, they are not mandatory. Our account is sensitive to the ‘optionality’ of the invisibility and change of state readings. 5. Generalizations and proposal 5.1. Core generalizations Somali encodes definiteness by means of (at least) two determiners: - KA and - KII. The choice of one over the other may give rise to change of state or invisibility readings. There are contexts in which these contrasts obtain (such as (5) for the temporal contrast and (6) for visibility) and contexts, like (3), where the implicatures are either cancelled or not generated. For convenience, the core data referenced throughout the paper is repeated below. (3) Context: Axmed was working home all day. He decides to go out and sees the sun. Marku baxay wux-uu arkay qorrax{-ka/-kii}. when went out FOC =3 S saw sun- KA /- KII ‘When he went out, he saw the sun.’ [03/07/2016] (5) Context: The year is 2016 and Barack Obama is the president of the United States. a. Madaxweynaha wux-uu ku nool yahay guriga cad. president-KA FOC =3 S at lives house white ‘The president lives in the White House.’ ≈ Barack Obama b. Madaxweynihii wux-uu ku nool yahay Texas. president-KII FOC =3 S at lives Texas ‘The president lives in Texas’. ≈ George Bush (6) V ISIBILITY CONTRAST between - KA and - KII Wax-aan fiirinayaa cadceed-da/-dii. FOC =1 S watching sun- KA /- KII I’m watching the sun. a. Inference with - KA: The sun is visible. b. Inference with - KII: The sun is eclipsed. c. - KII is odd if the sun is visible; - KA is odd if the sun is eclipsed. [01/30/2016] [01/30/2016] 10 Surprisingly, sun- KA is reportedly odd in (28), but would be felicitous in a context where the sun was rising. This is a puzzle which we leave for further research. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 635 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners The data points out that the distribution of NP- KII, given in (29), is broad. It may refer to visible entities of which the NP property is true at topic time (TT), as in (3), it may refer to visible entities of which the NP property is not true at TT, but true at some salient time before TT, as in (5), where Bush is a former president, and, finally, as in (6), to invisible entities of which the NP property holds true at TT, but the entities are not visible in the topic context. (29) D ISTRIBUTION OF NP- KII i. entites x that are in the topic context and NP(x)=1 at topic time, ii. entities x that are in the topic context and NP(x)=1 at some time preceding topic time, NP(x)=0 at topic time, iii. entities x that are not visible in the topic context and NP(x)=1 at topic time. With respect to NP- KA, its distribution, given in (30), is more restricted. In all of the contexts examined in this paper, - KA marked nominals referred to visible entities which satisifed the NP property at topic time. (30) D ISTRIBUTION OF NP- KA entities x that are in the topic context and NP(x)=1 at topic time Comparing the generalizations in (29) and (30), we observe that the range of meanings NP- KA is associated with is a proper subset of the range of meanings NP- KII is associated with. Consequently, we propose that a competition based account between the two definite determiners can capture the - KA and - KII contrasts discussed in this paper. 5.2. Proposal The contrasts observed in the Somali nominal TAM data can be explained by a competition based account, where the change of state and invisibility readings associated with - KII are derived from scalar implicatures.11 The first component of our proposal is Altshuler and Schwarzschild’s (2013) analysis of past stative sentences like the ones below. (31) a. We love this puzzle. b. We loved this puzzle. The core observation regarding (31) is that (31b) gives rise to the (cancellable) cessation implicature that the group denoted by ‘we’ no longer loves the puzzle. Example (31a), on the other hand, does not give rise to a comparable inference. Altshuler and Schwarzschild (2013) argue that the cessation implicature in a stative English past tense sentence like (31b) can be derived by setting up a competition between the past tense and the present tense. This competition is 11 A similar account is found in Thomas (2014) for Mbyá Guaranı́, where the morpheme -kue does not semantically encode change of state or existence, as described by Tonhauser for Paraguayan Guaranı́. Thomas argues that the cessation inference triggered by -kue is a scalar implicature. The existence inference is derived from the interaction between this implicature and general interpretive properties of noun phrases. His account relies on the use of the exhaustivity operator (Fox, 2007), which, depending on the meaning of the alternatives of the proposition, following Magri (2009), negates the contextually relevant alternatives of the given proposition. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 636 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners based on the assumption that a stative sentence in the present asymmetrically entails its past tense counterpart. Gricean pragmatic reasoning then derives the result that uttering the latter, e.g., (31b), gives rise to the inference that the former, e.g., (31a), is false. The rationale behind this entailment pattern is this. If (31a) is true now, that is, if the puzzle is loved now, the puzzle was also loved a moment ago. The hypothesis that a stative in the present tense asymmetrically entails a stative in the past tense, labeled by Cable (2017) as the Open Interval Hypothesis, is formalized in (32). (32) O PEN I NTERVAL H YPOTHESIS : The run-time of a state is an open interval. If s is a state and t is a temporal instant contained within the runtime τ(s) of s (t ⊆ τ(s)), then ∃t 0 such that t 0 < t and t 0 is also contained within τ(s) (t’ ⊆ τ(s)). In other words, if a tenseless stative clause is true at a moment m, it is also true at a moment that precedes m. Consequently, a present stative sentence entails both that the proposition is true at the time of utterance (by the contribution of present tense), and that it was true at some moment before utterance time (by the contribution of (32)). A past stative sentence, however, does not entail its present tense counterpart. This asymmetric entailment relation ensures that the use of a stative sentence in the past tense will give rise to the scalar implicature that its present tense counterpart is false. This, of course, unless independent factors block the implicature.12 This account can be extended to explain the contrasts between the use of Somali - KII and - KA, if we make the assumption that a sentence with a - KA marked nominal asymmetrically entails its counterpart with a - KII marked nominal. (That is, if we assume that the former determiner patterns like the present tense, and the latter, like the past tense.) Hence, we propose that the difference between - KII and - KA resides in a temporal presupposition encoded by - KII. Our analysis assumes that NPs are of type < e, it >. They denote functions from entities, to functions from times to truth values. We also extend the Open Interval Hypothesis in (32) to NP properties. The temporal interval tNP , the time at which the NP is evaluated (Tonhauser, 2007; Thomas, 2014) and represented in (33a), picks out topic time. Examples (33a) and (33b) recapitulate the structural assumptions for Somali DPs and the denotation of NPs. The lexical entries in (33c) and (33d) give our proposed denotations for the determiners - KA and - KII, both functions from NP denotations (< e, it >) to functions from times to generalized quantifiers. (33) a. b. c. d. 12 In [ [ NP D0 ] tNP ]DP where D0 is - KII or - KA JNPK = λ xe λti .P(t)(x) JKAKw,t,g = λ P<e,it> λti λ Q<e,t> : ∃!x[x ∈ C&P(t)(x)].Q(ιx[P(t)(x)]) JKIIKw,t,g = λ P<e,it> λti λ Q<e,t> : ∃t 0 ∃!x[t 0 < t&x ∈ C&P(t 0 )(x)]. ∃t 0 [t 0 < t&Q(ιx[P(t 0 )(x)])] Altshuler and Schwarzschild (2013) and Cable (2017) the cessation implicature arises only in the absence of a salient past topic time. (i) a. We love this puzzle. b. We loved this puzzle (yesterday). c. We loved this puzzle as soon as we started working on it. A cessation implicature is generated in (ib), but not in (ic). We predict the same to be true in Somali. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 637 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners According to the semantics in (33c) and (33d), both - KA and - KII introduce the familiar definiteness presupposition, that there is a unique x in the context such that the property denoted by the NP holds of x. For - KA, the property must hold at topic time. The determiner - KII, on the other hand, encodes the ‘precedence property,’ that there is a time t 0 (strictly) prior to topic time such that the property denoted by the NP holds of x at t 0 . Applying the Open Interval Hypothesis, if a proposition containing a - KA marked nominal is true at topic time, then it must also have been true at some interval preceding topic time. The fact that a proposition with a - KII marked nominal holds at topic time does not entail that its - KA marked counterpart holds at topic time. Consequently, a sentence with a - KA marked nominal asymmetrically entails its counterpart with a - KII marked one. We propose that the cessation implicature which arises in (24b), repeated below, is derived as in (34). We predict that this reasoning can be applied to any non-permanent property (event nominals, nouns denoting temporally bounded social functions like president or student). (24) a. Bandhig-ga ma=ad daawatay? exhibition-KA Q=2 S see.2 S . PAST ‘Have you seen the exhibition?’ b. Bandhig-gii ma=ad daawatay? exhibition-KII Q=2 S see.2 S . PAST ‘Have you seen the exhibition?’ → open at UT closed at UT [09/27/2015] The pragmatic reasoning is based on computing the minimally different alternatives of a given sentence. In this case, the - KA sentence is a minimally different alternative of the - KII sentence. Given that, according to the hypothesis in (32), (24a) asymmetrically entails (24b), asserting the weaker alternative (24b) triggers the implicature that the stronger (24a) is false. (34) P RAGMATIC R EASONING FOR (24 B ): CESSATION IMPLICATURE a. The speaker asserts (24b). b. The utterances in (24a) and (24b) are identical with the exception of the D0 node. c. exhibition- KA corresponds to the unique x which is an exhibition in context C at UT. d. exhibition-KII corresponds to the unique x which was an exhibition in context C at a time t 0 , prior to UT. e. The utterance in (24a) is stronger than (24b); (24a) entails (24b) according to the Open Interval Hypothesis. If x is an exhibition at UT, it must have also been an exhibition at some point in time before UT. f. If the speaker uttered (24b), then the stronger alternative with - KA, that x is an exhibition at UT, is false. g. Therfore, x is not an exhibition at UT. h. World knowledge: for x to stop being an exhibition, the exhibition must have closed. We argue that the (in)visibility contrast is also a derivable scalar implicature. The example in (35) is repeated from (27), where the use of - KII implies that the sun is eclipsed. We predict that the same reasoning can be applied to any noun which expresses a permanent property.13 13 Our attempts to obtain data regarding invisible non-permanent properties have been unsuccessful. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 638 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners (35) a. Shalay waxa=an firinayay cadcee-da yesterday FOC =1 S look.PAST sun-KA ‘Yesterday I looked at the sun’ → visible b. Shalay waxa=an firinayay cadcee-dii yesterday FOC =1 S look.PAST sun-KII ‘Yesterday I looked at the sun’ eclipsed [01/30/2016] Once again, minimally different alternatives are computed. Based on the hypothesis in (32), (35a) asymmetrically entails (35b), and the use of the weaker alternative implicates that the stronger alternative is false. (36) P RAGMATIC R EASONING FOR (35 B ): INVISIBILITY IMPLICATURE a. The speaker asserts (35b). b. The utterances in (35a) and (35b) are identical with the exception of the D0 node. c. sun-KA corresponds to the unique x which is a sun in context C at topic time. d. sun-KII corresponds to the unique x which was a sun in context C at a time t 0 , prior to topic time. e. The utterance in (35a) is stronger than the utterance in (35b); (35a) entails (35b) according to the Open Interval Hypothesis. If x is a sun at topic time, it must have also been a sun at some point in time before topic time. f. If the speaker uttered (35b), then the stronger alternative with - KA, that x is a sun at topic time, is false. g. Therefore, x is not a sun at topic time. h. World knowledge: the sun is permanent and unique, hence, x cannot stop being a sun. i. x is not a sun at topic time in C, but x is always a sun. j. The sun is invisible at topic time. 6. Concluding remarks This paper advances the understanding of the semantics of Somali definite determiners - KA and - KII, and compares them to nominal temporal markers crosslinguistically. The comparison between Somali and Guaranı́ led to the conclusion that the Somali remote definite determiner - KII does not encode the change of state or the existence properties attested in Guaranı́ NTMs (Tonhauser, 2007). Our data point in the direction of a temporal contrast between the two definite determiners in Somali, and support the conclusion that the change of state and invisibility readings are, in fact, cancellable implicatures. We proposed that this contrast is semantically encoded by means of an extra temporal presupposition in the case of - KII. Assuming our proposed semantics and the Open Interval Hypothesis (Altshuler and Schwarzschild, 2013; Cable, 2017), - KA asymmetrically entails - KII. Under this analysis, the competition between minimally different alternatives is responsible for generating the desired implicatures. References Altshuler, D. and R. Schwarzschild (2013). Moment of change, cessation implicatures and simultaneous readings. In Proceedings of Sinn und Bedeutung 17, pp. 45–62. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 639 R. Ivan & D. Özyıldız The temporal presuppositions of Somali definite determiners Barwise, J. and R. Cooper (1988). Generalized quantifiers and natural language. In J. Kulas, J. H. Fetzer, and T. L. Rankin (Eds.), Philosophy, Language, and Artificial Intelligence: Resources for Processing Natural Language, pp. 241–301. Dordrecht: Springer. Cable, S. (2017). The implicatures of optional past tense in Tlingit and the implications for ‘Discontinuous Past’. Natural Language & Linguistic Theory 35, 635–681. Chang, H. Y. (2015). Nominal aspect in Tsou. In E. 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On the interpretability of tense on D and its consequences for Case Theory. Lingua 113(7), 659–696. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 641 642 On the lexical semantics of property concept nouns in Basaá1 Peter JENKS — University of California, Berkeley Andrew KOONTZ-GARBODEN — The University of Manchester Emmanuel-Moselly MAKASSO — ZAS, Berlin Abstract. This paper considers the link between lexical category and lexical semantics, examining variation in the category of property concept (PC) words (Dixon, 1982; Thompson, 1989)—words introducing the descriptive content in translational equivalents of sentences whose main predicate is an adjective in languages with large open classes of them. Francez and Koontz-Garboden (2015) conjecture that nominal PC words might only have mass-type denotation (conceived in the spirit of Link 1983), as diagnosed by possession in predication (e.g., Kim has beauty/#Kim is beauty). In Basaá, a class of PC nominals we call substance nouns trigger possession in predication, while a class we call adjectival nouns do not, thereby falsifying Francez and Koontz-Garboden’s conjecture. We offer several diagnostics that confirm the substance denotation for the substance nouns, and an individual-characterizing denotation for the adjectival nouns, speculating on whether such nouns have a degree semantics, and whether they represent a crosslinguistically rare category or not. Keywords: lexical categories; semantic variation; adjectives; property concepts; mass nouns 1. Introduction: The meaning of lexical categories The nature of the major lexical categories is among the most foundational yet poorly understood areas of grammar (Baker and Croft, 2017). Among the outstanding questions is whether there might be a link between lexical categories, which play a clear role in syntax and morphology, and the kind of meaning a word has. Although this is a question of longstanding interest, it is rarely discussed in the model-theoretic literature, save for the occasional suggestion that there might be something to say (see e.g., Bach et al. 1995; von Fintel and Matthewson 2008: 152–153; Kaufman 2009: 32; Koch and Matthewson 2009: 129). This paper is a modest contribution toward development of a program of study in this area. We focus our attention on what Francez and Koontz-Garboden (2015, 2017) call property concept sentences—sentences like (1) whose main predicate is an adjective or, as with (2), whose main predicate is not an adjective but is translated by a sentence whose main predicate is an adjective in languages like English. (1) Your hair is long. (2) ‘Oku loloa ho ‘ulu. IMP long your hair ‘Your hair is long.’ (Tongan; Koontz-Garboden 2007: 117) We call the word in property concept sentences responsible for introducing the descriptive content (long in (1), loloa in (2)) the property concept (PC) word. Thanks to Dixon’s (1982; 1 This work has been supported financially by Arts and Humanities Research Council Grant AH/H033645/1. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 643 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá 2004) work, it is now widely known that property concept words vary in lexical category (both internal to and across languages). In (1), for example, long is an adjective, while loloa in (2) is a verb (see Koontz-Garboden 2007). Property concept words also vary in their lexical semantics. Our focus is on a two-way distinction based on behavior in predication pointed to by Francez and Koontz-Garboden (2015). They observe that there are PC words that require possessive morphosyntax in predication (possessive-predicating PC words) and those that do not (non-possessive predicating PC words), as illustrated for Spanish in (3) and (4) respectively. (3) Juan tiene miedo. Juan has fear ‘Juan is scared.’ (4) Juan es alto. Juan is tall ‘Juan is tall.’ Following Francez and Koontz-Garboden (2015), we take this contrast as diagnostic of a difference in the kind of meaning the PC words in the two classes of construction have: (i) those like miedo ‘fear’, which characterize substances (substance-type meanings, following Link 1983), and (ii) those like alto ‘tall’, which characterize individuals—specifically, those individuals that have the substance (e.g., a contextually salient portion of height) in question. Concomitant with the difference in meaning of the PC words in (3) and (4), reflected in the morphosyntax of predication, is a difference in lexical category. While the substance-characterizing PC word in (3) is a noun, the individual-characterizing PC word in (4) is an adjective. Crossclassifying the adjective and noun categories with this two-way semantic typology leads to the picture in (5), with two gaps. (5) Nominal and adjectival property concept denotations Individual-characterizing Substance-characterizing Adjective English, Spanish adjectives ??? Noun ??? PC nominals like miedo ‘fear’ Francez and Koontz-Garboden (2017: Chapter 5) argue that the gap in substance-characterizing adjectives depicted in the top right corner of (5) is genuine and principled. Substance denotations are not meanings well suited to the main function of adjectives—to act as attributive modifiers. Assuming that adnominal modification selects a subset of the denotation of the modified noun, Francez and Koontz-Garboden argue that there are no nouns with meanings that substance-characterizing adjectives could non-trivially modify. In the sample of languages that Francez and Koontz-Garboden (2015) examined, there were no languages with non-possessive predicating PC nominals, giving rise to the conjecture that the gap on the bottom left of (5) was genuine. The implication of this gap would be that nominal property concept words were always substance-characterizing, and never individualcharacterizing. Were this conjecture true, it would have implications for the semantics of nounhood. Yet in this paper we show that in Basaá (Bantu; Cameroon), PC nouns can have both substance-characterizing and individual-characterizing denotations. The conclusion is that nominal property concept words do not uniformly have substance-characterizing denotations. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 644 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá We begin with background on the semantic typology of property concept words, discussing the two kinds of meanings that these words can have. We then turn to the Basaá case study, in order to determine (i) the category of Basaá PC words, and (ii) their lexical semantics. We start by giving three arguments for the nominal categoriality of the relevant class of PC words. Drawing on a range of novel diagnostics and by contrasting these PC words with genuine substance-characterizing ones, we then show that rather than characterizing portions of substance, they instead characterize sets of individuals. We conclude with remarks on what exactly the individual-characterizing nature of the relevant class of Basaá PC nominals is, and also suggest that a comparable class of nouns exists in English. We close with discussion of the consequences of our observations for the understanding of the link between lexical category and lexical semantics. 2. Possessive-predicating PC nominals and their substance denotations Francez and Koontz-Garboden (2015) observe that nominal property concept words entail possessive morphosyntax for their sample of languages. Although we will argue below that there is a class of PC words in Basaá that falsify this generalization, there is also a class of PC words in the language that conforms with it. We call this class of words substance nouns (SNs), and they include mbOm ‘luck’; nguy ‘strength’; másÓdá ‘luck’; NÉm ‘courage’; hêmlE ‘hope/faith’. That such words are nominal in Basaá is uncontroversial, particularly given the fact that they are lexically associated with a noun class rather than agreeing with other nouns, fail to attributively modify nominals, can be used as the arguments of verbs, and have mass noun properties. SNs do not behave like common nouns in predicational contexts, as expected given Francez and Koontz-Garboden’s (2015) observations. Predication of a normal Basaá count noun (details of which are discussed further in §3) is copular, as shown in (6). (6) a ye m-alêt. 1. AGR COP 1-teacher ‘He is a teacher.’ (Hyman et al. 2012:8) Unlike with normal count nouns, attribution of a SN to an individual invokes the morphosyntax of possession. That is, the same morphosyntax—the verb gweé ‘have’—which is required to attribute the possession of some entity to another, whether inalienably (7a) or alienably (7b), is used to attribute the substance described by a SN to an individual, as shown in (8).2 2 In (i) Basaá, ‘have’ is morphologically complex, literally ‘be-with’, and has the paradigm in (i). Tense paradigm for áá-nâ ‘have’ Infin áánâ Past3 ááná Past2 áéena Past1 bákná Pres gweé Fut1 ḿ!ááná Fut2 gá!ááná Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde Fut3 aááná 645 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso (7) a. b. On the lexical semantics of property concept nouns in Basaá têble íní í gwé! é ma-koo mánâ AUG 7.table DEM AGR have 4-feet four ‘This table has four feet.’ Kim a gweé ! n-dáp Kim AGR has 9-house ‘Kim has a house.’ í (8) a gweé ma-sÓdá 1.AGR have 6-luck ‘(S)he is lucky.’ Drawing on the mereological approach to mass terms in Link (1983), Francez and KoontzGarboden (2015, 2017) treat the denotations of possessive-predicating PC words as related to the denotations of familiar substance mass terms such as gold and sand.3 For example, Nguy ‘strength’ has such a denotation, as shown in (9), where p is a variable over portions of abstract matter, and strength0 describes the property which characterizes all portions of strength. (9) JNguyK = λ p[strength0 (p)] Evidence that SNs have a mass-type semantics is offered in §4.1. A substance-characterizing denotation accounts for the possessive morphosyntax used with these PC nominals. Substances, as Francez and Koontz-Garboden discuss, cannot be predicated of individuals using a copula because substances are sets of abstract portions, not sets of individuals. To the extent that any meaning is generated in ordinary copular predication with substance-characterizing words, it is an odd or metaphorical one, a fact illustrated by (10).4 (10) a. b. Kim is strength. 6= Kim is strong. Kim has strength. = Kim is strong. Our hypothesis, following the treatment of similar examples in other languages in Francez and Koontz-Garboden (2015), is that the use of possessive morphosyntax with such PC nominals in predication is a direct reflection of their semantics. The idea is that because a substancecharacterizing PC word does not characterize a set of individuals, a relation has to be introduced to relate substances to individuals in order to attribute the substance to an individual. Francez and Koontz-Garboden call the general idea that a substance can be related to an individual with the semantics of possession substance possession, defining it as in (11). (11) Substance possession: For any individual a and substance P, a has P iff ∃p[P(p) & π(a, p)] In summary, the morphosyntax of possession with nominal PC terms arises due to the underlying semantics of substance possession. 3 See Koontz-Garboden and Francez (2010) for an inferior analysis in terms of Chierchia and Turner’s (1988) property theory. 4 In fact, in Basaá there is a group of ‘have’-predicating PC nominals which allows ‘be’-predication, but only in emphatic contexts. We take these cases to be direct ‘be’-predication of a SN, equivalent to English expressions like Kim IS beauty (incarnate), where the substance is predicated directly of the subject, meaning that Kim is literally a portion of beauty. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 646 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá No such possessive semantics is at play with property concept sentences showing normal predicative morphosyntax, e.g., those with adjectives. The precise semantics for the adjectival predicates in such sentences remains an open question (see e.g., Cresswell 1977; Klein 1980; von Stechow 1984; Heim 1985; Kennedy 1997; Barker 2002; Rett 2014; Menon and Pancheva 2014; Wellwood 2015; Burnett 2016, among others). For our purposes, it does not matter what the correct theory is. What matters is simply that adjectives do not denote substances. This is the case on all theories of adjectives (and is a point explicitly argued by Francez and KoontzGarboden 2017: Chapter 5). In one way or another, the adjectival word comes to characterize a set of individuals in some context, which can enter into ordinary processes of non-verbal predication. The headline finding of this paper is that contrary to Francez and Koontz-Garboden’s conjecture, nominal PC words can have a meaning of this type, whatever its precise formal details might be.5 In order to show this, we now make the case for the nominal status of ANs, and then show that they unequivocally have individual-characterizing meanings. 3. The lexical category of Basaá ANs The class of PC words in Basaá of primary interest, is what Hyman et al. (2013) call nominal adjectives and which we call here adjectival nouns (ANs), in view of the fact that they are nouns, following Hyman (2003).6 ANs constitute a large and open class of PC words in Basaá, with at least 100 members. Below we demonstrate that while ANs form a class of PC words that are demonstrably nominal in lexical category, they are not substance-characterizing, but rather characterize sets of individuals, falsifying the conjecture discussed in §1. In this section we argue for their nominal status, turning to their meaning in the section that follows. Like most Niger-Congo languages, Basaá nominals are distributed into a rich set of noun classes. Which noun class a particular noun belongs to can be determined based on the initial prefix of the noun as well as subject agreement and DP-internal concord. Members of each of these classes are provided in Table 1, drawn from Hyman (2003: 263) with some simplifications in the representation of prefixal morphology. The numerals in the left column refer to the numbering system for Bantu noun classes standard since Meinhof (1906). These numerals label each combination of number and gender a separate class. Hyman (2003) discusses the phonological and morphological traits of the prefixal morphology in detail, and also provides detailed paradigms for DP-internal concord and subject agreement. The example below illustrates both DP-internal concord and subject agreement—the verb and DP internal modifiers agree with the head noun nuní ‘bird’ in noun class. (12) dí-nuní dí-tân díí dí ń! tóp hémbí 13-bird 13.five 13.those 13.SBJ sing 19.song ‘Those five birds are singing a song.’ 5 It is possible, as suggested by Beck et al. (2010); Bochnak (2013, 2015) that there might be variation in the kinds of individual-characterizing meanings that there are. Quite how Basaá ANs fit into this picture is an interesting question for future research. 6 Our ANs are not to be confused with Hyman et al.’s adjectival nouns, which correspond to our substance nouns (SNs). Terminologically speaking, our adjectival nouns are their nominal adjectives, and our substance nouns are their adjectival nouns. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 647 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá Table 1: Noun classes in Basaá Class Singular Plural 1/2 3/4 3a/6 5/6 7/8 9/10 9/6 19/13 mudaá m-pék nyO li-pan tÓN pÉn kíN hi-tám áodaá mim-pék ma-nyO ma-pan bi-tÓN pÉn ma-kíN di-tám Singular Plural ‘woman’ ‘bag’ ‘mouth’ ‘forest’ ‘horn’ ‘arrow’ ‘neck, voice’ ‘kidney’ mut n-tómbá wOÓ j-alá y-oó N-gwÓ n-dáp hi-nuní áot min-tómbá mOÓ m-alá gw-oó N-gwÓ man-dáp di-nuní ‘man’ ‘sheep’ ‘hand’ ‘crab’ ‘yam’ ‘dog’ ‘house’ ‘bird’ Table 2: NAs are found in all noun classes (Hyman et al., 2013: 2) Class Num. NA Gloss Class Num. NA Gloss 1 3 5 7 9 19 sing. sing. sing. sing. sing. sing. n-lám n-laNgá li-múgÊ lÓNgÊ mbóm hi-peda ‘beautiful (sg.)’ ‘black (sg.)’ ‘taciturn (sg.)’ ‘good (sg.)’ ‘big (sg.)’ ‘small (sg.)’ 2 4 6 8 10 13 pl. pl. pl. pl. pl. pl. áa-lám min-laNgá ma-múgÊ bi-lÓNgÊ mbóm di-peda ‘beautiful (pl.)’ ‘black (pl.)’ ‘taciturn (pl.)’ ‘good (pl.)’ ‘big (pl.)’ ‘small (pl.)’ In example (12), the noun dí-nuní ‘birds’ controls agreement on the numeral, demonstrative, and the verbal prefix. We take lexically determined membership in one of the noun classes in Table 1 and the ability to control agreement to be definitional criteria for nounhood in Basaá. All earlier descriptions, including Dimmendaal (1988); Hyman (2003); Hyman et al. (2013), agree that the PCs we are calling ANs are nouns. Evidence for their nominal categorization comes from the fact that they have lexically determined inherent noun class (from Hyman et al. 2013), as described above. This is evidenced by the fact that ANs are found in all noun classes, as illustrated by Table 2. Further evidence for their nominal status comes from the fact that when they occur DP-internally, ANs subordinate the noun they modify via a connective particle, reminiscent of English of, and control agreement on higher adnominal modifiers (13). (13) a. b. lí-múgÉ ! lí hí-nuní líí lí ń! tóp hémbí 5-quiet 5.CON 19-bird 5-that 5.SBJ sing 19.song ‘That quiet bird is singing.’ má-múgÉ ! má dí-nuní máá má ń! tóp hémbí 6-quiet 6.CON 13-birds 6-that 6.SBJ sing 19.song ‘Those quiet birds are singing.’ The connective particle itself also agrees with the AN, as shown by Table 3; note that the connective which appears in this construction can be purely tonal, a low tone in class 1 and 9, and a high tone in class 3 and 7 (Hyman et al., 2013: ex. (10)). This is true generally of other Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 648 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá Table 3: Agreement of the connective with ANs Cl AN 1 3 5 7 9 19 n-lám n-laNgá li-múgÊ lÓNgÊ mbóm hi-peda of ! lí hí N hi-nuní hí-nuní hí-nuní hí-nuní hi-nuní hí-nuní ‘beautiful bird’ ‘black bird’ ‘quiet bird’ ‘good bird’ ‘big bird’ ‘small bird’ Cl AN of N 2 4 6 8 10 13 áa-lám min-laNgá ma-múgÊ bi-lÓNgÉ mbóm di-peda áá mí má ! bí í dí dí-nuní dí-nuní dí-nuní dí-nuní dí-nuní dí-nuní ‘beautiful birds’ ‘black birds’ ‘quiet birds’ ‘good birds’ ‘big birds’ ‘small birds’ DP internal modification where the modifier is nominal, as with possessive DPs and noun-noun compounds (Hyman et al., 2013). One important point to note about the construction illustrated in Table 3 is that the AN and N always agree in number, even if they occur in different genders or noun classes. Further evidence for the nominality of ANs comes from the existence of a separate class of true adjectival PCs (adjectives) in Basaá. Such genuine adjective is illustrated in (14), where the adjective kÉNı́ ‘big’ does not control agreement on the noun or subject auxiliary, but transparently reflects the noun class of the noun it modifies. Further, it modifies the head noun without a connective, unlike nominal modifiers (with AN or not), described previously. (14) hí-nuní hi-kÉNı́ híí hí ń! tóp hémbí 19-bird 19-big 19-that 19.SBJ sing 19.song ‘That big bird is singing.’ The number of adjectives in Basaá is relatively small, so Basaá is therefore like many languages of the world in having a closed adjective class (Hyman et al., 2013). Crucially for our purposes, we will see below that true adjectives and ANs cannot be distinguished semantically, so they are only distinguished by their syntactic category, revealed in their morphosyntactic behavior. 4. The lexical semantics of Basaá ANs Having demonstrated the nominality of ANs, we now examine their semantics. Given the discussion above, an obvious starting point is asking how they behave in predication. Here, as already mentioned, we find behavior different from that observed with nominal PCs elsewhere, both from SNs in Basaá, discussed above, and the nominal PCs from other languages discussed in Francez and Koontz-Garboden (2015). Basaá has a copula áá which occurs as the main verb in sentences with a variety of non-verbal predicates.7 This copula occurs with predicate nominals (15a), locatives (15b), and genuine 7 The (i) verb áá ‘be’ is characterized by extensive suppletion, as shown in (i). Tense paradigm for áá ‘be’ Infin Past3 Past2 Past1 áá áá áée bák Pres ye Fut1 ḿ! áá Fut2 gá! áá Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde Fut3 aáá 649 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá adjectives (15c), along with, crucial for our purposes, ANs (15d): (15) a. b. c. d. Victor a ye m-alêt Victor 1. SUB be 1-teacher ‘Victor is a teacher.’ hí-nuní híí hí yé í kedé ! É 19-bird 19.that 19. SUB be LOC inside tree ‘That bird is inside the tree.’ (e.g. in a hole) hí-nuní híí hí yé hi-kÉNı́ 19-bird 19.that 19. SUB be 19-big ‘That bird is big.’ hí-nuní híí hí yé li-mugÊ 19-bird 19.that 19. SUB be 5-quiet ‘That bird is quiet.’ (predicate nominal) (locative) (adjective) (adjectival noun) We assume that copular predication in contexts like those above is a transparent indication that the following predicate characterizes a set of ordinary individuals (cf. Partee 2002). Thus, the fact that adjectives and ANs are predicated with a copula is a transparent indication that adjectives and AN denote sets of ordinary individuals, like nominal and locative predicates. Below we present three additional arguments for this claim. 4.1. Atomicity In this section we illustrate that ANs and SNs are distinct in terms of atomicity: while ANs have atomic denotations, and are hence count nouns, SNs have non-atomic denotations and behave like mass nouns. Mass-like denotations are expected for SN given their substancebased semantics described in §2. The simplest evidence that ANs are count nouns while SNs are mass nouns comes from the number invariance of SNs. In §3, it was shown that ANs reflect the number of the noun they modify in the AN-of-N construction (Table 3). Thus, a distinction exists between nláám ‘beautiful’ and áaláám ‘beautiful’ depending on whether the noun is singular or plural in (13). By contrast, SNs do not inflect for number at all. This can be seen in both adnominal modifying and predicative environments. Beginning with attributive environments, the data in (16) demonstrate that like ANs, nominal modification with SNs requires a connective. But while ANs precede the connective, controlling agreement on higher modifiers (13), SNs follow the connective, and the modified noun controls agreement. What is crucial for our current purposes is that unlike ANs, SNs do not reflect the number of the noun which they modify. This is illustrated by (16), where the SN Ńgûy ‘strength’ is invariant regardless of whether it is modifying a singular or plural noun: (16) a. hi-nuní hí Ngûy hí ń! tóp hémbí 19-bird 19.CON 9.strength 19.SBJ sing 19.song ‘The strong bird is singing’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 650 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá Table 4: Substance nouns (SNs) in Basaá b. Class N of SN 1 3 4 5 6 7 8 9 hi-nuní hi-nuní hi-nuní hi-nuní hi-nuní hi-nuní hi-nuní hi-nuní hí hí hí hí hí hí hí hí máaNgÉ ń-saN mí-yaó lí-han má-sÓdá ságlá bí-sagda Ngûy ‘baby bird’ (bird of child) ‘peaceful bird’ (bird of peace) ‘likable bird’ (bird of charm) ‘mean bird’ (bird of meanness) ‘lucky bird’ (bird of chance) ‘annoying bird’ (bird of annoyance) ‘unsteady bird’ (bird of confusion) ‘strong bird’ (bird of strength) di-nuní dí Ngûy dí ń! tóp hémbí 13-birds 13.CON 9.strength 13.SBJ sing 19.song ‘The strong birds are singing’ Furthermore, while each lexical SN can be morphologically singular or plural, each individual SN is number-invariant, occurring in either a singular or plural noun class, as shown by the data in Table 4. Thus, the singular class 3 ǹsaN ‘peace’ has no class 4 plural counterpart *mı́saN. Likewise, the plural class 4 míyaó ‘charm’ has no singular class 3 counterpart *nyaó. The difference between ANs and SNs in the ability to mark number is thus directly manifested in DP-internal environments: only ANs reflect the number of the noun they modify. The number invariance of SNs also contrasts with ANs in predicational environments. Like adjectives and predicate nominals, ANs typically reflect the number of the subject: (17) dí-nuní díí dí yé ma-múgÊ 13-bird 13.that 13. SUB be 6-quiet ‘Those birds are quiet.’ The subject in (17) is plural, thereby triggering class 6 on the AN in this position.8 In contrast, SNs do not exhibit number agreement with the subject of ‘have’ in predicational environments, as shown by (18). (18) a. b. a gweé *n/mi-yáo 1.AGR have 3(SG)/4(PL)-charm ‘(S)he is likable.’ áá gwé! é *n/mi-yáo 2.AGR have 3(SG)/4(PL)-charm ‘They are likable.’ 8 Number agreement in the copular construction is not obligatory when the subject is plural. As discussed in Hyman et al. (2013), with predicates that allow collective readings, singular predicates overtly indicate a collective reading while plural predicates occur with distributive readings. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 651 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá Thus, a corollary of the general number-invariance of SNs is their inability to agree with nouns in number in both attributive and predicational environments. These diagnostics we believe are tied to atomicity—the question whether there are atomic parts in the denotation of the noun, as is the case with count nouns, or not, as is the case with mass nouns (Link, 1983). Consistent with our claim that SNs are substance-characterizing, then, these facts point to a non-atomic denotation for SNs. ANs, consistent with our claim that they characterize sets of (atomic) individuals, behave in the opposite manner. A more direct diagnostic for this distinction comes from numerals: while numerals can combine with ANs, they cannot with SNs, as shown by (19a,b) respectively.9 (19) ma-múgÉ ! má dí-nuní mátân 6-quiet 6.6. CON 13-bird 6.five ’five quiet birds’ b. *miyáo (míntân) mí hí-nuní (míntân) 4-charm (4.five) 4. CON 13-bird (4.five) (intended: *‘five charms of the bird’) a. In (19a), mátân ‘five’ agrees with the AN ma-múgÉ ‘quiet’, and as such the AN must preserve or share the count-status of the head noun it modifies. In contrast, (19b) illustrates that SNs cannot combine with numerals when they serve as the head of the noun phrase. As countability is a standard diagnostic for atomicity (and thereby count versus mass status, e.g. Rothstein 2010), we take the distribution of numerals to confirm that ANs have atomic denotations (and are count nouns) while SNs have non-atomic ones (and are mass), consistent with the claim that the former have individual-characterizing denotations, while the latter denote substances. 4.2. Weak quantifiers Additional circumstantial evidence for the individual-characterizing denotation for ANs comes from the syntactic behavior of various quantifiers in Basaá. Landman (2003) argues that while strong determiners are generalized quantifiers, i.e. interpreted as relations between sets (Montague 1973; Barwise and Cooper 1981) indefinite determiners have adjectival meanings, and are functions from nominal denotations to a subset of the nominal denotation with restricted cardinality. For example, while birds denotes the set of any plurality of birds, whether two or ten thousand, several birds denotes a much more restricted set of bird pluralities—namely those comprised of say, 3-10 atomic bird individuals. It turns out that in Basaá weak quantifiers, by contrast with strong quantifiers, pattern like ANs in several ways. This behavior, we argue, makes sense if weak quantifiers and ANs both characterize sets of individuals. The former is consistent with Landman’s claims, the latter with our claim about the semantic nature of ANs. 9 That the numeral is modifying the AN in (19a) and the SN in (19b) is shown by agreement—the numeral agrees in noun class with the AN in (19a) and the SN in (19b), as is typical for adnominal numeral modifiers in the language generally. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 652 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá NP-internally, weak quantifiers in Basaá pattern just like ANs. This is demonstrated by the data in (20), which shown that such quantifiers head the NPs they determine, triggering use of a linker particle the noun class agreement of which they control. (20) a. b. c. d. Ngandak í dínuní í yé mınlaNgá 3.many 3 19.birds 3. AGR be 4.black ‘Many birds are black.’ ndek dínuní í yé mınlaNgá 3.few (3)-19.birds 3. AGR be 4.black ‘Few birds are black.’ joga lí dínuní lí yé mınlaNgá 5.several 5 19.birds 5. AGR be 4.black ‘Several birds are black.’ pEs í dínuní í yé mınlaNgá 3.half 3 19.birds 3. AGR be 4.black ‘Half the birds are black.’ Unlike weak quantifiers, strong quantifiers do not pattern as ANs. The actual behavior of strong quantifiers is heterogeneous, as evidenced by the data in (21), where hígií ‘every’ appears prenominally and cÓdı́só ‘all’ appears postnominally. (21) a. b. hígií hinuní hí yé nlaNgá 19.every 19.bird 19.AGR be 3.black ‘Every bird is black.’ dínuní cÓdı́só ! dí yé mınlaNgá AUG -13.birds all 13.AGR be 4.black ‘All birds are black.’ In both cases, however, the quantifiers behave differently from the weak quantifiers in (20), in that neither of them heads the NP they determine or controls agreement. This is shown in (21a) by the lack of a linker particle and by the fact that hígií ‘every’ agrees with the head noun ‘bird’. The quantifier cÓdı́sô ‘all’ in (21b) simply does not agree, nor is there any question of it being in head position, as it is postnominal. This contrast in the behavior of weak and strong quantifiers makes sense if weak quantifiers and ANs are in the same semantic class (at some level), and if this class is individual-characterizing (as Landman independently argues for most weak quantifiers), the idea being that the head noun (whether AN or weak quantifier) composes with the post-linker noun through some form of predicate modification (as argued for weak quantifiers by Landman 2003: 2). We have already seen that ANs are copular-predicating, as expected for words that characterize sets of individuals. The same is expected of weak quantifiers on Landman’s theory. This prediction is borne out, as shown by (22).10 10 There are two exceptions to this, Ngim ‘some’ and tO ‘no’. In the case of quantifiers like the latter, Landman (2003: 12) argues for a special treatment on independent grounds. An explanation for the behavior of Basaá Ngim ‘some’ requires further investigation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 653 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso (22) a. b. c. d. On the lexical semantics of property concept nouns in Basaá dínuní tíní dí yé Ngandak birds these AGR be a.lot ‘These birds are many.’ dínuní tíní dí yé ndek birds these AGR be few ‘These birds are few.’ dínuní tíní dí yé joga birds these AGR be several ‘These birds are several.’ dínuní tíní dí yé pEs birds these AGR be half ‘These birds are half.’ Further, as expected if strong quantifiers are not individual characterizing, but rather have some other kind of non-predicative denotation (for example relations between sets, as Landman argues), then we expect strong quantifiers to be unacceptable in predicative environments, unlike weak quantifiers. This contrast is borne out, as evidenced by the data in (23). (23) a. *dínuní tíní dí yé hígií birds these AGR be every *‘These birds are every.’ b. *dínuní tíní dí yé cÓdı́sô birds these AGR be all *‘These birds are all.’ To reiterate, the basic observation is that weak quantifiers and ANs pattern together in some key ways. This behavior makes sense if they have the same kind of denotation, and if that denotation is an individual-characterizing one, as Landman argues for weak quantifiers on independent grounds, and as other diagnostics in this paper independently point to for ANs. 4.3. Pronominal anaphora A final argument for our claim that ANs characterize individuals comes from pronominal anaphora. The observation is simply that there is a predicate anaphor in Basaá that is restricted in the types of predicates it can be anaphoric to. Specifically, the particle in question is wEÉ, and it can be anaphoric to SNs (24), but not to ANs (25), adjectives (26), or common nouns (27). (24) (26) líhat, wEÉ Paul rich WEE Paul ‘Rich, that’s Paul.’ #NkÉNí, wEÉ Paul important WEE Paul ‘Important, that’s Paul.’ (25) (27) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde #nlám, wEÉ Paul pretty WEE Paul ‘Pretty, that’s Paul.’ #malêt wEÉ Paul. teacher WEE Paul ‘Teacher, that’s Paul.’ 654 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá This behavior makes sense if wEÉ is a sortally-sensitive anaphor, which can refer back to substance-characterizing denotations but not individual-characterizing ones.11 The key fact for the purposes of the discussion here is that ANs cannot be the antecedent of wEÉ, by contrast with SNs, consistent with the former’s lacking a substance-characterizing denotation and the latter’s having such a denotation. 5. Some questions The facts discussed above demonstrate that ANs do not have a substance-characterizing denotation, and have generally concluded that they are individual-characterizing. What they don’t answer are (i) what precise denotation ANs have, and (ii) whether Basaá is genuinely special in having property concept nominals with this kind of denotation. Beginning with the first question, the meaning of Basaá ANs is a difficult one because there is a fair amount of controversy about what exactly the denotation of adjectives is, with some researchers additionally claiming that adjectival meanings differ across languages (Beck et al., 2010; Bochnak, 2013; Bowler, 2016)). Three types of theory of adjective denotation are laid out in (28): (28) Three theories of adjectives a. Adjectives denote contextually sensitive sets of individuals (e.g., Kamp 1975; Klein 1980; van Rooij 2011). b. Adjectives denote relations between individuals and a degree argument, with the degree to which the adjective holds specified either morphosyntactically or in context (e.g., Cresswell 1977; von Stechow 1984; Kennedy 1999). c. Adjectives denote what have + substance nouns denote (see Menon and Pancheva 2014). If Bochnak’s (2013; 2015) analysis and diagnostics are taken at face-value, we can exclude (28a) from consideration for Basaá ANs, on the grounds that ANs behave like they have a degree (or alternatively, portion) argument—they can be used with measure phrases (29a) and in explicit comparatives (29b), for example. (29) a. b. N-koo ú yé n-tendéé méda mí-tân 3-rope AGR be 4-long 4.meter 4-five ‘The rope is five meters long.’ hí.ní hi-nuní hi yé hi-láám lÉl hí-í. 19-this 19-bird 19.AGR is 19-nice surpass 19-that.one ‘This bird is nicer than that one.’ 11 The proposed contrast is similar in spirit (if different in details) to the ability of it and that in English to have predicative (but not individual-denoting) antecedents, as discussed e.g., by Mikkelsen (2005), and shown by the data in (i). (i) a. b. The tallest girl in the class, that/it’s Molly. The tallest girl in the class, she/*it/*that’s Swedish. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde (Mikkelsen, 2005: 64) 655 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá The same points could be made for true adjectives in Basaá, illustrating more clearly that ANs and adjectives are semantically similar. In addition, Bassaá has a gradable modifier that can be used with ANs, Ngandak:12 (30) di-nuní dí yé min-laNgá Ngandak. 13-birds 13.AGR COP 4-black very ‘The birds are very black.’ While the same modifier can be used with adjectives (31), it can also be used SNs (32), a fact which might suggest that ANs and the have+SN constituent should have the same type of denotation in order to give a uniform denotation to Ngandak. (31) (32) hí-nuní híí hí yé hi-kÉNı́ Ngandak. 19-bird 19.that 19. SUB be 19-big very ‘That bird is big.’ kim a gweé Nguy Ngandak kim AGR has strength very ‘Kim is very strong.’ (adjective) (SN) Nevertheless, it is still an open question whether this denotation is one that invokes degrees (and scales) or portions (and substances). To a large degree, this is a conceptual issue, though Francez and Koontz-Garboden (2015: 552–556) point to some empirical considerations which could possibly distinguish between the two kinds of theories. The issue hinges largely on the nature of the ordering relation on the degrees/portions, and whether it is antisymmetric (as it is on degree-based theories) or not (as in Francez and Koontz-Garboden’s portion-based theory). Further work is needed to examine this issue in Basaá and more generally. The discussion thus far has been aimed simply at establishing the existence of individualcharacterizing property concept nominals, and has used Basaá for the purposes of an unambiguous existence proof. We have not explored whether Basaá is unique in having property concept nominals of this type, however. As it happens, there is a case that English in fact has property concept nominals similar to Basaá ANs, even if these might be less numerous. The issue hinges on whether nouns like those in (33) are property concept nominals or not. While some of these are restricted to human nouns (savant, genius) or to inanimate nouns (antique), others are less restricted (e.g., giant), much like adjectives that could be used to paraphrase them (e.g., huge), suggesting that these should be classed as property concept words.13 (33) idiot, savant, genius, giant, antique, disaster 12 We have not investigated closely whether this gradable modifier shows all the requisite properties of a genuine degree/portion modifier; see Beltrama and Bochnak 2015 for discussion. 13 These considerations point to the inductive nature of the notion of property concept word, and to the need for a property theory of what actually characterizes this class. This issue is one in need of work, and would answer the main question of Dixon (1982): why do adjectives have the meanings they have, particularly in languages with small closed classes of them, where such meanings are predictable? Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 656 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá This class of nouns use copular morphosyntax in predication, rather than possession. (34) a. This election is a disaster. b. #This election has disaster. Nouns like idiot and disaster have, in fact, been investigated in some detail by Morzycki (2012), who points out that there are gradable modifiers in English that can be used with just nouns like these (but not, for example, nouns like resident, teacher, etc.), a fact which coupled with their behavior in predication, again makes them look like the Basaá ANs: (35) a. an utter/huge/big disaster/idiot/genius b. #an utter/huge/big teacher/table In addition, these nouns can modify other nouns in a construction which closely resembles the Basaá AN-of-N construction (see Alexiadou et al., 2007: ch. 2 for an overview): (36) a. b. that idiot of a doctor the disaster of an election We can make sense of such facts if these nouns have a denotation like adjectives (a relation between degrees and individuals, or alternatively portions of substance and individuals), with the degree argument saturated by a degree modifier, as in (35), or by Pos, creating a predicate of individuals. This suggests that Basaá might be special not so much in having individualcharacterizing nominal property concept words, but rather having such a large, open, and productive inventory of them alongside the absence of a large open class of adjectives (cf. English). 6. Concluding remarks: Nominally encoded PCs have an argument in domain of substance It is widely known by now, thanks to Dixon’s (1982, 2004) observations, that property concept words can be nominal, adjectival, and verbal. More recently, Francez and Koontz-Garboden have shown that they also vary in their denotation—while property concept words in the familiar, best explored cases involving adjectives are individual-characterizing, there are many, particularly involving nouns, which are substance-characterizing. The program that the work in this paper fits into is that of determining whether all possible cross-classifications of category and meaning are attested, with the goal of using such a cross-classification to better understand the ways in which lexical categoryhood constrains word meaning. Limiting ourselves to adjectives and nouns, cross-classifying category with the two kinds of denotation identified by Francez and Koontz-Garboden leads to a picture like that in (37). (37) Nominal and adjectival property concept denotations Individual-characterizing Substance-characterizing Adjective English, Basaá adjectives Noun Basaá ANs 0/ Basaá SNs Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 657 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá The aim of the program is to determine whether the empty cells are genuinely empty, and if so why. In the case of substance-characterizing adjectives, for example, Francez and KoontzGarboden (2017: Chapter 6) argue that they are genuinely unattested, and that their absence (impossibility, they argue) follows from the very nature of the adjectival category itself. In this way, the program leads to a better understanding of the nature of lexical categoryhood, adjectives in particular. The question we have explored in this paper is whether the lower-left hand corner of the table in (37) is attested or not, i.e., whether there exist individual-characterizing property concept nouns. Previously, all known nominal property concepts have had substance-characterizing denotations, leading to the conjecture that they always had this denotation. We have shown that so-called Basaá adjectival nouns are at once nominal and individual-characterizing. Outstanding is still the question of precisely how Basaá adjectival nouns characterize individuals. As discussed briefly in §2, there is much debate in the formal literature about what precisely the denotation of adjectives are. The questions raised in that literature are relevant for the consideration of the precise denotation for Basaá adjectival nouns, and more work is needed. Further, it may well be that what is right for adjectives is actually not right for Basaá adjectival nouns, raising again the question of variation in denotation, and whether that might be tied to lexical category, albeit in a different form, with different kinds of denotations under consideration. In this paper, we have limited ourselves to the question of substance-characterizing denotations versus individual-characterizing denotations, without considering in a precise fashion what the latter are. Future work on Basaá should consider in a more precise fashion than we have done here what the denotations of Basaá adjectival nouns are, and what the observations made about these denotations tells us about the interface between lexical semantics and lexical category. For now, it is at least clear that property concept nominals need not be substance-characterizing. References Alexiadou, A., L. Haegeman, and M. Stavrou (2007). Noun Phrase in the Generative Perspective. Berlin: Mouton de Gruyter. Bach, E., E. Jelinek, A. Kratzer, and B. Partee (Eds.) (1995). Quantification in Natural Languages. Dordrecht: Kluwer. Baker, M. and W. Croft (2017). Lexical categories: Legacy, lacuna, and opportunity for functionalists and formalists. Annual Review of Linguistics 3(1), 179–197. Barker, C. (2002). The dynamics of vagueness. Linguistics and Philosophy 25, 1–36. Barwise, J. and R. Cooper (1981). Generalized quantifiers and natural language. Linguistics and Philosophy 4, 159–219. Beck, S., S. Krasikova, D. Fleischer, R. Gergel, S. Hofstetter, C. Savelsberg, J. Vandereist, and E. Villalta (2010). Crosslinguistic variation in comparison constructions. Linguistic Variation Yearbook 9, 1–66. Beltrama, A. and M. R. Bochnak (2015). Intensification without degrees cross-linguistically. Natural Language & Linguistic Theory 33(3), 843–879. Bochnak, M. R. (2013). Crosslinguistic Variation in the Semantics of Comparatives. Ph. D. thesis, University of Chicago. Bochnak, M. R. (2015). The degree semantics parameter and cross-linguistic variation. SeProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 658 P. Jenks, A. Koontz-Garboden, & E.-M. Makasso On the lexical semantics of property concept nouns in Basaá mantics and Pragmatics 8(6), 1–48. Bowler, M. (2016). The status of degrees in Warlpiri. In M. Grubic and A. Mucha (Eds.), Proceedings of The Semantics of African, Asian, and Austronesian Languages 2, Potsdam, pp. 1–17. Universitaetsverlag Potsdam. Burnett, H. (2016). Gradability in Natural Language: Logical and Grammatical Foundations. Oxford: Oxford University Press. Chierchia, G. and R. Turner (1988). Semantics and property theory. Linguistics and Philosophy 11(3), 261–302. Cresswell, M. (1977). The semantics of degree. In B. Partee (Ed.), Montague Grammar, pp. 261–292. Academic Press. Dimmendaal, G. J. (1988). Aspects du basaá: bantou zone A, Cameroun. Paris: Peeters/Selaf. Dixon, R. (1982). Where have all the Adjectives Gone? And other Essays in Semantics and Syntax. The Hague: Mouton. Dixon, R. (2004). Adjective classes in typological perspective. In R. Dixon and A. Y. Aikhenvald (Eds.), Adjective Classes: A Cross-linguistic Typology, pp. 1–49. Oxford: Oxford University Press. Francez, I. and A. Koontz-Garboden (2015). Semantic variation and the grammar of property concepts. Language 91(3), 533–563. Francez, I. and A. Koontz-Garboden (2017). Semantics and Morphosyntactic Variation: Qualities and the Grammar of Property Concepts. Oxford University Press. Heim, I. (1985). Notes on comparatives and related matters. UT Austin. Hyman, L. (2003). Basaá (A43). In D. Nurse and G. Philippson (Eds.), The Bantu Languages, pp. 257–282. New York: Routledge. Hyman, L., P. Jenks, and E.-M. Makasso (2013). Adjectives as nominal heads in Basaà. In Olanike Ola Orie and K. W. Sanders (Eds.), Selected Proceedings of the 43rd Annual Confer˙ ˙ ence on African Linguistics, Somerville, MA, pp. 151–162. Cascadilla Proceedings Project. Kamp, J. (1975). Two theories about adjectives. In E. Keenan (Ed.), Formal Semantics of Natural Language, pp. 123–155. Cambridge: Cambridge University Press. Kaufman, D. (2009). Austronesian nominalism and its consequences: A Tagalog case study. Theoretical Linguistics 35(1), 1–49. Kennedy, C. (1997). Projecting the Adjective: The Syntax and Semantics of Gradability and Comparison. Ph. D. thesis, UC-Santa Cruz, Santa Cruz, CA. Kennedy, C. (1999). Projecting the Adjective: The Syntax and Semantics of Gradability and Comparison. New York: Garland. Klein, E. (1980). A semantics for positive and comparative adjectives. Linguistics and Philosophy 4, 1–45. Koch, K. and L. Matthewson (2009). The lexical category debate in Salish and its relevance for Tagalog. Theoretical Linguistics 35(1), 125–137. Koontz-Garboden, A. (2007). Aspectual coercion and the typology of change of state predicates. Journal of Linguistics 43(1), 115–152. Koontz-Garboden, A. and I. Francez (2010). Possessed properties in Ulwa. Natural Language Semantics 18, 197–240. Landman, F. (2003). Predicate-argument mismatches and the adjectival theory of indefinites. In M. Coene and Y. D’Hulst (Eds.), From NP to DP, Volume 1: The Syntax and Semantics of Noun Phrases, Volume 1, pp. 211–237. Amsterdam: John Benjamins. 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A discourse approach to the cross-linguistic category ’adjective’. In R. Corrigan, F. Eckman, and M. Noonan (Eds.), Linguistic Categorization, pp. 245–265. Amsterdam: John Benjamins. van Rooij, R. (2011). Implicit versus explicit comparatives. In P. Égré and N. Klinedinst (Eds.), Vagueness and Language Use, pp. 51–72. New York: Palgrave. von Fintel, K. and L. Matthewson (2008). Universals in semantics. The Linguistic Review 25, 139–201. von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics 3, 1–77. Wellwood, A. (2015). On the semantics of comparison across categories. Linguistics and Philosophy 38(1), 67–101. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 660 Stativity and progressive: The case of Japanese ‘tokoro-da’1 Magdalena KAUFMANN — University of Connecticut Stefan KAUFMANN — University of Connecticut Abstract. The Japanese noun ‘tokoro’ (lit. ‘place’) has a grammaticalized variant with a temporal interpretation (Takubo 2011). Syntactically, this variant behaves like a noun and is typically modified by a sentence (or a suitable proform). The resulting NP ‘S-tokoro’ roughly means ‘time at which S’. With the copula ‘da/datta’ (Nonpast/Past) it can form a matrix sentence; but on its own it can also be used as a temporal adverbial. In these respects it is similar to other temporal expressions like ‘S-mae’ (‘time before S’), ‘S-ato’ (‘time after S), and ‘S-toki’ (‘time at which S’). But the acceptability and interpretation of ‘S-tokoro’ interacts with the temporal and aspectual properties of ‘S’ in puzzling ways. Focusing on matrix uses in this paper (embedded ones being similar), we develop an analysis that accounts for those interactions. Keywords: tense, aspect, temporal adverbs, modality, counterfactuality, progressive, Japanese 1. Introduction The Japanese noun ‘tokoro’ (lit. ‘place’) has a grammaticalized variant as a “formal noun” (形式名詞), a dependent category taking a sentential complement to form a compound which behaves outwardly like a noun phrase. In this paper we focus on sentences formed of such an ‘S-tokoro’ phrase and a tensed form of the copula ‘da’, shown schematically in (1).2 (1) [ [ Sentence ] tokoro ] { da / datta } Here Sentence stands for a tensed clause and ‘da, datta’ are the Nonpast and Past forms of the copula. On the temporal interpretation of ‘tokoro’ (other readings are possible, see below), (1) locates the matrix reference time relative to a time at which Sentence is or was true. The temporal and aspectual properties of Sentence play a crucial role in determining both whether the construction as a whole is well-formed, and if it is, how it is interpreted. Our goal in this paper is to give a semantic analysis which accounts for these interactions. The observation we are most interested in is that only non-stative and progressive Sentences are allowed under temporal ‘tokoro’, whereas lexical statives and perfects are not. 1 This paper is part of an extensive ongoing project with Yukinori Takubo, to whom we are grateful for much inspiration and discussion. However, the analysis presented here is our own and differs from his in important respects. We are also grateful to Setsuko Arita, Ikumi Imani, Yuya Okawa, Yukiko Atarashiya, the audiences the workshop on Modality as a window on cognition (19th International Congress of Linguistics, Geneva, 2013), the Meikai University Linguistics Colloquium (2015), Sinn und Bedeutung 21 (Edinburgh, 2016), and the Meaning Group at the University of Connecticut (2016), for comments and discussion. Part of this work was carried out during a semester at Kyoto University in Fall, 2015. We are grateful to Yukinori Takubo, the Japan Society for the Promotion of Science (Grant L-15504), and Kyoto University for their hospitality and support. 2 ‘S-tokoro’ can also occur in other environments, but its interpretation in such contexts does not differ significantly from that in (1), so we focus on the latter for the purposes of this paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 661 M. Kaufmann & S. Kaufmann Stativity and progressive 1.1. Temporal ‘tokoro’ with non-statives Our analysis of the tenses follows Kaufmann and Miyachi (2011; henceforth KM11). Sentences denote binary relations between temporal intervals, i.e., sets of pairs hi, ji. In a non-stative like (2a), the relation holds if and only if (i) j is the temporal trace of an event of Jon putting on a red jacket; and (ii) either i < j (for Nonpast) or j < i (for Past). In Reichenbachian terms, in matrix contexts i and j correspond to speech and reference time, respectively. (2) a. b. c. Zyon-ga akai zyaketto-wo { ki-ru / ki-ta } Jon-nom red jacket-acc put on-nonpast put on-past ‘Jon { will put on / put on } a red jacket’ [Zyon-ga akai zyaketto-wo ki-ru] tokoro { da / datta } ‘Jon { is / was } just about to put on a red jacket’ [Zyon-ga akai zyaketto-wo ki-ta] tokoro { da / datta } ‘Jon { has / had } just put on a red jacket’ In (2b), the Nonpast version of (2a) is embedded under ‘tokoro’ and the tensed copula. We aim to give (2a) a uniform analysis for matrix and embedded contexts, thus we assume that, as in (2a), the embedded clause ‘Zyon-ga akai zyaketto-wo ki-ru’ denotes a binary relation between intervals hi, ji. Now, however, i and j correspond to the reference times of the matrix clause and the embedded clause, respectively. Thus for (2b) and (2c) to be true, the matrix reference time must precede and follow that of the embedded clause, respectively. In both of (2b,c), the relation between the speech time and the matrix reference time is constrained by the tense on the copula. The presence of ‘tokoro da/datta’ means that (2b,c) are stative (in contrast to the non-stative (2a)). In this case, a co-temporal reading is available for Nonpast ‘datta’ under which speech and reference time coincide. Thus (2b,c) basically assert that the reference time is/was before or after the dressing event, respectively. One may wonder how they differ from their counterparts with ‘mae’ and ‘ato’, the more canonical Japanese counterparts of ‘before’ and ‘after’. We discuss this relationship in some detail below. For now, suffice it to say that (2b,c) are indeed close in meaning to their counterparts in (3a,b), with the important difference that (2b,c) carry a connotation of immediacy, expressed in (2) in our gloss using English ‘just’, which (3a,b) lack. (3) a. b. [Zyon-ga akai zyaketto-wo ki-ru] { mae / *ato } { da / datta } ‘Jon { is / was } just about to put on a red jacket’ [Zyon-ga akai zyaketto-wo ki-ta] { *mae / ato } { da / datta } ‘Jon { has / had } just put on a red jacket’ 1.2. Temporal ‘tokoro’ with lexical statives Stative clauses also denote binary relations between intervals but there are differences in detail which lead to markedly different patterns in well-formedness and interpretion under ‘tokoro’. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 662 M. Kaufmann & S. Kaufmann Stativity and progressive In matrix-level statives, the interpretation is similar to that of non-statives, except that Nonpast allows for speech and reference time to coincide. Thus in terms of the relationship between i, j, we have j < i for Past (as with non-statives) and i ≤ j for Nonpast (cf. i < j for non-statives). In embedded contexts, however, i must be contained in j; as a consequence, Past tense is disallowed (hence the ill-formedness of (4c)) and Nonpast lacks the futurate interpretation on which i < j. These facts are shared across a range of embedding contexts (see KM11 for data and discussion), but ‘tokoro’ adds even more constraints: the embedded Nonpast in (4b) is also peculiar. Most informants judge it to be marginal and, if acceptable at all, restricted to the counterfactual reading indicated in the gloss. (4) a. Ie-ni { i-ru / i-ta } home-loc be-nonpast be-past ‘I { {am/will be} / was } at home.’ b. ?[Ie-ni i-ru] tokoro { da / datta } ‘I would { be / have been } at home.’ c. *Ie-ni i-ta tokoro { da / datta } In this paper we aim to explain the absence of a temporal reading for (4b). We leave the analysis of the counterfactual reading for another occasion. 1.3. Temporal ‘tokoro’ with derived statives In addition to lexical statives, Japanese has aspectual operators which form derived statives from eventive complements. A well-studied expression of this kind is the suffix ‘-tei-’, which combines with the stems of non-stative verbs3,4 and can have either progressive or perfect readings, depending on the aspectual properties of the complement and contextual factors. This is illustrated by (5b), which has the two readings indicated in the translation. (5) a. Zyon-ga akai zyaketto-wo { ki-tei-ru / ki-tei-ta } Jon-nom red jacket-acc wear-tei-nonpast wear-tei-past Progressive: ‘Jon { is / was } putting on a red jacket’ Perfect: ‘Jon { is / was } wearing a red jacket’ b. [Zyon-ga akai zyaketto-wo ki-tei-ru] tokoro { da / datta } Progressive: ‘Jon { is / was } putting on a red jacket’ Perfect: ‘Jon would { be / have been } wearing a red jacket’ c. *[Zyon-ga akai zyaketto-wo ki-tei-ta] tokoro { da / datta } That one morpheme should have these two seemingly incompatible uses is puzzling and has made ‘-tei-’ one of the most written-about expressions in the Japanese linguistic literature. We postpone further discussion to the analysis below. For now, we only point out that the sentences derived with ‘-tei-’ exhibit an intriguing behavior when combined with ‘tokoro’, as 3 Certain other derivational morphemes can intervene between the verb stem and ‘-tei-’, for instance Passive, Causative and Potentialis, but not Negation. The details are not relevant here. 4 The claim that ‘-tei-’ combines only with non-statives is widely accepted in the literature. Incompatibility with ‘-tei-’ is Kindaichi’s (1950; 1976) main diagnostic for the class of stative verbs in his taxonomy (jôtaidôsi). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 663 M. Kaufmann & S. Kaufmann Stativity and progressive shown in (5b): On the Progressive reading of ‘-tei-’, ‘tokoro’ adds a purely temporal interpretation meaning ‘while/when’, even though no such interpretation is available either with lexical statives, which force a counterfactual reading in this case (cf. (4b)), or with eventives, on which the temporal interpretation would be ‘before’ (cf. (2b)). On the Perfect reading of ‘-tei-’, the sentence patterns with lexical statives in that only a counterfactual reading is available. Notice also that (5c) patterns with stative (4c) and not with eventive (2c) in that the string is ill-formed. This is the main puzzle to be addressed in this paper: On the one hand, Progressive and Perfect are generally considered derived statives, and the Japanese examples exhibit some properties that are expected under this analysis (e.g., the ill-formedness of (5c) and the relationship between the matrix and embedded reference times in (5b)). On the other hand, under ‘tokoro’ the Perfect is restricted to a counterfactual reading like other statives, while the Progressive has a temporal reading – which, however, is unlike that obtained with non-statives. 2. Theoretical background We develop our analysis in a slightly simplified version of the framework introduced by KM11.5 The major ingredients are shown in (6) along with their hierarchical structure in the sentence. (6) [ [ [ [ Sentence Radical ] Aspect ] Tense ] Environment ] Sentence radicals come in two major classes, stative and non-stative. We are not concerned here with the kind of sub-sentential aspectual composition that arises with quantification and distributivity, for instance, but we do need a formal representation of the stative/non-stative distinction. Aspectual operators impose temporal constraints on reference times and relate events to times. We assume that ‘-tei-’ is such an operator. But even sentences without ‘-tei-’ or other overt aspectual markers include a covert aspectual operator. In this we follow KM11. There are two tenses, Nonpast and Past, whose interpretation depends on the aspectual class of their complement as well as on the difference between matrix and embedded contexts. What we label as “Environment” in (6) is either the matrix context or one of a class of subordinating expressions which includes ‘tokoro’. 2.1. The model Let hT, ≺i be a non-empty set of temporal instants ordered by the transitive, irreflexive and connected relation ≺. The temporal period structure induced by hT, ≺i is a triple hI, ⊆, < i, where I is the set of non-empty convex subsets of T ,6 ⊆ is set-theoretic inclusion, and < is the relation of strict precedence on I × I. An event structure is a join-semilattice hE, vi, where E is a non-empty set of events and v is a partial order interpreted as the mereological “sub-event” relation. A temporal model is an octuple hI, ⊆, <, E, v, τ, s, Vi, where hI, ⊆, <i is a temporal period structure; hE, vi is an event structure; τ : E 7→ I maps events to their temporal traces, subject to the condition that for all e, e0 ∈ E, if e v e0 then τ(e) ⊆ τ(e0 ); s ∈ I is a (short) 5 The 6A simplification concerns KM11’s account of absolute tense under ‘toki’, which is orthogonal to this paper. set T 0 ⊆ T is convex iff for all t, t0 , t00 , if t ≺ t0 ≺ t00 and t, t00 ∈ T 0 , then t0 ∈ T 0 . Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 664 M. Kaufmann & S. Kaufmann Stativity and progressive interval representing the speech time; and V is an interpretation function mapping non-stative and stative sentence radicals to (characteristic functions of) subsets of E and I, respectively. We present our analysis as a compositional mapping from Japanese sentences to expressions in an extensional type-theoretical language which are then to be interpreted in temporal models. The basic types are i with Di = I (intervals),  with D = E (events) and t with Dt = {0, 1} (truth values). We do not define the language or its interpretetion explicitly because both will be obvious. We do assume that it has variables i, j, k, . . . ranging over intervals and e ranging over events; and symbols for unary predicates of intervals and events (corresponding to sentence radicals). We overload the symbols s, τ, <, ⊆ (mapped to the speech time s, the temporal trace function, the precedence relation <, and the subinterval relation). We will define further symbols below. 2.2. Sentence radicals Stative and non-stative sentence radicals denote properties of intervals and events, respectively. (7) Zyon-ga Nihon-ni iJon-nom Japan-loc be ‘Jon be in Japan’ { λi ∈ I[JonInJapan(i)] (8) Zyon-ga Nihon-ni ikJon-nom Japan-loc go ‘Jon go to Japan’ { λe ∈ E[JonToJapan(e)] 2.3. Aspectual operators Next up in the structure in (6) is a slot for aspectual operators. The suffix ‘-tei’ mentioned above is one of these operators; we also assume, following KM11, that sentences which do not have an overt operator in this location have a covert one.7 Semantically, aspectual operators map properties of intervals or events to binary relations between intervals. We use the symbols in (9) for relations between intervals, in addition to the “strict precedence” relation already defined in the model (see also Allen, 1983). (9) Relations between intervals a. i ∅ j B i < j ∨ j < i b. i b j B ∃k, l[k ⊆ j ∧ l ⊆ j ∧ k < i < l] [non-overlap] [non-initial, non-final subinterval] These relations are used in the translations of the aspectual operators. We adopt from KM11 the convention of using the names ϕ and ρ for variables over properties of intervals and properties of events, respectively.8 7 This simplifies the lexical entries of morphemes (such as tenses) that can combine with sentence radicals both directly and via the mediation of aspectual operators. 8 We deviate slightly from KM11’s definition of ∅ for non-statives: their τ(e) ⊆ j, corresponds to our j = τ(e). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 665 M. Kaufmann & S. Kaufmann (10) Stativity and progressive Aspectual operators a. ∅ { λϕhi,ti λiλ j[ϕ( j) ∧ [i , s → i b j]] ∪ λρh,ti λiλ j[∃e[ρ(e) ∧ j = τ(e)] ∧ i ∅ j] b. ‘-tei-’ { λρh,ti λiλ j[∃e[ρ(e) ∧ tei(e, j) ] ∧ [i , s → i b j]] At this point the expression “tei(e, j)” is just a placeholder. We return to this issue in Section 3, where we fill in the details that explain why ‘tokoro’ can have a temporal interpretation with the Progressive reading but not with the Perfect reading of ‘-tei-’. For now, we are more interested in the last conjunct of the formula in (10b), which establishes the relationship between the two intervals i, j. If i is not the speech time (i.e., in embedded contexts), it must be contained in j, otherwise (i.e., in matrix contexts) it is not so constrained. This condition mirrors the one imposed by the covert aspectual operator for lexical statives (the upper line in (10a)). This is the sense in which we think it correct to say that clauses modified by ‘-tei-’ are (derived) statives, regardless of whether the reading is Progressive or Perfect. The result of applying these aspectual operators to sentence radicals in (7) and (8) is given in (11). (11) Zyon-ga nihon-ni { a. i-∅ / b. ik-∅ / c. it-tei } Jon-nom Japan-loc be go go-tei Jon { be in / go to / go-tei to } Japan a. { λiλ j[JonInJapan( j) ∧ [i , s → i b j]] b. { λiλ j∃e[JonToJapan(e) ∧ j = τ(e) ∧ i ∅ j] c. { λiλ j[∃e[JonToJapan(e) ∧ tei(e, j) ] ∧ [i , s → i b j]] 2.4. Tense Next up in our structure (6) are the tenses. As mentioned above, there are two tenses in Japanese, Nonpast and Past, typically expressed on verbs with some allomorph of ‘-ru’ and ‘-ta’, respectively, except for the copula, whose forms are ‘-da’ and ‘-datta’.9 (12) Tenses a. nonpast { λiλ j[i ≤ j] (13) Zyon-ga nihon-ni { a. i-ru / b. i-ta / c. ik-u / d. it-ta / e. it-tei-ru / f. it-tei-ta } Jon-nom Japan-loc be-np be-p go-np go-p go-tei-np go-tei-p ‘Jon {is in / was in / is going to / went to / . . . } Japan’ a. { λiλ j[JonInJapan( j) ∧ i ≤ j ∧ [i , s → i b j]] b. { λiλ j[JonInJapan( j) ∧ j < i ∧ [i , s → i b j]]10 c. { λiλ j[∃e[JonToJapan(e) ∧ j = τ(e)] ∧ i < j] d. { λiλ j[∃e[JonToJapan(e) ∧ j = τ(e)] ∧ j < i] e. { λiλ j[∃e[JonToJapan(e) ∧ tei(e, j) ] ∧ i ≤ j ∧ [i , s → i b j]] f. b. past { λiλ j[ j < i] { λiλ j[∃e[JonToJapan(e) ∧ tei(e, j) ] ∧ j < i ∧ [i , s → i b j]]10 9 One class of adjectives also carries tense, expressed with ‘-i’ and ‘-katta’ for Nonpast and Past, respectively. The negative suffix ‘-na{-i/-katta}’ belongs to this paradigm. 10 Notice that (13b,f) imply that i = s, in line with the observation that Past statives only occur in matrix contexts. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 666 M. Kaufmann & S. Kaufmann Stativity and progressive 2.5. Embedding environments Next up we now reach the position filled by ‘tokoro’ or other embedding temporal expressions, such as ‘toki’ ‘when’, ‘mae’ ‘before’, etc. It is instructive to compare several such items to ‘tokoro’. In (14) we give four examples along with their interpretations from KM11. (14) a. b. c. d. mae ‘before’ { λϕhi,hi,tii λhλi∃ j[ϕ(i)( j) ∧ i < j] ato ’after’ { λϕhi,hi,tii λhλi∃ j[ϕ(i)( j) ∧ j < i] uti ‘while’ { λϕhi,hi,tii λhλi∃ j[ϕ(i)( j) ∧ i b j] toki ‘when’ { λϕhi,hi,tii λhλi∃ j[ϕ(i)( j)] All of these items are of the same type, viz. hhi, hi, tii, hi, hi, tiii (i.e., modifiers of binary relations between intervals). Their arguments are the denotations of tensed sentences – relations between intervals i, j which, in matrix sentences, are interpreted as the speech time and the reference time, respectively. In (14) we see that a new time is introduced when tensed sentences are embedded under temporal connectives. The idea is that now h, i are interpreted as the speech and reference time of the matrix sentence, and i anchors the temporal interpretation of the embedded clause. The relation that the embedded sentence imposes on i, j is now, in Reichenbachian terms, imposed on the reference time and event time of the embedded clause. The semantic contribution of most of the items in (14) is an added condition on the temporal relation between i, j (an exception is ‘toki’, which does not add any new constraint). This condition is conjoined with whatever the complement clause already requires of the two intervals. The result may be a contradiction, resulting in ill-formedness (e.g., in the case of ‘mae’ ‘before’ with Past tense or ‘ato’ ‘after’ with Nonpast). Some or the results are shown in (15) and (16). (15) (16) Zyon-ga nihon-ni { a. ik-u / b. *it-ta } mae Jon-nom Japan-loc go-npst go-pst before ‘before Jon {goes / went} to Japan’ a. { λhλi∃ j[∃e[JonToJapan(e) ∧ j = τ(e)] ∧ i < j ∧ i < j] b. { λhλiλ j[∃e[JonToJapan(e) ∧ j = τ(e)] ∧ i < j ∧ j < i] 3 7 Zyon-ga nihon-ni i-ru { a. *mae / b. *ato / c. uti / d. toki } Jon-nom Japan-loc be-npst before after while when ‘{before / after / while / when} Jon {is / was} in Japan’ a. { λhλi∃ j[JonInJapan( j) ∧ i < j ∧ i b j] 7 b. { λhλi∃ j[JonInJapan( j) ∧ j < i ∧ i b j] 7 c. { λhλi∃ j[JonInJapan( j) ∧ i b j ∧ i b j] 3 d. { λhλi∃ j[JonInJapan( j) ∧ i b j] 3 Table 1 shows the overall pattern resulting from the interaction between the various temporal constraints. iku ‘go’ and iru ‘be’ are non-stative and stative, respectively. The rightmost column shows the data with ‘tokoro’ that we outlined earlier. Our goal is to add a semantic entry for ‘tokoro’, replacing the question marks in the top row. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 667 M. Kaufmann & S. Kaufmann Stativity and progressive Table 1: Temporal constraints contributed by temporal connectives (top row) and their clausal complements (left column), and the resulting well-/ill-formedness of the combinations. mae ‘before’ i< j ik-u it-ta it-tei-ruprog it-tei-ruperf i-ru i-ta i< j j<i ib j ib j ib j 7 ‘before’ * * * * * ato ‘after’ uti ‘while’ toki ‘when’ j<i ib j · * ‘after’ * * * * * * ‘while’ ‘while’ ‘while’ * ‘before’ ‘after’ ‘while’ ‘while’ ‘while’ *11 tokoro ??? ‘right before’ ‘right after’ ‘while’ */cf */cf * There are three major challenges to this project. First, as seen in the table, ‘tokoro’ is sensitive to a distinction that the other particles do not track, distinguishing between the upper three rows (Nonstative ik-u/it-ta ‘go’; Progressive reading of ‘-teiru’) and the lower rows (Stative i-ru/ita ‘to be’, and Perfect reading of ‘-teiru’). None of the other connectives is sensitive to this distinction, nor is it expressed in the relation between the intervals i, j, which was sufficient to account for the patterns discussed so far. Secondly, ‘tokoro’ adds a connotation of “immediacy” to the temporal relations in the top rows, which our rendering in English as ‘right before’ and ‘right after’ is intended to convey. Finally, ‘tokoro’ alone has a counterfactual reading in cases in which a temporal reading is unavailable. 3. Analysis We address the challenges just discussed in terms of an interaction between ‘tokoro’’s aspectual properties and a certain notion of “immediacy.” For instance, recall that with non-stative complements, ‘tokoro’ comes to mean ‘right before’ or ‘right after’, depending on the embedded tense. We want to formalize this notion in such a way that the more peculiar properties of ‘tokoro’ – its well-formedness with Progressive but not with Perfect ‘-teiru’ and the availability of a counterfactual reading with Perfect ‘-teiru’ and statives – also fall out. One way to describe the peculiar behavior of ‘tokoro’ in combination with ‘-teiru’ is that on the Progressive reading of ‘-teiru’ these sentences behave like non-statives, whereas on the Perfect reading they behave like statives. We need to explain, not only why one and the same morpheme, ‘-tei-’, can have such disparate uses, but also why on the Progressive use it has a certain eventive “flavor” which is absent from the Perfect use. What is this eventive “flavor,” and how should it be represented? It is a widely held view that events involve change or development of some kind, and that their progress can be measured 11 Past statives can in principle occur in embedding contexts, but only with an absolute reading of the Past tense (i.e., one anchored to the speech time rather than the matrix reference time). Whether such a reading is available depends on the embedding connective. It is not available under ‘tokoro’, therefore we ignore it in this paper. It is available under ‘toki’, hence the asterisk in the corresponding cell in our table is a simplification. See Kaufmann and Miyachi (2011) for details. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 668 M. Kaufmann & S. Kaufmann Stativity and progressive in various ways, whereas states have none of those properties. The stative/non-stative distinction is often taken to be an ontological fact about different kinds of enventualities (Smith, 1991; Bach, 198612 ); the notion that events can be measured is discussed and formalized in various ways depending on whether the measurement draws on incremental themes, expressions of creation, changes of state or degree, paths, or yet some other notion (Dowty, 1991; Krifka, 1989, 1992; Tenny, 1994; Hay et al., 1999; Kennedy and Levin, 2008, i.a.). In this paper we stop short of committing ourselves to a particular view on the origins of event measurement. We are more interested in the question of how, once such measurement is introduced, it can have repercussions throughout the compositional process. For recall that ‘tokoro’ does not combine directly with event-denoting sentence radicals, and not even with ‘radical+-tei’ compounds. Instead, it combines with tensed clauses, and we have been assuming throughout that tensed clauses denote binary relations between temporal intervals. Since there is no direct link to the underlying eventualities, the “eventive flavor” of the Progressive cannot be implemented straightforwardly in terms of the denotatum of ‘tokoro’’s complement. Instead, we need a way to let the stative/non-stative distinction that is accessible lower in the derivation leave an “imprint” on the intervals higher up. To implement this, we enrich our representation of temporal traces. We do this in two steps: in Section, 3.1, give ‘-tei-’ access to different phases of an event (viz. its run-time and its result state, where available); in Section 3.2 we add a representation of event measurement. 3.1. The versatility of ‘-tei-’ While space does not permit us to do justice to the extensive literature on ‘-tei-’, we do need to introduce the basic facts about its semantic versatility. Most discussions of ‘-tei-’ distinguish at least three readings: Progressive, Resultative Perfect, and Experiential Perfect. Which of them are available for a particular sentence containing ‘-tei-’ depends on the prejacent’s aspectual properties (and possibly other factors). The clearest cases exhibiting all readings are accomplishments with an activity phase and a result state. The examples in (17) are from Igarashi and Gunji (1998), adjusted to our transliteration and glosses. (17a,b) illustrate the Progressive and Resultative Perfect readings, as highlighted by the English glosses. In (17c), the combination of the past adverbial ‘sannen mae-ni’ ‘three years ago’ with Nonpast tense forces the Experiential Perfect reading (Fujii, 1976; Ogihara, 1998). (17) a. b. Ken-wa ima tonari-no heya-de kimono-wo ki-tei-ru Ken-top now next-gen room-loc kimono-acc put on-tei-npst ‘Ken is now putting on a kimono in the next room’ Ken-wa kesa kara zutto ano kimono-wo ki-tei-ru Ken-top this morning from always that kimono-acc put on-tei-npst ‘Ken has been wearing that kimono since this morning’ [prog] [result] 12 Bach distinguishes states, processes and events, with the latter two being subsumed under the class of “nonstates.” We use the labels “non-stative” and “eventive” interchangeably. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 669 M. Kaufmann & S. Kaufmann c. Stativity and progressive Ken-wa ano kimono-wo sannen mae-ni ki-tei-ru [exp] Ken-top that kimono-acc three years before-loc put on-tei-npst (i) ‘Ken has the experience of putting on that kimono three years ago’ [exp ı] (ii) ‘Ken has the experience of wearing that kimono three years ago’ [exp ıı] Igarashi and Gunji (1998) argue that the Experiential (17c) can actually have two readings, depending on which of the two phases of the accomplishment – the putting on or the wearing of the kimono – is said to have taken place in the past. The two translations in (17c) are meant to bring out that difference. Gunji (2004) puts even more emphasis on this distinction, extending the traditional tripartite taxonomy by treating the two variants of the Experiential Perfect as distinct (though related) readings. This allows him to account for the full picture in terms of the interplay between two independent dimensions of variation: Activity vs. Result State reading of the prejacent, and Ongoing vs. Anterior reading of ‘-tei-’.13 The competing view of the traditional tripartite taxonomy is that the distinction between Activity and Resultative reading of the prejacent is only relevant under the Ongoing reading of ‘-tei-’, but neutralized under its Anterior reading (Ogihara, 1998). We adopt (Igarashi and) Gunji’s position that there is a major distinction between the Progressive and Resultative Perfect reading on the one hand, and the Experiential reading(s) on the other.14 This distinction seems related to a grammatical difference, as shown by the ability of past adverbials to co-occur with Present tense only under the Experiential reading.15 We stop short of postulating two distinct readings of the Experiential, however. This is in part because space is limited and a formal implementation which draws the distinction would require further modifications to the framework. Moreover, most informants report having a hard time seeing a clear semantic difference between the two readings. For the purposes of this paper, at least, we treat (17c) as one reading in which the Activity/Result State distinction is neutralized. For our formal analysis, this means that we need to encode two distinctions: the Activity/Result State distinction for the prejacent, and the Ongoing/Anterior distinction for ‘-tei-’. Furthermore, we follow those who assume that the two distinctions are not independent: Activity and Result State are only distinguished under Ongoing ‘-tei-’. Finally, we want to account for the fact that past adverbials can occur with Nonpast tense under Anterior but not Ongoing ‘-tei-’. 13 Gunji uses different terminology: at both levels, he distinguishes a basic view (基本視野; in our terminology, Activity at the level of the precedent and Ongoing at the level of ‘-tei-’) from a stative view (状態視野, our Result State (prejacent) and Anterior (‘-tei-’)). We prefer our terminologoy for its mnenomic value (for us), but nothing hinges on this choice. Notice also that Gunji considers ‘-tei-’ complex. He attributes the Ongoing/Anterior distinction to the semantics of ‘-te-’ alone, while taking ‘i’ to be semantically inert. 14 A separate class of approaches, which we do not discuss in detail here, seeks to unify the Resultative Perfect and the Experiential Perfect reading, setting them apart from the Progressive. See Ogihara (1998) for discussion. 15 Past adverbials can modify sentences with ‘-tei-’ under the other readings, but only if the matrix tense is Past: (i) Ken-wa ano kimono-wo sannen mae-ni ki-tei-ta Ken-top that kimono-acc three years before-loc wear-tei-pst ‘Ken was { putting on / wearing } that kimono three years ago.’ These cases do not pose a problem for our analysis on the assumption that the adverb here has ‘-tei-’ in its scope, rather than vice versa. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 670 M. Kaufmann & S. Kaufmann Stativity and progressive We start with Ongoing ‘-tei-’ and the two readings it gives rise to. Our preliminary definition of ‘-tei-’ from (10b) is repeated below. (10b) (preliminary) λρh,ti λiλ j[∃e[ρ(e) ∧ tei(e, j) ] ∧ [i , s → i b j]] We now need to spell out the expression tei(e, j) in the box in (10b). The idea is that ‘-tei-’ makes the inner stages of an event available for linguistic reference. We could simply replace the the box with the condition that j = τ(e), thus locating i within the runtime of the event in embedded contexts. However, this would only make the Progressive interpretation available, not the Perfect. To add the Perfect, we adapt from Igarashi and Gunji (1998); Gunji (2004) the main idea behind their classification. In principle, not one but two intervals can be associated with an event in the extension of a sentence radical: one is the familiar temporal trace of the event itself, the other is the interval over which its result state holds.16 Whether both of these intervals are available depends on the aspectual class: activities have no lexically encoded result state, whereas achievements may have a result state but no temporal extension in the triggering change-of-state event (i.e., no interval corresponding to an Activity part). Consequently, under ‘-tei-’, activities typically only have Progressive readings and achievements only Result state readings, whereas accomplishments can have both. Formally, we define an extended temporal trace function τ+ from events to sets of (one or two) intervals. The intention is that τ+ (e) is true of the conventional temporal trace τ(e) but also of the maximal interval of which e’s result state holds, in case the latter is defined. In (18) we use the auxiliary notation result for the partial function mapping events to their result states.17 (18) Extended temporal trace For all events e, τ+ (e) B λi[i = τ(e) ∨ ∃ j[ j = result(e) ∧ i = j]] Our definition for Ongoing ‘-tei-’ draws on this notion: (19) ‘-tei-’ ong { λρh,ti λiλ j[∃e[ρ(e) ∧ τ+ (e)( j)] ∧ [i , s → i b j]] We now turn to the Anterior reading of ‘-tei-’. What would seem to be the most straightforward way to include this reading – by modifying (19) to allow for the case that j < i – is not viable. 16 Note that Igarashi and Gunji’s implementation differs from ours: their constraints refert to the boundaries of the intervals in question, calling them the “start time” and “finish time” of the event (the latter also serving as the start time of the result state, where applicable), and the “reset time” marking the end of the result state. Aside from this difference, and modulo further fine distinctions that we cannot go into for lack of space, the intuitions are similar to our implementation, as far as we can see. 17 This way of implementing the idea has certain consequences for the underlying notion of events. Ogihara (Ogihara, 1998, p. 96) points out that two different descriptions of the same state of affairs can have different aspectual properties. For instance, different sentences referring to the same opening of a door may or may not have Progressive readings depending on the grammatical form. This means that the value of τ+ (e) may differ depending on the sentence used. In order to avoid untoward consequences of this possibility (e.g., ensuring that τ+ is a function), we have to assume that in such cases the model actually contains two distinct events representing the very same opening of the door which can serve as denotations of the different linguistic expressions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 671 M. Kaufmann & S. Kaufmann Stativity and progressive This is because Anterior ‘-tei-’ allows for the coexistence of past adverbs like ‘kyonen’ ‘last year’ with Nonpast tense. In our framework, this would mean that the adverb places j within the year preceding that of the speech time, while the Nonpast tense rules out the possibility that j precedes i, leading to contradictory constraints in matrix contexts (where i ends up referring to the speech time). We avoid this unwelcome consequence by giving Anterior ‘-tei-’ a denotation of an altogether different type and assuming that in the syntactic derivation it behaves in some respects more like a tense than an aspectual operator. Specifically, we assume that it co-occurs with, and outscopes, the covert aspectual operator ∅. Consequently, its complement denotes a relation between intervals, not a property of events, and this makes it possible for temporal adverbs to scope lower than ‘-tei-’. At the same time, as seen in the denotation in (20b), ‘-tei-’ introduces an additional interval k at which the prejacent ϕ is evaluated and which can be constrained by temporal adverbs. The tense above ‘-tei-’, meanwhile, constrains the relation between i and j. Thus past adverbs and present tense may co-occur without contradiction.18 (20) a. b. ‘-tei-’ ong { λρh,ti λiλ j[∃e[ρ(e) ∧ τ+ (e)( j)] ∧ [i , s → i b j]] ‘-tei-’ ant { λϕhhi,ti,hhi,ti,tii λiλ j[∃k[ϕ( j)(k) ∧ k < j] ∧ [i , s → i b j]] We illustrate with a few examples. (21) is a matrix sentence with the temporal adverb ‘kyonen’ ‘last year’. (21a) shows the denotation (the conditions imposed by Present or Past tense are listed in the last conjunct) which is then evaluated at the speech time s (fixed by the model) and reference time r (contributed by context). In this case the two constraints contributed by lastyear and tense are imposed on the same pair of intervals s, r. The ill-formedness of the Present-tense variant arises at this point due to the inconsistency of lastyear(s)(r) and s ≤ r.19 (21) Kyonen kimono-wo ki- { *ru / ta } last year kimono-acc wear npst pst [ [kyonen [ [kimono-wo ki ] ∅ ] ] { *ru / ta } ] a. { λiλ j[∃e[KimonoKi(e) ∧ j = τ(e)] ∧ i ∅ j ∧ lastyear(s)( j) ∧ {i ≤ j/ j < i}] (21a)(s)(r) ⇔ ∃e[KimonoKi(e) ∧ r = τ(e)] ∧ lastyear(s)(r) ∧ r < s We next turn to ‘-tei-’. For ease of exposition, we list examples of its Ongoing and Anterior use separately. The surface strings are indistinguishable, but we indicate the respective intended derivations in the bracketed representations. First consider Ongoing ‘-tei-’, which due to its type must combine directly with the sentence radical and scope under the temporal adverb. Only the Past-tense variant of the sentence can have this reading; the Nonpast is ruled out in the same way as the Nonpast of (21) above. Which readings (Activity and/or Result State Perfect) (22) can have depends on which intervals are made available by the extended temporal trace τ+ (e). Which reading it has in any particular instance further depends on how τ+ (e) applies 18 The reader may notice that according to (20b) the “high” ‘-tei-’ has the same type as the tenses – both are modifiers of binary relations between structured intervals. This means that the denotations do not by themselves enforce the observed structural relationship, i.e., that tense invariably sits higher in the syntactic tree than ‘-tei-’. We assume that this relationship is enforced independently by syntactic factors. 19 Note that it is not the past reference per se that is incompatible with Present tense. For instance, embedded under connectives like ‘toki’ ‘when’ and ‘mae’ ‘before’, Present tense is not interpreted as restricting s, r and can thus happily coexist with past intervals like ‘kyonen’. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 672 M. Kaufmann & S. Kaufmann Stativity and progressive to j (ultimately, r): it is a (non-initial and non-final) subinterval of either τ(e), giving rise to the Activity reading, or of result(e), corresponding to the Result State Perfect reading. (22) Kyonen kimono-wo ki-teiong - { *ru / ta } last year kimono-acc wear-tei npst pst [ [ kyonen [ [ kimono-wo ki ] tei ] ] ta ] [past activity/past result] + a. { λiλ j[∃e[KimonoKi(e) ∧ τ (e)( j)] ∧ lastyear(s)( j) ∧ j < i] (22a)(s)(r) ⇔ ∃e[KimonoKi(e) ∧ τ+ (e)(r)] ∧ lastyear(s)(r) ∧ r < s For the Anterior reading of ‘-tei-’, we do not predict that past adverbs with Nonpast tense result in inconsistency. This is shown in (23). (23) Kyonen kimono-wo ki-teiant -ru last year kimono-acc wear-tei-npst [ [ [ kyonen [ [ kimono-wo ki ] ∅ ] ] tei ] ru ] [pres exp] a. { λiλ j∃k[∃e[KimonoKi(e) ∧ k = τ(e)] ∧ k ∅ j ∧ lastyear(s)(k) ∧ k < j ∧ i ≤ j] (23a)(s)(r) ⇔ ∃k[∃e[KimonoKi(e) ∧ k = τ(e)] ∧ lastyear(s)(k) ∧ k < r ∧ s ≤ r] But we do not predict Anterior ‘-tei-’ to be inconsistent with Past tense either. In fact, we derive two readings for (24), corresponding to two positions of the adverb relative to ‘-tei-’. On the reading in (24a/b), the adverb restricts k, the event of putting on the kimono; the reference time r, which must lie strictly between k and s, is thus a time at which the experiential state holds. On this interpretation the sentence means that at some point in the recent past (say, a week ago) it was true (or it turned out) that the subject had worn a kimono last year. On the reading in (24c/d) the adverb restricts the reference time r, while the time k of wearing the kimono must be found at an even earlier time. In other words, it turned out last year that (already then) the subject had the experience of having worn a kimono. We take it that both readings exist. (24) Kyonen kimono-wo ki-teiant -ta last year kimono-acc wear-tei-pst a. [ [ [ kyonen [ [ kimono-wo ki ] ∅ ] ] tei ] ta ] [past exp] b. { λiλ j∃k[∃e[KimonoKi(e) ∧ k = τ(e)] ∧ k ∅ j ∧ lastyear(s)(k) ∧ k < j ∧ j < i] (24a)(s)(r) ⇔ ∃k[∃e[KimonoKi(e) ∧ k = τ(e)] ∧ lastyear(s)(k) ∧ k < r ∧ r < s] c. [ [ kyonen [ [ [ kimono-wo ki ] ∅ ] tei ] ] ta ] [past exp] d. { λiλ j∃k[∃e[KimonoKi(e) ∧ k = τ(e)] ∧ k ∅ j ∧ k < j ∧ lastyear(s)( j) ∧ j < i] (24c)(s)(r) ⇔ ∃k[∃e[KimonoKi(e) ∧ k = τ(e)] ∧ k < r ∧ lastyear(s)(r) ∧ r < s] 3.2. Event measurement Tradionally, the temporal trace of an event has been taken to be an interval (assigned to the event by the function τ, Krifka (1989)), and we have followed this convention thus far. The left-hand side of Figure 1 is an illustration. We propose a straightforward modification of this simple picture: The temporal trace function τS maps events to structured intervals, our term for sets Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 673 M. Kaufmann & S. Kaufmann Stativity and progressive e τ(e) ⊆ I i T E{i} Eτ(e) τK (e) ∈ I e Figure 1: Left: Temporal trace τ mapping events to intervals. Middle: Temporal trace τS mapping events to structured intervals (top) and induced order Eτ(e) on T (bottom). Right: Stative denotation i (top) and pre-order E{i} on T (bottom). of intervals which contain their own union.20 In our type-theoretic compositional framework, structured intervals are represented by their characteristic functions, i.e., in Dhi,ti , and we use variables i, j, etc. to range over them. For ease of exposition, we switch between talk of these characteristic functions and the sets of intervals they characterize, using variables like A, B, etc. for the latter. No confusion should result from this. (25) A set A of intervals is a structured interval iff ∪A is an element of A. The relations between intervals defined above can be extended to stuctured intervals straightforwardly as follows: (26) A < B B ∪A < ∪B A ∅ B B ∪A ∅ ∪B A b B B ∪A b ∪B A ⊃⊂ B B ∪A ⊃⊂ ∪B The shift from simple to structured temporal traces does not affect their durations, just their internal structure. Thus we assume that each τS (e) contains τ(e) as its greatest element. (27) A structured temporal trace is a function τS mapping events to structured intervals, subject to the condition that for all events e, τ(e) = ∪τS (e). Next, we use sets of intervals to derive a pre-order on the entire set T of times as in (28).21 For our example in Figure 1, the relative ranking of the equivalence classes of the pre-order induced by τ(e) is shown in the lower middle graph. (28) Induced pre-order on T Let A be a set of intervals. The pre-order EA on T induced by A is defined as follows: t EA t0 iff all intervals in A which contain t also contain t0 . 20 In fact, the structured intervals we consider here are nests of final subintervals; but we refrain from imposing those stronger properties by definition since nothing in our proposal depends on them. 21 This notion of an induced pre-order is inspired by Kratzer’s treatment of modality (Kratzer, 1981, i.a.); but notice that here the order is reversed, in the sense that times that are contained in more intervals are ranked higher, rather than lower. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 674 M. Kaufmann & S. Kaufmann Stativity and progressive This latter change also affects the interpretation of statives. Recall from above that they were mapped to properties of intervals. This remains unchanged, but now what gets passed up in the compositional process is the singleton sets containing those intervals. Singleton sets of intervals induce single-step pre-orders as shown on the right-hand side in Figure 1. There, all points in i are ranked equally and strictly higher than any point outside of i. This is in line with the intuition that the denotations of statives do not involve any notion of change or development. The switch to set-valued temporal traces requires minor adjustments to the overall system. Recall that our goal is to allow for expressions higher up in the syntactic tree, such ‘tokoro’, which do not directly compose with event-denoting sentence radicals, to have access to the structure of the temporal traces despite the intervening tenses (and possibly other temporal/aspectual material). We achieve this by generalizing to the worst case, as it were, using structured intervals throughout the compositional process. For the most part, that change is insignificant. For instance, the denotation of the covert aspectual operator ‘∅’, first given in (10a) above, changes to (29). The upper line, for stative complements, requires that there be an interval k of which ϕ is true and such that j is the singleton set containing k. The lower line, for non-statives, now implies that j encodes the structure of e. However, this information about the structure of e leaves no imprint on i, since i and j are required to be disjoint. (29) ∅ { λϕhi,ti λiλj∃ j[ϕ( j) ∧ j = λk[k = j]] ∧ [i , s → i b j]]∪ λρh,ti λiλj[∃e[ρ(e) ∧ j = τS (e)] ∧ i ∅ j] In fact, to keep things simple, it is a good idea to assume that the structured intervals used in the derivation are generally singleton unless they are non-trivially structured by the temporal trace of an event. Formally, this can be done by defining a predicate in the translation language that is true of structured intervals just in case they are singleton (e.g., sg(i) B ∃i[i = λ j[ j = i]]) and assert this predicate of all the intervals that are not used to record event measurement (i.e., i in (29), j in (31a), and both i,j in (31b)). We refrain from doing so in the interest of readability, but we do make the assumption that the structured intervals are singleton unless stated otherwise, and this assumption will in fact be significant below. For the denotation of ‘-tei-’, we redefine the notion of an extended temporal trace. Recall from (18) above that τ+ (e) is the property of being either the traditional temporal trace τ(e) or the result state result(e). From τ+ and the notion of a structured temporal trace τS we now define a function mapping events to properties of structured events: T(e) is the property of being either the structured trace τS (e) or the singleton set result(e). (30) Let τ+ be an extended temporal trace function and τS a structured temporal trace function defined on the same domain. The corresponding extended structural temporal trace function T maps events to properties of structured intervals as follows: T(e) = λi[i = τS (e) ∨ ∃ j[ j = result(e) ∧ i = λk[k = j]]] With this notion in place, we adjust our definition of ‘-tei-’ to structured intervals as in (31). (31) a. b. ‘-tei-’ ong { λρh,ti λiλj[∃e[ϕ(e) ∧ T(e)(j)] ∧ [i , s → i b j]] ‘-tei’ ant { λϕhhi,ti,hhi,ti,tii λiλj∃k[ϕ(j)(k) ∧ k < j ∧ [i , s → i b j] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 675 Stativity and progressive ibj j<i ibj 3 3 3 7 Ej i<j Ej M. Kaufmann & S. Kaufmann Figure 2: Permissible (left) and excluded (right) positions of i relative to the order induced by j. 3.3. ‘Tokoro’: the uphill condition ‘Tokoro’ takes as its complement a tensed clause, which as we saw denotes a binary relation between structured intervals, constrained by the temporal semantics of the complement. ‘Tokoro’ adds a single further condition on the pairs i,j in this relation: informally put, i must be adjacent to an interval with strictly higher “j-ness.” Somewhat more formally: i must abut an interval which ranks strictly higher than i on the order induced by j. We introduce special terms and notation for this relationship in (32) and give the denotation of ‘tokoro’ as in (33). Uphill and downhill Let i and j be structured intervals. i is downhill from j (and j is uphill from i), written i j , iff there is an interval k such that ∪i Ej k and ∪i ⊃⊂ k (33) ‘tokoro’ { λϕhhi,ti,hhi,ti,tii λhλi∃j[ϕ(i)(j) ∧ i  (32)  j] Figure 2 shows various possible locations of i relative to an order Ej , all of which may be delivered by the compositional semantics of the prejacent of ‘tokoro’. For instance, the pictures on the left are consistent with the denotations of a non-stative clause with simple Past, Progressive ‘-tei-’ plus Present, and simple Present. These options are illustrated in (34) and (35).22 In (34), where the precedence relation between i and j is fixed by the tense and aspect of the prejacent, ‘tokoro’ strengthens this requirement to immediate precedence. In (35), the inclusion of i within j is ensured by ‘-tei-’,23 and ‘tokoro’ imposes in the additional condition that j have internal structure, i.e., that it be the temporal trace of an activity (or of the activity phase of an accomplishment). This is the case for the Progressive reading of ‘-tei-’. (34)  Taro-ga { aruku // aruita } tokoro { da / datta } Taro-nom walk-npst walk-past tokoro cop-npst cop-past  ‘Taro {is/was} about to walk // {has/had} just walked’ a. λhλi∃j[∃e[TaroAruk(e) ∧ j = τS (e)] ∧ i ∅ j ∧ {i ≤ j//j < i} ∧ i j ∧ {h ≤ i/i < h}] (34a)(s)(r) ⇔ ∃j[∃e[TaroAruk(e) ∧ j = τS (e)] ∧ {r < j//j < r} ∧ r j ∧ {s ≤ r/r < s}]  22 Notice that the matrix tense in these sentences is irrelevant for the present discussion, since it constrains the relation between h and i, which does not interact with ‘tokoro’. 23 Here Past tense on the prejacent is ruled out because the position under ‘tokoro’ is an embedding context. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 676 M. Kaufmann & S. Kaufmann (35) Stativity and progressive  Taro-ga arui-tei- { ru // *ta } tokoro { da / datta } Taro-nom walk-tei- npst past tokoro cop-npst cop-pst ‘Taro {is/was} walking.’ a. λhλi∃j[∃e[TaroAruk(e) ∧ T(e)(j)] ∧ i b j ∧ {i ≤ j//j < i} ∧ i j ∧ {h ≤ i/i < h}] (35a)(s)(r) ⇔ ∃h[∃e[TaroAruk(e) ∧ T(e)(j)] ∧ r b j ∧ r j ∧ {s ≤ r/r < s}]  Statives, on the other hand, do not have the right temporal denotations to serve as the prejacents of ‘tokoro’. This is shown for lexically statives in (36). Here i is placed within j, similarly to the Progressive reading available for (35) above; this time, however, the order induced by j is flat around i, thus the contour condition imposed by ‘tokoro’ is not met, as on the right-hand side in Figure 2. The Perfect reading of (35) is ruled out in the same way. (36)  Zyon-ga Nihon-ni { iru // *ita } tokoro { da / datta } Jon-nom Japan-loc be-npst be-past tokoro cop-npst cop-past a. λhλi∃j[∃ j[JonInJapan( j) ∧ j = λk[k = j]] ∧ i b j ∧ i j ∧ {h ≤ i/i < h}] (36a)(s)(r) ⇔ ∃j[∃ j[JonInJapan( j) ∧ j = λk[k = j]] ∧ r b j ∧ r j ∧ {s ≤ r/r < s}]  Finally, the Anterior reading of ‘-tei-’ is also incompatible with ‘tokoro’. The corresponding structure and interpretation for (35) is shown in (35’). (35’)  [ [ [ [ [ [Taro-ga aruk ] ∅ ] teiant ] {ru/*ta} ] tokoro ] {da/datta} ] ‘Taro {has/had} the experience of walking.’ a. λhλi∃j∃k[∃e[TaroAruk(e) ∧ k = τS (e)] ∧ k < j ∧ i b j ∧ i j ∧ {h ≤ i/i < h}] (36a)(s)(r) ⇔ ∃j∃k[∃e[TaroAruk(e) ∧ k = τS (e)] ∧ k < j ∧ r b j ∧ r j ∧ {s ≤ r/r < s}]  It is worth noting that the formula in (35’a) as it stands does not imply contradiction and illformedness, since it does not require j to be a singleton structured interval. This is not as it should be, since ‘-tei-’ does not in fact have an experiential reading under ‘tokoro’ (except for the counterfactual reading, which we do not deal with in this paper). It is here that our assumption that all structured intervals are singleton unless stated otherwise comes into play. We predict the unavailability of this reading if (and since) we assume that j in (36) is singleton, even though in the interest of readability we refrain from enforcing this in the formulas. 4. Conclusion Rather than summarize what we have accomplished in this paper, we mention two things we left for future work. We already mentioned that we did not deal with counterfactual readings of lexical statives and non-Progressive ‘-tei-’ under ‘tokoro’. We also did not touch on cases in which contextually given information can rescue a temporal reading. For instance, (37) can have a temporal interpretation even under a resultative reading of ‘-tei-’, as indicated by the English gloss, if the state in question occurs as part of a set sequence of eventualities, as for instance in describing which outfit a model is wearing at this point as part of an ongoing fashion show. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 677 M. Kaufmann & S. Kaufmann (37) Stativity and progressive Tada ima kimono-wo ki-tei-ru tokoro da. right now kimono-acc wear-tei-npst tokoro cop-npst ‘She’s in the kimono right now.’ We leave a full analysis of these cases to a future occasion. References Allen, J. F. (1983). Maintaining knowledge about temporal intervals. Communications of the ACM 26, 832–843. Bach, E. (1986). The algebra of events. Linguistics and Philosophy 9, 5–16. Dowty, D. (1991). Thematic proto-roles and argument selection. Language 67, 547–619. Fujii, T. (1976). “Dōshi + teiru” no imi. See Kindaichi (1976). [The semantics of Verb + teiru]. Gunji, T. (2004). Nihongo no asupekuto to hanzizitu kasô. Theoretical and Applied Linguistics at Kobe Shoin 7, 21–34. [=Japanese Aspects and Counterfactuals]. Hay, J., C. Kennedy, and B. Levin (1999). Scale structure underlies telicity in ‘degree achievements’. In T. Matthews and D. Strolovitch (Eds.), Proceedings of SALT 9, Ithaca, NY, pp. 127–144. CLC Publications. Igarashi, Y. and T. Gunji (1998). The temporal system in Japanese. In T. Gunji and K. Hasida (Eds.), Topics in the Constraint-Based Grammar of Japanese, pp. 81–97. Dordrecht: Kluwer. Kaufmann, S. and M. Miyachi (2011). On the temporal interpretation of Japanese temporal connectives. Journal of East Asian Linguistics 20, 33–76. Kennedy, C. and B. Levin (2008). Measure of change: The adjectival core of degree achievements. In L. McNally and C. Kennedy (Eds.), Adjectives and Adverbs: Syntax, Semantics, and Discourse, pp. 156–182. Oxford, UK: Oxford University Press. Kindaichi, H. (1950). Kokugo dōshi no ichibunrui. Gengo Kenkyū 15. [A classification of Japanese verbs]. Kindaichi, H. (Ed.) (1976). Nihongo Dōshi no Asupekuto. Mugi Shobō. [Japanese verb aspect]. Kratzer, A. (1981). The notional category of modality. In H.-J. Eikmeyer and H. Riesner (Eds.), Words, Worlds, and Contexts, pp. 38–74. Walter de Gruyter. Krifka, M. (1989). Nominal reference, temporal constitution and quantification in event semantics. In R. Bartsch, J. van Benthem, and E. Bos (Eds.), Semantics and Contextual Expression, pp. 75–115. Foris Publication. Krifka, M. (1992). Thematic relations as links between nominal reference and temporal constitution. In I. Sag and A. Szabolcsi (Eds.), Lexical Matters, pp. 29–53. Stanford, CA: CSLI Publications. Ogihara, T. (1998). The ambiguity of the -te iru form in Japanese. Journal of East Asian Linguistics 7, 87–120. Smith, C. S. (1991). The Parameter of Aspect, Volume 43 of Studies in Linguistics and Philosophy. Kluwer. Tenny, C. L. (1994). Aspectual Roles and the Syntax-Semantics Interface. Dordrecht: Kluwer. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 678 Parentheticality, assertion strength, and discourse1 Todor KOEV — University of Düsseldorf Abstract. Sentences with so-called SLIFTING PARENTHETICALS (e.g. The dean, Jill said, flirted with the secretary; Ross 1973) grammaticalize an intriguing interaction between speech act function and conventional meaning, one that is not found in regular embedding constructions (e.g. Jill said that the dean flirted with the secretary). In such sentences, the main clause is independently asserted and at the same time is interpreted in the scope of the parenthetical, which typically serves an evidential function. The discourse effect of this pragmasemantic setup is that slifting parentheticals modulate the strength with which the main part of the sentence is asserted (Urmson 1952, Asher 2000, Rooryck 2001, Davis et al. 2007, Simons 2007, Maier and Bary 2015). Building on Davis et al. (2007), this paper proposes a probabilistic discourse model that captures the role of parentheticality as a language tool for qualifying speaker’s commitments. The model also derives two empirical properties that set apart slifting parentheticals from regular embedding constructions, i.e. (i) the fact that slifting parentheticals invariably express upward entailing operators and (ii) the fact that they usually do not occur in subordinate clauses. Keywords: parentheticals, evidence, assertion, polarity, embedding, probability. 1. Introduction The interpretational properties of sentences with SLIFTING PARENTHETICALS (Ross 1973) are perhaps best illustrated by direct comparison to regular embedding constructions. Consider the minimal pair of sentences below. (1) The dean, Jill said, flirted with the secretary. (2) Jill said that the dean flirted with the secretary. The slifting sentence in (1) is largely synonymous with its embedding counterpart in (2). In most contexts, uttering either sentence would imply, in some weak sense, that the dean flirted with the secretary and attribute this information to Jill. The strength of such weak implications is contingent on the additional information provided, including the lexical properties of the attitude predicate (e.g. say leads to a weaker claim than discover) and the quality of the source (e.g. Jill might be a more trustworthy source than Marissa when it comes to the dean’s flirtations). We see that parentheticals as well as embedding constructions can both be used to express claims with a varying degree of strength. However, slifting sentences exhibit a range of properties that set them apart from regular embedding constructions. Here I discuss two such differences. The first difference concerns the 1I would like to thank Dan Lassiter, Roger Schwarzschild, Peter Sutton, and the audiences at Backgrounded Reports 2016 and Sinn und Bedeutung 21. For judgments, I am indebted to Kurt Erbach, Jeremy Perkins, and Peter Sutton. All mistakes are my own. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 679 T. Koev Parentheticality, assertion strength, and discourse observation that the former constructions obey certain polarity restrictions. Jackendoff (1972), Ross (1973), Hooper (1975), and Maier and Bary (2015) already notice that slifting parentheticals usually cannot host negation. Generalizing this observation, we could say that slifting parentheticals may create upward entailing but not downward entailing environments. This is illustrated in (3), where I think expresses an upward entailing operator and I doubt expresses a downward entailing operator. In contrast to parentheticals, the matrix clause of embedding constructions is not sensitive to the direction of the polarity it creates (4). (3) Snowden is a Russian spy, (4)  I think I doubt   I think #I doubt  . Snowden is a Russian spy. Second, slifting parentheticals have a more limited syntactic distribution than embedding clauses. The former do not easily modify subordinate clauses and thus do not appear in the scope of a propositional operator (5). This is in contrast to the latter constructions, which can easily be further embedded (6). (5) #Selena thinks that Justin, the vocal coach said, is a talented singer. (6) Selena thinks the vocal coach said that Justin is a talented singer. The upshot of this preview of properties is that any good semantic theory of slifting sentences needs to explain why such sentences give rise to claims comparable in strength to the claims expressed by embedding constructions. At the same time, the theory should be able to derive the unique properties of slifting sentences that distinguish them from embedding constructions. Section 2 states the main assumption of the paper. In Section 3, I show how graded claims can be modeled by using standard tools from probabilistic reasoning. Section 4 discusses the polarity and scopal properties of slifting parentheticals. Section 5 is the conclusion. 2. One sentence, two assertions The main claim of this paper is that slifting sentences stand apart from regular embedding constructions because of a single basic fact. Following similar claims in previous literature, I assume that slifting sentences make two semantic contributions as part of their conventional meaning (cf. Urmson 1952, Hooper 1975, Bach 1999, Asher 2000, Potts 2005, Simons 2007, Maier and Bary 2015, Hunter 2016). More specifically, I assume that the slifted clause (the nonparenthetical part of the sentence) invariably encodes the main assertion while the sentence as a whole expresses secondary, typically evidential information. Hooper and Simons put this idea succinctly: “[. . . ] the effect of complement preposing is to make the complement proposition the main assertion of the sentence while reducing the original main clause to parenthetical or secondary status. [. . . ] there are two assertions, or two claims to Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 680 T. Koev Parentheticality, assertion strength, and discourse truth. The first one, from the preposed complement, is given more importance in this construction, and the parenthetical assertion is clearly subordinated.” (Hooper 1975: 95) “From a discourse or usage point of view, it seems quite clear that the main point of an utterance of a slifted sentence will be the content of the slifted (i.e. nonparenthetical) clause, with the syntactically parenthetical clause serving a parenthetical function.” (Simons 2007: 1039) This assumption can be summarized as follows. (7) D OUBLE A SSERTION H YPOTHESIS A slifting sentence makes two assertions. The main assertion is expressed by the slifted clause and the parenthetical asserts secondary information. This hypothesis implies that the sentence in (8), repeated from (1), asserts both (8a) and (8b). (8) The dean, Jill said, flirted with the secretary. a. The dean flirted with the secretary. b. Jill said that the dean flirted with the secretary. (MAIN ASSERTION) (PARENTHETICAL ASSERTION) I argue that the Double Assertion Hypothesis can explain the potentially weakening effect of slifting parentheticals on the main claim and derive the ways in which such sentences differ from regular embedding constructions. While the latter constructions can be used to trigger weak implications as well, these implications need not be written into the semantics and can be derived through reasoning. It is important to emphasize that the privileged semantic role of slifted clauses correlates with their apparent syntactic status as main clauses. Grimshaw (2011) presents a battery of arguments in support of the claim that English slifted clauses are indistinguishable in form from main clauses. She shows that, unlike subordinate clauses, slifted clauses cannot be non-finite (9), cannot be headed by a complementizer (10), require subject–auxiliary inversion when the parenthetical includes an interrogative predicate (11), and generally block quantifier binding from the parenthetical (12). The following data are adapted from Grimshaw (2011: 4–6). (9) a. *To leave, I promised them. b. I promised them to leave. (10) a. *That it was raining hard, they thought. b. They thought that it was raining hard. (11) a. Had she made a mistake, he wondered. b. *He wondered (whether) had she made a mistake. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 681 T. Koev (12) Parentheticality, assertion strength, and discourse a. ??Shei liked the film, every girli said. b. Every girli said that shei liked the film. This argues for a main clause analysis of slifted clauses (Jackendoff 1972) over one which views them as raised or “s(entence-)lifted” complements (Ross 1973). While the precise syntactic analysis of slifting sentences is not the focus of this paper, given the weight of the empirical evidence, I will assume that slifted clauses are main clauses and treat slifting parentheticals as adjuncts. 3. Modulating assertion strength We have already seen that the strength with which a clause is implied can be qualified by parenthetical modification or through semantic embedding. For example, the unqualified claim in (13) can be weakened as in (13a) or (13b). (13) Jack is married to a nurse. a. Jack, Emmy said, is married to a nurse. b. Emmy said that Jack is married to a nurse. There are two simple yet important observations to be made about (13a)–(13b). The first observation is that the degree to which (13) is implied is modulated by the quality of the evidence stated in the parenthetical or the matrix clause. For example, changing Emmy said to Emmy discovered, Emmy might have said, or Everyone claims may result in a stronger or a weaker claim. The second observation is that if the context is held constant, the relative strength with which (13) is implied by each sentence is roughly the same. If we schematically represent slifting sentences as C, E and embedding constructions as E(C), where C and E are mnemonics for “claim” and “evidence” (respectively), these two empirical observations can be summarized as follows. (14) If C, E and E(C) are uttered in the same context, then: a. S TRENGTH D EPENDENCE: The implication strength of C is contingent on E in both C, E and E(C). b. S TRENGTH S IMILARITY: C is implied with approximately the same strength by C, E and E(C). I take it that Strength Dependence is quite uncontroversial. One piece of evidence for Strength Similarity is the fact that the main claim put forward by slifting or embedding sentences can be doubted or denied by the speaker with a comparable degree of ease. (15) (16) Jack, Emmy said, is married to a nurse, but  Emmy said that Jack is married to a nurse, but I doubt he really is I’m sure he isn’t   . I doubt he really is I’m sure he isn’t  . There appears to be some variation in judgment regarding the strength of slifted clauses, though. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 682 T. Koev Parentheticality, assertion strength, and discourse Jackendoff (1972), Asher (2000), Murray (2014), and Hunter (2016) claim that slifted propositions cannot always be denied, even when the respective embedded proposition can.2 (17) a. b. (18) Myrtle will come tomorrow, Margaret believes, (#but she actually came yesterday). Margaret believes that Myrtle will come tomorrow, but she actually came yesterday. (examples from Jackendoff 1972: 97) a. #John, Mary assures us, can be trusted, but I don’t trust him. b. Mary assures us that John can be trusted, but I don’t trust him. (examples from Asher 2000: 36) If these data are real, one possible explanation is that the contrast in judgment may have to do with the central discourse status of slifted clauses (see Section 4.2). However, I discovered that English speakers tend to accept (17a) and (18a). Moreover, all speakers I consulted find such sentences felicitous if a weaker follow-up (e.g. but I seriously doubt it) is used, such that the possibility that the slifted clause is true is left open. I will then assume that slifted clauses imply commitments that more or less match the commitments implied by the respective embedded propositions. How can we model weak assertions? Davis et al. (2007) hypothesize that there are two major language strategies for qualifying a claim. The first strategy involves semantic embedding under an appropriate modal operator, which weakens the original claim by manipulating its truth conditions. This is the strategy illustrated by embedding constructions. Under the second strategy, first suggested in Lewis (1976), the speaker specifies the source of information and may weaken the original claim by lowering the quality threshold for asserting it.3 Since slifting parentheticals provide evidential support for the main claim, slifting sentences arguably lexicalize this latter strategy (see also Simons 2007, Murray 2014, Hunter 2016). To illustrate the evidential strategy, Davis et al. (2007: 81) outline the following three-step procedure (here slightly adapted). (19) If a parenthetical sentence C, E is uttered by an agent a and in a context c, then: i. a assumes a commitment to having E-type evidence for C, ii. the quality threshold θ c is readjusted to the reliability of E, and then iii. a asserts C against θ c . One intuitive way of fleshing out Davis et al.’s idea is to assume that propositions enter the common ground as indexed by quality thresholds, which impose a lower bound on their certainty level. The threshold against which a slifted clause C is asserted will depend not only on the context but also on the reliability of the evidence E provided by the slifting parenthetical. This threshold could then be less than the default for the given context. In contrast to parentheticals, 2 For reasons of uniformity and in order to do justice to the proposal, in borrowed examples I will often substitute ungrammaticality marking (*) with pragmatic unacceptability marking (#). 3 Davis et al. (2007) call these the MODAL and the EVIDENTIAL strategy, respectively. I find this terminology confusing in both directions. On one hand, slifting parentheticals contain modals as main predicates; on the other hand, modal verbs often contribute evidential meanings (von Fintel and Gillies 2010, Lassiter 2016). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 683 T. Koev Parentheticality, assertion strength, and discourse an embedding sentence E(C) will always be evaluated against the unmodified threshold. If C is weakened, this is because it is interpreted in the semantic scope of E, not because it is weakly asserted. As an illustration, consider a context with a quality threshold of 0.9 and one in which the likelihood of Emmy’s words being true is 0.7. If Jack, Emmy said, is married to a nurse is uttered, we will add to the common ground both the proposition that Emmy said Jack is married to a nurse (indexed by 0.9) and the proposition that Jack is married to a nurse (indexed by 0.7). In turn, if Emmy said Jack is married to a nurse is uttered, only the former proposition will be added to the common ground, and it will be indexed by 0.9. This way of looking at things does not yet derive Strength Dependence or Strength Similarity. We still need to explain why embedded clauses, although not asserted, are implied with a comparable degree of confidence to slifted clauses, and why in both cases this degree depends on the quality of the evidence. Both of these constraints can be accounted for if we assume that contexts are associated with PROBABILITY MEASURES.4 Probability measures are functions µ from propositions (sets of possible worlds) to real numbers between 0 and 1 such that (i) µ maps the universal set of worlds to 1 and (ii) µ maps the union of any two disjoint propositions p and q to the sum of µ(p) and µ(q). Instead of representing common grounds as sets of indexed propositions, i.e. as objects of the form CG = {hp1 , θ1 i, . . . , hpn , θn i}, we can view them as effectively specifying a probability measure, i.e. a function µ such that µ(p1 ) = θ1 , . . . , µ(pn ) = θn . We now want to model the intuition that discourse-new information may modify the likelihood of discourse-old information. Assume that we are given a prior probability for p and just learned that q. How should we update the probability of p in light of the new evidence q? One could employ the mechanism of CONDITIONALIZATION, which involves redistributing probability weights after new information is obtained. In its simple form, the probability measure µ conditionalized on the proposition q is defined as follows, for any proposition p. (20) S IMPLE CONDITIONALIZATION µ(p ∩ q) , where µ(q) 6= 0 µq (p) = µ(q) However, simple conditionalization is too rigid for our threshold-based discourse model. It presumes that the newly obtained information q is certain and tells us how much of its probability weight is assigned to p ∩ q. But what if q itself is uncertain, e.g. asserted against a threshold of θ = 0.9? Work in philosophy and cognitive science has adopted a slightly more complicated mechanism, called J EFFREY CONDITIONALIZATION (Jeffrey 1990). While not previously used in formal semantics to the best of my knowledge, it gives us what we want because it is expressed in terms of simple conditionalization but also factors in the uncertainty of the evidence.5 4 Probability measures have been widely studied and have well-understood properties. Less-familiar tools for modeling uncertainty include Dempster–Shafer belief functions, possibility measures, etc. (see Halpern 2003 for an overview). 5 Jeffrey himself called this generalized form of conditionalization “probability kinematics”. Notice that this Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 684 T. Koev (21) Parentheticality, assertion strength, and discourse J EFFREY CONDITIONALIZATION (Jeffrey 1990) µhq, θ i (p) = θ µq (p) + (1 − θ ) µ¬q (p), where 0 < µ(q) < 1 Here the evidence is made sensitive to its likelihood: µhq,θ i (p) stands for the probability of p, given that the likelihood of q is θ . It is easy to see that when the evidence is certain, i.e. θ = 1, Jeffrey conditionalization reduces to its simple relative. That is, µhq, 1i = µq , for any q. The following example illustrates the usefulness of Jeffrey conditionalization in accumulating new evidence. Example Let p stand for the proposition It is raining, q stand for the proposition Mary said it is raining, and µ(p) = 0.5, µ(q) = 0.5, µq (p) = 0.7. That is, we are completely ignorant as to whether p or q are true but we know that learning q would substantially increase the likelihood of p, e.g. because Mary is a fairly reliable source of weather information. What is the posterior probability of p if q is uttered at a 0.9 quality threshold? • By Bayes’ rule, the prior probability of q given p is: µ p (q) = 0.7. µq (p) µ(q) 0.7 × 0.5 = = µ(p) 0.5 • By the complement rule, the prior probability of ¬q is: µ(¬q) = 1− µ(q) = 1−0.5 = 0.5. • By Bayes’ rule and the complement rule: µ¬q (p) = (1 − 0.7) × 0.5 = 0.3. 1 − 0.5 µ p (¬q) µ(p) (1 − µ p (q)) µ(p) = = µ(¬q) 1 − µ(q) • By the Jeffrey conditionalization rule and given that q is uttered at a threshold of 0.9, the posterior probability of p is: µhq, 0.9i (p) = 0.9 µq (p) + (1 − 0.9) µ¬q (p) = 0.9 × 0.7 + 0.1 × 0.3 = 0.66. The probability of rain thus increases from 50% to 66%. This is lower than the 70% produced by simple conditionalization, since the latter rule does not take into account that we are only 90% certain that Mary said it was raining. End of example The effect of slifting and embedding sentences on the probability measure of the context can now be rendered as follows. h[[E(C)]], θ i h[[C]], µ 0 ([[C]])i µ −−−−−−→ µ 0 −−−−−−−→ µ 00 (22) Slifting sentences C, E: (23) Embedding sentences E(C): µ −−−−−−→ µ 0 h[[E(C)]], θ i rule falls out from a few basic facts of probability theory. Proof: µ(p) = µ(p ∩ q) + µ(p ∩ ¬q) total probability law = µ(q) µq (p) + µ(¬q) µ¬q (p) conditional probability = µ(q) µq (p) + (1 − µ(q)) µ¬q (p) complement = θ µq (p) + (1 − θ ) µ¬q (p) θ = µ(q) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde QED 685 T. Koev Parentheticality, assertion strength, and discourse If a slifting sentence C, E is uttered, the probability measure is first conditionalized on h[[E(C)]], θ i and then conditionalized on h[[C]], µ 0 ([[C]])i (22). The strength of the evidential proposition [[E(C)]] is then the threshold value θ and the strength of the main proposition [[C]] is its prior probability µ conditionalized on the evidential proposition at θ . In turn, if an embedding sentence E(C) is uttered, the probability measure is conditionalized on h[[E(C)]], θ i alone (23). Even though in this latter case the embedded clause is not asserted, speech participants may employ probabilistic reasoning to infer that the likelihood of C, given that E(C) was asserted against θ , is µh[[E(C)]], θ i ([[C]]). This story accounts for both Strength Dependence and Strength Similarity: the strength of C depends on the strength and relevance of E(C) in both cases. Slifting sentences and embedding sentences are then predicted to play a similar role when it comes to what inferences speakers may draw from them. They only differ in that the former assert (perhaps weakly) the slifted clause while the latter do not assert the embedded clause. 4. The uniqueness of slifting parentheticals The analysis of varying assertion strength proposed in the previous section does not directly predict any substantial interpretational differences between slifting and embedding sentences. However, as already mentioned in the Introduction, the two constructions differ in polarity and distribution. This section discusses these differences in depth and argues that they both are rooted in the Double Assertion Hypothesis and general principles of discourse organization. 4.1. Polarity restrictions Other things being equal, one might expect that slifting parentheticals can have the same grammatical make-up as matrix clauses. For example, the fragment Jill said can be used parenthetically and it can also serve as a matrix clause. However, Jackendoff (1972), Ross (1973), Hooper (1975), and Maier and Bary (2015) notice that, unlike matrix clauses, slifting parentheticals need to make a “positive” or “affirmative” import. At least initially, it appears that slifting parentheticals cannot contain negation or lexically negative predicates. (24) (25)    I think  #I don’t think John is, , a fink.   #I doubt (Jackendoff 1972: 97)    I think  I don’t think John is a fink.   I doubt The same authors also observe that there is no syntactic ban on slifting parentheticals hosting negation or negative predicates. If a slift contains a lexically negative verb (like doubt or deny) that is negated, the sentence becomes acceptable. (26) John is, I don’t doubt, a fink. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde (Jackendoff 1972: 97) 686 T. Koev Parentheticality, assertion strength, and discourse (27) Mushrooms are great on diets, I don’t doubt. (28) It’s a long shot, I don’t deny. (Ross 1973: 155) (Hooper 1975: 107) The positive/affirmative import generalization must then be a semantic one and it must constrain the entire slifting parenthetical, not just its main predicate. I propose that it should be stated in terms of monotonicity.6 The monotonicity properties of operators have been widely discussed in the literature on polarity items and elsewhere. The two crucial notions of upward and downward entailingness are standardly defined as follows (e.g. Ladusaw 1980). (29) a. b. An operator O is UPWARD ENTAILING iff for any propositions p and q, if p ⊆ q then O(p) ⊆ O(q). An operator O is DOWNWARD ENTAILING iff for any propositions p and q, if p ⊆ q then O(q) ⊆ O(p). Asher (1987) develops a semantic typology of a wide range of propositional attitude predicates. He proposes that verbs like say, think, believe are upward entailing while verbs like deny or doubt are downward entailing.7 Indeed, if Jimmy believes I own a Porsche (and he also knows that Porsches are cars), then he must believe that I own a car. In turn, if Jimmy doubts I own a car (and knows that Porsches are cars), then he must doubt that I own a Porsche as well. The polarity generalization about slifting parentheticals can now be stated as follows. (30) U PWARD M ONOTONICITY A slifting sentence C, E can be felicitously uttered only if E expresses an upward entailing operator. Assuming that no operator can be both upward and downward entailing, Upward Monotonicity correctly bans slifts from creating downward entailing environments. It also rules out slifts that express non-monotone operators, i.e. operators that are neither downward nor upward entailing. The verb lie is one example of a non-monotone propositional operator; e.g. there is no entailment relation between (31a) and (31b).8 Upward Monotonicity then correctly predicts that the sentences in (32), which host non-monotone slifts, are not acceptable. (31) a. b. Jeremy lied that he resides in Vancouver. Jeremy lied that he resides in Canada. 6 There appear to be further restrictions on what can go into slifting predicates that go beyond polarity and that are not addressed in this paper. See Ross (1973), Hooper (1975), and Haddican et al. (2014) for discussion. 7 I will sometimes loosely talk of lexical items themselves as being upward or downward entailing. What is meant is that the operators that those items denote have the claimed monotonicity. 8 The reason lie is non-monotone might be that a lied that p implies both a said p and not-p. Since a said is upward entailing while not is downward entailing, the combined effect is that of non-monotonicity. I am indebted to Emar Maier for the suggestion that lie expresses a non-monotone operator. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 687 T. Koev (32) Parentheticality, assertion strength, and discourse a. #Paul had never known his mother, he lied. b. #The CEO, his girlfriend lied, is a true gentleman. There are two cases of seeming violations of Upward Monotonicity that deserve further mentioning. The first case involves situations when the speaker echoes a previous utterance and disagrees with it by using a segment that resembles a negated slifting parenthetical. This use is illustrated in (33), and can be read as Mushrooms are great on diets? I don’t think so. The second case involves what looks like a negated slifting parenthetical attached to a negated main clause (34). The apparent function of such parentheticals is to qualify the categorical denial of a claim expressed by the first part of the sentence. (33) Mushrooms are great on diets, I don’t think so. (34) Matt doesn’t like phonology, I don’t think. It is fairly clear that (33) is not a slifting sentence at all. This is because the argument slot in the second segment is filled by a so-anaphor and without it the sentence becomes unacceptable. Genuine slifts do not allow so-insertion (cf. *The dean, Jill said so, flirted with the secretary). While examples as in (34) do exhibit the grammatical form of slifting constructions, they turn out to have a very limited distribution and quirky interpretational properties. Ross (1973) and Hooper (1975) observe that in such examples the negation in the parenthetical is licensed by a negation in the main clause. Just any downward entailing operator in the main clause cannot support a negated slift (cf. *Few people like phonology, I don’t think) and just any downward entailing slift cannot be licensed by a negated main clause (cf. *Matt doesn’t like phonology, I doubt). In addition, the putative parenthetical may modify a non-clausal argument (cf. Matt doesn’t like phonology, I don’t think he does) and has to appear at the end of the sentence (cf. *Matt, I don’t think, doesn’t like phonology). Ross (1973) also notices that such doublynegated sentences are restricted to Neg-Raising predicates (cf. Matt doesn’t like phonology, I don’t think / *I don’t fear). Most importantly, as noted in Huddleston and Pullum (2002: 845), the negation in the slift is semantically vacuous, and (34) is synonymous with Matt doesn’t like phonology, I think. I will then tentatively assume that such constructions illustrate some sort of negative concord and are actually upward entailing. If so, the data in (33)–(34) do not challenge the Upward Monotonicity restriction. Where does Upward Monotonicity come from? Two explanations have been suggested in the literature, although none of them seems able to explain the full range of data. One idea is that this generalization falls out from the relative strength with which a main clause is asserted. Hooper (1975), Scheffler (2009), and Hunter (2016) propose that, roughly, upward entailing slifts imply the main clause with a sufficiently high level of confidence while downward entailing slifts do not. Assuming that τ is the minimal threshold that any assertion (whether weak or strong) in the given context should meet, we could then propose the following constraint. (35) A SSERTION S TRENGTH A slifting sentence C, E can be felicitously uttered only if µh[[E(C)]], θ i ([[C]]) ≥ τ. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 688 T. Koev Parentheticality, assertion strength, and discourse However, this constraint immediately runs into empirical difficulties. A segment like it seems entails its propositional argument in a fairly weak sense but can serve as a parenthetical (cf. Noah majored in psychology, it seems). In contrast, a segment like he regrets contains a factive predicate that presupposes the truth of its propositional argument, yet it is unacceptable as a parenthetical (cf. #Noah majored in psychology, he regrets). Assertion Strength leaves these facts unexplained. A related idea is that Upward Monotonicity is tied to the evidential role of slifting parentheticals. Haddican et al. (2014) and Maier and Bary (2015) suggest that upward entailing operators provide a good source of evidence while downward entailing operators do not. We could then require that parentheticals raise the likelihood of the main sentence being true. (36) E VIDENTIAL S UPPORT A slifting sentence C, E can be felicitously uttered only if µh[[E(C)]], θ i ([[C]]) > µ([[C]]). The main challenge for this constraint is negative evidence. Evidential Support predicts that in the given context (37a) is infelicitous, and it would not let us expect that there is anything wrong with (37b). Indeed, if Putin rarely tells the truth, what he says is likely to be false and what he denies is likely to be true. The attested data are the exact opposite of what is predicted. (37) Putin is a rogue leader who typically makes false claims in order to deceive his enemies. a. There are Russian troops in Ukraine, Putin said. b. #There are Russian troops in Ukraine, Putin denied. I propose that Upward Monotonicity has less to do with the semantics of slifting parentheticals and more to do with the fact that slifted clauses do double duty: they are independently asserted (albeit perhaps weakly) and they serve as arguments to slifting parentheticals, as stated by the Double Assertion Hypothesis. Slifting parentheticals are upward entailing because slifted clauses in particular and main clauses in general act like POSITIVE POLARITY ITEMS (PPIs). For example, (38) hosts a main clause interpreted under an upward entailing (UE) operator and the sentence is acceptable; (39) hosts a main clause interpreted under a downward entailing (DE) operator and the sentence is unacceptable. (38) [Snowden is a Russian spy]PPI , [Mary thinks]UE . (39) #[Snowden is a Russian spy]PPI , [Mary doubts]DE . The positive polarity status of slifted clauses may be taken to follow from fact that assertions should allow speech participants to draw entailments, which are weaker inferences. In other words, asserted sentences need to be closed under their entailments, as stated by the following constraint. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 689 T. Koev (40) Parentheticality, assertion strength, and discourse E NTAILMENT C LOSURE A sentence S can be felicitously uttered only if S and all of its entailments meet the quality threshold of the context. This type of general constraint may appear to be of little value when it comes to single assertions, because entailments are less specific than what is said and Entailment Closure will always be met. But some constraint along those lines becomes important in slifting sentences, where the slifted clause serves an argument of the parenthetical yet it is also independently asserted, as per the Double Assertion Hypothesis. It is then plausible to require that parenthetical assertions are closed under the entailments of the slifted clause. (41) PARENTHETICAL E NTAILMENT C LOSURE A slifting sentence C, E can be felicitously uttered only if, for any entailment C0 of C, E(C0 ) meets the quality threshold whenever E(C) does. This constraint can be further elucidated by drawing attention to the fact that the two assertions C and E(C) associated with a slifting sentence C, E are proportional with respect to their informativity. When E is upward entailing, the strength of E(C) is directly proportional to the strength of C and any weakening of C makes E(C) weaker, i.e. truth is always preserved. If, however, E is downward entailing, the strength of E(C) is inversely proportional to the strength of C. In this case, a weaker C makes E(C) stronger, and truth need not be preserved. In other words, only upward entailing slifting parentheticals will obey Parenthetical Entailment Closure. To illustrate, notice that speakers may draw all sorts of entailments from the main clause in (39), including that Snowden is a spy. However, this would violate Parenthetical Entailment Closure, because the parenthetical assertion does not guarantee that Mary doubts Snowden is a spy; it only guarantees that Mary doubts Snowden is a Russian spy. No such problem arises in (38), because here the truth of the parenthetical assertion is preserved for all entailments of the main clause. In particular, if Mary thinks that Snowden is a Russian spy, it follows that she also thinks Snowden is a spy. Before closing this section, one should point out that the positive polarity status of main clauses is visible from data that go beyond slifting sentences, thereby strengthening the case for an entailment closure constraint of the form proposed above. As Ross (1973), Szabolcsi and Zwarts (1993), and Potts (2002) notice, an upward monotonicity restriction is operational in as-parentheticals as well. (42) John is our hero,  as you know #as no one knows  . (after Szabolcsi and Zwarts 1993: 246) Verb second embedding in German is restricted in the same way. Although main clauses are verb second and embedded clauses are verb final, German draws a grammatical distinction between regular embedding of dass/‘that’ complements with a verb final syntax and embedding of verb second clauses. Importantly, Scheffler (2009) points out that while attitude verbs of any monotonicity can occur in regular embedding constructions, verb second embedding is restricted to upward entailing attitudes. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 690 T. Koev (43) Parentheticality, assertion strength, and discourse a. Peter glaubt, Maria ist schwanger. Peter believes Maria is pregnant ‘Peter believes that Maria is pregnant.’ b. #Maria bereut, sie ist nach Berlin gezogen. Maria regrets she is to Berlin moved (Scheffler 2009: 184) Finally, certain speaker-oriented adverbs exhibit similar behavior. Jackendoff (1972) and Bellert (1977) mention the fact that discourse adverbs do not have negative counterparts. (44) a. b.    Truthfully  Honestly , I can’t tell you the answer.    Sincerely   #Falsely  #Dishonestly , I can’t tell you the answer.   #Insincerely (Jackendoff 1972: 99) Apparently, these polarity restrictions have a common source. I suggest that they are all based on a mechanism similar to the one proposed for English slifting sentences. 4.2. Main clause modifiers A second difference between slifting and embedding sentences concerns their embeddability. It has been noticed that slifting sentences typically modify main clauses and cannot appear in subordinate clauses (Ross 1973, Rooryck 2001). Embedding constructions do not have this property and can readily be further embedded. (45) a. #Martin now realizes that Sheila is, I had claimed, a luscious yummy. (Ross 1973: 152) b. #Selena thinks that Justin, the vocal coach said, is a talented singer. (46) a. b. Martin now realizes that I had claimed Sheila is a luscious yummy. Selena thinks that the vocal coach said Justin is a talented singer. The data in (45) also show that the scope of slifting parentheticals is clause-bounded, i.e. that slifts obligatorily modify their host clause. If that were not the case, (45a) and (45b) would be acceptable under a reading whereby the parenthetical takes scope over the entire sentence. I propose that the main clause restriction on slifting parentheticals once again follows from the Double Assertion Hypothesis. Recall that this hypothesis states that slifted clauses play a primary discourse role while the parenthetical component serves a subsidiary function. An empirical reflex of this contrast in pragmatic status is the fact that a slifted clause but not the entire parenthetical sentence can resolve a question, as demonstrated below. (47) Q: Why is Fred not here? A: He has quit his job, the secretary told me. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 691 T. Koev (48) Parentheticality, assertion strength, and discourse Q: What happened next? A: #There is life on Mars, she announced. In a similar vein, Asher (2000: 33) gives the following example. (49) A: The party, Mary assures us, is over. B: #Does she? How can we flesh out the non-central discourse status of slifting parentheticals? Asher assumes that the parenthetical component of a slifting sentence is connected to the main clause through an Evidence discourse relation. But evidentiality alone would not explain why (48) and (49) are unacceptable, since in principle evidential information can answer questions (cf. A: Lena is dating someone. B: How do you know? A: She always leaves work early.). The subordinate status of slifting parentheticals must then come from somewhere else. I propose that what is wrong with (48)–(49) is not that the parenthetical assertion cannot resolve a question but rather that the main assertion must but does not do so. I assume, quite plausibly, that main clauses are conventionally marked as AT- ISSUE, where the property of at-issueness is understood as relevance to the question under discussion, as argued in Simons et al. (2010) and much subsequent work. Arguably, this is the reason why the discourses below are degraded. (50) A: B: (51) Who was  Louise with  last night?  (?)hopes  ?wishes Henry that she was with Bill.   ?dreamt (Simons 2007: 1036) Q: What is Peter’s favorite color? A: ?Peter, whose favorite color is blue, never wears white shirts. The following constraint requires that main clauses pick out one of the alternatives introduced by the question under discussion. (52) AT-I SSUENESS A (declarative) main clause C can be felicitously uttered in a context with a question under discussion Q only if [[C]] ∈ Q. Given that slifted clauses are main clauses, At-Issueness entails that a slifting sentence C, E can be felicitously uttered only if [[C]] ∈ Q, where Q is the question under discussion in the given context. One way to read this is that slifting parentheticals attach to clauses that are obligatorily at-issue, i.e. main clauses. It is then to be expected that such parentheticals do not occur in syntactically subordinate positions. Since embedded clauses need not be marked for discourse status, embedding predicates can freely be further embedded. In the remaining part of this section, I address one type of exception to the non-embeddability of slifting parentheticals. The following sentence is acceptable and the parenthetical seems to take narrow scope with respect to the matrix verb (see also Ross 1973). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 692 T. Koev (53) Parentheticality, assertion strength, and discourse Sarah said that Will, she thinks, has strong qualifications. One possible reaction would be to say that embedded clauses too can take on at-issue status.9 However, this begs the question of why slifting parentheticals do not embed on a regular basis. What I would like to suggest is that examples as these are likely based on some sort of an agreement mechanism whereby the slift restates what is already expressed by the matrix clause. In support of this view, notice that (53) deteriorates if the slift presents a fresh perspective by introducing a different attitude holder (54). Also, such examples seem to require predicates that can describe the same attitude, e.g. say and think. (53) becomes unacceptable if the matrix and the slifting predicates do not line up semantically (55). (54) ?Sarah said that Will, the committee thinks, has strong qualifications. (55) #Sarah imagined that Will, she thinks, has strong qualifications. I leave the precise analysis of such examples to further research, here merely noting their special properties. 5. Conclusion This paper investigated the semantic properties of sentences with slifting parentheticals. The main claim was that such constructions function as a means of modulating assertion strength. I proposed a probabilistic account whereby the assertion strength of the slifted clause is derived from the background discourse information conditionalized on the evidence described by the parenthetical component. The account was shown to capture the intuition that the implication strength of slifted clauses varies depending on the quality and certainty of the evidence. Importantly, slifting sentences were not reduced to embedding constructions and their unique properties were preserved. In particular, the proposal was able to explain why slifting parentheticals express upward entailing operators and why they typically modify main clauses. The paper argued that those properties follow from the double assertion nature of slifting sentences and general principles of discourse management. References Asher, N. (1987). A typology for attitude verbs and their anaphoric properties. Linguistics and Philosophy 10(2), 125–197. Asher, N. (2000). Truth conditional discourse semantics for parentheticals. Journal of Semantics 17, 31–50. Bach, K. (1999). The myth of conventional implicature. Linguistics and Philosophy 22, 327– 366. Bellert, I. (1977). On semantic and distributional properties of sentential adverbs. Linguistic Inquiry 8(2), 337–351. Davis, C., C. Potts, and M. Speas (2007). The pragmatic values of evidential sentences. In Proceedings of Semantics and Linguistic Theory 17, pp. 71–88. 9 Cf. so-called DISCOURSE PAENTHETICAL uses of matrix clauses (Urmson 1952, Simons 2007, Hunter 2016). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 693 T. Koev Parentheticality, assertion strength, and discourse Grimshaw, J. (2011). The place of slifting in the English complement system. Generative Initiatives in Syntactic Theory 3, Handout. https://docs.google.com/file/d/ 0B1DtOqeuIhA3Nzg2NDNmNzEtMmFkZC00N2VjLThjYmUtNmM0MTA1MzUxMWNj/edit?hl= en_US. Haddican, B., A. Holmberg, H. Tanaka, and G. Tsoulas (2014). Interrogative slifting in English. Lingua 138, 86–106. Halpern, J. Y. (2003). Reasoning about Uncertainty. MIT Press. Hooper, J. B. (1975). On assertive predicates. In J. Kimball (Ed.), Syntax and Semantics 4, pp. 91–124. Academic Press. Huddleston, R. and G. Pullum (2002). The Cambridge Grammar of the English Language. Cambridge University Press. Hunter, J. (2016). Reports in discourse. Dialogue & Discourse 7(4), 1–35. Jackendoff, R. (1972). Semantic Interpretation in Generative Grammar. MIT Press. Jeffrey, R. (1990). The Logic of Decision (second ed.). The University of Chicago Press. Ladusaw, W. A. (1980). Polarity Sensitivity as Inherent Scope Relations. Ph. D. thesis, University of Texas, Austin. Lassiter, D. (2016). Must, knowledge, and (in)directness. Natural Language Semantics 24, 117–163. Lewis, D. (1976). Probabilities of conditionals and conditional probabilities. Philosophical Review 85, 297–315. Maier, E. and C. Bary (2015). Three puzzles about negation in non-canonical speech reports. In Proceedings of the 20th Amsterdam Colloquium, pp. 246–255. Murray, S. (2014). Varieties of update. Semantics & Pragmatics 7(2), 1–53. Potts, C. (2002). The syntax and semantics of as-parentheticals. Natural Language & Linguistic Theory 20, 623–689. Potts, C. (2005). The Logic of Conventional Implicatures. Oxford University Press. Rooryck, J. (2001). Evidentiality I. Glot International 5(4), 25–133. Ross, J. R. (1973). Slifting. In The Formal Analysis of Natural Language, pp. 133–169. Mouton. Scheffler, T. (2009). Evidentiality and German attitude verbs. In Proceedings of Penn Linguistics Colloquium 32, pp. 183–192. Simons, M. (2007). Observations on embedding verbs, evidentiality, and presupposition. Lingua 117, 1034–1056. Simons, M., J. Tonhauser, D. Beaver, and C. Roberts (2010). What projects and why. In Proceedings of Semantics and Linguistic Theory 20, pp. 309–327. Szabolcsi, A. and F. Zwarts (1993). Weak islands and an algebraic semantics for scope taking. Natural Language Semantics 1, 235–284. Urmson, J. O. (1952). Parenthetical verbs. Mind 61, 480–496. von Fintel, K. and A. S. Gillies (2010). Must . . . stay . . . strong! Natural Language Semantics 18, 351–383. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 694 Simple even hypothesis: NPIs and differences in question bias1 David KRASSNIG — University of Konstanz Abstract. The even-based approach to NPI licensing arose as a competitor to the traditional idea that NPIs are licensed by some monotone environments. The approach itself equates NPIs with even + existential quantification. As such, distributional differences between NPIs and the expression even ONE are undesirable. There are, however, a small number of known differences: (i) They behave differently in the restrictor of a universal quantifier, and (ii) questions containing even ONE are negatively biased, whereas questions with an NPI are not. Under our proposal, we decompose weak EVEN into two focus particles. One is identical to the original EVEN , whereas the other particle has a directly opposite scalar presupposition and an additional presupposition of exclusivity. In doing so, we can derive both problematic cases for the even-based approach in a straightforward fashion. Keywords: negative polarity item, NPI, even, question bias, local accommodation, projection 1. Introduction Accounting for the entire distribution of negative polarity items (NPI) has been an ongoing issue for linguists for nigh a century: Formally starting with the work of Jespersen (1917) and Klima (1964), we have yet to discover a model that is capable of accounting for the entire set of known empirical data. Traditionally, NPIs are analysed as being licensed by certain monotone environments (cf. Fauconnier, 1975; Ladusaw, 1979): Namely, NPIs are generally considered to be licensed by (Strawson) downward-monotone environments. However, alternative models to NPI licensing have recently been on the rise (e.g. Krifka, 1995; Chierchia, 2013: and others). One of the major alternative NPI models would be the even-based approach to NPI licensing (cf. Lee and Horn, 1994; Lahiri, 1998; Crnič, 2011a). Essentially, this approach states that any NPI is covertly licensed by the focus particle even at logical form (LF). The NPI itself is equivalent to weak existential quantification (i.e. any would be equivalent to even ONE). With most of the objections to this approach (cf. Heim, 1984) having been defused by Crnič (2014a, b), only a few major obstacles remain: One of them is the difference in polar question bias between questions containing the expression even ONE (hereafter referred to as even-questions) and questions containing the unstressed NPI any (hereafter referred to as NPI-questions). Whereas the former type appears to be negatively biased (i.e. rhetorical by nature), the latter question type corresponds to normal information-seeking questions. A dissimilarity that is not predicted by equating both expressions, as is done in the even-based approach. Another difference in distribution is that even ONE and any behave differently within the restrictor of a universal quantifier. This paper explores how the even-based approach may be reconciled with this set of empirical data. To achieve this, we propose (i) that EVEN be decomposed into the two focus parti1 We would like to thank Maribel Romero and Marı́a Biezma for their continued guidance and valuable input. We would also like to thank Andreas Walker for his insightful comments. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 695 D. Krassnig cles Simple even hypothesis and EVEN MAX (cf. Crnič, 2012; Lahiri, 2010), (ii) that any is only licensed by EVEN MIN , (iii) that overt even is licensed by the combination of EVEN MIN and EVEN MAX , (iv) that, crucially, EVEN MAX carries an additional presupposition of exclusivity, (v) that the difference in the universal quantifier’s restrictor is derivable via local accommodation of EVEN MAX ’s aforementioned presupposition, and (vi) that the difference in question bias is the result of the same projected presupposition of exclusivity from EVEN MAX . (1) EVEN MIN a. b. LF for any [ evenMIN [
↑ . . . [↑ . . . oneF . . . ] ] ] LF for even ONE [ evenMIN [
↑ . . . [ evenMAX [↑ . . . oneF . . . ] ] ] ] In §2 we go into how NPIs are traditionally viewed and how they are modelled under the evenbased approach to NPIs (see §2.1). In §3 we go into how rhetorical questions can be derived (see §3.1), how polar questions are analysed according to Guerzoni and Sharvit’s (2014) question model (see §3.2), and how these question models fail to handle the difference in question bias with a non-decomposed EVEN. In §4 we then decompose the NPI-licensing EVEN into the two focus sub-particles EVEN MIN and EVEN MAX . We then show in §4.2 how the difference in question bias is obtained with this decomposed model of weak EVEN. 2. NPI licensing Accounting for NPIs is a complex issue in formal semantics. Any model that seeks to license them needs to have a unified analysis for a wide range of different licensing environments. See below for a (non-exhaustive) list of NPI-licensing and non-licensing constructions. (2) a. #John read any book. b. John didn’t read any book. c. Exactly two students read any book. d. Every student who read any book passed the exam. e. Did John read any of the relevant books? NPIs are not licensed within simple affirmative declarative sentences. They are licensed under negation, within the restrictor of universal quantification, under only, within the antecedent of a conditional, within questions, and within the scope of some non-monotone quantifiers. The first workable model that covered a wide range of the known empirical data was put forth by Fauconnier (1975) and Ladusaw (1979). Their model of licensing was based upon the monotonicity of the environment containing the NPI in question: According to their model, an NPI is licensed iff it occurs within a downward-monotone environment. Later on, their model was improved upon by von Fintel (1999, 2001), who extended their account to cover more empirical data, by lessening the restrictions to Strawson downward-monotone environments (environments that are shown to be downward-monotone given the right circumstances). Together, they form the traditional mainstream line of thought concerning how NPIs are licensed. We refer to Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 696 D. Krassnig Simple even hypothesis their model, and other models like them, as the monotonicity-based approach to NPI licensing (or, alternatively, the Fauconnier-Ladusaw-Fintel approach). Naturally, over the years, other models developed that diverged from these monotonicity-based models: Krifka (1995) and Chierchia (2013), to name two of the more substantive ones. However, recently one particular line of thought rose to greater prominence: the even-based approach to NPI licensing. Originally ruled out as a viable candidate by Heim (1984), the idea that NPIs are to be licensed by a (covert) EVEN at LF was nevertheless picked up by a number of authors over the years. Amongst them are Lee and Horn (1994), Lahiri (1998), and Crnič (2014a, b). 2.1. Even-based approach to NPI licensing An alternative approach to NPI licensing is based upon the focus particle even. The essential idea behind this approach is that every NPI is covertly licensed by EVEN at LF. This notion was first considered by Heim (1984) as she noted the similarity in distribution between the expression even ONE and the NPI any. See below for the even ONE counterparts to (2). (3) a. #John read even ONE book. b. John didn’t read even ONE book. c. Exactly two students read even ONE book. d. Every student who read even ONE book passed the exam. e. Did John read even ONE book? As we can see, there is an exact match between the felicity distribution of even ONE and the NPI any (at least for this limited range of data). However, this approach was initially ruled out by Heim (1984) herself, after she encountered some differences that are not easily accounted for: First, that the felicity of even ONE in (3d) is context-dependent, as can be seen below, whereas its NPI counterpart is felicitous, regardless from contextual influences. (4) a. Every student who read any book wore blue jeans. b. #Every student who read even ONE book wore blue jeans. Second, it was noted that questions containing the expression even ONE are negatively biased (i.e. the positive answer is strictly unexpected), whereas their NPI counterparts are not. (5) a. b. Did John read any book? (i) Yes, he did. (ii) No, he didn’t. Did John read even ONE book? (i) #Yes, he did. (ii) No, he didn’t. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 697 D. Krassnig Simple even hypothesis As mentioned before, the even-based approach was nevertheless picked up by a number of authors. Prominent examples would be Lee and Horn (1994), who first proposed that NPIs are always composed of a covert EVEN and an existential quantifier; Lahiri (1998), who has shown that this approach is a natural selection for Hindi (its NPIs are transparently consist of an even-like particle and existential quantification); and Crnič (2014a, b), who has shown that this approach is able to account for the distributional difference in (4) and the licensing of NPIs in non-monotone environments such as in (2c). The approach also accounts for the infelicity of NPIs in upward-monotone environments and the felicity in downward-monotone ones. Now that we have an overview over the empirical data, the history of the even-based approach, and what the approach is currently able to account for, we must consider how it accounts for them. To do this, we first list a number of assumptions most adherents to this approach typically make: (i) EVEN may move freely at LF (Karttunen and Peters, 1979); (ii) focus generates a set of possible alternatives to the focused element (Rooth, 1992); (iii) EVEN has no assertive contribution, but presupposes that its prejacent proposition is the least likely member of its set of focus alternatives (Karttunen and Peters, 1979; Kay, 1990); (iv) NPIs are semantically equivalent to indefinites (Lee and Horn, 1994; Lahiri, 1998); (v) NPIs also induce alternatives that are utilized by some alternative-sensitive operators (Krifka, 1995; Chierchia, 2013); (vi) NPI-licensing EVEN only associates with weak predicates (therefore also referred to as weak EVEN ) (Crnič, 2011a, 2014a, b); and (viii) predicates are considered weak, iff they are the most probable member of their focus set (Crnič, 2011a, 2014a, b). See below for the formal definition of weak EVEN, where Cc represents the function less likely than: (6) JevenK(C)(p)(w) = p(w) is defined iff ∀q ∈ C[p 6= q → p Cc q] Another important piece of formal machinery is Kolmogorov’s (1933) third axiom of probability that says that any proposition φ that entails any proposition ψ is at most as likely ψ: (7) Kolmogorov’s (1933) third axiom of probability If φ ⇒ ψ, then φ Ec ψ. Equipped with these assumptions we may now review the current state of the literature on how the (in-)felicity of the different environments are derived. We review how the even-based approach handles upward-, downward-, and non-monotone environments. We furthermore review how the Crnič (2014a) accounts for the differences in the universal restrictor and how the difference in question bias can not be accounted for with the current model. We refer to the aforementioned literature on even and the even-based approach for details on those environments which we do not expand upon. U PWARD -M ONOTONE E NVIRONMENTS and their infelicity are easily accounted for under the even-based approach. For the sentence (8), we would derive the following presupposition: (8) #John read any/even ONE book. a. even [ John read oneF book ] b. For n > 1: ∃1 x[BOOK(x) ∧ READ( j, x)] Cc ∃n x[BOOK(x) ∧ READ( j, x)] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 698 D. Krassnig Simple even hypothesis In an upward-monotone environments, entailing relations are preserved. Ergo, the original prejacent entails all of its focus alternatives, as can be seen below. (9) John read at least n books ⇒ John read at least one book Thereby, according to the axiom of probability in (7), it must be the most probable alternative. This is diametrically opposed to EVEN’s felicity requirements, causing the sentence to crash. D OWNWARD -M ONOTONE E NVIRONMENTS, on the other hand, reverse entailing relations: (10) John didn’t read at least one book ⇒ John didn’t read at least n books Therefore, the same principle of probability now enforces that not at least one is the least likely member of its focus set. Thus, there can never be a downward-monotone environment in which even ONE (and thereby NPIs) are infelicitous, explaining the NPIs perceived link to them. (11) John didn’t read any/even ONE book. a. even [ not [ John read oneF book ] ] b. For all n > 1: ¬∃1 x[BOOK(x) ∧ READ( j, x)] Cc ¬∃n x[BOOK(x) ∧ READ( j, x)] N ON -M ONOTONE E NVIRONMENTS suspend all entailing relations. As such, Kolmogorov’s (1933) third axiom of probability holds no influence over the felicity of such sentences. Therefore, it comes as no surprise that not all non-monotone environments license NPIs. Critically, Crnič (2011a, 2014b) noted that for sentences containing the expression exactly n, it appears that the varying number n is the most decisive factor for felicity. Consider this scenario: (12) Context: There is a lecture with 500 enrolled students. The professor announced ten relevant books before the start of the semester. The first class is now over. The professor relates her experience to one of her colleagues. a. Exactly two students read any/even ONE book. (i) even [ exactly two students read oneF book ] (ii) For all n > 1: ∃!2 x[STUDENT(x) ∧ ∃1 y[BOOK(y) ∧ READ(x, y)]] Cc ∃!2 x[STUDENT(x) ∧ ∃n y[BOOK(y) ∧ READ(x, y)]] b. #Exactly 250 students read any/even ONE book. (i) even [ exactly 250 students read oneF book ] (ii) For all n > 1: ∃!250 x[STUDENT(x) ∧ ∃1 y[BOOK(y) ∧ READ(x, y)]] Cc ∃!250 x[STUDENT(x) ∧ ∃n y[BOOK(y) ∧ READ(x, y)]] It appears that the sentence is only felicitous, if n refers to a contextually low quantity. Crnič (2014b) advocates that the fulfillment of the scalar presupposition is determined by our expectations and general world knowledge, as there are no axioms of probability to guide us. In our example, our general expectations would have been (i) that most students read at least one book, (ii) some students read more than one book, and (iii) that very few students read all ten books. The further the number of students having read n books deviates from these assump- Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 699 D. Krassnig Simple even hypothesis tions, the more unexpected the respective proposition becomes. See figure 1 for a graph that represents our general expectations for this scenario. Figure 1: Expectedness graph of (12) and its alternatives. The x-axis represents the number of students having read n books. The y-axis to the expectedness of the assertion. By converting our expectations of the world into probabilities, we can see that the original assertion of (12a) scores the lowest available probability for its value of n (fulfilling the scalar presupposition of EVEN). The infelicitous sentence in (12b), however, does not. I N THE RESTRICTOR OF UNIVERSAL QUANTIFICATION, we have a seeming difference in distribution between weak even and NPIs. Whilst NPIs are universally felicitous, its counterpart even ONE is not. Below is the expected LF and presupposition for the NPI sentence: (13) Every student who read any book passed the exam. a. [ even [ Every student who read oneF book passed the exam ] ] b. For all n > 1: ∀x[STUDENT(x) ∧ ∃1 y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] Cc ∀x[STUDENT(x) ∧ ∃n y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] Being (Strawson) downward-monotone, one can easily see that this scalar presupposition is fulfilled, regardless of any correlation between the restrictor of the quantifier and its verb phrase. As such, the general felicity of NPIs in this environment is derived. But how do we account for the context-sensitivity of even ONE? According to Crnič (2014a), the focus particle in (16) violates Crnič’s (2011b) principle of non-vacuity (see his paper for details on how): (14) Principle of Non-Vacuity “The meaning of a lexical item used in the discourse must affect the meaning of its host sentence (either its truth-conditions or its presuppositions)” (Crnič, 2011b) or its presence must be required on structural grounds (Crnič, 2014a: p. 133). As a means to rescue the use of even, he proposes that there is a covert exhaustifying operator E XH that asserts that all alternatives that are not entailed by the original are false. This operator is obligatorily used to ensure that the contribution of EVEN is non-vacuous. (15) JExhK = ∀q ∈ C[p 6⇒ q → q(w) = 0] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 700 D. Krassnig (16) Simple even hypothesis Every student who read any book passed the exam. a. [ even [ Every student whx [ exh(C) x read oneF book ] passed the exam ] ] b. For all n > 1: ∀x[STUDENT(x) ∧ ∃!1 y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] Cc ∀x[STUDENT(x) ∧ ∃!n y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] It accomplishes this purpose by changing the weak existential existential at least one into exactly one, since all higher-numbered alternatives are negated. This suspends the entailing relations that enforce the felicity of even. Since the axiom of probability in (7) no longer affects our judgment, we have to rate the asserted proposition against its alternatives based upon our world knowledge and expectations. As there is a correlation between reading (relevant) books and passing the exam, we would expect that the more books you read, the more likely you are to pass it. As such, our presupposition would be fulfilled. If we exchange our VP with wore blue jeans (see (4)), however, our world-knowledge should dictate an expected correlation between wearing blue jeans and the number of books read. 3. The issue of questions Before we go on to see how the even-based approach has problems with deriving the (non-)bias of questions, we first give a sketch on how bias/rhetoricity is derivable. This is followed by an overview of Guerzoni and Sharvit’s (2014) question model and the problems contemporary question models have with a non-decomposed version of EVEN (with respect to the even-based approach to NPI licensing). 3.1. Rhetoricity There are multiple theories concerning how rhetorical questions derive their rhetoricity. Not all of them are mutually exclusive. In this paper, we present two known ways to derive rhetoricity. The first was proposed by Guerzoni (2003), whereas the second theory was first proposed by van Rooy (2003) and Rohde (2006). Guerzoni (2003) proposes that a question must be considered rhetorical, if only one felicitous answer to the question is derived by the LF of the question form. The second approach is based upon the average informativity of the question (or rather, the lack thereof) and requires some general explanations. The first approach to rhetoricity was designed by Guerzoni (2003), who focused entirely on the distribution of even in questions and how it can be used to derive its negative bias. In her semantics, there are two possible structures for questions containing a focus particle such as even. In either structure, however, the focus particle would scope above both answers to the polar question. The only possible difference is whether or not the particle scopes above or below the negation in the negative answer. For even, this would result in the following possible structures: (17) Did John read even ONE book? a. {#JevenK(C)(JJohn read oneF bookK), #JnotK(Jeven C [John read oneF book]K)} b. {#JevenK(C)(JJohn read oneF bookK), JevenK(C)(Jnot [John read oneF book]K)} Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 701 D. Krassnig Simple even hypothesis In (17a), EVEN always associates with an upward-monotone environment. As such, as detailed in §2.1, both answers would be considered infelicitous, since the scalar presupposition is unfulfillable. In (17b) the affirmative answer is still infelicitous. However, the negative answer has EVEN associated with a downward-monotone environment, thereby fulfilling its scalar presupposition (as detailed before). Therefore, the only possible answer that fulfills the scalar presupposition would be the negative answer of the second LF. This renders the question itself rhetorical, as reasoned by Guerzoni (2003), since there is but one possible felicitous answer. The second approach is based upon the informativity of a question and was mostly characterised by van Rooy (2003). The essential idea is, that you seek to gain the most information possible to the question you ask. Starting with very general questions, the more knowledge you already possess about the respective state of the world, the more specific your questions become. In his paper, he explains how we can derive the rhetoricity of minimizer questions: (18) Did John (even) LIFT A FINGER to help? The minimizer, which is licensed by EVEN, invokes a presuppositional scale of helpful contributions. It also presupposes that the value is known for all units of help except for two: one and zero. In essence, according to van Rooy (2003), the minimizer restricts the range of helpful contributions to the lowest part of the contextually relevant scale. The question whether he did the minimal amount of work or no work at all still remains uncertain. The rhetorical effect is then achieved, according to van Rooy (2003), as follows: Whilst either answer is equally probable, due to the fact that either answer reflects very negatively on John, the actual answer itself does not really matter. As such, the informativity of the question can be judged to be considerably lower than its minimizer-less alternative which does not restrict John’s helpfulness to such a degree. 3.2. Environments in questions approach The approach to polar questions by Guerzoni and Sharvit (2014) contrasts with traditional question models (cf. Karttunen, 1977) in that they encode all possible answers to the question within the syntax of the question’s LF. They do this by arguing that polar questions are alternative yes-or-no questions containing an optionally silent whether (or not). Instead of assuming that a question operator derives both answers from a single LF, they assume that both answers are present within the LF and linked via disjunction. One of them is pragmatically omitted, however, via ellipsis. They would argue that a question like Did John kiss Mary(, or not)? would have the following LF: (19) [whetherL ] [ 7 ? [[John kissed Mary] (or7 [not) [John kissed Mary]]]] Within this structure, one of the options is elided by pragmatical omission. This can only be done when both answers share an identical structure, which is a necessity of any polar question (under the assumption that negation scopes over a proposition and is not analysed in situ). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 702 D. Krassnig Simple even hypothesis The definitions for the relevant lexical items, JwhetherL K, J?K, and Jor7 K, are provided below. Note that the or has a co-indexation to the trace left by the movement of whether, deviating from its standard form insofar that it is considered to be a Heimian indefinite.2 This assumption was adopted from Rooth and Partee (1982). (20) a. b. c. JwhetherL K = [λ Qhhs,ti,hhs,ti,tii .[λ qhs,ti .∃!rhs,ti [Q(r)(q) = 1 ∧ q(w) = 1]]] Jor7 K = [λ Phσ ,ti .[λ Qhσ ,ti .[λ zσ .(g(7) = P ∨ g(7) = Q) ∧ g(7)(z) = 1]]] J?K = [λ phs,ti .[λ phs,ti .p = q]] Using these definitions, the sentence structure in (19) derives the following Hamblin set in (21) as its meaning. Compare this meaning to the LF structure in (19). (21) JDid John kiss Mary?K = {JJohn kissed MaryK, Jnot [John kissed Mary]K} Notice the exact correspondence of the individual answers to how the LF was structured. One of the major reason’s for Guerzoni and Sharvit (2014)’s approach’s perceived elegance is this exact one-to-one correspondence. As such, we do not go into details concerning exactly how the final Hamblin set is derived. We refer to Guerzoni and Sharvit (2014: p. 212ff.) for details. The major difference to Guerzoni (2003) in relation to NPIs also lies with the expanded alternative structure of polar questions: If the negative clause is directly represented at LF, then the EVEN need not be applied to both sides simultaneously (cf. Guerzoni, 2003). In Crnič (2014a, b)’s adaptation of Guerzoni and Sharvit (2014)’s question model, we assume that NPI-licensing EVEN is only generated in the downward-monotone environment underneath the negation. The EVEN is then raised above the negating element, leaving the substructures of the affirmative and negative answer identical: (22) [whetherL ] [ 7 ? [[John kissed one girl] (or7 [ even C [not) [John kissed oneF girl]]]]] Since the constituents are equal to one another, the elision of the affirmative answer is licensed as a pragmatic omission. As such, we arrive at the following generalized structure for sentences containing an NPI-licensing even: (23) [whetherL ] [ 7 ? [CP (or7 [even [not) CP]]]] Which, in turn, derives the following Hamblin sets: (24) a. b. JDid John kiss even oneF girl?K = {JJohn kissed one girlK, JevenK(C)(¬JJohn kissed oneF girlK)} JDid even CP?K = {JCPK, JevenK(C)(¬JCPK)} Accordingly, under this question model, any questions containing an NPI-licensing EVEN are predicted not to exhibit any kind of bias, since either answer is considered to be felicitous. 2A Heimian indefinite is a restricted variable bound by another operator further up in the LF. See Heim (1982) for further details on this topic. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 703 D. Krassnig Simple even hypothesis Under the assumption of the simple even hypothesis, this would correctly predict the non-bias of questions containing NPIs. Therein also lies the problem: Since we do not make a distinction between even ONE and any, questions containing an overt even ONE are incorrectly predicted to be unbiased. So far, two attempts have been made to rectify this erroneous prediction: The first correction was attempted by Guerzoni and Sharvit (2014: p. 216, footnote 18) themselves. They proposed the following LF to derive negative bias for such questions: (25) [whetherL ] [ 7 ? [[[even C] CP] (or7 [[even C] [not) CP]]]] This structure would correctly assign an infelicitous reading to the affirmative question. However, Crnič (2014a) correctly pointed out that such structures violate the constraint on ellipsis: (26) Constraint on Ellipsis A constituent α may be elided if it is contained in a constituent β that contrasts with an antecedent constituent β 0 (where β contrasts with β 0 if and only if the meaning of β 0 is in the focus value of β ). The second attempt to correct the erroneous prediction was carried out by Crnič (2014b). He had drawn parallels to the conundrum he faced with Strawson downward-monotone environments and suggested that the use of covert exhaustification might improve matters. As such, he considered the following LF structure: (27) [whetherL ] [ 7 ? [John kissed one girl (or7 [[even C] [not) Exh John kissed oneF girl]]]] Crnič (2014b: p. 206) reasons that the sentence’s scalar presupposition entails that John is less likely to have kissed a high number of girls in contrast to having kissed fewer girls. (28) JevenK(C)(¬JExh C [John kissed oneF girl]K) is defined iff for all n > 1 : That John did not kiss exactly one girl Cc that John did not kiss exactly n girls. Crnič (2014b) himself states that this presupposition is not an exact match to the negative bias observed. It might, however, be an additional presupposition that accompanies NPI questions anyway. But that is beside the point. So far, no solution has been found regarding the difference in bias between even ONE and unstressed NPI questions. 4. Decomposing weak even This still leaves us, however, with the problem of how to derive the presuppositions that induce the questions’ rhetoricity. Having exhausted all possible configurations with Guerzoni and Sharvit’s (2014 question model, we need to innovate to find an LF that might derive the question’s negative bias. In line with Lahiri (2010) and Crnič’s (2012) analyses of weak scalar particles, we therefore propose that even is morphologically complex. That is to say, EVEN decomposes into two separate focus particles. In Crnič’s (2012) analysis, he proposes that some scalar particles decompose into JevenK and its antonym J¬evenK. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 704 D. Krassnig (29) Simple even hypothesis a. b. JevenK(C)(p)(w) = p(w) is defined iff ∀q ∈ C[p 6= q → p Cc q] J¬evenK(C)(p)(w) = p(w) is defined iff ∀q ∈ C[p 6= q → q Cc p] We propose that EVEN decomposes into two similar focus particles: EVEN MIN and EVEN MAX . The former is identical to standard weak EVEN, whereas the latter has no at-issue contribution but two separate presuppositions: First, that its prejacent is the most probable alternative, and second, that all alternatives that are not entailed by its original prejacent are false. In essence, we adopt Crnič’s (2012) model, with the exception of an added presupposition of exclusivity.3 (30) a. b. JevenMIN K(C)(p)(w) = p(w) is defined iff ∀q ∈ C[p 6= q → p Cc q] JevenMAX K(C)(p)(w) = p(w) is defined iff ∀q ∈ C[p 6= q → q Cc p], and ∀q ∈ C[p 6⇒ q → q(w) = 0] We independently motivate this decomposition by two factors: (i) Some element is required to enforce weak EVEN’s pairing with weak predicates, and (ii) to account for the presupposition of exclusivity exuded by sentences of the same type as below: (31) a. b. John doesn’t even know how to START a computer. ⇒ John doesn’t know how to do any activity with a computer.4 Exactly two of her friends even know how to START a computer. ⇒ None of her friends know how to do anything else with a computer. While the first sentence would be easily accounted for with an additive particle that might accompany EVEN, the latter would not be (Crnič, 2011a: p. 157). With our account, however, both of the above readings are derivable, as shown below. (32) John doesn’t even know how to START a computer. a. [ evenMIN [ not [ evenMAX [ John knows how to startF a computer ] ] ] ] b. Presupposition of EVEN MIN : For all R: It is less likely that John doesn’t know how to start a computer than John doesn’t know how to R a computer. c. Presupposition of EVEN MAX : For all R 6= JstartK: It is more likely that John knows how to start a computer than John knows how to R a computer, and John does not know how to R a computer. The computation of the other sentence is less straightforward, as it contains an instance of presupposition projection. For the purposes of this paper, we assume that presuppositions under quantifiers project universally (cf. Heim, 1983).5 Under this assumption, we derive the following presuppositions: 3 It should be noted that adding a presupposition of exclusivity virtually renders EVEN MAX identical to Guerzoni’s (2003) only2 in her analysis of German scalar particle auch nur. 4 Note that we intentionally do not use a predicate that is entailed by all of its alternatives. If the alternatives were entailed, then the negation itself would already result in the correct reading. Theoretically, people exist who might not know how to start a computer, but are perfectly able to use it for specific tasks (e.g. writing). 5 This assumption, however, is not crucial, and existential projection leads to a weaker, but also tenable claim. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 705 D. Krassnig (33) Simple even hypothesis Exactly two of her friends even know how to START a computer. a. [ evenMIN [ exactly two of her friends [ 1 [ evenMAX [ t1 knows how to startF a computer ] ] ] ] ] b. Presupposition of EVEN MIN : For all R: It is less likely that Exactly two of her friends know how to start a computer than John doesn’t even know how to R a computer. c. Presupposition of EVEN MAX : For all R 6= JstartK: It is more likely for all of her friends to know how to start a computer, rather than how to R a computer (individually, not collectively), and all of her friends do not know how to R a computer. Now that we have sufficiently motivated our decision to decompose EVEN, we proceed to show how this analysis would fare with the different kinds of environments we find it in (cf. §2). Note that this analysis simply adds additional presuppositions upon the already existing analysis. As such, any LF that was already ruled out by our previous non-decomposed approach, will also be ruled out under this approach, as their presuppositions will still remain unfulfilled. We therefore refrain from showing the presuppositions of EVEN MAX under upward monotone environments. Also note that we propose that only overt even requires to be licensed by EVEN MAX . As such, the analysis for sentences containing an NPI remains the same and is not reiterated here. D OWNWARD -M ONOTONE E NVIRONMENTS remain as straight-forward as they used to be under the original even-based account. In downward-monotone environments, EVEN MAX moves to take scope over the upward-monotone expression, beneath the downward-monotone operator. As such, if the predicate is weak, the presupposition is an automatic success due to Kolmogorov’s third axiom of probability. (34) John didn’t read even ONE book. a. [ evenMIN [ not [ evenMAX [ John read oneF book ] ] ] ] b. Assertion: J(34)K = ¬∃1 x[BOOK(x) ∧ READ( j, x)] c. Presupposition of EVEN MIN : For all n > 1: ¬∃1 x[BOOK(x) ∧ READ( j, x)] Cc ¬∃n x[BOOK(x) ∧ READ( j, x)] d. Presupposition of EVEN MAX : For all n > 1: ∃n x[BOOK(x) ∧ READ( j, x)] Cc ∃1 x[BOOK(x) ∧ READ( j, x)], and ¬∃n x[BOOK(x) ∧ READ( j, x)] The presupposition of exclusivity is also successful and precludes the possibility of John having read more than one book, which is entirely compatible with the sentence’s asserted content. N ON -M ONOTONE E NVIRONMENTS remain as context-sensitive as they used to be. The presupposition of EVEN MIN remains responsible for the context-sensitivity of the expression. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 706 D. Krassnig (35) Simple even hypothesis Exactly three students read even ONE book. a. [ evenMIN [ exactly three students [ 1 [ evenMAX [ t1 read oneF book ] ] ] ] ] b. Assertion: J(35)K = ∃!3 x[STUDENT(x) ∧ ∃1 y[BOOK(y) ∧ READ(x, y)]] c. Presupposition of EVEN MIN : For all n > 1: ∃!3 x[STUDENT(x) ∧ ∃1 y[BOOK(y) ∧ READ(x, y)]] Cc ∃!3 x[STUDENT(x) ∧ ∃n y[BOOK(y) ∧ READ(x, y)]] d. ∀-projected presuppositions of EVEN MAX : For all n > 1: ∀y[y ∈ P → ∃n x[BOOK(x) ∧ READ(y, x)] Cc ∃1 x[BOOK(x) ∧ READ(y, x)]], and ∀y[y ∈ P → ¬∃n x[BOOK(x) ∧ READ(y, x)]] The presuppositions of EVEN MAX , on the other hand, are a tad more complicated as they must be projected. The scalar presupposition remains trivial, as it still associates with an upwardmonotone environment. The presupposition of exclusivity, however, projects in such a way that for all members of P it is true that they did not read more than one book. The set P represents the domain of the projection, which corresponds to the entire set of students (not only those three that have been mentioned). Coupled with the asserted content this entails that amongst all students, only the three students in question have read anything at all. Having shown that the standard non-problematic environments are also accounted for by our extension of the original account, things are now ready to get interesting. We now go into how our account handles those cases that were considered problematic by Heim (1984). As demonstrated in the next two subsections, our account is able to explain the unwanted differences in a straightforward fashion and requires no added assumptions or mechanisms. 4.1. Restrictor of universal quantification In the restrictor of universal quantification, things turn more complicated and, by extension, more interesting. Let us review what the LF of a relevant NPI sentence looks like. Being downward-monotone, the felicity is fulfilled and not influenced by external factors. (36) Every student who read any book passed the exam. a. [ even [ Every student who read oneF book passed the exam ] ] b. For all n > 1: ∀x[STUDENT(x) ∧ ∃1 y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] Cc ∀x[STUDENT(x) ∧ ∃n y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] For the LF of the corresponding even-counterpart, we first need to decide what happens with the presupposition under quantification. Let us consider the following possible projections: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 707 D. Krassnig (37) Simple even hypothesis Every student who read even ONE book passed the exam. a. [evenMIN [[every[student that[1[evenMAX [t1 read oneF book]]]]] [passed the exam]]] b. Unprojected presuppositions of EVEN MAX : For all n > 1: ∃n x[BOOK(x) ∧ READ(g(1), x)] Cc ∃1 x[BOOK(x) ∧ READ(g(1), x)], and ¬∃n x[BOOK(x) ∧ READ(g(1), x)] c. ∀-projected presuppositions of EVEN MAX : For all n > 1: ∀y[y ∈ P → ∃n x[BOOK(x) ∧ READ(y, x)] Cc ∃1 x[BOOK(x) ∧ READ(y, x)]], and ∀y[y ∈ P → ¬∃n x[BOOK(x) ∧ READ(y, x)]] d. ∃-projected presuppositions of EVEN MAX : For all n > 1: ∃y[y ∈ P ∧ ∃n x[BOOK(x) ∧ READ(y, x)] Cc ∃1 x[BOOK(x) ∧ READ(y, x)]], and ∃y[y ∈ P ∧ ¬∃n x[BOOK(x) ∧ READ(y, x)]] For the universally projected presupposition of exclusivity, the reading we get would be far too strong for our intuitions. The sentence (37) does not give rise to the intuition that no student at all read more than one book. The existentially projected presupposition, too, does not match the intuitions that arise from this sentence: In this case, the exclusivity presupposition would presuppose that there is some student who has not read more than one book. Since the sentence is perfectly fine in a scenario where all students have read all the required books and it is taken to be a general statement, this also excludes the existentially projected presupposition. This leaves us with a third option: Shifting the presupposed content to the assertive level via local accommodation. And indeed, under the assumption that the presuppositions of EVEN MAX are locally accommodated in the restrictor of the universal quantifier, we would derive the following assertion and presuppositions:6 (38) Every student who read even ONE book passed the exam. a. [evenMIN [[every[student that[1[evenMAX [t1 read oneF book]]]]] [passed the exam]]] b. Assertion with local accommodation of EVEN MAX : J(37)K = ∀x[STUDENT(x) ∧ ∃!1 y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] c. Presupposition of EVEN MIN with local accommodation of EVEN MAX : For all n > 1: ∀x[STUDENT(x) ∧ ∃!1 y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] Cc ∀x[STUDENT(x) ∧ ∃!n y[BOOK(y) ∧ READ(x, y)] → PASS(x, ιv[EXAM(v)])] These assertive and presuppositional levels are nigh-equivalent to the ones derived by Crnič (2014a) in (16). As such, under the assumption of local accommodation, we derive the required context-sensitivity of even without resorting to the introduction of additional rescue operators (i.e. Exh). Under the assumption that NPIs were licensed by weak EVEN (i.e. by both of its sub-particles), we would also introduce context-sensitivity to (37)’s NPI counterpart. This is undesirable. To circumvent this problem, we proposed the following alteration to the original 6 Note that we make no assertion on what happens to the scalarity presupposition of EVEN MAX . There are two possible options. (i) The presupposition projects as usually, or (ii) the presupposition is also locally accommodated. However, this would lead to infelicitous propositions, and, as such, should be avoided as an option. Further research is required for how a presupposition trigger with multiple presuppositions projects with regard to its individual presuppositions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 708 D. Krassnig Simple even hypothesis even-based approach: Weak NPIs are licensed by covert EVEN MIN at LF. Overt instances of weak even and strong NPIs (e.g. minimizers), on the other hand, are licensed by the combination of EVEN MIN and EVEN MAX . This means that we leave the existing analysis of weak NPIs under this approach entirely untouched: We only change the semantics of overt even and strong NPIs. (39) Summary of our proposal so far a. Weak NPIs are licensed by EVEN MIN b. Strong NPIs and overt weak even are licensed by EVEN MIN and EVEN MAX c. E VEN MAX is locally accommodated in the restrictor of universal quantification, and thereby introduces the required context-sensitivity of weak even Now that we have covered the environments that the even-based approach already accounted for, let us turn our eye to how questions are affected by our proposal. 4.2. Decomposed even and English polar questions Given that we now assume that NPIs are licensed only by EVEN MIN , the analysis for NPI questions remains the same as presented in §3.2. That is, they do not derive any kind of question bias or feeling of rhetoricity. Concerning the LF of even-questions, on the other hand, we would derive the following structure and Hamblin set: (40) Did John read even ONE book? a. [whetherL ] [ 7 ? [[John read oneF book] (or7 [evenMIN [not) evenMAX [John read oneF book]]]]] b. JDid John read any book?K = {JJohn read oneF bookK, JevenMIN K(C0 )(Jnot [evenMAX C [John read focusF book]]K)} The negative answer would have the following presuppositions: (41) John didn’t read even ONE book. a. [ evenMIN [ not [ evenMAX [ John read oneF book ] ] ] ] b. Presupposition of EVEN MIN : For all n > 1: ¬∃1 x[BOOK(x) ∧ READ( j, x)] Cc ¬∃n x[BOOK(x) ∧ READ( j, x)] c. Presupposition of EVEN MAX : For all n > 1: ∃n x[BOOK(x) ∧ READ( j, x)] Cc ∃1 x[BOOK(x) ∧ READ( j, x)], and ¬∃n x[BOOK(x) ∧ READ( j, x)] Under the assumption that questions inherit the presuppositions of all of their possible answers (cf. Abrusán, 2014: p. 40, amongst others), this would entail that the question itself is only defined if we already preclude the possibility that John has read more than one book.7 This 7 Note that we can arrive at the same requirements, even if we do not assume that questions inherit all of their answer’s presupposition. Under the assumption that questions only inherit presuppositions shared by all of their answers, we can simply maximize the ellipsis to ensure that EVEN MAX is also contained by the affirmative answer: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 709 D. Krassnig Simple even hypothesis would mean that the speaker has already settled for herself that John will not have read any great amount of books. In fact, she assumes that he could have read at most one book, if any, which she also communicates to the addressee via the question form itself. This situation is identical to van Rooy’s (2003) analysis of minimizer questions. We simply derive the necessary conditions for his derivation of rhetoricity in a different fashion. In fact, under our assumptions, minimizer-questions would derive their rhetoricity through the very same process as above, since we assume that strong NPIs are also licensed by the combination of both types of EVEN.8 One caveat, however: Since overt even does not always associate with ludicrously minimal amounts (in comparison to lifting a finger), the derivation of rhetoricity is dependent upon the judgment of the speaker/addressee. Is the difference between nothing and one relevant to the situation? If so, the question would still be information-seeking. If not, the question would be considered rhetorical. As such, our proposal makes the following prediction: Not all instances of even-questions are rhetorical in nature. This difference would be determined by context. 5. Conclusion The aim of this paper was to consider how the even-based approach NPI licensing can be reconciled with the differences in distribution between NPIs and the expression even ONE with the general assumption that NPIs are also licensed by EVEN. We have achieved this in §4, §4.1 and §4.2, where we have altered the semantics of overt even, whilst we left the analysis of NPIs untouched. Under our account, the impression that even ONE and any are licensed by the same factors was fabricated due to the fact that they share one important licensing factor: EVEN MIN . In our account, however, overt even requires a second licensing EVEN MAX that is solely responsible for all of the distributional differences pointed out by Heim (1984). We are aware that our approach may have problems with accounting for the correct reading of some sentences such as the ones below. (42) a. b. c. John regrets opening even ONE book. John knows that asking out even ONE girl is a difficult task. If John opens even ONE book, he will learn something new. More precisely, our account is likely to make some predictions of exclusivity that are too strong to match our general intuitions for such sentences. A point for future research would be to examine how our account interacts with these environments and whether the presupposition of exclusivity might be dealt with in a similar fashion to the solution we provided for the universal quantifier’s restrictor (or an entirely different approach for that matter). Another potential point for future research would be the empirical examination of our prediction concerning the (i) Did John read even ONE book? a. [whetherL ] [ 7 ? [[evenMAX John read oneF book] (or7 [evenMIN [not) evenMAX [John read oneF book]]]]] 8 It is interesting to note that minimizers and other strong NPIs are often considered to bear obligatory stress. The indefinite in even ONE also bears stress. A possibility for future research might be, whether an interaction with the stress itself somehow derives EVEN MAX , possibly explaining why any turns into a strong NPI once stressed. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 710 D. Krassnig Simple even hypothesis contextually-determined rhetoricity of even-questions. Another important point for future research is to analyse the projection of multiple presuppositions triggered by the same focus particle and empirically test whether all of them obligatorily project in the same manner. References Abrusán, M. (2014). Weak Island Semantics. Oxford University Press. Chierchia, G. (2013). Logic in Grammar. Oxford University Press. Crnič, L. (2011a). Getting even. Ph. D. thesis, Massachusetts Institute of Technology. Crnič, L. (2011b). On the meaning and distribution of concessive scalar particles. In N. LaClara, L. Fainleib, and Y. Park (Eds.), Proceedings of NELS 41. Crnič, L. (2012). On the typology of scalar particles: Morphological complexity and scope rigidity. Talk at Ben Gurion University of the Negev. Crnič, L. (2014a). Against a dogma on NPI licensing. In L. Crnič and U. Sauerland (Eds.), The Art and Craft of Semantics: A Festschrift for Irene Heim, Volume 1, pp. 117–145. MIT Working Papers in Linguistics 70. Crnič, L. (2014b). Non-monotonicity in NPI licensing. Natural Language Semantics 22, 169– 217. Fauconnier, G. (1975). Polarity and the scale principle. In Chicago Linguistic Society 11, pp. 188–199. Guerzoni, E. (2003). Why Even Ask? On the Pragmatics of Questions and the Semantics of Answers. Ph. D. thesis, Massachusetts Institute of Technology. Guerzoni, E. and Y. Sharvit (2014). ‘Whether or not anything’ but not ‘whether anything or not’. In L. Crnič and U. Sauerland (Eds.), The Art and Craft of Semantics: A Festschrift for Irene Heim, Volume 1, pp. 199–224. MIT Working Papers in Linguistics 70. Heim, I. (1982). The Semantics of Definite and Indefinite Noun Phrases. Ph. D. thesis, University of Massachusetts, Amherst. Heim, I. (1983). On the projection problem for presuppositions. In Proceedings of the 2nd West Coast Conference on Formal Linguistics, pp. 114–125. Stanford University Press. Heim, I. (1984). A note on negative polarity and downward entailingness. In Proceedings of NELS, Volume 14, pp. 98–107. GLSA Publications. Jespersen, O. (1917). Negation in English and Other Languages. A. F. Høst. Karttunen, L. (1977). Syntax and semantics of questions. Linguistics and Philosophy 1, 3–44. Karttunen, L. and S. Peters (1979). Conventional implicature. In C.-K. Oh and D. A. Dinneen (Eds.), Syntax and Semantics 11, pp. 1–56. Academic Press. Kay, P. (1990). Even. Linguistics and Philosophy 13(1), 59–111. Klima, E. (1964). Negation in English. In J. A. Fodor and J. J. Katz (Eds.), The Structure of Language, pp. 246–323. Prentice Hall. Kolmogorov, A. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung: Ergebnisse der Mathematik. Chelsea Publishing Company. Translated as Foundations of Probability, 1950. Krifka, M. (1995). The semantics and pragmatics of weak and strong polarity items. Linguistic Analysis 25, 209–257. Ladusaw, W. A. (1979). Polarity Sensitivity as Inherent Scope Relations. Ph. D. thesis, University of Texas, Austin. Lahiri, U. (1998). Focus and negative polarity in Hindi. Natural Language Semantics 6, 57– Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 711 D. Krassnig Simple even hypothesis 123. Lahiri, U. (2010). Some even’s are even if . . . only: The concessive even in Spanish. Manuscript. Lee, Y. S. and L. Horn (1994). Any as indefinite plus even. Unpublished ms. Rohde, H. (2006). Rhetorical questions as redundant interrogatives. San Diego Linguistic Papers 2, 134–168. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1, 75–116. Rooth, M. and B. Partee (1982). Conjunction, type ambiguity and wide scope “or”. In D. P. Flickinger, M. Macken, and N. Wiegand (Eds.), Proceedings of the 1st West Coast Conference on Formal Linguistics, pp. 353–362. Stanford University. van Rooy, R. (2003). Negative polarity items in questions: Strength as relevance. Journal of Semantics 20, 239–273. von Fintel, K. (1999). NPI licensing, Strawson entailment, and context dependency. Journal of Semantics 16, 97–148. von Fintel, K. (2001). Counterfactuals in a dynamic context. In M. Kenstowicz (Ed.), Ken Hale: A Life in Language, pp. 123–152. MIT Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 712 Polarity reversals under sluicing1 Margaret KROLL — University of California, Santa Cruz Abstract. This paper presents novel English sluicing data that challenge even the most successful existing theories of the relationship between antecedent and elided content in sluicing constructions. The data supply robust evidence for a previously unobserved phenomenon in which the elided content and the antecedent content in a sluiced construction contain opposite polarity. The phenomenon challenges current accounts of identity conditions on ellipsis by demonstrating that a greater mismatch between antecedent and elided content is possible than previously thought; specifically, the paper shows that the identity condition for sluicing must be sensitive to pragmatic as well as to semantic content. This observation motivates a proposal in which sluicing is treated as a pragmatics-sensitive phenomenon licensed by local contextual entailment. Keywords: ellipsis, sluicing, dynamic semantics, formal pragmatics, polarity 1. Introduction Sluicing, first noted by Ross (1969), is an ellipsis phenomenon in which the TP of an interrogative is elided under some identity condition, stranding an overt wh-phrase in the CP domain. An example is given in (1) below. (1) Bernie knows that someone in Iowa voted for Trump, but he doesn’t know whoi [TP ti in Iowa voted for Trump]. This paper discusses the previously unobserved phenomenon of polarity reversals2 under sluicing. The phenomenon I am calling polarity reversal is that in which the antecedent and elided material in a sluicing construction contain opposite polarity. For example, the antecedent content (A) in (2), Trump will comply, has positive polarity while the elided content (E), Trump won’t comply, has negative polarity. (2) I don’t think that [Trumpi will comply]A, but I don’t know why [TP hei won’t comply]E.3 1 Thank you to Pranav Anand, Rachelle Boyson, and Jim McCloskey for bringing this phenomenon to my attention and for inspiring/providing much of the project’s data. Thank you to Pranav Anand, Sandy Chung, Dan Hardt, Bill Ladusaw, Jim McCloskey, and Deniz Rudin for invaluable discussion of the ideas presented here, as well as audiences at UCSC, UC Berkeley, and SuB21. Finally, thank you to the undergraduate annotators of the Santa Cruz Ellipsis Project for their work in classifying the original corpus data. This project has in part been supported by a UC Santa Cruz Institute of Humanities Research cluster grant to the Santa Cruz Ellipsis Consortium, and by the National Science Foundation Grant No. 1451819: The Implicit Content of Sluicing. 2 I use this label pre-theoretically and for convenience. As we will see, no actual “reversal” of polarity takes place between an antecedent and elision site. 3 Note that there is a reading in which the antecedent includes the matrix clause, but this reading is pragmatically odd. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 713 M. Kroll Polarity reversals under sluicing I show that data like (2) require a shift in current beliefs about the identity conditions that license sluicing constructions. I propose a theory of sluicing that builds on the advances made in previous accounts while allowing for greater mismatches between antecedent and elided content in order to accommodate the newly observed data.4 The paper proceeds as follows. Section 2 provides an overview of Merchant’s (2001) theory of e-GIVENness and demonstrates that it fails to predict the polarity reversal data. Section 3 proposes an alternative theory and steps through its predictions for three polarity reversal examples. Section 4 addresses the concern of overgeneration that arises for pragmatic accounts of sluicing, and Section 5 concludes. 2. e-GIVENness Numerous theories of sluicing have been proposed since the original syntactic isomorphy approach given in Ross (1969). The dominant semantics-based account of sluicing is Merchant’s (2001) theory of e-GIVENness, which imposes a bidirectional semantic entailment identity condition on ellipsis. More recent theories have constrained the eGIVENness account in various ways (Merchant 2005; Chung 2006, 2013; Barker 2013; AnderBois 2014). As these accounts are designed to be more restrictive than Merchant’s original account, the objection outlined here that e-GIVENness undergenerates the polarity reversal data applies equally to these theories.5 2.1. Bidirectional semantic entailment Merchant (2001) proposes that sluicing constructions are formed via wh-movement of a remnant constituent and subsequent deletion at PF of the remaining TP. e-GIVENness is a modification of Schwarzschild’s (1999) GIVENness, which itself is a theory of focus and deaccenting. Schwarzschild proposes, drawing upon Rooth’s (1985, 1992) theory of focus, that an expression can be deaccented if it is GIVEN, where GIVENness is defined as follows: Formal GIVENness Condition: An utterance B counts as GIVEN iff it has an antecedent A and: ∀<w,g> ∈c ∃h [ExClo(⟦A⟧g )(w) → ExClo(⟦B⟧g , h )(w)] Informally, GIVENness says that an expression can be deaccented if the existential focus closure of the expression is contextually entailed by the existential closure of an antecedent.6 4 A methodological aside on the data used throughout: The corpus examples given here were identified by undergraduate annotators trained on the Santa Cruz Ellipsis Consortium. The properties of the sluices, including the provided pre-sluices, are those given by (at least) two independent annotators. After the annotation process, the judgments were verified by (an average of) ten trained linguists, including faculty and graduate students, in consultation with naïve speakers. Many of the examples presented here have more than one possible interpretation for the pre-sluice. The claim here is not that the pre-sluices provided for these examples are the only interpretation available for these examples, but merely that they are a felicitous, freely available interpretation in the context in which the sluice was found or constructed. 5 Barros (2014) and Ginzburg and Sag (2001) take a different approach, combining syntactic and pragmatic constraints. See Kroll (in prep) for a discussion of these theories. 6 Existential closure is a type-shifting operation that raises expressions to type ‹t› by existentially binding unfilled arguments. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 714 M. Kroll Polarity reversals under sluicing Because Schwarzschild was concerned with deaccenting, his theory does not discuss ellipsis. However, Merchant draws upon the idea from Rooth (1992) and Romero (1997) that the licensing conditions for deaccenting and ellipsis are related, the strong version of which is to say that ellipsis is just an extreme version of deaccenting. Merchant notes, though, that the theory of GIVENness runs into a problem if applied faithfully to cases of ellipsis. Specifically, it fails to rule out impossible sluices such as (3), in which the elided content is entailed by the labelled antecedent (assuming calling x an idiot → insulting x), but is not judged to be a possible interpretation of the sluiced sentence. (3) [Abby called someone an idiot]A, but I don’t know who [Abby insulted t]E. Based on such examples, Merchant proposes that GIVENness alone is not strong enough to act as a licensing condition for ellipsis. Merchant therefore strengthens GIVENness by requiring that the entailment relationship between the antecedent and elided expression be bidirectional instead of unidirectional. The account is given as follows: Focus condition on TP-ellipsis: A TP α can be deleted only if α is e-GIVEN. e-GIVENness: An expression E counts as e-GIVEN iff E has a salient antecedent A and, modulo ∃ type-shifting, i) A entails F-clo(E), and ii) E entails F-clo(A). Note that condition (ii) is the novel aspect of the theory. Note also that the entailment requirement here is that of semantic entailment and, unlike GIVENness, does not leave room for contextual entailment. The bidirectional entailment requirement of e-GIVENness will correctly rule out the problematic example given in (3), repeated below, as the elided expression does not entail the F-closure of the antecedent expression. (3) [Abby called someone an idiot]A, but I don’t know who [Abby insulted t]E. A entails F-clo(E): Yes. A = ∃x.Abby called x an idiot F-Clo(E) = ∃x.Abby insulted x E entails F-clo(A): No. E = ∃x.Abby insulted x F-Clo(A) = ∃x.Abby called x an idiot 2.2. e-GIVENness predictions The semantic identity condition of e-GIVENness is permissive enough to allow for certain observed syntactic mismatches between sluiced clauses and their antecedents, such as tense (Merchant 2001); however, the bidirectional entailment requirement is too restrictive to allow for polarity mismatches. Let’s look again at (2), repeated below as (4). (4) I don’t think that [TP Trumpi will comply]A, but I don’t know why [TP hei won’t comply]E . Applying e-GIVENness to A and E yields the following: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 715 M. Kroll Polarity reversals under sluicing A entails F-clo(E): No. A = comply(t) F-Clo(E) = ¬comply(t) E entails F-clo(A): No. E = ¬comply(t) F-Clo(A) = comply(t) Neither the antecedent expression nor the elided expression in (4) entails the other. An alternate possibility is to include the matrix clause in the antecedent, thereby capturing its negation in the antecedent expression. This is given in (5). (5) [TP I don’t think that Trumpi will comply]A, but I don’t know why [TP hei won’t comply]E. A entails F-clo(E): No. A= ¬∀w[w ∈W dox, s → comply(t)(w)] F-Clo(E) = {w: ¬ comply(t)(w)} E entails F-clo(A): No. E = {w: ¬ comply(t)(w)} F-Clo(A)= ¬∀w[w ∈W dox, s → comply(t)(w)] As (5) shows, expanding the antecedent to include the matrix negation does not yield entailment in either direction. Indeed, my lacking a belief that Trump will comply does not semantically entail that Trump will not comply, as my lack of beliefs about an event does not entail any truth about the event itself. Notice that even if one argues that the stronger negraised interpretation of the antecedent, e.g. along the lines of Gajewski (2007) (see §3.1), counts as semantic content, we still do not have mutual entailment, as my thinking that Trump will not comply does not entail that he won’t, as I can have false beliefs. Similarly, it will not work to take the matrix as antecedent, and the complement of but as the potential elided phrase,7 as my thinking that Trump will not comply does not semantically entail my not knowing why he won’t, as I may indeed know the reason he won’t. I leave it to the reader to confirm the formal predictions here. In summary, bidirectional semantic entailment accounts such as e-GIVENness are too restrictive and fail to predict the existence of polarity reversal data. The next section proposes an alternative account that builds off the insights of both GIVENness and e-GIVENness. 3. A modified account This section presents a theory of sluicing that abandons semantic identity in favor of pragmatics-based entailment. The spirit of the proposal is indebted to those accounts already discussed and to the contextual entailment allowance that was included, though not given an exposition, in Schwarzschild’s GIVENness. Informally, I propose that the TP of an interrogative can be elided if and only if the proposition expressed by the TP, modulo existential closure, is entailed by the context in which the proposition would be uttered. Formally, Local Givenness is expressed as follows: 7 If one wanted to argue that, similar to focus licensing (Rooth 1985, 1992), one can have a larger expression license the deletion of a smaller contained expression. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 716 M. Kroll Polarity reversals under sluicing Local Givenness (Preliminary):A TP α can be deleted iff ExClo(⟦α⟧g ) expresses a proposition p such that c L ⊆p. The relevant notion of context we are concerned with is the local context, cL, in which p is expressed. The local context of a proposition p is more constrained and therefore not necessarily identical to the global context of the discourse in which p is uttered. For Stalnaker, the context set is updated as propositions are entered into the discourse and accepted by speakers as true for the purposes of the discourse (2002). However, propositions can be entered into local contexts without being entered into the context set, i.e. without being accepted as true of the actual world by the speakers of the discourse. Note that this means that, throughout a discourse, cL is not a continually narrowing set of worlds. Instead, cL is the set of worlds compatible with the presuppositions of the local proposition. While the account presented here is compatible with a range of dynamic theories, I assume the following basic formal reasoning (Kadmon 2001 and citations within): Context update: a. If cL entails the presuppositions of p, then cL + p = {cL ∩ p} b. If cL does not entail the presuppositions of p, then either: i. undefined, or ii. the presuppositions of p are accommodated, cL + p = {(cL ∩ ps(p)) ∩ p} The following sections apply Local Givenness to three categories of polarity reversal sluices.8 3.1. Neg-raising polarity reversals One class of polarity reversal sluices contains neg-raising verbs. For example, (2) is repeated below as (6): (6) [I don’t think that Trumpi will comply]A, but I don’t know why [TP hei won’t comply]E. That neg-raising is the relevant property in (6) can be seen by swapping the neg-raising verb think with the non-neg raising verb hope, as in (7a). Example (7a) cannot receive the polarity reversal interpretation; the only available interpretation is that in which the matrix clause acts as antecedent, given in (7b). (7) a. b. Mary doesn’t hope that Trumpi will comply, and she can’t explain why [# hei won’t comply]. Mary doesn’t hope that Trump will comply, but she can’t explain why [shei doesn’t hope that Trump will comply]. Neg-raising verbs are clause-embedding verbs that when negated allow a reading in which matrix negation takes scope in an embedded clause. As it is arguably the dominant approach 8 See Kroll (in prep) for derivations of polarity reversal examples containing until, doubt, and say. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 717 M. Kroll Polarity reversals under sluicing in the literature, I use here the account of neg-raising given in Gajewski (2007).9 Gajewski’s account draws importantly on an idea from Bartsch (1973) that the inference from the literal interpretation of a neg-raising sentence like (6A), where negation takes matrix scope, to the neg-raised interpretation, where negation takes embedded scope, is a pragmatic inference. Specifically, Bartsch argues that neg-raising verbs license an excluded middle presupposition as a pragmatic inference. For a sentence like (6A) that contains the neg-raising verb think, the presupposition is that the subject either believes that the proposition expressed by the complement of the verb is true, or believes that it is false. The assertion of (6A) combined with this presupposition then pragmatically entails that the speaker in (6) has a belief that Trump will not comply. The pragmatic nature of the reasoning involved explains how negation comes to be interpreted low and also explains why the neg-raised reading is cancellable in context. The criticism leveled against Bartsch's original account is that no principled reason is given for why some verbs are neg-raising verbs and others are not (Horn 1978). For example, no explanation is given for why the verb think can neg-raise while the epistemically stronger verb know cannot, or why neg-raising verbs are idiosyncratically distributed across different languages. Gajewski proposes to alleviate this objection by categorizing the excluded middle presupposition of neg-raising verbs as a soft-trigger presupposition in the sense of Abusch (2005). Abusch’s soft-trigger presuppositions are presuppositions that are easily cancellable in context and as such are distinct from hard-trigger presuppositions, which are not. Softtrigger presuppositions are carried by predicates that invoke lexically-stipulated alternatives as a matter of convention. The invocation of these alternatives triggers a pragmatic presupposition that one of the alternatives is true. In the case of neg-raising verbs, the alternatives invoked are the literal interpretation of the sentence and the neg-raised interpretation of the sentence. To summarize this discussion, Gajewski proposes to treat neg-raising predicates as soft triggers that invoke a pragmatic excluded-middle presupposition. This captures the behavior described in Bartsch’s account while providing a more principled explanation for why some verbs allow neg-raising and others do not. With this theoretical background in place we can now return to example (6). I have proposed that the assertion of (6A) combined with the excluded-middle presupposition invoked by the verb think entails that the speaker in (6) has the belief that Trump will not comply. Formally, this is expressed as follows: (6) [I don’t think that Trumpi will comply]A, but I don’t know why [hei won’t comply]E. (6') ⟦I don't think that Trump will comply⟧wA, g = ¬∀w[w ∈Wdox, s → comply( t)(w)] Via the excluded middle presupposition conventionally associated with the verb think, A presupposes the following: Excluded Middle Presupposition of (6A): [∀w[w ∈Wdox, s → comply(t)(w)]∨∀w [w ∈Wdox, s → ¬ comply(t)(w)]] 9 I ask my syntactically-inclined readers to please preview §3.2 to assuage objections to this choice. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 718 M. Kroll Polarity reversals under sluicing The denotation of think assumed here can therefore be given as follows: ⟦think⟧w ,g = λp.λx:[∀w[w ∈Wdox, x → p(w)]∨∀w [w ∈W dox, x → ¬ p(w)]]. [∀w[w ∈W dox, x → p(w)]] Because A expresses that the first disjunct of the excluded middle presupposition is false, the presupposition of A and the assertion of A together entail the second disjunct of the presupposition. This entailment produces the stronger reading that the speaker uttering (6) has a belief that Trump will not comply. Local Givenness requires that the proposition elided in (6)—Trump will not comply—is entailed in its local context; however, as discussed, the strengthened neg-raising reading in (6)—that the speaker believes that Trump will not comply—does not semantically entail the elided proposition, as the speaker can have false beliefs. I argue here that the speaker’s assertion of her belief of p can, in context and under certain conditions, be taken to assert p itself. This move relies on the proposal that, while doxastics such as think primarily report on the private mental state of an individual and therefore do not directly reference the common ground (or context), think p can be used in conversation to pragmatically assert p, as proposed in Anand and Hacquard (2014, 84). The following steps apply Local Givenness to (6). i. Starting Context: c=W ii. (6A) asserts that it is not true that the speaker believes that Trump will comply. Semantic Denotation of (A): ⟦A⟧w ,g = ¬∀w[w ∈W dox, s → comply( t)(w)] iii. The pragmatic excluded middle presupposition of (6A)—conventionally associated with the verb think—requires that the speaker either believes that Trump will comply or believes that Trump will not comply. Excluded Middle Presupposition of (A): [∀w[w ∈Wdox, s → comply(t)(w)]∨∀w [w ∈Wdox, s → ¬ comply(t)(w)]] iv. Steps (ii) + (iii) derive the strengthened neg-raised interpretation: Because (ii) asserts that it is not true that the speaker believes that Trump will comply, it follows from (iii) that the speaker believes that Trump will not comply. The utterance of (6A) thus asserts the strengthened meaning given below. Strengthened Neg-Raised Interpretation of (A): ∀w[w ∈Wdox, s → ¬comply(t)(w)] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 719 M. Kroll Polarity reversals under sluicing v. The assertion in step (iv) creates a local context cL in which the worlds under consideration are only those compatible with the speaker’s doxastic state, namely those worlds in which Trump does not comply. cL for E: W ∩ {w: w ∈W dox, s }= {w: ¬comply(t)(w)}= cLE vi. Semantic Denotation of (E): {w: ¬ comply(t)(w)} vii. The local context includes only those worlds in which Trump will not comply, which entails the elided proposition that Trump will not comply (in fact there is mutual entailment between the world sets). Local Givenness: cLE ⊆ExClo(⟦E⟧)w ,g = {w:¬comply(t)(w)}⊆{w:¬comply( t)(w)} The entailment satisfies the Local Givenness requirement that the elided proposition be entailed by its local context, and we predict felicitous elision of the proposition expressed by (6E). 3.2. Polarity reversals over remember The reader may, at this point, raise an objection that the previous example wrongly dismissed the possibility of a syntactic account of neg-raising as an explanation for the inference from ¬φp → ¬p. Indeed, the classic analysis of neg-raising—originally advanced by, among others, Fillmore (1963) and Ross (1973) and revived recently by Collins and Postal (2014)— argues for a syntactic explanation. However, I show in this section that an appeal to a syntactic account of neg-raising will not save a semantic entailment account of sluicing. Instead, the inference ¬φp → ¬p must, at least in some cases, be purely pragmatic in nature. Example (8) is a corpus polarity reversal sluice containing remember. (8) [corpus example 91594, Santa Cruz Ellipsis Project] Context: [O]n the day the Japanese invaded Pearl Harbor, Hummel was rounded up and locked in an internment camp along with about 2,000 other foreigners… So he and a British friend engineered an escape with the help of Nationalist guerrillas concealed nearby. He crawled over barbed-wire and walked most of the night and the next day. He was 20 and had no military training. But he was handed a small Belgian pistol, and he had little choice but to stay and help, harassing Japanese patrols by night and trying to defend a small patch of land against a communist takeover. Sluice: “I don’t know why [I wasn’t scared], but I really can not remember being scared,” [Hummel] said. “It all seemed like great fun.” Example (8) is illustrative in that it appears to behave like the neg-raising examples; specifically, ¬remember p is interpreted in context as entailing ¬p. However, remember is Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 720 M. Kroll Polarity reversals under sluicing not classified as a neg-raising verb in the literature and, indeed, the inference is more contextually dependent than that carried by neg-raising verbs. For example, A’s utterance in (9) is perfectly acceptable, while A’s utterance in (10) is grammatical but a bit unwieldy. (9) I don’t remember being scared, but apparently I was! (10) ? I don’t think that John went to the party last night, but that’s because I don’t know anything about his whereabouts last night. Karttunen (1971) classifies remember as an implicative verb. As such, remember has the following properties when taking an infinitival complement: remember p → p, ¬remember p → ¬p. For example, in (11) below there is a strong intuition that the assertion of the sentence commits the speaker to believing that she did not shut the door. (11) I didn’t remember to shut the door. Higginbotham (2003) proposes that remember (along with imagine) in its usage with a gerund complement carries an obligatory de se reading when the embedded subject is PRO. For example, while (12) has both a possible de re and a possible de se reading, (13) carries only the de se reading, under which John remembers he himself going to the movies. (12) John remembered his going to the movies. (13) John remembered going to the movies. [Higginbotham 7&10] Based on these discussions, I propose that the licensing of the inference ¬remember p → ¬p in (8) is licensed by two defeasible contextual assumptions. The first assumption is that the speaker has a memory about the particular event represented by p.10 I argue that this assumption is stronger in cases in which the subject of remember is remembering their own experience of the particular event, as in Higginbotham’s de se examples. The second assumption is based on the idea that insofar as our memory of eventualities track with our beliefs about those eventualities, a speaker’s memory represents the speaker’s beliefs about the way the actual world was in the past. An assertion of memory can therefore in context be taken as doxastic evidence for or against a description of a particular eventuality and license inferences from memory to belief. These assumptions are defeasible in that a speaker can have the reliability of her memory challenged. The following steps apply Local Givenness to (8). (8) I don’t know why [I wasn’t scared]E, but [I can not remember being scared]A. 10 I abstract away here from concerns about negative events, and assume that the event in question in (8) exists and that it was either an event of being scared or an event of being not scared. Another way to approach this is to say that the speaker either remembers the event e or remembers the maximal eventuality S of all eventualities e' in the relevant time period and e ⊈ S (cf. Krifka (1989) and de Swart (1996), in which the following definition of event negation is used: λ P.λ s.[ MAX(s)∧¬∃e[ P(e)∧e⊆s]] ). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 721 M. Kroll Polarity reversals under sluicing i. Starting Context: c=W ii. The presupposition associated with A is that the speaker has a memory of the particular event being discussed, namely an event of being scared or being not scared. Presupposition of A:11 [∀w[w ∈W MEM,s→∃e[¬ scared(s)(e)(w)]]∨∀w[w ∈W MEM,s→∃e[scared(s)(e)(w)]]] iii. The semantics of A expresses that the speaker does not remember an event of being scared: in all the worlds compatible with the memory of the speaker there was no event (in the relevant time period) in which the speaker was scared. WMEM,s here acts as an information state of the speaker containing all those worlds compatible with the memory of the speaker. Semantic Denotation of A: ⟦A⟧w ,g = ∀w[w ∈W MEM,s → ¬∃e[scared(s)(e)(w)]] iv. Steps (ii) and (iii) together entail the proposition that the speaker remembers an event of his being not scared. Therefore, an assertion of A expresses the following: Presuppositionally-enriched Denotation of A: ∀w[w ∈W MEM,s → ∃e[¬scared(s)(e)(w)]] v. Under the inference that the speaker’s memories of the past represent the speaker's beliefs about the history of the actual world, we can infer the following from Step (iv). Inference of Speaker’s Belief: ∀w[w ∈W DOX,s → ∃e[¬ scared(s)(e)(w)]] vi. Step (v) pragmatically asserts that the speaker was not scared.12 The context is then updated with this proposition. Context Update: W ∩ {w: ∃e[¬scared(s)(e)(w)]} = {w: ∃e[¬scared(s)(e)(w)]} = cLE vii. Existential Closure of E: ExClo(⟦E⟧w ,g )= {w: ∃e[¬ scared( s)(e)(w)]} viii. Local Givenness: cLE ⊆E = {w: ∃e[¬ scared( s)(e)(w)]}⊆{w: ∃e[¬scared(s)(e)(w)]} 11 Contextual domain restriction assumed throughout. One could also argue that the assertion creates a subordinating context for the embedded why question. I see no crucial difference between the two implementations here. 12 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 722 M. Kroll Polarity reversals under sluicing The existential closure of E is entailed by its local context, and we correctly predict felicitous elision of E. As a closing note, the fact that example (8) is a cataphoric sluice was ignored for our purposes here. Something must, of course, be said about these sluices, which are common in the Santa Cruz sluicing corpus. I leave this aside for further investigation, besides noting that these sluices seem to involve some sort of processing hold in which the sluice is not interpreted until a relevant antecedent is encountered, analogous to instances of pronominal cataphora. 3.3. Polarity reversals with exclusive disjunction The resourceful reader might at this point object that, instead of jettisoning our familiar bidirectional entailment account, a simpler path is to simply enrich the bidirectional entailment condition to include pragmatic and not merely semantic content. I show here that a pragmatically enriched bidirectional entailment account still fails to generate the full range of polarity reversal data. The polarity reversal examples discussed in this section involve exclusive disjunction. A corpus example is given in (14) and a constructed example in (15). (14) [corpus example 22987, Santa Cruz Ellipsis Project] Context: On Dec. 10, [Senator] McCain sent a letter to the FCC urging the fivemember board to end two years of deliberations and decide whether Paxson Communications should be given a license for a Pittsburgh station. Angela J. Campbell, an attorney for opponents to the deal, told the Globe that McCain’s letter likely ‘tipped’ the scales in favor of the decision. Sluice: “Senator McCain said, ‘Do it by December 15 or explain why [you didn’t do it by December 15],’ and the commission jumped to it and did it that very day,” Campbell told the Globe. (15) [constructed example] Context: Students in a semantics class were given the option to do an extra credit problem, and were required to mark the number of the problem that they did on a spreadsheet accessible by the course’s professor and TA. Both the professor and TA thought that John, a student in the class, would have chosen to do a problem. They look at the spreadsheet and see that nothing is marked down under John’s name. The TA says to the professor: Sluice: Either [Johnj didn’t do an extra credit problem]A, or hej didn’t mark which onei [hej did ti]E. Note that these examples illustrate that negation can be either “added” into the ellipsis site, as in (14), or “deleted” from the ellipsis site, as in (15).13 13 Thank you to Jason Merchant (p.c.) for pointing out that these data run counter to the claim made in Merchant (2013: 15) that negation present in the antecedent of a sluicing construction requires a corresponding negation present in the ellipsis site. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 723 M. Kroll Polarity reversals under sluicing I focus here on example (15), the utterance of which asserts that either (A) John didn’t do an e.c. problem or (E) John did an e.c. problem. The disjunction is exclusive because the two disjuncts are opposites: they cannot both be true (or false) at the same time. The analysis of (15) given here relies on Karttunen’s (1974) proposal of the local contexts for exclusive disjunction constructions. Specifically, Karttunen gives the following asymmetric proposal for disjunctive constructions: Karttunen’s Local Context for Exclusive Disjunction: For propositions p, q such that p ˅ q is uttered in a context c: cL for p = c, cL for q = c + ¬p. The proposal says that the local context for the first disjunct of an exclusive disjunction construction—that is, the context in which the disjunct can be felicitously uttered—is the global conversational context. The local context for the second disjunct is the global conversational context intersected with the negation of the first disjunct. The intuition for this proposal is that for an exclusive disjunction to be true one of the disjuncts must be true, but not both. Therefore, the context in which the first disjunct is admitted is just the global conversational context, but the context in which the second disjunct is admitted takes into account its opposition to the first disjunct, and so all the worlds in which the first disjunct holds are excluded. The following steps apply Local Givenness to the disjunction in (15). i. Starting Context: c=W ii. Denotation of A: ⟦A⟧w ,g = {w:¬∃x[extra credit problem( x)(w)∧do( x)( j)(w)]} iii. Denotation and Existential Closure of E:14 ExClo(⟦E⟧w ,g )= {w: ∃x[extra credit problem(x)(w)∧do(x)( j)(w)]} iv. Karttunen’s Local Context for A and E: c LA = c = W v. Local Givenness: cLE ⊆ExClo(⟦E⟧w , g )= {w: ¬¬∃x[extra credit problem( x)(w)∧do( x)( j)(w)]} ⊆{w: ∃x[extra credit problem(x)(w)∧do( x)( j)(w)]} 14 Note that the wh-phrase which one is d-linked in the sense of Pesetsky (1987), meaning that it ranges over a salient set in the discourse. One could assume here, following Cinque (1989), that d-linked wh-phrases are referential and therefore leave behind a referentially indexed trace. Existentially closing over this trace would then restrict the possible identity of the thing to which the existentially bound variable can refer to a member of a particular set present in the discourse. However, as the d-linking is orthogonal to the example here, I suppress this issue for the sake of expositional clarity. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 724 M. Kroll Polarity reversals under sluicing Local Givenness is satisfied in step (iv) because the local context for E entails the proposition expressed by E, assuming a classical logic in which a doubly negated proposition equals its unnegated equivalent. We therefore correctly predict felicitous elision of E. The possibility of polarity reversal sluices in disjunction constructions illustrates the necessity of local contextual entailment in the current account. The global context of (15) does not entail the proposition that John did any extra credit problems, as both possibilities— of John having done extra credit problems and of him not having done any—are being entertained as possibilities. It is only in the local context of the second disjunct that the proposition that John did extra credit problems is entailed, as the local context excludes those worlds in which John didn’t do any extra credit problems. Furthermore, examples such as (15) show that a pragmatically-enriched bidirectional entailment account is insufficient to explain the polarity reversal data, as no pragmatic enrichment of the semantic content of A and E in (15) will yield bidirectional entailment of the propositions. Instead, the crucial licensing factor in this example is the disjunctive operator—which contributes its heritage properties15 to A and E—and not the propositional content of A and E themselves. 4. Concerns of overgeneration The analysis proposed here is necessarily more permissive than syntactic or semantic entailment accounts of sluicing; this additional permissiveness is required in order to capture the structural and semantic differences between the antecedent and elided phrases in polarity reversal sluices. However, there are concerns that a pragmatics-based sluicing account will overgenerate or be overly permissive. I sketch here several constraints to alleviate these concerns.16 First, I adopt the constraint that focus-marked constituents cannot be elided (Rooth 1992; Heim 1997; Merchant 2001). Second, I adopt what I call the Well-Formedness Condition on Sluicing (see Dayal and Schwarzschild 2010): The Well-Formedness Condition on Sluicing: If a pre-sluice is infelicitous, then the corresponding sluice will not be well-formed.17 Dayal and Schwarzschild propose the restriction in order to rule out cases such as (16), comparable to (3) above, which motivate the bidirectionality condition of e-GIVENness: (16) Abbyi called Brian an idiot, but I don’t know who [#shei insulted t]E. The Condition is both empirically supported and intuitively satisfying. It seems desirable that a question that is infelicitous when uttered overtly will remain infelicitous when partially elided. By adopting the Well-Formedness Condition we are able to rule out examples like 15 See Karttunen and Peters (1979), Heim (1983), and Kadmon (2001). See a more extensive discussion of overgeneration concerns in Kroll (in prep). Additional concerns with a pragmatic approach are case matching facts (Merchant 2001) and the Chung’s Generalization facts (Chung 2006, 2013). Case matching facts are captured in this account’s adoption of Merchant’s PF deletion account (2001); see Kroll (in prep) for an account of the Chung’s Generalization facts. 17 The term infelicitous was chosen here in order to allow for the proposed amelioration of islands under sluicing (Merchant 2001). 16 Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 725 M. Kroll Polarity reversals under sluicing (16) independently, obviating the need for a stronger bidirectional entailment condition in these cases. A question naturally raised at this point is why the pre-sluices of examples like (16) are infelicitous. I propose that this is because it is infelicitous to ask a question that already has a partial answer available in the discourse (Romero 1997; Fitzpatrick 2005; Barros 2014; a.o.).18 19 For example, B’s question in (17) is infelicitous without the inclusion of other: (17) A: I saw some tigers today at the zoo. B: {What/which} #(OTHER) animals did you see today at the zoo?20 B’s response is infelicitous without other because A has already asserted that she has seen some tigers that day at the zoo, which is a partial answer to the question ‘What animals did you see today at the zoo?’. Other contributes a presupposition that A has seen some particular animal at the zoo that day. Unlike previous discussions of this discourse requirement on questions, I propose that the behavior be accounted for using Heim’s (1991) Maximize Presupposition: Maximize Presupposition: Given two contextually equivalent alternatives, speakers must use the alternative whose presuppositions are stronger and happen to be met in the context of use. Maximize Presupposition captures exactly the generalization that we want, which is that a question must ask for only new information in a discourse and must presuppose the existence of any partial answers that are already available. The additional benefit of using Maximize Presupposition is that it relates this characteristic of questions to a more general constraint on felicitous utterances in a discourse, making it unnecessary to posit a separate constraint purely for questions. Last, I integrate into the current account an intuitively satisfying pragmatic constraint that for a proposition to be elided it must be uniquely salient at the time the sluice is uttered. The idea is motivated by the common sense principle that in order for a speaker to felicitously not pronounce some part of an utterance, the meaning of the unpronounced piece of the utterance must be recoverable by the speaker’s interlocutor in the discourse. The integration of this constraint correctly rules out the infelicitous sluice in (18), which is not ruled out by Local Givenness as given in §3 nor by the Well-Formedness Condition. (18) [Abby called [Joe]F an idiot]A, but I don’t know who [else]F [#Abby insulted]E. The saliency constraint is integrated into the final version of Local Givenness, provided below. 18 See also Barker’s (2013) Answer Ban and Ginzburg’s (2012) Question Introduction Appropriateness Condition. While the Answer Ban is intended to apply to sluices, this is clearly a more general constraint on questions in a discourse. The QIAC deals with the resolution (complete answers) of questions in the discourse. 19 I assume here a definition of partial answers based on partition semantics (Groenendijk and Stokhof 1981, 1984; Lahiri 2002, a.o.). 20 Where animals is given a kind reading, so the relevant alternatives are tigers, lions, llamas, etc. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 726 M. Kroll Polarity reversals under sluicing Local Givenness (Final):A TP α can be deleted iff ExClo(⟦α⟧g ) expresses a proposition p, such that c L ⊆ p and p is uniquely salient. Additionally, the following test of saliency is proposed: Test for saliency: p is salient at time t if p can be picked out by a propositional discourse anaphor, such as that, at time t. That positive polarity sentences license the propositional discourse anaphor that is pointed out in Webber (1988), among others. That negative sentences also license discourse anaphora is observed in Asher (1993), Hwang (1992), and de Swart (1996): (19) John didn’t knowi the answer to the problem. Thisi lasted until the teacher did the solution on the board. [Asher, pg. 53] The propositional discourse anaphor that is anaphoric to “activated” entities in the sense of Gundel et al. (1990); that is, it is anaphoric to entities that the speech participants are currently aware of, i.e. have access to due to the entities’ presence in the immediate discourse context. Note that this type of anaphoric reference to the sluiced content is possible in the polarity reversal cases: (20) A: I don’t know why [I wasn’t scared]i, but I really can not remember being scared. B: Thati’s impossible! You were just a child. In (20), the deictic demonstrative that is anaphoric to the sluiced proposition I wasn’t scared. That is, the meaning of the first sentence in B’s utterance is “It’s impossible that you weren’t scared.” The strong claim that anaphoric reference with that is a necessary and sufficient condition to test the salience of a proposition in all cases is not being advocated here. Salience is a more complicated notion than can be captured in a single test, as the extensive literature on pronominal salience and reference attests. The anaphora test is merely intended to be one way to probe this issue. The larger question of how to determine the saliency of a proposition in a given discourse requires more thought and investigation than space allows here.21 5. Conclusion Polarity reversal sluicing data present a new challenge to the enterprise of determining the conditions under which linguistic content can be felicitously elided. This paper shows that, counter to its dominant treatment in the syntactic literature, ellipsis is an inherently pragmatics-sensitive phenomenon subject to contextual licensing. I argue that the ability to elide linguistic content fits naturally into general theories of constraints regulating coherent discourses, and have detailed one way to account for the pragmatic sensitivity of data that 21 Note that the claim here is that the sluiced proposition licenses the anaphora; the antecedent material may contribute a discourse referent equivalent to the pragmatically enriched proposition, but the theory here does not predict that it necessarily does. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 727 M. Kroll Polarity reversals under sluicing present serious challenges for non-pragmatic theories. Many challenges to developing a complete theory of sluicing and ellipsis, of course, remain. References Abusch, D. 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Mouton. Schwarzschild, R. (1999). GIVENness, AVOIDF, and other constraints on the placement of accent. Natural Language Semantics 7, 141–77. Stalnaker, R. (2002). Common ground. Linguistics and Philosophy 25, 701–721. Webber, B. L. (1988). Discourse deixis: Reference to discourse segments. Proceedings of the 26th Annual Meeting of the Association for Computational Linguistics, pp.113–122. SUNY Buffalo. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 729 730 Common nouns as variables: Evidence from conservativity and the temperature paradox1 Peter LASERSOHN — University of Illinois at Urbana-Champaign Abstract. Common nouns and noun phrases have usually been analyzed semantically as predicates. In quantified sentences, these predicates take variables as arguments. This paper develops and defends an analysis in which common nouns and noun phrases themselves are treated as variables, rather than as predicates taking variables as arguments. Several apparent challenges for this view will be addressed, including the modal non-rigidity of common nouns. Two major advantages to treating common nouns as variables will be presented: Such an analysis predicts that all nominal quantification is conservative, rather than requiring conservativity to be stipulated as a constraint on determiner denotations; and it makes possible some improvements to the analysis of the temperature paradox, allowing for quantificational examples without adding a spurious layer of modal variability. Keywords: common nouns, variables, rigidity, conservativity, temperature paradox 1. Introduction Common nouns are frequently analyzed semantically as predicates. Beginning logic students are trained to represent sentences like (1)a. using formulas like (1)b., in which the 1-place predicate M seems to correspond directly to the common noun man, just as the 1-place predicate S corresponds to the verb smiles: (1) a. Every man smiles. b. ∀x[M(x) → S(x)] M and S here are syntactically and semantically similar in every way: Both combine with an argument to form a formula; both are the sort of thing which can be truthfully or falsely predicated of an individual; and therefore both are naturally analyzed as denoting the set of individuals of which they can be truthfully predicated (or almost equivalently, the characteristic function of this set). Montague (1973) treated common nouns as belonging to logical type 〈〈s, e〉, t〉 — that is, as 1-place predicates of “individual concepts.” Following Bennett (1975), most subsequent literature in the Montague-derived tradition (including major textbooks such as Dowty, et al. (1981), Gamut (1991), Heim and Kratzer (1998) and many others) has analyzed them as belonging to type 〈e, t〉 — as 1-place predicates of individuals. In both approaches, common nouns are treated identically to intransitive verbs. Exceptions are sometimes made for relational nouns such as mother, brother, top, bottom, etc., which are then treated as being of type 〈e, 〈e, t〉〉; but this still gives such nouns the status of predicates — just 2-place predicates rather than 1-place. 1 This paper was presented to the Harvard Linguistics Circle and at the University of Chicago in addition to Sinn und Bedeutung. Thanks to the audiences at both talks, and especially to Nicholas Asher, Gennaro Chierchia and Uli Sauerland for comments and suggestions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 731 P. Lasersohn Common nouns as variables Proper names, in contrast, are most often treated as being of type e. That is, each proper name is analyzed in such a way that it denotes some particular individual, rather than “holding true” of all the individuals in some class. This results in a sharp division of semantic function with proper names on one side but verbs and common nouns together on the other. This division is preserved even in most analyses which do not treat proper names as individualdenoting — for example by assimilating proper names to quantifiers, as in Russell’s (1910) theory of proper names as “disguised definite descriptions” or in more modern treatments of names and quantifiers as second order predicates (whether of type 〈〈e, t〉, t〉 or Montague’s more baroque 〈〈s, 〈〈s, e〉, t〉〉, t〉). Occasionally, proper names have been analyzed as predicates (Quine (1960), Fara (2015)), but then, of course, common nouns are treated as predicates too: verbs, common nouns and proper names are all treated similarly, with no clear semantic correlate to the morphosyntactic distinction between verbs and nouns (whether proper or common). What I will argue in this paper is that common nouns are similar in semantic type to proper names, and differ in type from verbs. The morphosyntactic distinction between nouns and verbs thus corresponds directly to a difference in semantic type. More particularly, I will argue that common nouns are variables, in roughly the same sense as the variables of predicate logic. Man is more like the x in (1)b. than the M. This is not an entirely new idea. Lepore and Ludwig (2007), for example, say “In ‘All men’, ‘men’ functions as if it were a variable restricted to taking on as values only men…” But this suggestion appears only in their informal discussion. In their formalization, common nouns are not treated this way — or analyzed at all, really: Lepore and Ludwig give formalized rules only for interpreting a simplified artificial version of English which does not contain sentences like (1)a. but only predicate-logic-like formulas such as (2): (2) [Every x : x is a man](x smiles) No interpretation rule is given for the single word man (or any other common noun), but only for the whole open formula ‘x is a man’. If any semantic analysis of the single word man is intended, it is not made explicit; and the notation here, with separate elements ‘x’ and ‘man’, does not suggest that the noun itself is a variable, despite Lepore and Ludwig’s informal discussion. To my knowledge, the idea that common nouns are variables has never been developed or defended in detail.2 The idea faces a number of technical and theoretical challenges: How can we deal with relational nouns? With mass nouns? With quantification? With intensionality? Can such an analysis be made compositional? Even if all these challenges are met, is there any advantage to treating common nouns as variables, or does this idea turn out to be equivalent (or inferior) to a treatment of common nouns as predicates? 2 Aside from Ludwig and Lepore, an interesting comparison may be made to Luo (2012). The idea that common nouns are variables is also, I suspect, the motivating intuition behind Breul (2013), but I must confess an inability to make sense of Breul’s formalism. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 732 P. Lasersohn Common nouns as variables I think that each of these challenges can be answered, and that there are in fact several advantages to treating common nouns as variables, over treating them as predicates. Showing this in detail is a larger project than can be presented in this short paper, so I will focus here on meeting just one of the “challenges” and two of the “advantages.” Specifically, I will show how we can reconcile an analysis of common nouns as variables with the fact that typical common nouns are modally non-rigid; and I will argue that such an analysis predicts that all nominal quantification is conservative, so that conservativity does not need to be stipulated as a condition on determiner denotations; and that it makes possible some improvements to the analysis of the temperature paradox, allowing for quantificational examples without adding a spurious layer of modal variability. 2. First pass: Common nouns as variables What does it mean to say that common nouns are variables? This will depend on exactly what a “variable” is, of course. Unfortunately, there is no universally agreed-on, standard definition of variables, so our main thesis is somewhat obscure at the outset. We shall therefore have to begin with a technique for the semantic analysis of variables which I think most readers will at least find familiar, and show how common nouns can be treated as variables using this technique. In the end, I will adopt a somewhat different approach to the semantics of variables; but starting with a more familiar technique should at least clarify the intuition underlying the claim that common nouns are variables. In this familiar technique, expressions are assigned denotations relative to a series of parameter values, including an assignment of values to variables. Semantic rules are given in such a way that one can derive equations of the form in (3), where α is a linguistic expression, g is an assignment of values to variables, and the three dots abbreviate whatever other parameters denotations are relativized to: (3) ⟦α⟧…, g = a Variables are expressions whose denotations are fixed directly by the assignment of values to variables. That is, α is a variable iff for all g (and all ways of filling in the three dots): (4) ⟦α⟧…, g = g(α) Variable binding is analyzed as the assignment of denotations relative to a given assignment g based on denotations relative to assignments which agree with g in what they assign to all variables other than the one being bound.3 For example, we can define standard variable binding operators like ∀ and ∃ as in (5): (5) a. ⟦∀αφ⟧…, g = 1 iff ⟦φ⟧…, h = 1 for all h agreeing with g on all variables other than α. b. ⟦∃αφ⟧…, g = 1 iff ⟦φ⟧…, h = 1 for at least one h agreeing with g on all variables other than α. 3 This phrasing does not imply that the relevant assignments differ from g in what they assign to the variable being bound. Any assignment g agrees with itself on all variables other than α (for any variable α). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 733 P. Lasersohn Common nouns as variables With this understanding of what variables and binding are as background, how can we treat common nouns as variables? Instead of giving lexical stipulations like those in (6), we may specify the meanings of common nouns as part of the definition of an assignment of values to variables, as in (7): (6) a. ⟦student⟧ = λx . x is a student a. ⟦professor⟧ = λx . x is a professor (7) g is an assignment of values to variables iff a. g is a function with domain {x | x is a common noun token4 or …}; b. If α is a token of student, then g(α) is a student; c. If α is a token of professor, then g(α) is a professor; d. etc. It should be noted that under (7), student and professor are of type e, not 〈e, t〉. We shall have to revise the definition in (7) several times before the end of this paper; but let us adopt it for the moment, and explore how it may function in a larger theory of quantification and binding for English. I assume that LF representations are derived via an operation of Quantifier Raising, which adjoins a quantifier phrase to its scope, leaving a trace in its original position. I will also assume here that Quantifier Raising is clause-bounded. This means we normally cannot use it to obtain transparent readings for quantifier phrases in opaque contexts; but alternative techniques are available, and perhaps better motivated anyway.5 By the antecedent of a trace, let us mean the NP of the DP whose trace it is. That is: (8) Where δ is a determiner token and κ is a common noun phrase token: antecedent(trace(δ κ)) = κ. Note that this is a slightly non-standard use of the term antecedent. In [every professor [e smiles]], professor, not every professor, is the antecedent of e. We do not assume that traces are co-indexed with their antecedents (or with the DPs containing their antecedents). The analysis is compatible with such co-indexation, but does not require it, provided there is some way of identifying the antecedent of each trace. Traces will be interpreted as variables, with a requirement that (relative to any assignment of values to variables g) a trace co-denotes with its antecedent: (9) g is an assignment of values to variables iff a. g is a function with domain {x | x is a common noun token, trace token or…}; b. If α is a token of student, then g(α) is a student; c. If α is a token of professor, then g(α) is a professor; 4 Instead of assigning values to expression tokens, we could assign values to pairs of an expression type and a context of use. In the long run, this may be the preferable option; but a consideration of the issue here would force a long digression from our central concerns in this paper, so I assign values to tokens here in the interest of simplicity. 5 See, e.g., Cresswell (1990). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 734 P. Lasersohn Common nouns as variables d. etc.; e. If ε is a trace token, then g(ε) = g(antecedent(ε)). We write “g ~κ h” to mean that assignment h agrees with assignment g on all common noun phrases other than κ. Now we can define every syncategorematically: (10) ⟦every κ φ⟧g = 1 if ∀h [g ~κ h → ⟦φ⟧h = 1]; 0 if ∃h[g ~κ h & ⟦φ⟧h = 0]. It is easy to confirm that this gives the correct result that Every professor e smiles is true iff for every x such that x is a professor, x smiles. Other quantifiers can be defined analogously (but revisions will be necessary to deal with more complex cases). It is perhaps worth noting at this point that if we analyze quantification in the way just sketched, there is no semantic motivation any more to have QR move whole DPs, rather than just determiners, or to have QR leave traces. We could get the same effect simply by moving the determiner, and leaving the NP in situ. But let us leave that issue aside, in order to concentrate on semantic matters rather than syntax. 3. First advantage: Conservativity is predicted Even though our analysis is not in its final form, we can already see one advantage to treating common nouns in this way, rather than treating them as predicates: The analysis predicts that all nominal quantification is conservative.6 This claim must be clarified, because the relevant notion of conservativity here is not exactly the traditional textbook sense. The standard definition is in (11): (11) D is conservative iff for all A, B: D(A, B) iff D(A, A∩B) But if we take D to be a determiner denotation, A to be a common noun phrase denotation, and B to be a predicate denotation, this definition presupposes that common nouns denote sets. Analyses which treat common nouns in some other way will never claim that determiners are conservative in exactly this sense. In order to compare theories, we need a more general notion of conservativity, which is not tied so tightly to a particular approach to the analysis of common nouns and determiners. A more useful way to conceptualize conservativity for our current purposes is to recognize that the intuitive content of the standard definition is that A functions as a domain of quantification. That is, in ascertaining whether D(A, B), one need not consider those members of B which are not in A. Put differently (and more sloppily and Englishspecifically): in determining the truth value of a sentence of the form D N VP, you only need to consider the N’s: Which N’s does VP apply to and which N’s doesn’t VP apply to? You never need to consider the truth value that results from applying VP to something which isn’t an N. 6 The suggestions made in this section may be interestingly compared to proposals like those in Fox (2002), Sauerland (2004), Sauerland (2007), Romoli (2015); but such a comparison will have to wait for another occasion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 735 P. Lasersohn Common nouns as variables In any analysis, some distinction must be drawn between the things which a given noun accurately describes and those which it doesn’t. If common nouns are analyzed as denoting sets, these are the members of the set denoted by the noun; if common nouns are analyzed as denoting functions of type 〈e, t〉, these are the things mapped onto 1 by the function denoted by the noun; if common nouns are analyzed as variables, these are the things assigned to the noun by the various assignments of values to variables. No matter which approach is taken, a theory claims that determiner quantification is conservative iff whenever a determiner-noun combination combines with a predicate P to form a sentence, the truth value of that sentence can be ascertained by considering only how P applies to the things accurately described by the noun, so that the truth values which result from applying P to things not accurately described by the noun are irrelevant. Now we can see how conservativity falls out from the general approach to determiner quantification just outlined. Assignments of values to variables, in this approach, are functions from common noun phrases (and traces) to individuals. For any such function, the individual assigned to a given noun N is something which “is an N” — something which would be a member of the extension of N in a more conventional analysis. As one considers a class of assignments which differ from one another at most in what they assign to N, therefore, one is effectively considering the things which are accurately described by the noun. As long as object-language quantification over individuals is analyzed in terms of metalanguage quantification over assignments of values to variables, and as long as determiner-noun combinations are interpreted by quantifying over those assignments which agree on all variables other than the noun with which the determiner combines, conservativity is automatic. To give just a little more detail: Assume that interpretation rules for quantifiers conform to the following general template, based on the rule for every: (12) ⟦δ κ φ⟧g = 1 if for δ-many assignments of values to variables h such that g ~κ h, ⟦φ⟧h = 1; = 0 if it is not the case that for δ-many assignments of values to variables h such that g ~κ h, ⟦φ⟧h = 1. Rules conforming to this template derive a value for ⟦δ κ φ⟧g based on ⟦φ⟧h , for various assignments h which differ from g at most in what they assign to κ (and any trace with κ as its antecedent). But h(κ) will always be something which is accurately described by κ, and so will h(ε), where antecedent(ε) = κ. There simply are no assignments of values to variables relative to which ε receives a value which is not accurately describable by κ, so it makes no sense to ask whether the truth value of φ is relative to such assignments is relevant to the truth value of the whole sentence [δ κ φ]. That is, quantification is just over those individuals which are accurately described by the noun, which is to say, the quantification is conservative — and this follows from the general architecture of the theory. In contrast, if we assume simply that determiners denote 2-place Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 736 P. Lasersohn Common nouns as variables relations between sets (or functions of type 〈〈e, t〉, 〈〈e, t〉, t〉〉), nothing guarantees conservativity; it must be independently stipulated.7 4. Adding intensionality: Non-rigid variables Analyzing common nouns as variables will not work properly in an intensional semantics, if we treat variables in the traditional way. Standard versions of intensional logic and quantified modal logic incorporate a principle like that in (13): (13) If α is a variable, then ⟦α⟧M,w,g = g(α). This gives the effect that for all w, w′, ⟦α⟧M,w,g = ⟦α⟧M,w′,g. That is, variables are modally rigid. But now recall (9)b.: “If α is a token of student, then g(α) is a student.” In which world must g(α) be a student? Since no world is mentioned, we standardly assume the condition is meant to apply in the actual world w@. Since variables are rigid, this gives the effect that for any w, ⟦student⟧M,w,g is a student in w@ — but nothing requires ⟦student⟧M,w,g to be a student in w. This is obviously wrong — it results in incorrect truth conditions for sentences like (14): (14) John believes that every student e smiles Assuming our current semantics including (9), (10) and (13), combined with a standard possible-worlds analysis of believe along the lines of Hintikka (1969), (14) is assigned a reading which is true (in the actual world w@) iff in every world w compatible with John’s belief state (in w@), everyone who is a student in w@ smiles in w. It is not assigned a reading which is true (in w@) iff in every world w compatible with John’s belief state (in w@), everyone who is a student in w smiles in w. In other words, the analysis wrongly predicts that all common nouns should be interpreted transparently. To allow opaque readings, we need to allow modally non-rigid variables.8 This requires us to revise our definition of an assignment of values to variables: (15) g is an assignment of values to variables iff a. g is a partial9 function with domain {x | x is a common noun token, trace token or…}⨯W; b. If α is a token of student: for all w, if there exists an x such that x = g(α, w), then g(α, w) is a student in w; c. If α is a token of professor: for all w, if there exists an x such that x = g(α, w), then g(α, w) is a professor in w; d. etc.; e. If ε is a trace token, then for all w, g(ε, w) = g(antecedent(ε), w). 7 Our discussion in this section raises the question of how to deal with only and other quantifiers which appear not to be conservative. I assume in such cases, the quantifier binds a variable which is constructed in part based on intonational focus or other factors, rather than simply binding the NP (if any) which serves as its syntactic complement. That is, the quantification in such cases is not strictly “nominal.” A detailed consideration of such cases will have to await another occasion. 8 These have rarely been suggested before, but see e.g. Hughes and Cresswell (1968: 195–201). 9 We allow g to be a partial function because in some worlds, there aren’t any students or professors. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 737 P. Lasersohn Common nouns as variables Making this change necessitates corresponding revisions to our definition for the double brackets, and to our definition of what it means for one assignment to agree with another on all values other than a particular one: (16) If α is a variable, then for all worlds w and assignments g: ⟦α⟧w,g = g(α, w). (17) g ~κ,w h iff a. there exists some x such that h(κ, w) = x; and b. for all common noun phrases ν and worlds w′: if ν ≠ κ then g(ν, w′) = h(ν, w′). We also need to revise our rule for every to reflect the change made in (17): (18) ⟦every κ φ⟧w,g = 1 if ∀h [g ~κ,w h → ⟦φ⟧w,h = 1]; 0 if ∃h[g ~κ,w h & ⟦φ⟧w,h = 0]. It is easy to confirm that our rules now give the desired modal profile for sentences like Every student e smiles. However, our revisions have introduced another problem. Some variables should be rigid — specifically pronouns, assuming these can be bound across the borders of intensional contexts. For example, consider (19), assuming that professor is the antecedent of she. (19) [Every professor e believes [that she smiles]] If we treat the pronoun here the way we have treated traces — as codenoting, in each world w, with its antecedent — we assign the wrong truth conditions. Intuitively, (19) is true in w@ only if for every x such that x is a professor in w@, in every world w compatible with x’s belief state in w@, x smiles in w. But if we require, for every assignment g, world w and pronoun π, that g(π, w) = g(antecedent(π), w) — like we did with traces — we do not get that reading, because nothing requires that g(she, w) = g(professor, w@). Quantifying on assignments that agree with g on all values other than g(professor, w@) will not quantify over values for she in the “belief worlds”. To solve this problem, we must again revise our definition of assignment functions, so that each one is keyed to a particular world: (20) g is an assignment of values to variables for w (or “w-assignment”) iff a. g is a partial function with domain {x | x is a common noun token, trace token, pronoun token, or…}⨯W; b. If α is a token of student: for all w′: if there exists an x such that x = g(α, w′), then g(α, w′) is a student in w′; c. If α is a token of professor: for all w′: if there exists an x such that x = g(α, w′), then g(α, w′) is a professor in w′; d. etc.; Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 738 P. Lasersohn Common nouns as variables e. If ε is a trace token, then g(ε, w′) = g(antecedent(ε), w′); f. If π is a pronoun token, then g(π, w′) = g(antecedent(π), w). Note the difference between clauses e. and f. Relative to each world wʹ, a trace is required to denote the same thing as the denotation of its antecedent in wʹ, but a pronoun is required to denote the same thing as the denotation of its antecedent in w, the world to which the assignment is keyed. This guarantees that relative to any given assignment, the denotation of a pronoun is modally rigid. Now we revise the tilde notation so that agreeing assignments must be keyed to the same world: (21) g ~κ,w h iff a. g and h are both w-assignments; b. there exists some x such that h(κ, w) = x; and c. for all common noun phrases ν and worlds w′: if ν ≠ κ then g(ν, w′) = h(ν, w′). Our rule for every in (18) can remain notationally the same, but operates differently due to the replacement of (17) with (21). In (18), g and h are now both required to be w-assignments — so relative to h, any pronouns in φ will rigidly denote what κ denotes relative to h in w. This ensures that (19) will be true relative to a world w only if for every x such that x is a professor in w, for every w′ compatible with x’s belief state in w, x smiles in w′. The person who smiles in each professor’s belief worlds is correctly required to be that same person who is a professor in w, and holds the belief. There is no requirement that every professor must be a professor in all her belief worlds. 5. Second advantage: The temperature paradox We can now turn to a second major advantage to treating common nouns as variables: It allows some improvements in how we analyze the temperature paradox. The paradox and its proposed solution in Montague (1973) are familiar to most readers and will only be briefly sketched here: The argument in (22) is of a form which seems naturally representable as in (23), but (23) is a valid argument and (22) is not. (22) The temperature is rising. The temperature is 90. Therefore, 90 is rising. (23) ∃x[temperature(x) & ∀y[temperature(y) → x = y] & rise(x)] ∃x[temperature(x) & ∀y[temperature(y) → x = y] & x = n] ∴ rise(n) Montague’s solution is to treat rise as a predicate of functions from indices (including times) to individuals, but treat is as holding (at a given index) between two such functions iff they Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 739 P. Lasersohn Common nouns as variables return the same value for that index.10 Under this analysis, (22) can be paraphrased as (24), which is easily seen as invalid: (24) The unique temperature function is a rising function. The unique temperature function and the 90 function currently yield the same value. Therefore the 90 function is a rising function. The analysis is made more formal through the use of ∧- and ∨-operators, defined as in (25) and (26): (25) ⟦∧α⟧M,w,t,g = that function f with domain W⨯T such that for all w′ ∈ W, t′ ∈ T: f(w′, t′) = ⟦α⟧M,w′,t′,g (26) ⟦∨α⟧M,w,t,g = ⟦α⟧M,w,t,g(w, t) Now the argument may be represented as (27) rather than (23): (27) ∃x[temperature(x) & ∀y[temperature(y) → x = y] & rise(x)] ∃x[temperature(x) & ∀y[temperature(y) → x = y] & ∨x = ∨n] ∴rise(n) In (27), the variables x and y are of type ⟨s, e⟩, not of type e. Hence rise and temperature must both be of type ⟨⟨s, e⟩, t⟩. In the case of rise, this is intuitive and appropriate. What counts as rising at a time t depends on how things are at times other than t. It is impossible to ascertain whether the temperature is rising at a moment by examining a photograph of a thermometer taken at that moment; one needs multiple photographs, taken at different times. It therefore makes sense to treat rise as taking functions from times to numbers as its arguments, so that rise can “see” what is going on at other times; there is a clear intuitive basis for treating rise as temporally intensional. But the situation with temperature is quite different: To tell whether a particular value is the temperature at a given moment, a single photograph taken at that moment suffices, and photographs taken at other times are irrelevant. There isn’t the same intuitive basis for letting temperature take functions from times to numbers as its arguments as there is for rise; temperature is not temporally intensional in its conditions of application like rise is. This feature of Montague’s analysis leads to a problem pointed out by Anil Gupta.11 Intuitively, the argument in (28) is valid. But it is translated into Intensional Logic as in (29), and (29) is not a valid argument: (28) Necessarily, the temperature is the price. The temperature is rising. Therefore, the price is rising. 10 I have simplified Montague’s analysis here by setting aside some irrelevant complications with type assignment. 11 Gupta’s problem is outlined in Dowty, et al. (1981: Appendix III) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 740 P. Lasersohn (29) Common nouns as variables □∃x[temperature(x) & ∀y[temperature(y) → x = y] & ∃z[price(z) & ∀y[price(y) → z = y] & ∨x = ∨z] ∃x[temperature(x) & ∀y[temperature(y) → x = y] & rise(x)] ∴∃x[price(x) & ∀y[price(y) → x = y] & rise(x)] To see that (29) is invalid, let T1, T2, T3, P1, P2, P3 be the functions given in (30). Now consider a model where temperature holds at ⟨w1, t1⟩ uniquely of T1, at ⟨w1, t2⟩ of T2, and at ⟨w1, t3⟩ of T3, and where price holds at ⟨w1, t1⟩ uniquely of P1, at ⟨w1, t2⟩ of P2, and at ⟨w1, t3⟩ of P3: (30) T1(w1, t1) = 99 T1(w1, t2) = 100 T1(w1, t3) = 101 T2(w1, t1) = 89 T2(w1, t2) = 90 T2(w1, t3) = 91 T3(w1, t1) = 79 T3(w1, t2) = 80 T3(w1, t3) = 81 P1(w1, t1) = 99 P1(w1, t2) = 98 P1(w1, t3) = 97 P2(w1, t1) = 91 P2(w1, t2) = 90 P2(w1, t3) = 89 P3(w1, t1) = 83 P3(w1, t2) = 82 P3(w1, t3) = 81 It is easy to see that the first premise of (29) is true: at each world-time pair there is a unique temperature function, and a unique price function, and the two functions return the same current value — 99 at ⟨w1, t1⟩, 90 at ⟨w1, t2⟩, and 81 at ⟨w1, t3⟩. The second premise of (29) is also true at all indices, under an intuitive definition of rise and an assumption that t1 precedes t2 and t2 precedes t3: At each index, the unique temperature function is a rising function, returning a higher value at each successive time. For example, at ⟨w1, t2⟩ the unique temperature function is T2, which returns 89 at ⟨w1, t1⟩, 90 at ⟨w1, t2⟩, and 91 at ⟨w1, t3⟩. However, the conclusion of (29) is false at every index, since at every index the unique price function is a falling function, not a rising one. In Lasersohn (2005) I suggested a solution to this problem, which unfortunately did not work. I argued that the source of the problem was in treating the as a variable-binding quantifier. In the sentence The temperature is rising, this quantificational analysis of the requires temperature to take the same variable as its argument as is rising does, which in turn forces temperature into the intuitively unjustified type ⟨⟨s, e⟩, t⟩, which allows different temperature functions (and not just different temperature values) at different times, which leads to Gupta’s problem. But if we switched to a non-quantificational analysis of the, I argued, we could avoid using a single variable both as argument to temperature and as argument to is rising. Specifically, if we represent the temperature as ℩x temperature(x), where temperature is of type ⟨e, t⟩ and the iota-operator is interpreted as in (31), then The temperature is rising can be represented as in (32): (31) ⟦℩x P(x)⟧M,w,t,g = the unique element u such that ⟦P⟧M,w,t,g(u) = 1 if there is such a unique element, undefined otherwise. (32) rise(∧℩x temperature(x)) At each index, ℩x temperature(x) denotes the unique temperature (value) at that index. By the semantics of the ∧-operator in (25), ∧℩x temperature(x) will rigidly denote the function Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 741 P. Lasersohn Common nouns as variables mapping each index onto the unique temperature at that index. In this way, we derive just one temperature function — the same one at every index — and just one price function. Hence, if at every index the temperature function yields the same value as the price function (so they are really the very same function), and the temperature function is a rising function, then the price function must be a rising function too. Gupta’s problem is eliminated. However, this solution cannot be correct, as Romero (2008) was quick to point out. By tying the solution to a non-quantificational analysis of the, I made it impossible to deal with more clearly quantificational examples in the same way. But such examples exist; in fact, Montague himself gave such an example, perhaps because he anticipated the kind of analysis I was proposing: (33) A price rises. Every price is a number. Therefore, a number rises. In light of such examples, I concede the point that the temperature paradox does not really provide us with evidence for a non-quantificational theory of the definite article. Considerations of space preclude a review of Romero’s very interesting analysis here, but it should be acknowledged that it accounts successfully for the validity of Gupta’s argument. However, it also retains an odd feature of Montague’s original analysis, which seems to me to be very unintuitive: It allows nouns like temperature to denote different sets of functions relative to different times. That is, we can have temporal variation not just in what values get returned by the temperature function (or functions), but in which functions count as temperature functions in the first place. Intuitively, that can’t happen. Suppose we are talking about the temperature of one particular object, in one particular world. If at time t1, the temperature function for that object in that world maps t1 to 90, t2 to 91, and t3 to 92, then it cannot happen that at t2, the temperature function for that object in that world maps t1 to 85, t2 to 84, and t3 to 83. This kind of temporal variation is easy enough to rule out by meaning postulate (or some similar lexical stipulation), but it would be preferable, if possible, to find a more “architectural” solution, which prevented a case like this from coming up in the first place. If we analyze common nouns as variables, and allow variables to be temporally non-rigid in the same way as we allowed them to be modally non-rigid, such a solution is available. First, to allow for temporal intensionality, we revise the definition of assignment functions in (20) so that assignments give values to variable-world-time triples, and add a clause for the noun temperature: (34) g is an assignment of values to variables for w, t (or “w,t-assignment”) iff a. g is a partial function with domain {x | x is a common noun token or trace token or pronoun token or …}⨯W ⨯T b. If α is a token of student: for all w′, t′: if there exists an x such that x = g(α, w′, t′), then g(α, w′, t′) is a student in w′ at t′; Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 742 P. Lasersohn Common nouns as variables c. If α is a token of professor: for all w′, t′: if there exists an x such that x = g(α, w′, t′), then g(α, w′, t′) is a professor in w′ at t′; d. If α is a token of temperature: there is some pragmatically relevant object or location x, such that for all w′, t′: x exists at w′, t′ iff g(α, w′, t′) is the temperature of x in w′ at t′ (in the relevant scale — ˚F, ˚C, etc.) e. etc.; f. If ε is a trace token: for all w′, t′: g(ε, w′, t′) = g(antecedent(ε), w′, t′); g. If π is a pronoun token: for all w′, t′: g(π, w′, t′) = g(antecedent(π), w, t). Notice that according to (34)d., for each assignment function g and token of the noun temperature there is one particular object or location whose temperature at various times and worlds is tracked by the values which g assigns to that token (relative to those times and worlds). The value which g assigns to a token of temperature relative to a world w and time t is just a number — an entity of type e — not a function or set of functions. So for any given world and any given object, there will be just one function which picks out the temperature of that object in that world at each time — not different such functions at different times. This eliminates the source of Gupta’s problem. In a semantic theory using (34), the intension of a token of temperature relative to a given assignment g will naturally be a function mapping each world-time pair onto the temperature of one particular object or location in that world at that time. Verbs like rise must remain at type ⟨⟨s, e⟩, t⟩. But now we have a problem: If traces are required to co-denote with their antecedents, and nouns like temperature are type e, then the trace left by phrases like the temperature or every price will also be of type e, so it will not be of the right type to serve as argument to rise. Therefore, we now allow traces (and pronouns) of type ⟨s, e⟩. If a trace or pronoun is in position to fill an ⟨s, e⟩ argument place, the trace/pronoun must be of type ⟨s, e⟩. If it is in position to fill a type e argument place, it must be of type e. If a trace or pronoun is of type ⟨s, e⟩, its denotation must be the same as the intension of its antecedent, rather than its extension. More formally, we replace (34)f., g. with (35)a., (35)b.: (35) a. If ε is a trace token: for all w′, t′: g(ε, w′, t′) = g(antecedent(ε), w′, t′) or g(ε, w′, t′) = that function f: W⨯T→De such that for all w″, t″, f(w″, t″) = g(antecedent(ε), w″, t″), according as ε is of type e or of type ⟨s, e⟩; b. If π is a pronoun token: for all w′, t′: g(π, w′, t′) = g(antecedent(π), w, t) or g(π, w′, t′) = that function f: W⨯T→De such that for all w″, t″, f(w″, t″) = g(antecedent(ε), w″, t″), according as π is of type e or of type ⟨s, e⟩. Finally, we need to make the obvious updates to the notation used in our rules and definitions, to reflect the fact that assignments are now to a time parameter in addition to a world. We replace (21) with (36): (36) g ~κ,w,t h iff a. g and h are both w,t-assignments; b. there exists some x such that h(κ, w, t) = x, and Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 743 P. Lasersohn Common nouns as variables c. for all common noun phrases ν, worlds w′ and times t′: if ν ≠ κ, then g(ν, w′, t′) = h(ν, w′, t′). And (18) with (37): (37) ⟦every κ φ⟧w,t,g = 1 if ∀h [g ~κ,w,t h → ⟦φ⟧w,t,h = 1]; 0 if ∃h[g ~κ,w,t h & ⟦φ⟧w,t,h = 0]. Now our semantics (unlike that of Lasersohn (2005)) will assign a coherent interpretation to sentences like [Every temperature [e rises]]. In order to serve as argument to rises, the trace e must be of type ⟨s, e⟩. Therefore, relative to any assignment g, it must denote the intension of its antecedent, temperature, relative to g. Relative to g, the intension of temperature is a function tracking the temperature of one particular object or location — but relative to another assignment, the intension of the temperature might be a function tracking the temperature of some other relevant object or location. The sentence is true relative to an assignment g iff [e rises] is true relative to every assignment h agreeing with g on all nouns other than temperature. That is, it is true if the temperature function of each relevant object or location is a rising function. The original temperature paradox argument correctly comes out invalid, even if we adopt a quantificational analysis of definites. We may define the as in (38): (38) ⟦the κ φ⟧w,t,g = 1 if ∃h[g ~κ,w,t h & ∀i [g ~κ,w,t i → h = i] & ⟦φ⟧w,t,h = 1]; 0 if ¬∃h[g ~κ,w,t h & ∀i [g ~κ,w,t i → h = i] & ⟦φ⟧w,t,h = 1]. Consider the truth condition assigned to (39) under this rule: (39) [The temperature [e rises]] In order for (39) to be true relative to an assignment g (in w, at t), there must be exactly one assignment h which agrees with g on all common noun tokens other than the token of temperature in this example. If h agrees with g in this way, there must be some pragmatically relevant object or location, whose temperature h assigns to this token at each world and time. Since h is unique, there can be only one function which maps a pragmatically relevant object or location onto its temperature at each world and time. That is to say, despite the fact that temperature is of type e, according to our rules (39) requires a unique temperature function, not just a unique temperature value. Of course this unique temperature function must also be a rising function in order for (39) to be true. In contrast, (40) is true (relative to w, t, g) iff the value of the unique temperature function at w, t is 90; the trace here is of type e, and therefore denotes the extension, not the intension of its antecedent. (40) [The temperature [e is ninety]] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 744 P. Lasersohn Common nouns as variables Assuming that the intension of ninety is the constant function mapping each world-time pair onto 90, (41) will always be false, even if (39) and (40) are true: (41) [Ninety rises] It is also easy to see that Gupta’s argument comes out valid. Sentence (42)a. equates, at all world-time pairs, the value of the unique temperature function with the value of the unique price function. If the unique temperature function yields the same value at every pair as the unique price function, then they are the same function; so if the temperature function is rising, the price function is rising. (42) a. Necessarily, the temperature is the price. b. The temperature is rising. c. Therefore, the price is rising. 6. Conclusions Common nouns which are usually analyzed predicates of type ⟨e, t⟩ may instead by analyzed as being of type e by treating them as restricted variables. Treating them this way, in combination with a standard understanding of what variable-binding is, predicts that all nominal quantification is conservative, and does so without any independent restriction on determiner meanings. In order to assign correct truth conditions to sentences in which common nouns appear in intensional contexts, an analysis which treats them as variables must allow variables to be modally non-rigid. Certain other variables, notably pronouns, should continue to be analyzed as rigid. Allowing modally non-rigid variables makes possible an analysis of the temperature paradox which can deal with quantificational examples, without requiring extra stipulations to rule out modal variation in which functions count as temperature functions, thus solving “Gupta’s problem.” These arguments are not by themselves sufficient to establish that common nouns should be analyzed as variables. That would be a far larger project, requiring much more thorough and intensive investigation than can be accomplished in a single paper. Several important challenges to this view have not been addressed here: How can we deal with relational nouns? With complex noun phrases containing modifiers? With mass and plural nouns? Can the treatment of quantification be formulated in such a way that determiners are assigned denotations, instead of being interpreted syncategorematically, as they were in this paper? I believe all these challenges can be met; but demonstrating this will have to wait for another occasion. Additional advantages to analyzing common nouns and noun phrases as variables also suggest themselves: Such an analysis may allow for a closer, more systematic correlation between syntactic categories and semantic types. If complex phrases like farmers who own a donkey can be treated as type e variables, a new pathway opens for the analysis of the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 745 P. Lasersohn Common nouns as variables “proportion problem” in sentences like Most farmers who own a donkey beat it. Treating common nouns as type e variables promises a more natural analysis of “collectivizing” conjunction of common nouns, as in the reading of this man and woman where it denotes a group whose members are a man and a woman. These and other topics must here be left to later investigation. References Bennett, M. R. (1975). Some Extensions of a Montague Fragment of English. Indiana University Linguistics Club. Breul, C. (2013). Zu Artikeln und dem Logisch-Semantischen Typ von Nomina. Linguistische Berichte 235, 309–336. Cresswell, M. J. (1990). Entities and Indices. Kluwer Academic Publishers. Dowty, D., R. E. Wall, and S. Peters (1981). Introduction to Montague Semantics. Reidel. Fara, D. G. (2015). Names are predicates. Philosophical Review 124(1), 59–117. Fox, D. (2002). Antecedent-contained deletion and the copy theory of movement. Linguistic Inquiry 33(1), 63–96. Gamut, L. T. F. (1991). Logic, Language and Meaning, Volume 2: Intensional Logic and Logical Grammar. University of Chicago Press. Heim, I. and A. Kratzer (1998). Semantics in Generative Grammar. Blackwell. Hintikka, J. (1969). Semantics for propositional attitudes. In J. W. Davis, D. J. Hockney, and W. K. Wilson (Eds.), Philosophical Logic, pp. 21–45. Reidel. Hughes, G. E. and M. J. Cresswell (1968). An Introduction to Modal Logic. Metheun. Lasersohn, P. (2005). The temperature paradox as evidence for a presuppositional analysis of definite descriptions. Linguistic Inquiry 36(1), 127–130. Lepore, E. and K. Ludwig (2007). Donald Davidson’s Truth-Theoretic Semantics. Oxford University Press. Luo, Z. (2012). Formal semantics in modern type theories with coercive subtyping. Linguistics and Philosophy 35(6), 491–513. Montague, R. (1973). The proper treatment of quantification in ordinary English. In K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes (Eds.), Approaches to Natural Language: Proceedings of the 1970 Stanford Workshop on Grammar and Semantics, pp. 221–242. Reidel. Quine, W. V. O. (1960). Word and Object. MIT Press. Romero, M. (2008). The temperature paradox and temporal interpretation. Linguistic Inquiry 39(4), 655–667. Romoli, J. (2015). A structural account of conservativity. Semantics-Syntax Interface 2(1), 28–57. Russell, B. (1910). Knowledge by acquaintance and knowledge by description. Proceedings of the Aristotelian Society 11, 108–128. Sauerland, U. (2004). The interpretation of traces. Natural Language Semantics 12(1), 63– 127. Sauerland, U. (2007). Flat binding: Binding without sequences. In U. Sauerland and H.-M. Gärtner (Eds.), Interfaces + Recursion = Grammar? Chomsky's Minimalism and the View from Syntax-Semantics, pp. 197–254. Mouton de Gruyter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 746 Bayes nets and the dynamics of probabilistic language Daniel LASSITER — Stanford University Abstract. This paper is about a shared concern of linguistic semantics and pragmatics, epistemology, and many other areas of cognitive science: the formal representation of information and uncertainty. It is common in many of these areas, and increasingly in linguistics, to represent agents’ information using probability—an enrichment of classical semantics. However, each application of probability must answer difficult questions about whether a probabilistic representation is rich enough to capture the nuances of our information states. Two such problems—the epistemological distinction between uncertainty and ignorance, and the dynamic effects of probabilistic language in formal pragmatics—seem to suggest a negative answer, and to support a more complicated model that repesents uncertainty in terms of sets of probability measures. Following insights due to Judea Pearl (1988), I argue that the simplest probabilistic approach may be sufficient to handle these problems if we pay close attention to the hierarchical structure of information states, as encoded explicitly in the graphical representation of relationships among questions known as “Bayesian networks” or “Bayes nets”. Keywords: epistemic modality, probability, dynamics, epistemology 1. Three scenarios and two puzzles (1) Two teams, A and B, are about to compete in a soccer game. You’ve seen them compete many times, and you are certain that they are evenly matched. What probability should you assign to the sentence “A will win”? (2) Two teams, A and B, are about to compete at soccer. You know nothing at all about these two teams. What probability should you assign to the sentence “A will win”? If pushed, most people will give the same answers to these questions: “50%”. But our reason for giving these answers is obviously different in (1) and (2). In (1), we have a lot of relevant information to justify making this choice with confidence. In (2), our choice is made in ignorance: we just don’t have any reason at all to favor one team over the other. Obviously, there is an epistemologically relevant difference, and it would be a mistake to represent our information identically in (1) and (2). But probabilistic representation seems not to make a distinction here. (3) As in example (2), there are two teams, A and B, who are about to compete, and you know nothing at all about them. However, a knowledgeable friend assures you that “Team A is likely to win.” What probability should you assign to “A will win”? Here we move from a mainly epistemological question to one that lies at the border of epistemology, formal pragmatics, and computational cognitive science. Epistemologists and psychologists worry about the way that people do (or should) modify their states of information in light of new information, however acquired. Formal pragmaticists and dynamic semanticists worry about the way that people do (or should) modify their states of information in light of new information acquired by linguistic means. The latter kind of question being a special case Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 747 D. Lassiter Bayes nets and the dynamics of probabilistic language of the former, both groups of theorists should care about what information is conveyed by the sincere assertion of a statement with probabilistic import, like “Team A is likely to win”. This is a particularly important problem for theorists of a Bayesian bent, since for them probability— or “credence”—is the basic currency of belief. Unfortunately, there is no general theory of the informational effects of probabilistic language to date. An attempt to frame one must balance three considerations, each difficult in its own right: getting the empirical facts right, integrating with existing accounts of linguistic dynamics, and remaining plausible in light of a broader accounts of epistemology and the cognitive science of learning and reasoning. This paper treats the dynamics of probabilistic language and the confidence/ignorance distinction as two sides of an epistemological coin. The first approach takes ordinary probability to be inadequate as a representation of agents’ credence states, and opts for a richer model using imprecise credences—i.e., sets of probability measures. Probabilistic language, in turn, is modeled in terms of filtering on this set. The second approach tries to explain both the confidence/ignorance distinction and the dynamic effects of probabilistic language in terms of a single probability model that incorporates a hierarchical structure—such as that of a Bayes net. The need to include hierarchical structure in probabilistic models employs enjoys vast psychological, philosophical, and computational motivation (e.g., Pearl 1988, 2000; Glymour 2001; Sloman 2005; Woodward 2003; Tenenbaum et al. 2011; Danks 2014). Hierarchical models can also be used to model the interplay between statistical and causal reasoning, which is crucial in many linguistic, cognitive, and philosophical applications. There is an obvious gain in theoretical simplicity, then, if we can apply this independently motivated modeling approach to resolve the problems discussed here as well. However, I will argue that the primary motivation for the hierarchical approach is that it yields a better account of the basic empirical facts. None of this calls directly into doubt whether further phenomena might motivate the use of imprecise probabilities in epistemology, psychology, or linguistics. Nor does it bear on the rather different question of whether imprecise-probability models are useful in modeling epistemic phenomena that extend beyond the minds of individuals, such as group belief or conversational common ground. (See brief comments on the latter in §5 below.) The main claim of the current work is rather that certain phenomena which appear to problematize Bayesian models of individual agents’ informational states and their (linguistic and non-linguistic) dynamics in fact already have an illuminating explanation within these models. 2. Precise and imprecise credences Say that an agent a has precise credences just in case a’s state of information is well-represented by a probability measure Pa . Since this function is being used here to model a’s state of belief, or “credence”, we’ll also call it a “credence function”. Pa assigns a number between 0 and 1 to each proposition A P ℘pW q, subject to the usual laws of probability (Kolmogorov, 1933): Pa pW q “ 1, and Pa pA Y Bq “ Pa pAq ` Pa pBq ´ Pa pA X Bq. (These definitions assume that W is finite, inessentially, in order to simplify the math.) Just what it means for a’s information to be “well-represented” by Pa is a difficult theoretical question that I will leave at an intuitive level here. Explicit judgments about probability, other linguistic behaviors, overt choices, and dispositions to choose in particular ways are some of the many ways that we might want to Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 748 D. Lassiter Bayes nets and the dynamics of probabilistic language evaluate whether a candidate Pa is a good representation of a’s information. Notice that this model does not compete with classical semantics, but rather presupposes and extends it: a set of worlds W generates a Boolean algebra ℘pW q whose elements are propositions that receive probabilities. Probability assignments are constrained by classical logic. For example, if A and B are contradictory—A X B “ H—then PpA X Bq “ 0. If A entails B—A Ď B—then Pa pAq ď Pa pBq. (Indeed, the probabilistic model inherits some important limitations of the classical semantics, such as problems around logical omniscience and hyperintensionality.) Precise credence models have many epistemological and cognitive advantages, and are also subject to many kinds of objections. One well-known objection involves experimental evidence that ordinary people make systematic errors in probabilistic reasoning (e.g., Tversky and Kahneman 1974; Kahneman et al. 1982). While this kind of critique is surely relevant, I want to set it aside here with a few quick comments. First, there are many additional experiments in which people seem to reason appropriately with probabilities. Second, experiments in which people are asked to reason explicitly about probabilities may be less theoretically revealing than those in which probabilistic inference is implicit in the way that uncertainty informs judgment and decision (e.g., Griffiths and Tenenbaum 2006; Trommershäuser et al. 2008). The logic is essentially the same as that which motivates linguists to pay closer attention to unreflective linguistic productions and judgments than to explicit metalinguistic judgments. Third, recent work has suggested a reconciliation, where at least some errors and biases in probabilistic reasoning may be explicable in terms of performance factors, interactions among cognitive systems, or strategies for efficient approximation (Griffiths et al., 2012; Vul et al., 2014). The objections that motivate imprecise credence models are primarily of a different kind. Kahneman and Tversky argued that ordinary people’s credence states, to the extent that they are not consistent with a precise credence model, fail to meet a normatively correct epistemological standard. Proponents of imprecise credences, in contrast, argue that it would in many cases be normatively inappropriate for an agent to have a credence state that is consistent with a precise credence model. A typical example is scenario (2): two teams compete in a game, and you know nothing at all about their relative skills. Joyce (2005, 2010) argues that, in such a scenario, you are making a mistake if you have any precise credence in team A winning. What possible grounds could you have for such “extremely definite beliefs ... and very specific inductive policies”, when “the evidence comes nowhere close to warranting such beliefs and policies” (Joyce 2010, p.285)? Depending on the teams’ relative skills, the right credence to have might be any value in the range r0, 1s! You don’t know enough to exclude any of these. This objection is closely related to the problem of insufficient expressiveness that we began with. When asked for a probability estimate in scenarios (1) and (2), I might produce “50%” in both cases—but confidently in (1), and with hesitation and confusion in (2). Similarly, I would immediately reject an uneven bet on either team in (1), but might have a harder time making up my mind in (2). Either way, the precise model seems to miss at least two important differences between these judgments: differences in their evidential basis, and in their phenomenology. Any two events to which I give credence 0.5 just have credence 0.5, end of story. As a result, precise credences are not fine-grained enough to provide a good model of my credence state. As Halpern (2003, p.24) puts it, “Probability is not good at representing ignorance”. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 749 D. Lassiter Bayes nets and the dynamics of probabilistic language 3. Confidence and ignorance: An imprecise model The proposed alternative is to represent an agent a’s information not by a single measure Pa , but by a set of measures Pa (e.g., Levi 1974; Jeffrey 1983). This is sometimes called a’s “Representor” (van Fraassen, 1990). Each P P Pa conforms to the probability axioms. This model has no expressive difficulty in the sporting examples. In the first scenario, where I am confident that the teams are evenly matched, my P has the property that, for every P P P, PpA winsq “ 0.5. In the second scenario, where I have no relevant information, my P has the property that, for every r P r0, 1s, there is a measure P P P such that PpA winsq “ r. In the first case I have an “extremely definite belief” (Joyce, 2010) that PpA winsq “ 0.5, and I am right to. In the second I have no definite belief about the value of PpA winsq, and I am right not to. Despite this apparent success, some important objections have been made to the use of imprecise probabilities. One is that it is difficult to frame a plausible decision theory for agents with imprecise credences. Elga (2010), in particular, canvasses a number of options and shows that each makes pathological predictions in certain cases; see also White 2010. A second kind of objection involve examples where imprecise models seem to predict, rather oddly, that learning a new fact should lead to a net loss of information (“probabilistic dilation”: Seidenfeld and Wasserman 1993), or where learning something that is intuitively irrelevant to an event A leads to a gain of information about A’s probability (White, 2010). (However, see Pedersen and Wheeler 2014 for important subtleties that may help to improve the plausibility of dilation.) These particular objections are two of many, and they are still a matter of active controversy in the epistemological literature. I don’t want to take a stand on whether they are decisive, but I do think they give us sufficient reason to look for a model that combines naturally with well-understood, well-behaved Bayesian models of learning and decision. First I will discuss a third objection which introduces some of the motivation for the hierarchical alternative. Perhaps the most troubling objection to imprecise probability models, from our current perspective, is the observation that they “preclude[] inductive learning in situations of extreme ignorance” (Joyce 2010, p.290; see also White 2010; Rinard 2013). For example, consider a biased coin example analogous to scenario 2 above. Suppose I am uncertain about the probability of getting heads when a certain coin is tossed. This probability could in principle be anywhere in r0, 1s. On any given toss, the probability of getting heads—Ppheadsq—is equal to the coin’s bias π, which is a fixed fact about the world, determined by the coin’s objective properties. My uncertainty about Ppheadsq reduces to uncertainty about the value of π. Suppose I had precise credences, with a prior distribution on π—say, a Beta distribution. If I wanted to be maximally noncommittal, I might use a Betap1, 1q distribution, which puts equal prior probability on every bias π P r0, 1s (see Fig. 1, left). Given this model, after conditioning on the observation of n heads and m tails my posterior probability is given by Betap1`n, 1`mq. (In general, conditioning a Betapa, bq prior on n heads/successes/wins and m tails/failures/losses yields a Betapa ` n, b ` mq posterior. See Griffiths et al. 2008; Hoff 2009 for introductions to the Beta-Binomal model.) So, for example, if I had a maximally noncommittal Betap1, 1q prior, after observing 150 heads in 300 tosses my beliefs about the bias π would be updated to a Betap151, 151q distribution. This prior-to-posterior mapping is pictured in Fig. 1. The quite Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 750 D. Lassiter Bayes nets and the dynamics of probabilistic language 10 12 14 8 6 4 2 0 2 4 6 8 Probability density 10 12 14 Posterior after 150 heads out of 300 0 Probability density Prior 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 π 0.4 0.6 0.8 1.0 π Figure 1: Prior-to-posterior mapping for an agent with precise credences and a Beta(1,1) prior, after observing 150 heads/successes out of 300 trials. The red line indicates the expected value of the parameter π, which does not change with this evidence even though our uncertainty about the estimate (i.e., the variance of π) decreases dramatically. reasonable prediction is that, after observing 150/300 heads, you can be quite confident that the coin’s bias π is close to 0.5—even if you were maximally noncommittal about π to begin with. Not so in the imprecise credence model with the standard update rule of pointwise conditioning. I have no idea about the probability of heads initially, so my initial representor P0 contains, for every r P r0, 1s, a credence function P such that Ppheadsq “ r. For example, P0 might contain, for every possible Beta prior, a measure that encodes a binomial model with that prior. P0 “ tP | Ppπq „ Betapa, bq, @a, b P r0, 8qu (Using only Beta priors is a significant restriction relative to Joyce’s philosophical desiderata, but using the full range of possible distributions would only make the problem worse.) Now, suppose I observe 150/300 heads and update P0 to P1 by pointwise conditionalization, discarding measures that assign probability 0 to the observations and so cannot generate the sequence. In this case, the latter condition requires us to discard any Beta prior with a 0 in either position, which could only generate “all heads” or “all tails” sequences. All other measures in P0 assign positive probability to the observed sequence of 150 heads and 150 tails, and survive in conditionalized form as Betapa ` 150, b ` 150q measures: P1 “ tP | Ppπq „ Betapa ` 150, b ` 150q, @a, b P p0, 8qu “ tP | Ppπq „ Betapa1 , b1 q, @a1 , b1 P p150, 8qu When we look at a few of these distributions, it is clear that something has gone wrong. Alongside reasonable-ish posteriors like Betap160, 200q [so Ppheadsq « .44] and Betap200, 160q [so Ppheadsq « .56], the posterior belief state contains a Betap150.1, 1014 q posterior [where Ppheadsq ă 10´10 ] and a Betap1014 , 150.1q posterior, where Ppheadsq is indistinguishable from 1. This is truly remarkable, since the probability that we would have seen 150 or more heads in 300 if Ppheadsq “ 10´10 is around 10´87 —but this failure of prediction is not taken into account in update by pointwise conditioning. In fact, for every r in the open interval p0, 1q, there is a measure in P1 such that Ppheadsq “ r. As far as the spread of probabilities for heads is concerned, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 751 D. Lassiter Bayes nets and the dynamics of probabilistic language all that we have gained from our observations is to contract the interval r0, 1s to p0, 1q, ensuring that both heads and tails are possible outcomes. We have learned nothing else about the coin’s bias. But in reality, a sequence of 150 heads and 150 tails can and should teach us a lot, even if we know nothing at all about the coin to begin: it is almost certainly fair, or very close to it. Inductive learning is possible from a starting point of ignorance. Several responses are possible here. First, we could search for an alternative to pointwise conditioning as an update rule. I won’t speculate about how this would go. A second option would be to rule out representors where Ppheadsq may fall anywhere in r0, 1s or p0, 1q. This would avoid the narrow problem addressed here, but it seems poorly motivated. If imprecise credences are motivated in the first place by considering belief under ignorance, how can we justify dealing with theoretical problems by pretending to know something that we don’t? (Never mind that many such restricted models will still exhibit no learning, or will learn at an unbelievably slow rate.) A third option, floated by Joyce (2010), is to conclude that it is in fact not possible to learn in a rational way from a starting point of total ignorance. However, Joyce continues, real people employ non-rational heuristics to help them get by psychologically, such as restricting attention to measures that give high enough probability to the observed evidence. This response seems desperate, and if taken seriously it may imply that all of our beliefs are irrationally held: after all, for each of my beliefs there was some point at which I was totally ignorant on the subject.1 A fourth option is to take this problem to demonstrate the impossibility of providing a precise formal model of belief states (Rinard, 2013). This could be correct, but I hope it isn’t. My preferred response is to reject imprecise credences as a model of individuals’ belief states. To plump for this option, let me point out the key technical difference between precise- and imprecise-credence models that is creating this problem: whether we place a probability distribution on top of the set of credence functions in P0 . Imprecise models decline to assign probabilities to the elements of P0 , leaving it as an unstructured set. If we did put a distribution on P0 , we would end up with a precise-credence model with a hierarchical structure, as I will describe in the next section. In this case, many kinds of (hyper-)priors on P0 would yield plausible results with ordinary conditioning. We can see why this small change makes a difference if we break down conditioning using Bayes’ rule. With a distribution on the measures in P0 , the posterior probability of each P P P0 would be proportional to the product of the prior and the likelihood, where the latter is the probability that we would have observed the data if P were the true distribution. Conditioning re-ranks credence functions to take into account such facts—e.g., that 150/300 heads is moderately likely under a Betap160, 200q distribution, and astronomically unlikely under a Betap150.1, 1014 q distribution. In contrast, imprecise models do not represent information about the relative plausibility of the measures in the representor, and pointwise conditioning does not take into account how well the measures in P0 fare in the goal of predicting the data (a likelihood term). This seems to be the basic reason why imprecise models fare so poorly when confronted with simple examples of inductive learning. In order to extract a plausible treatment of learning from imprecise credence models we need 1 We all began, in the womb, in a state of total ignorance, though we must presumably have been endowed with inductive biases. As psychologists and machine learning researchers are fond of reminding us, learning without initial biases (i.e., a hypothesis space and priors) is impossible: see, for example, Perfors 2012. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 752 D. Lassiter Bayes nets and the dynamics of probabilistic language to put a distribution on P0 so that we can apply ordinary conditioning. In other words, we need a prior on our priors, which is the basic idea of hierarchical models. 4. Confidence and ignorance: A hierarchical model This is, to be sure, a roundabout way of getting to a simple objection. We just don’t need imprecise credences to represent the difference between confidence and ignorance in the sporting scenarios we started with. Arguments against precise models based on a supposed failure to represent this distinction are simply misdirected. Confidence and ignorance can be given a satisfying treatment within hierarchically structured models, which are well-developed formally and strongly motivated psychologically and computationally. Recall Joyce’s (2010, p.285) objection to precise models quoted above: in a situation of ignorance, it is not justifiable for you to have “extremely definite beliefs ... and very specific inductive policies”, because “the evidence comes nowhere close to warranting such beliefs and policies”. Already in the coin-bias example, though, this objection is at least partly misplaced.2 If your prior on the bias parameter π is a Betap1, 1q distribution (Fig. 1, left), your belief is anything but definite. It is true that π has a precise expected value 0.5, and also that your marginal belief about Ppheadsq is 0.5. However, you are extremely uncertain about both of these beliefs: depending on what evidence you receive, you could come to a very definite conclusion that π and Ppheadsq are both 0, both 1, or anywhere in between. For example, after observing 0/300 heads, your posterior distribution on π would be Betap1, 301q, with Ppheadsq indistinguishable from 0. This would be an “extremely definite” opinion, and one that is justified by the evidence. Similarly, after seeing 150/300 heads, you have a fairly definite opinion that π and Ppheadsq are close to 0.5 (Fig. 1, right). Even though the summary estimate Ppheadsq “ 0.5 (red dashed line) does not change, the transition from the information state described by the left of Fig. 1 to the one on the right clearly represents a significant change in your beliefs about Ppheadsq. More generally, I suggest—building on observations made in another context by de Finetti 1977 and Pearl 1988 (p.357ff.)—that many of the intuitive arguments for imprecise probabilities discussed above can be accounted for in a better-motivated way once we take into account the hierarchical structure of belief. Our beliefs are interconnected, and probability estimates involving one variable usually depend on uncertain beliefs about others. Uncertainty about one variable—e.g., the bias π of a coin—may influence our uncertainty about a probability estimate of interest—e.g., the probability that the coin will come up heads on a given flip. Given the richness of our belief systems, there will usually be many layers of uncertainty. Even though such a model will always yield a precise numerical probability for any event of interest, this 2 The part that may well hit home nonetheless is the accusation that precise credence models give rise to “very specific inductive policies” which are not warranted by the evidence. This is essentially the same point as the correct observation that precise credence models require priors that are not chosen on the basis of experience. Some authors have argued that priors should be chosen so as to maximize entropy (Jaynes, 2003; Williamson, 2009), though there are well-known objections to this move (van Fraassen, 1989). Does this mean that no choice of priors can be uniquely justified? Perhaps, but it is not clear why this should be so troubling. Since learning without priors is impossible, Bayesian cognitive models imply that evolution has supplied us with priors that are good enough to enable successful learning, starting in the womb. These may well vary between individuals, and there is no reason to expect that nature’s choice of priors should be uniquely justified or rational. All we can expect is that they should get the job done with respect to the ultimate goals of survival and reproduction. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 753 D. Lassiter Bayes nets and the dynamics of probabilistic language numerical value does not have any special place in the model: it is just what you get when you marginalize over the uncertainty of other relevant variables. In a hierarchical model, probability estimates can vary enormously in how “definite” they are—more precisely, in their variance. Hierarchical models are used in many modern applications in psychology, philosophy, artificial intelligence, and statistics. In these models, probabilities are derived from graphs representing causal relations among variables, together with the conditional distribution on each variable given its parents. Uncertainty about one variable may influence the kind and degree of uncertainty in the value of another. For simplicity I will focus on Bayesian networks (“Bayes nets”), a simple propositional language for describing hierarchical models. (For discussion of richer languages for describing hierarchical Bayesian models that can treat uncertainty about individuals, properties, relations, etc., see for example Goodman et al. 2008; Goodman and Tenenbaum electronic; Tenenbaum et al. 2011 and, for a linguistically-oriented presentation, Goodman and Lassiter 2015.) I will impose a causal interpretation on the Bayes nets described in this paper. While this is not obligatory, it helps to gain intuitions about their meaning, and it is crucial to their psychological motivation (e.g., Glymour 2001; Sloman 2005). The sporting example that we began with allows us to illustrate Bayes nets and their ability to represent confidence and ignorance alike. Formally, a Bayes net B is an enrichment of familiar intensional semantics models, consisting of a set of possible worlds W together with: 1. A set of “variables” V P V, where each V is a partition of W . (A cell is a “value” of V .) 2. A set of “arrows”, i.e., an acyclic binary relation on V. (The inclusion of an arrow from Vi to V j indicates that Vi is immediately causally relevant to V j .) 3. A set of conditional probability tables which assign a distribution PpV | ParentspV qq to each V P V, where ParentspV q “ tV 1 | xV 1 ,V y P Vu. A probability measure P is compatible with Bayes net B if and only if P satisfies the Markov condition: each V P V is probabilistically independent of its nondescendents, given its parents. To situate the hierarchical modeling concept within our sporting examples, consider: In case (2), when asked to reason about the competition between unknown teams A and B, did you really know nothing at all about these teams? I doubt it. Most likely, you brought to bear on the problem a rich network of relevant background knowledge. You knew that the outcomes of matches are determined largely by the performance of the teams; that teams are composed of players who have different roles; that they have latent characteristics like skill and consistency; that not all teams are equally skilled or consistent; and so forth. In addition, your experience may have provided you with relevant population statistics which can help you to make an informed guess about the distribution of these characteristics among teams, even without any specific knowledge of the team. All of this background knowledge enabled you to make a reasonable guess about how a randomly chosen team would perform, and what factors you should attend to if you want to use observations to improve your forecast of a team’s performance. As a start in modeling the richer background knowledge that we implicitly bring to bear on Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 754 D. Lassiter Bayes nets and the dynamics of probabilistic language such problems, consider the simplified representation in Fig. 2.3 This model represents two key features of teams that are relevant to their performance: their skill and their consistency. Performance of team i is modeled as a Gaussian (normal) distribution with parameters µi (skill) and σi (consistency). As a result, the team’s performance in any given competition is a noisy reflection of the team’s true skill. Skill and consistency are, in turn, objects of uncertainty that we are trying to estimate when observing the outcomes of competitions. This means that we must place a prior on them as well. In a realistic model, these variables might be connected to many further factors—e.g., the team’s composition, quality of coaching, motivation, etc. To simplify the example, I will summarize all of these sources of uncertainty with simple priors on the parameters: µA and µB are both distributed as N p0, 1q, and σA “ σB “ .1. µA µB σA perf A σB perf B winner @i : µi „ N p0, 1q @i : σi “ .1 @i : perf i „ N pµi , σi q winner “ A iff perf A ą perf B Figure 2: Hierarchical model of a match between teams A and B. In this model PpA winsq is equal to Ppperf A ą perf B q—the probability that A’s noisy performance exceeds B’s. Note that this model does not generate a single, determinate prediction about A’s performance in any given match. Instead it generates for each team a distribution over an infinite set of performance values p´8, 8q. A few of these distributions are shown in the top left of Fig. 3. As a result, the model encodes a distribution over an infinite set of values for PpA winsq, which could be anywhere in p0, 1q depending on subsequent observations. While the model does yield a precise best guess about the performance difference—and so about PpA winsq—this guess has no special status in the model: it is merely the result of marginalizing over our uncertainty about the parent variables (skill and consistency). Indeed, two models that generate the same probability estimate for this event—say, PpA winsq “ .5— may vary considerably in how confident (“definite”, “determinate”) the probability estimate is.4 A key factor is, of course, how much evidence the estimate is based on. 3 The model is directly inspired by the Microsoft Trueskill system that is used to rank Xbox Live players in order to ensure engaging match-ups in online games: see Bishop 2013. It is also closely related to the tug-of-war model explored by Gerstenberg and Goodman (2012); Goodman and Lassiter (2015). 4 As Pearl (1988, p.361-2) writes: “The point is to notice that by specifying a causal model for predicting the outcome ... we automatically specified the variance of that prediction. In other words, when humans encode probabilistic knowledge as a causal model of interacting variables, they automatically specify not only the marginal and joint distributions of the variables in the system, but also a particular procedure by which each marginal is to be computed, which in turn determines how these marginals may vary in the future. It is this implicit dynamic that makes probabilistic statements random events, admitting distributions, intervals, and other confidence measures.” As a consequence, Joyce (2010, p. 283) is simply wrong in his assertion that “Proponents of precise models ... all agree that a rational believer must take a definite stand by having a sharp degree of belief” in situations of ignorance. While Joyce is right that taking a “definite stand” in case of ignorance is unreasonable, his conclusion Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 755 D. Lassiter Bayes nets and the dynamics of probabilistic language Marginal on performance 0.4 0.3 Density 0.2 2 0 0.0 0.1 1 Density 3 0.5 4 Candidate performance distributions −2 −1 0 1 2 3 −3 −1 0 1 2 Performance Performance difference, case (i) Performance difference, case (ii) 2.5 3 0.0 1.5 0.0 0.5 1.0 Density 2.0 0.3 0.2 0.1 Density −2 Performance 0.4 −3 −3 −2 −1 0 1 Performance difference 2 3 −3 −2 −1 0 1 2 3 Performance difference Figure 3: Some distributions implicit in the Fig. 2 model. Top left: some of the 8 performance distributions that could turn out to be the true distribution for either team. Top right: Marginal on perfA{B with no specific evidence. Bottom row: Distribution of perfA ´ perfB with no observations (left) and after observing that each team won 15 of 30 matches (right). Consider our two leading examples again. In case (1), we “know nothing”—i.e., only general domain knowledge is available. As a result, the variance of the estimated performance difference is high, and confidence in the estimate PpA winsq “ .5 is low (Fig. 3, bottom left). In case (2), there is ample evidence to indicate equal skill—many previous matches, with each team winning an equal number. In this case, the variance of the estimated performance difference is low, and confidence in the estimate PpA winsq “ .5 is high. The bottom right panel of Fig. 3 shows the model’s predictions about Ppperf A ą perf B q once we have observed each team winning 15 of 30 matches. Here we can infer that the teams have roughly equal skill, and that we should forecast roughly equal performance in the next game: PpA winsq “ .5. Bayes nets offer a precise credence model that represents the distinction between confidence and ignorance in a straightforward way. The need to represent this distinction does not, therefore, give us a reason to abandon precise credence models in favor of a more complex representation that also introduces new problems involving learning and decision. The apparent problem with precise models—that radically different credal states could generate the same probability estimate PpA winsq “ .5—was not due to any expressive limitation. Instead, the problem is generated by our habit as theorists of treating such numerical estimates as representations of belief states, forgetting that they give only a narrow window into the rich structure of a probability distribution and its potential to change in response to experience. 5. Dynamics of probabilistic language: An imprecise model The third puzzle that we started with was how to understand the informational effect of explicitly probabilistic language. Example (3) is repeated here: that precise credence models are inappropriate is a non sequitur: precise probability estimates can be extracted from hierarchical models, but these models do not generally imply a “definite stand” on these estimates. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 756 D. Lassiter (4) Bayes nets and the dynamics of probabilistic language Two teams A and B who are about to compete, and you know nothing at all about them. However, a knowledgeable friend assures you that “Team A is likely to win.” What probability should you assign to “A will win”? This puzzle is a special case of the more general question of how we should update our beliefs on the basis of new information. However, in (3) the new information is provided in linguistic form, and so we have the dual problem of supplying an interpretation and an update procedure that will generate the right mapping from information states to modified information states. In familiar models of linguistic dynamics, information states I are usually modeled as sets of worlds—or sometimes as sets of structured objects that segment out different kinds of information and handle them separately. Sentences S pick out, relative to a context c, properties of the kind of objects contained in I. So, if I is a set of worlds, JSKc is a set of worlds as well. The algorithm for incorporating the information conveyed by S in c into state I is simple: we transition from state I to state I X JSKc , eliminating from I any worlds that are not in JSKc . On this approach to conversational dynamics, information states and sentence-meanings-in-context must be objects of the same type. This means that, if our language contains sentences whose meaning is not well treated as a set of worlds, an eliminative theory of update requires us to enrich the representation of information states accordingly.5 Now, recent work has given considerable semantic motivation to the claim that the interpretation of A is likely to win in (4) makes direct reference to a probability—roughly, “PpA winsq ą .5” (Swanson, 2006; Yalcin, 2007, 2010; Lassiter, 2010, 2011, 2017a; Moss, 2015). This leaves us with a theoretical dilemma. If we want to hold to the eliminative conception of update, we can either try to give this probability statement a world-relative interpretation, or we can assign it some other interpretation and enrich our model of information states to compensate. Yalcin 2012 proposes a simple eliminative model of update for both factual and probabilistic statements, building on Yalcin 2007. On this account epistemic statements—including probabilistic statements—do not have a world-relative interpretation. Instead, they depend on the value of a sui generis information state parameter which varies independently of the choice of evaluation world, and which determines a probability measure P. Briefly, the idea is that a conversational common ground C is a set of pairs i “ xsi , Pi y, where si is a set of worlds and Pi is a probability measure with Pi psi q “ 1. For factual statements such as It’s raining, update eliminates from C those i for which it is not raining everywhere in si , without constraining Pi . I “ñ I X txs, Py | @w P S : It’s raining at wu. update For probabilistic statements such as It’s likely to rain, update eliminates points i P C that do not assign sufficiently high probability to rain, but places no direct constraints on si . I “ñ I X txs, Py | Pprainq ą .5u. update 5 An alternative is to modify the definition of update, giving pointwise definitions for individual expressions, as Veltman (1996) does for might and several other epistemic operators. However, this approach is not promising for likely, and I will not consider it further. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 757 D. Lassiter Bayes nets and the dynamics of probabilistic language This formal model of conversational dynamics bears a striking resemblance to the sets-ofmeasures model of credence that we considered above. However, there are two very different ways to interpret it. Yalcin’s proposal is to use it to model the dynamics of conversational common ground, in the mold of Stalnaker 1978. The idea is that, as a conversation proceeds, the acceptance of utterances leads to an accumulation of constraints on interlocutors’ information. Once “It’s likely to rain” is accepted, the common ground contains the information that Pprainq ą .5, meaning that interlocutors are publicly committed to this constraint. This interpretation is conceptually close to the “group belief” interpretation of imprecise probability models discussed above. As mentioned above, I have no quarrel with the group belief interpretation of imprecise credences, where measures in the set represent assignments of probability that are consistent with existing group commitments; the objections canvassed were specifically leveled at an application to individual psychology. For similar reasons, Yalcin’s interpretation seems unproblematic as a way of treating the way that conversational commitments constrain the way that common ground constrains (but does not determine) probability assignments. Solving the puzzle in (3)/(4) requires a more ambitious theory, though. It is not enough to require that someone who accepts A is likely to win must assign PpA winsq ą .5. This constraint does not tell us enough about what that person should come to believe about PpA winsq, other than the bare fact that PpA winsq cannot fail to exceed .5. What we are interested in is a mapping from an individual’s prior state of information to a posterior state, which would determine what she should believe if she begins in state I and then gains some explicit information about the likelihood of events. While it was not proposed for this purpose, Yalcin’s formal apparatus could equally be put to use in this way (cf. also Rothschild 2012). On this interpretation, an individual’s state of information I is a set of pairs i “ xsi , Pi y, and we have a simple algorithm for updating with the information conveyed by A is likely to win: as in Yalcin’s proposal, map I to the subset of I containing all xsi , Pi y for which Pi pA winsq č .5. While this proposal is prima facie plausible, it encounters some serious difficulties. First, as a representation of individual psychological states its plausibility is threatened by general objections to the use of imprecise credence models for this purpose: problems with framing a decision theory, with updating beliefs from a starting point of ignorance, and so forth. Second, even if we were to accept imprecise credence models along the lines of Joyce (2005, 2010), the update procedure just described would not be sufficiently general. The problem is that imprecise probabilities are intended to represent situations where probabilities are not known— but probabilistic statements can be informative about known and unknown probabilities alike. Consider a scenario in which a ball is drawn from one of two urns. Urn A contains 10 red and 5 blue balls, so Ppred | Aq “ 2{3. Urn B contains 5 red and 10 blue balls, so Ppred | Bq “ 1{3. A fair coin was flipped to determine which urn the ball would come from—A if heads, B if tails. So, PpAq “ PpBq “ 1{2. If someone who knows what urn was selected tells us The ball is probably red, how should we respond? Clearly, we can conclude that the coin toss came up heads and A was selected. So the posterior probability of red, after update with The ball is probably red, should be equal to Ppred | Aq “ 2{3. However, it is not possible to model this kind of update by filtering in a standard imprecise Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 758 D. Lassiter Bayes nets and the dynamics of probabilistic language probability model: paradoxically, we know too much. That is, we could attempt to represent this situation in terms of an imprecise model where some measures have Ppredq “ 2{3 and some have Ppredq “ 1{3. Then, upon learning that the ball is probably red, we could model the update effect of this information by eliminating the measures where Ppredq “ 1{3. But as Joyce (2005, 2010) emphasizes, this model is inappropriate: it leaves out known probabilities, i.e., the information that the choice of urn was determined by the flip of a fair coin. Since PpAq “ PpBq “ 1{2, all measures P in our information state have Ppredq “ Ppred | Aq ˆ PpAq ` Ppred | Bq ˆ PpBq “ 2{3 ˆ 1{2 ` 1{3 ˆ 1{2 “ .5 But if Ppredq “ .5 according to all measures in our information state, the model of probabilistic update under consideration—“throw out all measures on which Ppredq č .5”—will yield the empty information state. If only we didn’t know that the choice of urn was determined by a fair coin toss, we could update with the information that the ball is probably red! The filtering approach to update with probabilistic language does not, it appears, play nicely with the kinds of imprecise credence models that have been given independent motivation in the philosophical and statistical literature. 6. Dynamics of probabilistic language: A hierarchical model Our problem is to explain why, in the urn model just given, update with The ball is probably red leads to a coherent result—and to one which somehow yields the judgment that Ppredq is precisely 2{3. As in the general discussion of precise vs. imprecise credence models, I suggest that the solution to our problem is to pay closer attention to the hierarchical structure of information states. Consider a causal Bayes net representing this process (Fig. 4). The key thing to observe about this model is that the intuitive update effect of The ball is probably red is exactly the same as the intuitive update of The coin came up heads. Our goal is to find a way to use the structure of the Bayes net to guarantee that this will be the result, against this informational background. Once this is done, we may be able to define a general update procedure that applies to probabilistic and non-probabilistic language alike. Ppheadsq “ .5 Pptailsq “ .5 coin flip PpA | headsq “ 1 PpA | tailsq “ 0 urn Ppred | Aq “ 2{3 Ppred | Bq “ 1{3 color Figure 4: Causal Bayes net modeling the urn scenario. A Bayes net defines a way of partitioning the space of possible worlds into increasingly finegrained cells as a causal process unfolds. The first step in the process is the flip of a coin, which has two possible outcomes with specified probabilities. If we happen to be at a world w in which the coin came up heads, then an urn is selected. In this model, the urn is A with probability 1 in this case. So, w–and any other heads-world—is also an A-world. The red/blue mix of the urn selected in w is 10/5, and so the probability that the ball selected will be red is 2/3. The Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 759 D. Lassiter Bayes nets and the dynamics of probabilistic language next step is the choice of a ball: at any w, either the ball chosen is actually red, or it is actually blue. Nevertheless, it is a fact about w that the probability of a red ball being selected is 2/3, even if the random selection process actually unfolds so that a blue ball is chosen. The Bayes net thus suggests a world-relative probability concept, where probabilities are dissociated from the actual occurrence of events. As long as our observations do not include the ball’s color or any downstream effects of this variable, it is true at any such w that the ball is probably red, because this is a world at which the coin came up heads and the urn selected was A. My suggestion, then, is to interpret probability statements as involving a kind of world-bound probability, but relativized to a Bayes net B. (At least probability statements with an “objective” flavor—see caveats below.) Suppose that the statement is The ball is probably red. Rather than looking for a global, world-independent parameter P and checking the value of Ppredq (as in Yalcin 2007, 2012), we look to Pw predq, the probability that B assigns to red at world w. With a world-bound probability concept available, we could then model update with The ball is probably red as simple conditionalization, a procedure that works equally for factual statements. Here, update means conditioning on the set of worlds w1 such that Pw1 predq ą .5. (5) a. b. JThe ball is probably redKB,w “ 1 iff Pw predq ą .5. P “ñ Pp¨ | tw1 | Pw1 predq ą .5uq. update with (5a) If this is to work, the key question is how B and w conspire to determine Pw . Recall from above that the intuitive update resulting from The ball is probably red is the same as the update from Urn A was selected: both tell us, in effect, that Ppredq “ 2{3. Relative to the Bayes net in Fig. 4, then, the set of worlds in which The ball is probably red is true should be the same as the set of worlds in which Urn A is selected is true. As a first approximation, we could define Pw predq, relative to B, to be equal to the conditional probability of red in B given the actual value(s) at w of the immediate parent(s) of the variable of which red is a value. Since the only parent of color is urn, this means that Pw predq “ Ppred | urnw q, where urnw is the actual value of urn at w. If the urn is A in w, then Pw predq “ 2{3. If the urn is B at w, then Pw predq “ 1{3. If we define Pw in terms of the structure of a Bayes net in this way, the contextual equivalence of The ball is probably red and Urn A was selected follows immediately. Relative to the Bayes net in Fig. 4, the set of worlds w where Pw predq ą .5 is the same as the set of worlds where Ppred | urnq ą .5, relative to the actual value of urn at w. Relative to this model, the intension of The ball is probably red—tw | Pw pred ą .5u—is the same as the intension of The Urn selected is A. So, of course, conditioning on either has the same update effect. We can now return to the puzzle around how to update with (3)/(4), Team A is likely to win. If we know nothing about these teams beyond general domain knowledge, our information might be represented by the Bayes net in Fig. 2 above. On the present proposal the intension of Team A is likely to win, relative to this Bayes net, is tw | Pw pwinner “ Aq ą .5u. The parents of winner in this model are perf A and perf B . So, by the definition of Pw offered above, this is the set of worlds w where the probability of A winning is greater than .5, given the actual values of perf A and perf B at w. This result is problematic, since it implies that Pw pwinnerq should be 1 or 0 at every world. This is because the value of winner is a deterministic function of its Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 760 D. Lassiter Bayes nets and the dynamics of probabilistic language parents—winner “ A if perf A ą perf B , otherwise “ B. My suggestion is that we should look not necessarily to a variable’s immediate parents, but to its closest non-deterministic parents. Final proposal: Pw pV “ vq is equal to the conditional probability of A given the actual values at w of V ’s closest non-deterministic ancestors in B. On this proposal, the truth-value of Team A is likely to win at any w, relative to this model, is determined by the values of µA , σA , µB , and σB at w. These variables represent the facts at w about the teams’ skill and consistency, respectively. Given the assumptions that we made in setting up the Fig. 2 model, Team A is likely to win ends up having a sensible update effect: it is equivalent to µA ą µB , i.e., the proposition that Team A is more skilled than Team B. Fig. 5 shows graphically the effect of updating an uninformed prior distribution with this information. Posterior Prior of B A Ski ll Skil Skil l of l of A ity ity Dens Dens Ski ll of B Figure 5: Left: 2-dimensional Gaussian representing an uninformed prior on the teams’ skills. Right: posterior after learning that Team A is likely to win. This proposal is tentative and subject to important caveats: I will mention only two for reasons of space. First, the final proposal might need to be circumscribed so that it applies only when neither V nor any of its descendants has been observed. After all, if we have observed that A won, then Ppwinner “ Aq should be 1. However, note that this observation could not have been made in the scenario under consideration, since the key example was a prediction about a future event which could not in principle have been observed. In general, a complete theory along these lines will need to be more explicit about the role of time—about the way that causal processes unfold in time, about the way that probability estimates change over time in response to new observations, and any interactions between the two. While I do not feel that I have a complete grasp of the complex issues at stake here, it does seem worth noting that it is often unproblematic to assert an explicitly tensed statement of the form φ was likely and φ —e.g., Team A was likely to win, but they didn’t win. This is striking, since present-tense statements of the form φ is likely, but φ are generally infelicitous (Yalcin, 2007). The difference in the past-tense case seems to be that there are two different times involved: an earlier time at which the “worldly” probability of A winning was greater than .5, e.g., because A is a more skilled team; and a later time at which the speaker learned that A didn’t win, despite their advantageous position. So, we should not redefine Pw such that Pw pV “ vq is always 0 or 1 whenever the value of variable V has been observed. Instead, we need to explicitly incorporate an element of time: Ppw,tq pV “ vq is 0 or 1 if V has been observed at or before t. However, I will not attempt it in this Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 761 D. Lassiter Bayes nets and the dynamics of probabilistic language space to working out the temporal aspect in detail or its connections to Yalcin’s observations about “epistemic contradictions”. A second caveat is that my proposal may apply only to certain kinds of probability statements. Theoretical and corpus studies have found evidence that what we have called “probabilistic” language is ambiguous between multiple kinds of probability that are ontologically and psychologically distinct (Kahneman and Tversky, 1982). The probability statements that I have analyzed in the second part of this paper seem to relate to a kind of “objective”, “worldly”, or “stochastic” probability, relating to the unfolding of an indeterministic causal process. In contrast, most theorists in the semantic literature on probability expressions have explicitly or implicitly assumed that the subject matter of probabilistic language is subjective uncertainty. These positions are not in competition: Ülkümen et al. (2016), in particular, have shown that English has the semantic resources to talk about both kinds of uncertainty. They show that the two kinds of uncertainty are even distinguished lexically to some extent, with items such as likely and chance favoring stochastic interpretations while confident, certain, etc. favor subjective interpretations. Lassiter (2017b) gives further corpus evidence for this conclusion, and argues for several more semantically distinct interpretations of probability expressions. The proposal floated here is most clearly suited to language describing stochastic causal processes, including (but not limited to) many future-oriented uses of probability expressions. I am exploring ways to extend it to clearly subjective uses like that in the corpus example in (6) (Lassiter, 2017b), where there is a clear fact of the matter and information is simply lacking. (6) [T]he residential-scale reservoirs ... were likely used around 900 B.C. It’s likely that the systems were lined with a thick, clay “plaster” ... I am unsure whether this effort will be successful. I believe that it would be also be consistent with the proposal given here to model the update effect of such examples from a different perspective, such as Madsen’s (2015) framework of “multi-agent statistics”. 7. Conclusion Imprecise credence models, which represent uncertainty using sets of probability measures, have a good deal of philosophical and linguistic motivation. However, their scope is more limited than has generally been recognized. Where the formal representation of uncertainty is concerned, imprecise credences may well be useful as a treatment of group belief. However, they encounter severe problems as a representation of individual-level uncertainty, particularly involving learning from a starting point of ignorance. I argued that these problems can be resolved by adopting an explicitly hierarchical perspective on belief states, and that hierarchical models already account for the confidence/ignorance distinction that has been used to motivate imprecise models as a representation of individual-level uncertainty. While I formalized this perspective using causal Bayes nets, there are also other, richer hierarchical models based on probabilistic programming techniques, which will probably be needed in a fuller treatment. A second puzzle involving the update effects of expressions like φ is likely and probably φ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 762 D. Lassiter Bayes nets and the dynamics of probabilistic language seemed initially to point to a formally parallel model, where information states are sets of measures (or something strictly richer). This model may well be sufficient as a common-ground model. However, it fails as a solution to the psychological problem of how agents can/should incorporate such statements into their information states, because it predicts that they should have trivial update effects when probabilities are known. I argued that we may be able to resolve this issue as well by attending to the hierarchical structure of belief states, interpreting at least some probabilistic statements as factual claims about stochastic causal processes rather than expressions of subjective uncertainty. While there is much more to be done to shore up this suggestion, I hope at least to have demonstrated that direct engagement between semantics and pragmatics, formal epistemology, computational cognitive science, and Bayesian statistics has significant potential to generate new concepts and useful theoretical models. References Bishop, C. M. (2013). Model-based machine learning. 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Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 765 766 Quantified indicative conditionals and the relative reading of most1 Sven LAUER — University of Konstanz Prerna NADATHUR — Stanford University Abstract. Kratzer (in press) notes a curious ‘reverse’ reading for certain quantified conditionals with most. The existence of this reading is problematic for accounts that aim at compositionally deriving the perceived interpretation of quantified conditionals, especially for those that take if -clauses to semantically restrict the domain of nominal quantifiers. We show how the reverse reading can be derived on such a restrictor account, as an instance of the relative reading of most. The derivation closely parallels a recent account of the ‘reverse proportional’ reading of many (Romero, 2015). Our account is entirely compositional and draws on independently motivated assumptions about the interpretation of most. Keywords: conditionals, quantifiers, most, superlatives 1. Introduction: an old ‘embarrassment’ Conditionals that appear to be embedded under other operators present a difficult testing ground for semantic theories of the natural language conditional. In this paper, we are concerned with quantified indicative conditionals (QICs), which combine an if -clause and a nominal quantifier: (1) a. b. Every student passed if she studied hard. No student failed if she studied hard. Although (1a) and (1b) are intuitively paraphrases (assuming that failing is not passing), analyses of QICs which simply embed an if -conditional under the quantifier have struggled to produce equivalent interpretations for these statements: “The embarrassment had been known for a long time, but nobody dared talk about it. Then Higginbotham (1986) dragged it into the open” (Kratzer, in press), by demonstrating the insufficiency of the classical material conditional analysis of if for interpreting the sentences in (1). While ⊃ arguably produces acceptable truth conditions for (1a), the interpretation that results for (1b) is not equivalent — and, moreover, is patently inappropriate: (1b) does not entail that all students studied hard. (2) a. b. (1a) ≡ ∀[STUDENT][STUDY- HARD ⊃ PASS] All students are such that studying hard ensured passing. (1b) ≡ ¬∃[STUDENT][STUDY- HARD ⊃ ¬PASS] ≡ ∀[STUDENT][STUDY- HARD & PASS] All students are such that they both studied hard and passed. This unfortunate result arises from the (now unpopular) identification of the material conditional ⊃ with if. However, simply embedding the influential ‘restrictor’ conditional of Kratzer 1 We would like to thank Doris Penka and audiences at the 2016 Stanford SemFest, CUSP 9 at UC Santa Cruz, and Sinn und Bedeutung, for comments and discussion. This research was kindly supported by the EU FP7 Marie Curie Zukunftskolleg Incoming Fellowship Programme, University of Konstanz (grant no. 291784) for Sven Lauer. This support is gratefully acknowledged. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 767 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most (1986) does not fare much better. Kratzer treats if -clauses as restricting the domain of a (covert) universal modal quantifier; (3) shows the results of embedding this under nominal quantifiers. (3) a. b. (1a) ≡ ∀[STUDENT][[STUDY- HARD][PASS(x)]] All students are such that studying hard must have resulted in success. (1b) ≡ ¬∃[STUDENT][[STUDY- HARD][¬PASS]] ≡ ∀[STUDENT][♦[STUDY- HARD][PASS]] All students are such that it is possible that studying hard resulted in success. 1.1. The ‘folkloric’ solution: if -clauses restrict nominal quantifiers One route around this problem questions whether QICs truly comprise embedded structures à la (2)-(3). A suggestion in the spirit of the Lewis-Kratzer conditional comes from von Fintel (1998). He suggests interpreting the if -clauses as restricting the nominal quantifiers directly. This yields the truth conditions in (4), which are both intuitively sensible and equivalent. (4) a. b. (1a) ≡ ∀[STUDENT & STUDY- HARD][PASS] All students who studied hard passed (1b) ≡ ¬∃[STUDENT & STUDY- HARD][¬PASS] No student who studied hard did not pass. This ‘folkloric’ solution (named by von Fintel and Iatridou, 2002) is challenged by von Fintel and Iatridou (2002), Higginbotham (2003), and Huitink (2009). The main thrust of their objections involves comparisons between QICs and corresponding sentences where the if -clause is replaced by a relative clause attached directly to the overt restriction of the quantifier: (5) a. b. Every coin is silver if it is in my pocket. Every coin that is in my pocket is silver. On the account in (4), these two sentences have identical truth conditions: treating the if -clause as restricting the quantifier domain should reduce it, functionally, to a restrictive relative clause. However, the sentences are not intuitively equivalent: (5a) suggests a non-accidental or rulebased connection between the location of a coin and its composition, which (5b) does not. Leslie (2009) defends the restrictor analysis against this objection. She points out that the problematic QICs seem rule-oriented precisely because they appear to involve a generalization over multiple instances. That is, in the same way that (6a), on the standard restrictor account, has truth-conditions which require the specified coin to come up heads across all situations in which it is flipped, (6b) requires the same to hold of all the coins in the relevant domain. (6) a. b. This coin comes up heads if it is flipped. In all accessible worlds in which this coin is flipped, it comes up heads. Every coin comes up heads if it is flipped. In all accessible worlds, all of these coins that are flipped come up heads. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 768 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most Leslie points out that a fair coin intuitively falsifies (6b), even if it happens to come up heads in a particular trial or set of trials. Thus, the truth conditions of (6) require quantification over situations, and suggest modalizing the restrictor account. On Leslie’s proposal, if -clauses restrict nominal quantifiers, but, in cases like (6), this occurs below a wide-scope modal. This gives the truth conditions in (7) for our original QIC examples: (7) a. b. (1a) ≡ ∀[STUDENT & STUDY- HARD][PASS] All accessible worlds are such that all students who studied hard passed. (1b) ≡ ¬∃[STUDENT & STUDY- HARD][¬PASS] All accessible worlds are such that no students who studied hard did not pass. As with von Fintel’s (1998) solution, Leslie’s modalized restrictor conditional provides sensible and equivalent truth conditions for these QICs. Her proposal arguably solves the problem of the contrast between QICs and restrictive relative clauses in cases like (5): the first case necessarily involves a modal quantifier, whereas the second does not. (8) a. b. (5a) ≡ ∀[COIN & IN - MY- POCKET][SILVER] In all accessible worlds, all coins in my pocket are silver. (5b) ≡ ∀[COIN & IN - MY- POCKET][SILVER] In the actual world, all coins in my pocket are silver. The ‘non-accidental’ connection in (5a) on this account emerges from quantification over accessible worlds. On the other hand, (5b) simply describes an actual-world situation. 1.2. The road ahead Against this backdrop, Kratzer (in press) observes a new and surprising reading for certain QICs. In her examples, the conditional consequent appears to enter into the restriction of a nominal quantifier, and the conditional antecedent provides its scope (see Section 2). This seems to provide direct evidence against any kind of restrictor analysis. This paper defends the restrictor conditional against this challenge. We argue that the key to ‘reversed’ readings of QICs comes from reverse proportional readings of quantified statements with many and few (Westerståhl, 1985). Building on Romero (2015), we propose that ‘reverse’ readings of most-QICs are instances of the relative reading of most, analyzed as the composition (Hackl, 2009; Romero, 2016) of parametrized MANY and the superlative, focus-sensitive morpheme -est (Heim, 1999). When composed with a restrictor analysis of conditionals, this predicts reverse readings for most-QICs in precisely the circumstances that Kratzer describes. We argue that our account improves on Kratzer’s (in press) in terms of predictive power: reverse readings are predicted only for determiners (e.g., most, many, few) which contain the right focus-sensitive components, but not for other determiners (every, all, or no). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 769 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most 2. The reverse reading of most-QICs Kratzer’s empirical challenge centers on a previously unobserved reading for certain QICs: (9) Most kids asked for calculators if they had to do long divisions. [Kratzer: pp.20-21] a. Vanilla reading: (standard) The majority of kids who had to do long divisions asked for calculators. |long-division kids ∩ calculator kids| > |long-division kids − calculator kids| b. Reverse reading: (novel) The majority of kids who asked for calculators had to do long divisions. |calculator kids ∩ long-division kids| > |calculator kids − long-division kids| Given the standard interpretation (10) for most, the vanilla reading of (9) is easily generated. The contents of the if -clause appear to enter into the restriction (A = KID ∩ DO - LONG - DIV) of most, while the matrix clause provides its nuclear scope (B = USE - CALCULATOR). This produces an interpretation equivalent to (9a). (10) Most[A][B] := |A ∩ B| > |A − B| The reverse reading, on the other hand, is not so neat. Given (10), the matrix clause appears to enter the quantifier’s restriction, while the if -clause provides its nuclear scope. This is a startling result, and it presents a serious problem for any restrictor analysis of if -clauses. We concur with Kratzer that this new reading exists, and that it only emerges under very particular contextual conditions. (11) gives an appropriate context for reversal. Crucially, the matrix clause is backgrounded, while the if -clause provides new, or focused information. (11) You: Did you see kids using calculators when you volunteered in your son’s school yesterday? What did they use the calculators for? Me: Most kids asked for calculators if they had to do long divisions. But I am pleased to report that most kids in my son’s school do long divisions by hand. The felicity of the sentence which follows (9) in the dialogue in (11) clearly demonstrates the reality of the reverse reading in this scenario. On the vanilla reading (9a), the final sentence directly contradicts the content of the QIC. On the other hand, if (9) is taken to mean (9b), it is perfectly coherent to continue with the information that the number of children doing long division by hand is greater than the number doing long division by other means. Reverse readings do not seem to exist without the topic-focus structure illustrated in (11). In support of this point, consider (12), which backgrounds long division instead of calculator use. (12) You: Did you see kids doing long division when you volunteered in your son’s school yesterday? Were they able to do it by hand? Me: Most kids asked for calculators if they had to do long divisions. #But I am pleased to report that most kids in my son’s school do long divisions by hand. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 770 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most Ultimately, the existence of reverse QIC readings in any context presents a serious challenge to restrictor analyses, whether folkloric, modalized, or otherwise. If the contents of an if -clause are entered into the restriction of a quantifier, it is not at all clear how they are available to provide its nuclear scope as well. Given the tools to hand, including the quantifier meaning (10) for most, it seems that we must give up on the concept of if as an operator on quantifier domains if we wish to be able to account for the empirical QIC terrain. 3. Kratzer’s analysis 3.1. A bomb defused Based on the arguments mentioned in the introduction, Kratzer’s approach to the QIC problem begins from the premise that if -clauses do not restrict nominal quantifiers. Instead, she postulates a embedded structure in which a binary conditional operator (.) and its sentential arguments are fully contained in the nuclear scope of the quantifier, as shown in (13). (13) a. b. (1a) ≡ ∀[STUDENT][STUDY- HARD . PASS] (1b) ≡ ¬∃[STUDENT][STUDY- HARD . ¬PASS] Given this structure, Kratzer argues that . must support the following set of logical inferences: (14) a. b. c. d. Modus ponens. φ . ψ and φ jointly entail ψ Contraposition. φ . ψ entails ¬ψ . φ Conditional excluded middle. For all φ , ψ: either φ . ψ or φ . ¬ψ Weak Boethius’ thesis. φ . ¬ψ entails ¬(φ . ψ) The first two patterns are relatively standard assumptions in the literature on conditionals, although they are not without challenge (see McGee, 1985). (14c) follows from the structural assumption in (13), and the desired equivalence between (1a) and (1b): (15) ∀x[φ . ψ] ≡ ¬∃x[φ . ¬ψ] =⇒ ∀x[φ . ψ] ≡ ∀x¬[φ . ¬ψ] =⇒ φ . ψ ≡ ¬[φ . ¬ψ] =⇒ ¬[φ . ψ] ≡ φ . ¬ψ (desired equivalence, cf (1)) (DeMorgan’s law) (14d) follows from (14c), on the assumption that at most one of φ . ψ or its negation (φ . ¬ψ) can be true. Given a bivalent logic, these inferences lead to a ‘bombshell’ for the semantics of conditionals (Pizzi and Williamson, 2005). Any connective . which satisfies all of the properties in (14) must be equivalent to the material biconditional: φ . ψ ≡ φ ⊃ ψ ∧ ψ ⊃ φ ! This result leaves Kratzer in a difficult position, since it is not plausible that natural language if . . . then semantically expresses the material biconditional outside of QICs. The only apparent workaround is to suggest, as Kratzer does, that “some element in the syntactic environment of the embedded conditionals . . . obscures their compositional meaning contribution.” The particular element she appeals to is pragmatic domain restriction (von Fintel, 1994; Stanley and Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 771 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most Szabó, 2000), associated with the determiner. The argument proceeds as follows. Kratzer proposes that (past-tense) QICs embed a material conditional. This leaves us with Higginbotham’s original problem: (1a) and (1b) are no longer equivalent, and the truth conditions for (1b) (reproduced below) do not reflect its intuitive meaning. (16) No student failed if she studied hard. ¬∃[STUDENT][STUDY- HARD ⊃ ¬PASS] All students both studied hard and passed. Now, however, the quantificational determiner comes along with a domain variable. This variable is valued pragmatically, and its value ends up in the quantifier restriction. (17) NoD student failed if she studied hard. ¬∃[STUDENT & D][STUDY- HARD ⊃ ¬PASS] Kratzer suggests that a natural default for the value of D is the if -clause. Since this is also part of the material conditional, this means that if -clauses in ‘neutral’ QICs perform double duty: as pragmatic restrictors of nominal quantifiers and as antecedents of embedded conditionals. (18) NoD student failed if she studied hard. ¬∃[STUDENT & STUDY- HARD(= D)][STUDY- HARD ⊃ ¬PASS] If the conditional antecedent is pragmatically assigned to the domain variable, as in (18), its role in the conditional becomes redundant, and we wind up with the interpretation in (19c). von Fintel (1998)’s folkloric solution, (4), in which the if -clause was taken to semantically restrict the quantifier domain. As a result of this, the combination of an embedded conditional with pragmatic domain restriction does indeed produce interpretive equivalence between (1a) and (1b). (19) EveryD student passed if she studied hard. a. Semantic meaning: ∀[STUDENT][STUDY- HARD ⊃ PASS] b. After pragmatic restriction: ∀[STUDENT & STUDY- HARD][STUDY- HARD ⊃ PASS] c. Equivalent to: ∀[STUDENT & STUDY- HARD][PASS] (20) NoD student failed if she studied hard. a. Semantic meaning: ¬∃[STUDENT][STUDY- HARD ⊃ ¬PASS] b. After pragmatic restriction: ¬∃[STUDENT & STUDY- HARD][STUDY- HARD ⊃ ¬PASS] c. Equivalent to: ¬∃[STUDENT & STUDY- HARD][¬PASS] The semantic meanings in (19a) and (20a) do not reflect the perceived equivalence of (1a) and (1b). This means that the conditional operator ⊃ need not satisfy conditional excluded middle (14c) and weak Boethius’ thesis (14d), and Pizzi and Williamson’s bombshell does not apply. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 772 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most 3.2. Reversal Reverse readings enter the picture at this point, as evidence of the process of pragmatic domain restriction. In the unmarked case, domain restriction proceeds as above: the antecedent enters into the restriction of the quantifier, and we obtain the vanilla reading for a conditional like (9). (21) MostD kids asked for calculators if they had to do long divisions. a. Semantic meaning: Most[KID][LONG - DIV ⊃ CALC] b. After pragmatic restriction: Most[KID & LONG - DIV][LONG - DIV ⊃ CALC] c. Equivalent to: Most[KID & LONG - DIV][CALC] d. Paraphrase: Most kids who had to do long divisions used calculators. However, since domain restriction occurs pragmatically, it should be possible for something other than the conditional antecedent to value the domain variable D. Kratzer suggests that this happens in marked (non-neutral) cases, like the context in (11). Specifically, a reverse reading is predicted if the domain variable picks up the conditional consequent as its value: this situation plausibly occurs when the consequent is backgrounded and the antecedent is focused. (22) MostD kids asked for calculators if they had to do [long divisions]F . a. Semantic meaning: Most[KID][LONG - DIV ⊃ CALC] b. After pragmatic restriction: Most[KID & CALC][LONG - DIV ⊃ CALC] c. Paraphrase: Most kids who used calculators either did not have to do long divisions or used calculators (to do them). If D is the conditional consequent, the embedded material conditional is not reducible, and we get the interpretation in (22). This is not quite the meaning we are after: note that (22) is satisfied if most of the students who used calculators simply did not have to do long-divisions. To get us to the correct interpretation, on which most of the calculator users did in fact have to do long divisions, Kratzer posits that the conditional operator in this case must be interpreted biconditionally, via an embedded application of conditional perfection (Geis and Zwicky, 1971). (23) MostD kids asked for calculators if they had to do long divisions]F . a. Semantic meaning: Most[KID][LONG - DIV ⊃ CALC] b. After pragmatic restriction: Most[KID & CALC][LONG - DIV ⊃ CALC] c. After embedded perfection: Most[KID & CALC][LONG - DIV ≡ CALC] d. Equivalent to: Most[KID & CALC][LONG - DIV] e. Paraphrase: Most kids who used calculators had to do long divisions. If perfection turns the embedded conditional into a biconditional, we wind up in a similar position as in (19) and (20). In this case, since it is the consequent that enters the restriction of the quantifier, it is the consequent that is redundant. This results in the interpretation indicated in (23d) and (23e), which effectively reverses the roles of conditional antecedent and consequent as compared to the neutral case in (21). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 773 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most 3.3. The consequences Kratzer’s approach represents a rather radical move. The account she presents is ultimately noncompositional: even the accessible vanilla interpretation of QICs like (1a)-(1b) does not result from the simple composition of a conditional with a wide-scope nominal quantifier, but also requires the input of a pragmatic operation which – crucially – can have a different outcome. In addition, the appeal to conditional perfection for the reverse reading is not wholly innocent. For one, it must be applied in an embedded position, which throws into question its widely-accepted status as a pragmatic inference. Moreover, conditional perfection in many cases strengthens a conditional to something weaker than a full biconditional: for instance, if p, then q may suggest that q is not unconditional, rather than the full converse, if not p, then not q (von Fintel, 2001; Franke, 2009). If conditional perfection is to unerringly produce the result required for the derivation in (23), it seems that we will require a new, more direct, mechanism. Finally, there is a rather more immediate problem with Kratzer’s account: it makes incorrect predictions. Concretely, the crucial feature in producing a reverse interpretation for a conditional is the presence of focus within the antecedent; properties of the wide-scope quantifier do not play a role. As a result, reverse readings should exist, given the right context, for QICs with any quantifier, not just with most. This is not the case: these readings are unattested with the universal quantifier (24), and do not arise even when the appropriate context is provided (25).2 (24) Every kid asked for a calculator if she had to do long divisions. a. Predicted vanilla reading (attested): All kids who had to do long divisions asked for calculators. b. Predicted reverse reading (unattested): All kids who asked for calculators were ones who had to do long divisions. (25) You: Did you see kids using calculators when you volunteered in your son’s school yesterday? What did they use the calculators for? Me: Every kid asked for a calculator if she had to do long divisions. #But I am pleased to report that some kids in my son’s school do long divisions by hand. As in (11), a reverse reading of the conditional in (25) would be compatible with the given continuation, but the vanilla reading produces a contradiction. We find only the latter case, against the prediction made by Kratzer’s account. We suggest that it is not an accident that the first attestation of a reverse reading uses the quantifier most. Rather, it is because the choice of quantifier plays a role in the availability (and derivation) of these interpretations. Together with the theoretical issues noted above, Kratzer’s problematic predictions make holding out for a different analysis of QICs an attractive option. A suitable analysis, we propose, should (i) derive the equivalence of (1a) and (1b) as the outcome of semantic composition. It should also (ii) account for the existence of reverse readings in the contexts described by Kratzer – but it should, crucially, only do this for the quantifiers which actually exhibit these readings. 2 The two readings are equivalent under no, due to the symmetric property of this determiner. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 774 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most We have already seen that a restrictor analysis can deliver on (i). In the remainder of this paper, we show that it can also deliver on (ii): when the properties that differentiate quantifiers like most from those like every (and no) are taken into account, a restrictor analysis is not only able to produce reverse readings but also improves on Kratzer’s predictions in this regard. Crucial inspiration for our account comes from recent work on reverse proportional readings of many. 4. The reverse-proportional reading of many Descriptively, we can distinguish at least three meanings for sentences of the form Many Ps are Qs. The first two are the cardinal reading in (27) and the proportional reading in (28). (26) Many Scandinavians have won the Nobel Prize in literature. (27) Cardinal: Manycard [P][Q] ≡ |P ∩ Q| > n, where n is ‘large’ number. The number of Scandinavians NP-lit winners is large. (28) Proportional: Manyprop [P][Q] ≡ |P∩Q| |P| > k, where k is a ‘large’ proportion. The ratio of Scandinavian NP-lit winners to all Scandinavians is high. Westerståhl (1985) points out that, with 14 Scandinavian Nobel winners (as of 1984) and millions of Scandinavians, both these readings likely come out false. And yet, (26) appears to have a reading on which it is true, and this is intuitively so because 14 Scandinavians out of 81 Nobel Prize winners “seems rather (too?) many” (p. 403). But neither (27) nor (28) compares the number of Scandinavian winners (|P ∩ Q| = 14) to the number of all winners (|Q| = 81). We can characterize this ‘reverse proportional’ reading as in (29). (29) Reverse proportional: Manyr-prop [P][Q] ≡ |P∩Q| |Q| > k, where k is a ‘large’ proportion. The ratio of Scandinavian NP-lit winners to all NP-lit winners is high. Note that the reverse proportional reading is just the proportional reading with the arguments reversed, i.e., Manyr-prop [P][Q] ≡ Manyprop [Q][P]. Just as antecedent and consequent seem to ‘switch places’ in the reverse readings of most-QICs, the nominal complement and the VP seem to ‘switch places’ in the reverse proportional reading of many. Stipulating (29) as a separate lexical meaning of many is undesirable not only on general grounds (Grice’s ‘modified Occam’s razor’), but also because, if (29) were the meaning of a lexicalized determiner, it would violate the conservativity universal (Barwise and Cooper, 1981; Keenan and Stavi, 1986). Consequently, several authors have sought to reduce (29) to one of the the other recognized readings. Here, we draw on Romero (2015)’s analysis of the reverse proportional reading, as it is the one most readily adapted to our purposes. Romero extends Hackl’s (2000, 2009) account of more and most as the combination of an underlying operator MANY with the comparative -er and the superlative -est, respectively. Likewise, Romero takes English many to decompose into MANY plus the (silent) positive morpheme POS that is also present in the positive form of adjectives (von Stechow, 1984). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 775 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most Romero also draws on arguments by Schwarz (2010) showing that POS displays a relative/absolute ambiguity, and combines this with Herburger’s (1997) observation that the reverse proportional reading is facilitated by stress on the first argument of the determiner. Consequently, she provides a lexical entry for POS that is dependent on a set of alternatives generated by an alternative semantics (Rooth, 1992), much as in Heim (1999)’s analysis of the superlative. Romero takes the underlying operator MANY to be ambiguous between a cardinal and a proportional reading. Both are ‘parameterized determiners’ in the sense of Hackl (2000), i.e., they have generalized determiner meanings with an extra (degree) argument. MANYcard simply counts the individuals that jointly satisfy both its non-degree arguments, while MANYprop computes their proportion. Both of these meanings are conservative for any fixed degree d. (30) a. b. MANY card MANY prop := λ dn λ Pet λ Qet . |P ∩ Q| ≥ d, where n is the degree-type. := λ dn λ Pet λ Qet .(|P ∩ Q| : |P|) ≥ d In order to yield a truth-evaluable statement, both these operators must combine with a degree operator like POS (for surface many), comparative -er (more) or superlative -est (most). POS combines with a property P of degrees and claims that there is a degree d of which P is true and which exceeds the standard of comparison θ . Crucially, this standard of comparison is calculated on the basis of a comparison class C (a set of degree properties):3 (31) = λ Cnt,t λ Pnt .∃d[P(d) ∧ d > θ (C)] where θ is a function that maps comparison classes to degrees.4 POS As in Heim (1999)’s analysis of the superlative, the degree morpheme scopes independently and uses focus structure to constrain C: the comparison class must be a subset of the focusalternative value of the sister of POS. With these ingredients, Romero derives the two proportional readings (standard and reverse) from the single lexical entry for MANYprop , as follows: on both readings, POS moves out of the DP to the sentence level. As is standard for QR in LF-based theories, POS leaves behind a trace (of type n in this case) that is bound by a lambda abstract created by the movement operation. That is, on both proportional readings, the sentence in (32a) has a logical form like the one sketched in (32b). (32) a. b. vacation in the countryside. Many Scandinavians     [POS C] 1 t1 - MANYprop [ Scandinavians ] [ vacation in countryside ] ∼ C What differs between the two readings is the focus structure of the sentence, which results in 3 Romero’s entry is more complicated because she also aims to decompose few into MANY, POS and an antonymizing morpheme LITTLE, à la Heim (2006). To achieve this, Romero uses the analysis from von Stechow (2009), according to which POS claims that its degree property argument is true of all degrees contained in the ‘neutral segment’ of the scale. This complication is not relevant for our purposes here. 4 Romero takes the value delivered by θ to be dependent on the distribution of values over its comparison class argument, cf. Fernando and Kamp 1996; Schöller and Franke 2015. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 776 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most different comparison classes. If the focus (or contrastive topic)5 is outside of the restriction of the quantifier, a regular proportional reading results: (33) Many Scandinavians vacation [in the countryside]F . a. Logical form:      [POS C] 1 t1 -MANYprop [ Scandinavians ] [ vacation in countrysideF ] ∼ C b. Alternatives: c. d.  λ d 0 .d 0 -MANYprop [      λ d 0 .d 0 -MANYprop [ λ d 0 .d 0 -MANYprop [ JCK ⊆   λ d 0 .d 0 -MANYprop [    ... Scandinavians Scandinavians Scandinavians Scandinavians ][ ][ ][ ][ vacation in countryside vacation at the beach vacation in the mountains vacation in urban centers ], ], ], ],            Truth-conditions: ∃d : d-MANYprop [ Scandinavians ][ vacation in countryside ] & d > θ (JCK) Paraphrase: The proportion of Scandinavians who vacation in the countryside is high compared to the proportion of Scandinavians vacationing in other places. The reverse proportional reading emerges if the focus/contrastive topic instead occurs within the restrictor of many: (34) Many [Scandinavians]F vacation in the countryside. a. Logical form:      [POS C] 1 t1 -MANYprop [ ScandinaviansF ] [ vacation in countryside ] ∼ C b. Alternatives: c. d.  λ d 0 .d 0 -MANYprop [      λ d 0 .d 0 -MANYprop [ λ d 0 .d 0 -MANYprop [ JCK ⊆   λ d 0 .d 0 -MANYprop [    ... Scandinavians Mainland Europeans Americans East Asians ][ ][ ][ ][ vacation in countryside vacation in countryside vacation in countryside vacation in countryside ], ], ], ],            Truth-conditions: ∃d : d-MANYprop [ Scandinavians ][ vacation in countryside ] & d > θ (JCK) Paraphrase: The proportion of Scandinavians who vacation in the countryside is high compared to the proportion of people from other world regions who vacation in the countryside. Romero’s truth-conditions are not exactly those characterized in (28)–(29). For example, applying the semantics of (29) to (32a) would require that the ratio comparing Scandinavian countryside-vacationers to all countryside-vacationers worldwide is ‘high’. (34) instead compares the ratio of Scandinavian countryside-vacationers to Scandinavians against the analogous ratio for other world regions. Romero argues that her truth-conditions are superior.6 5 Romero leaves open whether stress marks focus (as assumed by Herburger 1997) or contrastive topic (as argued by Cohen 2001). We follow her in this regard, but to ease readability we will mark the stressed constituent with F rather than F/CT. 6 Cohen (2001) argues that the number of all Scandinavians is relevant to the inverse proportional reading. To this, Romero adds examples showing that the individual alternative ratios must be taken into account. Whether or Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 777 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most 5. The reverse reading as a relative reading of most 5.1. Our proposal In a nutshell, our proposal is that the reverse reading of most-QICs arises as an instance of the relative reading of most/-est, which is analyzed in the manner of Heim (1999) and Hackl (2009). The only assumption that needs to be added is that the if -clause restricts the underlying ‘parameterized determiner.’ With this, the derivation of the reverse reading of most-QICs is entirely parallel to Romero’s derivation of the reverse proportional reading of many. (35a) repeats the definition of MANYcard . In (35b), we give a Heim (1999)-style meaning for -est. Following Romero’s analysis, -est moves to the sentence level to gain scope. With focus in the if -clause, a restrictor analysis gives us the logical form sketched in (35c).7 (35) a. b. c. := λ dn λ Pet λQet . |P ∩ Q| ≥ d  J-estK = λ Cdt,t λ Pdt .∃d P(d) & ∀C ∈ C[C 6= P → ¬C(d)] Most students asked for calculators if they had to do [long divisions]F . Logical form: MANY card [[-est C] [1 [t1 -MANYcard [kid & had to do [long division]F ] [asked for calculator]]] ∼ C] Again, C is required to be a subset of the focus-semantic value of the LF-sister of -est. This leads to a set of alternatives like (36), where long divisions contrasts with other problem types. (36) Alternatives:  λ d 0 .d 0 -MANYcard [ kid    λ d 0 .d 0 -MANYcard [ kid JCK ⊆ λ d 0 .d 0 -MANYcard [ kid    ...  & had-to-do-long-division ][asked-for-calc],    & had-to-do-multiplication ][asked-for-calc], & had-to-do-decimals ][asked-for-calc],    The resulting truth-conditions are spelled out in (37a) and paraphrased in (37b): (37) a. Truth-conditions: b. ∃d : d-MANYcard [kid & had-to-do-long-division][asked-for-calc] ∧ ∀C ∈ C : C 6= λ d 0 .d 0 - MANY[kid & had-to-do-long-division][asked-for-calc] → ¬C(d) Paraphrase: The number of calculator-using kids who had to do long divisions was larger than the number of calculator-using kids doing any other problem type. not this dependence on ratios needs to be part of the denotation of many is subject to debate. For example, Penka (2018) proposes that, semantically, all three readings are derived from a version of MANYcard , and that the apparent dependence on ratios in certain examples instead results from the way the function θ determines the standard on the basis of the comparison class. For our purposes, we can set this debate aside. We will be using MANYcard in our analysis of most-QICs, remaining agnostic whether there is, in addition, a MANYprop . 7 In our LF-sketches, we add the content of the if -clause as a conjunct of the restrictor of MANY card . This is done for ease of exposition only, and we do not intend to claim that if -clause is actually part of the first argument of the determiner. In fact, there are good reasons to think that any workable restrictor analysis must reject this possibility, as we discuss in Section 5.2 below. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 778 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most The truth-conditions in (37) importantly differ from the ones in Section 2, repeated in (38): (38) |calculator kids ∩ long-division kids| > |calculator kids − long-division kids| (37) characterizes a true relative reading, which only requires that the set of kids doing long divisions contained the largest group of calculator users. By contrast, (38) requires that more than half of the calculator users were long-divisioners. It is easy to see that the two readings can come apart in a situation where there are more than two problem types, namely if the largest group of calculator users for a given problem type is less than half of all calculator users. We think that the reading we derive is at least as appropriate as the alternative.8 This account correctly predicts that the reverse reading is only available when material in the if clause is focused. More importantly, it also correctly predicts that this reading is only available for determiners that are focus-sensitive in the right way, and hence, unlike Kratzer’s account, it does not predict the reverse reading for QICs with every.9 We do predict reverse readings for many and few, paraphrased in (39) and (40), respectively, on the assumption that these contain a Romero-style parameterized determiner. According to our intuitions, (39) and (40) are true in scenarios which satisfy their putative paraphrases. It is hard, however, to evaluate what this shows, given that with many (unlike with most), truth-value judgements are dependent on judgements of what counts as a ‘high’ number or proportion, relative to a comparison class. (39) Many kids asked for calculators if they had to do [long divisions]F . Putative ‘reverse’ reading: The number/proportion of calculator users among the long-division kids was high compared to the number/proportion of calculator users doing other problem types. (40) Few kids asked for calculators if they had to do [long divisions]F . Putative ‘reverse’ reading: The number/proportion of calculator users among the long-division kids was low compared to the number/proportion of calculator users doing other problem types. 5.2. If-clauses vs. relative clauses Any restrictor account has to deal with the fact that QICs are not always equivalent to the analogous sentence where a relative clause replaces the if -clause. Our example sentences are a case in point: (41) has the vanilla reading, but does not have the reverse reading. 8 Suppose the speaker has visited three classes of 20 children each. Each class did different kinds of problems: long division, logarithm and multiplication. 3 students in the logarithm class and 3 students in the multiplication class asked for calculators, and 8 students in the long division class did. To our ears, (35c) can be true in this situation, but we admit that the intuitions are somewhat subtle. 9 Hallman (2016) proposes to analyze all as a superlative(-like) operator. Depending on the implementation, this analysis potentially predicts the reverse reading for a sentence like All students asked for calculators if they had to do long divisions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 779 S. Lauer & P. Nadathur (41) Quantified indicative conditionals and the relative reading of most Most kids who had to do long divisions asked for calculators. The absence of the reverse reading for (41) arguably can be attributed to a constraint that is independently needed (and hence motivated, see Romero 2015, 2016): (42) Constraint: On a relative reading, the F-associate of -est cannot be internal to the DP where -est originates. This constraint is active in examples with adjectival superlatives and the most (Pancheva and Tomaszewicz 2012): (43) John has the best albums by [U2]F . # ‘John has better albums by U2 than by any other band.’ (44) John has the most albums by [U2]F . # ‘John has more albums by U2 than by any other band.’ Pancheva and Tomaszewicz (2012) provide an account of these facts. They also account for the fact that these readings actually are available in languages like Bulgarian and Polish as long as the DP where -est originates is not marked as definite. This explanation obviously does not directly translate to English DPs headed by most without a definite determiner, but the same constraint is needed for ‘bare’ most on any analysis that allows the determiner to have relative readings.10 Otherwise, such accounts predict the analogue of the ‘reverse proportional’ reading of many for (45), contrary to fact: (45) Most [Scandinavians]F have won the nobel prize in literature. # ‘The number/proportion of Scandinavian NP-lit winners is larger than the number/proportion of NP-lit winners from any other world region.’ We want to suggest the following view. Even though in QICs, if -clauses restrict the quantifier in subject position, they are not ‘internal to the DP’ in the sense relevant to the constraint in (42), while relative clauses are. Thus, if -clauses allow speakers of English to circumvent the constraint and hence are the only environment where reverse readings of most can be produced. Interestingly, as Romero (2016) notes, the putative ambiguity of the underlying parameterized determiner (MANYcard vs MANYprop ) is obscured with most unless the focus falls within the restriction of the determiner. This means that, in English, QICs are are the only known environment where one could test whether there is a MOSTprop (MANYprop + -est) in addition to MOST card ( MANY card + -est). The crucial kind of scenario is given in (46). 10 There is documented inter-speaker variation with respect to the acceptability of relative readings with bare most. Kotek et al. (2011, 2015) found evidence that only about a third of speakers could access a relative reading (which they dub the ‘superlative reading’). To our knowledge, no speakers perceive a reverse reading for (45). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 780 S. Lauer & P. Nadathur (46) Quantified indicative conditionals and the relative reading of most In a class of 35 students, 10 had to practice long division, the rest had to practice multiplication problems. 5 of the long division kids asked for calculators, while 7 of the multiplication kids did. According to our intuitions, Kratzer’s example does not seem to have a true reading in this scenario, i.e., there is no evidence for MOSTprop . This is in line what Romero reports for Bulgarian and Polish, where the difference between MOSTcard and (putative) MOSTprop can be tested outside of conditionals as well. 5.3. Alternative accounts? It might be thought that all that is needed to account for reverse readings is the basic idea underlying our analysis, viz., that reverse readings are relative readings. With this, one might think, any analysis of relative readings of most and any analysis of QICs can be combined to account for reverse readings. But this is not so: the space of options is actually quite constrained. Our account is built on a Romero/Hackl-style analysis of most which has several salient alternatives that may be preferable on independent grounds. Penka (2018) develops a more parsimonious version of Romero’s account, insofar as she dispenses with the need for MANYprop in addition to MANYcard . Likewise, Beaver and Coppock (2014) provide an alternative analysis of (the) most, which Coppock and Josefson (2014) have argued is better equipped to handle the crosslinguistic variation in the distribution of the different readings of (the) most. What both these alternatives share in common is that they analyze most not as a ‘parameterized determiner’, but instead as a noun phrase modifier. As a consequence, it is not immediately obvious that these analyses can be combined with a restrictor analysis of QICs. The problem is that the sentences in question must contain a quantifier for if to restrict. Penka’s analysis, in theory, features such an operator, as she assumes that sentences with bare most receive their quantificational force from a silent existential determiner 0. / But it is not clear that it is plausible to assume that if -clauses restrict 0/ in our examples, because quantifiers headed by overt existential determiners generally cannot be restricted by if -clauses: Some students passed if they studied hard does not have a reading on which it says that there are some students that both studied hard and succeeded. Things are even worse on Beaver and Coppock’s account, where there is no quantificational operator in the structure of sentences with definites and indefinites (including the most)—instead, these DPs gain quantificational force (or reference) via a type-shifting operation when they are in argument position. As a consequence, it is not clear how a restrictor analysis would combine with their account. This is not to say that either of these accounts could not be made compatible with a restrictor analysis, suitably spelled out. Maybe Penka’s 0/ is different from overt existentials in a way that allows it to be restricted by if -clauses. Likewise, a suitable specification of the syntax-semantics interface could allow if clauses to restrict the output of the type shifting operation in Beaver and Coppock’s account.11 All that we want to note here is that such a combination will not work ‘out of the box.’ 11 Alternatively, Beaver and Coppock allow for the possibility that bare most is a an operator that is not derivationally related to the most in the most-DPs. This most could be a bona fide determiner, which if could restrict. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 781 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most Proponents of such alternative accounts may hence be especially interested in alternative accounts of QICs. Unfortunately, such alternatives do not seem workable to us. Let MOSTrel be an arbitrary account of relative most, and suppose that QICs have a full conditional structure embedded under the quantifier, as in (47): (47) MOSTrel [kids] [had to do long divisions . asked for calculators] In order to derive the truth conditions we derive, MOSTrel has to compare the number of calculator users that had to do long division in relation to the number of calculator users that had to do other problem types. The question is how it can do that on an analysis like (47) without assuming that if . . . then can mean and when embedded under a quantifier. 6. Conclusion and outlook We have shown that the reverse reading does not provide an insurmountable challenge for a restrictor analysis of QICs. On the contrary, on a restrictor analysis, the reverse reading emerges rather straightforwardly as an instance of the relative reading of most, given a number of independently motivated ingredients. Some open issues remain. Empirically, it is worth noting that not all speakers can access the reverse reading in most-QICs. Even those that can perceive the reading, do so only under favorable circumstances. This is not entirely unexpected on our account, as it has been shown (e.g., Kotek et al., 2015) that only a subset of speakers can access relative readings with bare most, and that even for those speakers, this reading is not dominant. Our account of the reverse reading makes a clear prediction that lends itself to experimental testing: The speakers who can access reverse readings of most-QICs should be the same ones that perceive relative readings with most more generally. Theoretically, while Leslie’s extended restrictor analysis is promising, it remains to be seen whether it can be spelled out in a way that deals with all challenges that have been identified in the literature. An additional question is why the presence of an if -clause restricting a nominal quantifier forces the presence of a wide-scope modal. At the same time, the interaction of if -clauses, the putative wide-scope modal, and tense deserves closer attention. Kratzer notes that some of the problematic differences between if -clauses and relative clauses disappear in the past tense. For example, consider the pair in (48). (48a) appears to quantify not only over actual goofers, but also students who could goof off, even though in actuality they do not (Leslie 2009). (48b), by contrast, only makes a claim about students who actually goofed off. (48) a. b. Every student will fail if she goofs off. Every student failed if she goofed off. This contrast can arguably be accounted for if the wide-scope modal in Leslie’s analysis quantifies over historical alternatives at the utterance time (Condoravdi, 2002). This quantification is trivialized in the past-tense, but not in the present and the future. More generally, we conjecture that many, if not all, apparent challenges for a restrictor analysis can be explained by a combination of (i) the presence of a wide-scope modal, (ii) temporal interpretation, and (iii) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 782 S. Lauer & P. Nadathur Quantified indicative conditionals and the relative reading of most the fact that domain restriction proceeds differently with if -clauses than with relative clauses. We intend to investigate the details of this idea in future work. Open issues notwithstanding, we think that the existence of reverse readings (for some speakers) evens the score a bit: As noted in Section 5.3, it is not at all clear that non-restrictor accounts can analyze reverse readings as relative readings. Such accounts consequently face the challenge of how to predict these readings in a way that accounts for their distribution across determiners. As we have shown, restrictor accounts succeed on this front: hence, even skeptics should agree that they deserve another look. References Barwise, J. and R. Cooper (1981). Generalized quantifiers and natural language. Linguistics and Philosophy 5, 159–219. Beaver, D. and L. Coppock (2014). A superlative argument for a minimal theory of definiteness. In Semantics and Linguistic Theory (SALT) 24, pp. 177–196. Cohen, A. (2001). Relative readings of many, often and generics. Natural Language Semantics 69, 41–67. Condoravdi, C. (2002). 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(2009). “If”, “unless”, and quantification. In R. J. Stainton and C. Viger (Eds.), Compositionality, Context and Semantic Values, pp. 3–30. Springer. McGee, V. (1985). A counterexample to modus ponens. Journal of Philosophy 9, 462–71. Pancheva, R. and B. Tomaszewicz (2012). Cross-linguistic differences in superlative movement out of nominal phrases. In Proceedings of WCCFL 30. Penka, D. (2018). One many, many readings. In Sinn und Bedeutung 21 (this volume). Pizzi, C. and T. Williamson (2005). Conditional excluded middle in systems of consequential implication. Journal of Philosophical Logic 34, 333–362. Romero, M. (2015). The conservativity of many. In Proceedings of the Twentieth Amsterdam Colloqium, pp. 20–29. Romero, M. (2016). POS, -est and reverse readings of many and most. In North-Eastern Linguistics Society (NELS) 46, pp. 141–154. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1, 75–116. Schöller, A. and M. Franke (2015). Semantic values as latent parameters: Suprising few & many. In Semantics and Linguistic Theory (SALT) 25, pp. 143–162. Schwarz, B. (2010). A note on for-phrases and derived scales. Handout, Sinn und Bedeutung 15. von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics 3, 1–77. von Stechow, A. (2009). The temporal degree adjectives früher/später ‘early(er)’/‘late(r)’ and the semantics of the positive. In A. Giannakidou and M. Rathert (Eds.), Quantification, Definiteness and Nominalization, pp. 214–233. Oxford University Press. Stanley, J. and Z. G. Szabó (2000). On quantifier domain restriction. Mind & Language 15(2), 219–261. Westerståhl, D. (1985). Logical constants in quantifier languages. Linguistics and Philosophy 8, 387–413. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 784 The number sensitivity of modal indefinites1 Jess H. K. LAW — Rutgers, The State University of New Jersey Abstract. In this study, I take up the interaction between modal flavor and the number morphology of existential wh-indefinites in Mandarin, a phenomenon first discussed in Lin (1998). I argue that there are three essential theoretical pieces to this interaction: (i) types of nominal reference (quantized vs. cumulative), (ii) degrees of modal variation (total vs. partial), and (iii) achieving modal variation by exhaustification. I show that while exhaustifying alternatives contributed by quantized wh-indefinites may give rise to either total or partial modal variation, exhaustifying alternatives contributed by cumulative wh-indefinites may only give rise to partial modal variation. Keywords: alternatives, exhaustification, modal indefinites, plurality 1. Introduction Indefinites that give rise to modal inferences are called modal indefinites. Well-known examples of modal indefinites include those introduced by determiners like English any (Kadmon and Landman 1993, Dayal 1998, Chierchia 2013, a.o.) German irgendein (Kratzer and Shimoyama 2002, a.o.,) Spanish algún (Alonso-Ovalle and Menéndez-Benito 2010) and Romanian vreun (Fălăus 2014). Take German irgendein indefinites as an example. They give rise to different modal inferences under the scope of epistemic modals and deontic modals (Aloni and Port 2010, Aloni and Franke 2013), as exemplified by (1) and (2) (taken from Aloni and Franke 2013). Specifically, in (1), the irgendein indefinite is in the scope of a deontic modal, and it gives rise to an inference that any man can be a marriage option for Mary; by contrast, in (2), the irgendein indefinite is in the scope of an epistemic modal, and it leads to an inference that signals speaker ignorance or indifference. (1) Mary musste irgendeinen Mann heiraten. Mary had-to irgend-one man marry ‘Mary had to marry a man.’ Any man was a permitted marriage option for Mary. (2) Juan muss in irgendeinem Zimmer im Haus sein. Juan must in some room in-the house be ‘Juan must be in some room of the house’ The speaker does not know or does not care about which room Juan is in. Aloni and Franke (2013) called the inference in (1) ‘total variation inference,’ and the inference in (2) ‘partial variation inference.’ These terms are based on the Modal Variability Hypothesis, which attributes distinct degrees of modal variation to epistemic and deontic modals (see also Aloni and Port 2010). According to Aloni and Franke (ibid), deontic modals require total 1I am indebted to Simon Charlow, Veneeta Dayal and Anthony Gillies for their generous comments on earlier versions of this work. I also thank Lucas Champollion, Yi-Hsun Chen, Mingming Liu and Haoze Li for helpful discussions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 785 J. H. K. Law The number sensitivity of modal indefinites modal variation, but epistemic modals only require partial modal variation, where total and partial modal variations are defined below (Aloni and Franke 2013:110): 2 (3) a. b. Total (modal) variation: ∀x ⋄ φ (x) All alternatives in the relevant domain qualify as a possible option. Partial (modal) variation: ∃x∃y(⋄φ (x) ∧ ⋄φ (y) ∧ x 6= y) More than one (but not necessarily all) alternatives in the relevant domain qualify as a possible option. The inference in (1) clearly follows the definition of total variation. The inference in (2) is identified as partial variation, because it is felicitous in the ‘hide and seek’ scenario described by Alonso-Ovalle and Menéndez-Benito (2010). (4) Marı́a, Juan, and Pedro are playing hide-and-seek in their country house. Juan is hiding. Marı́a and Pedro haven’t started looking for Juan yet. Pedro believes that Juan is not hiding in the garden or in the barn: he is sure that Juan is inside the house. Furthermore, Pedro is sure that Juan is not in the bathroom or in the kitchen. As far as he knows, Juan could be in any of the other rooms in the house. In the above scenario, Pedro can felicitously utter (2), even though not all the rooms are epistemic possibilities for him—he knows that Juan is not in the bathroom or in the kitchen. In this paper, I extend this line of research to include modal indefinites in Mandarin. I demonstrate that the distinction in total vs. partial modal variation has a reflex on the number morphology of modal indefinites. Adopting the Alternatives and Exhaustification approach outlined in Chierchia (2013), I show that total modal variation is not compatible with domain alternatives triggered by a modal indefinite that exhibit cumulative reference in the sense of Krifka (1989, 1998). This analysis is able to account for a long standing puzzle in Mandarin, i.e., a modal indefinite must occur with a numeral classifier under the scope of deontic modals (Lin 1998). This paper is organized as follows. Section 2 introduces the core data and clarifies the correlation between modal flavor and degrees of modal variation. Section 3 provides an account for the interaction, which incorporates plurality into the framework of Alternatives and Exhaustification (Chierchia 2013, Fox 2007, a.o.). Section 4 concludes. 2. Modal indefinites in Mandarin Mandarin makes use of wh-phrases, rather than a distinct determiner, to construct modal indefinites (Lin 1998, see also Li 1992). Consider the example in (5). This sentence makes an existential claim, but additionally conveys a modal inference that the speaker does not know 2 As a terminological note, the term total (modal) variation is often taken to be synonymous with free choice, while the term partial (modal) variation is often simply referred to as modal variation, after Alonso-Ovalle and Menéndez-Benito (2010). I take modal variation to be a cover term for both total and partial modal variation in this paper. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 786 J. H. K. Law The number sensitivity of modal indefinites which book(s) Zilu read.3 Due to the modal inference, the speaker of (5) may not identify the book, whether by its name or its physical ostension, as suggested by the infelicity of the ‘namely’ continuation (see also Liao 2011: 8–9). The same infelicity is not shared by an ordinary indefinite, which lacks the modal inference, as shown in (6). (5) Zilu kenengE kan-le shenme shu. # Jiushi Halibote. Zilu possibly read-ASP what book namely Harry.Potter ‘Zilu possibly read some book(s), namely Harry Potter.’ (6) Zilu kenengE kan-le yi-ben shu. Jiushi Halibote. Zilu possibly read-ASP one-CL book namely Harry.Potter ‘Zilu possibly read a book, namely Harry Potter’ In addition, Mandarin wh-indefinites can also occur within the scope of deontic modals (subscripted with D), as exemplified in (7). Intuitively, this sentence conveys that any book in a contextual relevant set can be an option for Zilu. (7) Zilu keyiD du yi-ben shenme shu. Zilu can read one-CL what book ‘Zilu can read any book.’ Based on this set of data, Liao (2011) argues that wh-indefinites in Mandarin should be taken to be modal indefinites. She proposes an analysis based on Alternatives and Exhaustification (Chierchia 2006, 2013, Fox 2007) to capture the modal variation effect and the fact that modals are required for these wh-indefinites to be well-formed. Mandarin wh-indefinites are similar to German irgendein indefinites in their interactions with modals with different flavors. Specifically, a wh-indefinite under an epistemic modal expresses partial modal variation, but the same indefinite under a deontic modal expresses total modal variation. This contrast is verified by the following contexts. Context 1: Total variation John and Mary were planning a trip to Europe. John suggested: (8) Women keyiD qu yi-ge Ouzhoude shenme chengshi. we can go one-CL European what city ‘We can go to an European city (whichever will work).’ Mary knew that they could only visit an European city where they had a friend to stay with. Since they only had a friend in London and a friend in Berlin, she added:4 3 Mandarin lacks plural morphology, so depending on the context Zilu could have read one or more books. This property of bare noun phrases is central to the discussion of this paper. 4 I chose not to narrow down the domain to a single city so that it can be clear that the objection is not to the lack of modal variation, but to how freely one can choose among the cities in Europe. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 787 J. H. K. Law (9) The number sensitivity of modal indefinites Bu dui. Women zhi keyiD qu Lundun huo Bolin. no right we only can visit London or Berlin. ‘No, we can only go to London or Berlin.’ Mary’s response is felt to be felicitous in this context. Under the deontic modal, which requires total modal variation, the sentence in (8) expresses that all the cities in Europe that are in the domain are open options for their visit. This total modal variation inference can be challenged by a denial, as shown in (9). Context 2: Partial variation John and Mary knew that Peter went on a trip last week, but they did not know where he went. They were talking about where Peter could have gone. John suggested: Ta kenengE qu-le yi-ge Ouzhoude shenme chengshi. he possibly go-ASP one-CL European what city ‘He could have gone to an European city.’ (10) Mary knew that Peter stayed with a friend during his trip, and Peter only had two overseas friends, one in London and one in Berlin. So, she added: (11) #Bu dui. Ta zhi kenengE qu-le Lundun huo Bolin. not right he only possible go-ASP London or Berlin ‘No, he could only have gone to London or Berlin. This time, the response is felt to be infelicitous. Although modal variation is still perceived with (10), partial modal variation is enough for the epistemic environment. This means that not necessarily all European cities in the domain are taken into consideration. In this case, challenging total modal variation is not felicitous, because no total modal variation inference is generated. I argue that this is the reason why the response is odd.5 Although Mandarin wh-indefinites have modal variation inferences similar to German irgendein indefinites, they show a lesser known and intriguing interaction between the types of licensing modals and numeral classifiers in wh-phrases. In particular, as observed by Lin (1998), modal wh-indefinites under deontic modals must be accompanied by a numeral classifier (underlined), as evidenced by (12), whereas epistemic modals are compatible with wh-phrases 5A limitation of this diagnostic is that the contrast fails to hold between deontic and epistemic necessity modals. Using English as an example, we can see that (ib) is way more natural as a objection to (ia) than (iib) is to (iia): (i) a. b. A: John may read a book from the shelf. B: No. He may not read Harry Potter. (ii) a. b. A: John must read a book from the shelf. B: # No. He may not read Harry Potter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 788 J. H. K. Law The number sensitivity of modal indefinites with or without numeral classifiers, as illustrated by the well-formedness of (13).6 This generalization is true regardless of the modal force. (12) Zilu yaoD /keyiD kan *(yi-ben) shenme shu. Zilu must/can read one-CL what book ‘Zilu must/can read some book(s) (I don’t care which).’ (13) Zilu kendingE /kenengE kan-le (yi-ben) shenme shu. Zilu certainly/possibly read-ASP one-CL what book ‘Zilu possibly read some book(s) (I don’t know which).’ Represented configurationally, the classifier puzzle has the following form: (14) a. b. Epistemic modal . . . (NUM - CL) wh-phrase Deontic modal . . . *(NUM - CL) wh-phrase Combining the terminology used in the literature of bare noun phrases and modal indefinites, I refer to existential wh-indefinites without numeral classifiers as ‘bare wh-indefinites’. In contrast, I refer to existential wh-indefinites with numeral classifiers as ‘non-bare wh-indefinites’. In this paper, I develop an account for the classifier puzzle, couched primarily in the Alternatives and Exhaustification approach (Chierchia 2006, 2013, Liao 2011, a.o.), but incorporates insights from research on nominal reference (Link 1983, Krifka 1989, a.o.). Assuming that wh-indefinites are translated as existential quantifiers (Karttunen 1977), I argue that it is possible to tease apart bare and non-bare wh-indefinites in terms of their domain restrictions. The former are restricted by nominal predicates which denote sets containing atomic and plural individuals closed under sum formation. Following the classical terminology, we say that this type of predicates exhibit cumulative reference. The latter are restricted by nominal predicates whose denotations are not closed under sum formation. These predicates are known to exhibit quantized reference. The cumulativity-quantization distinction goes back at least to Link (1983) (who credits Quine 1960 for cumulativity) and is discussed in detail by Krifka (1989). In addition, I adopt an emerging view from the literature of modal variation that epistemic modals and deontic modals have different free choice potentials (see Aloni and Port to appear b, Fălăus 2014). Once this contrast is in place, we can see that wh-indefinites under epistemic modals express partial modal variation, while those under deontic modals express total modal variation. After incorporating the distinctions between cumulativity vs. quantization and between total vs. partial modal variation, an analysis based on Alternatives and Exhaustification reveals the source of the classifier puzzle. Specifically, deriving total modal variation with a modal indefinite restricted by a cumulative predicate results in a contradictory inference. This contradiction can be avoided in two ways, either by replacing a cumulative predicate (i.e., a bare 6 Some aspect markers on verbs that are available under epistemic modals are not so under deontic modals. Le is such an example. At this stage, it’s not clear to me whether this difference in aspect marking is related to the classifier puzzle. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 789 J. H. K. Law The number sensitivity of modal indefinites wh-indefinite) with a quantized predicate (i.e., a non-bare wh-indefinite), or by lowering the degree of modal variation. The former explains why numeral classifiers can help deontic modals ‘license’ wh-indefinites. The latter accounts for the optionality of numeral classifiers with whindefinites in epistemic modal environments. 3. An Alternatives and Exhaustification approach to modal variation 3.1. Key ingredients My proposal is based on the Alternatives and Exhaustification approach initiated by Chierchia (2006, 2013) and Fox (2007), and especially follows the extension of these studies to Mandarin wh-indefinites by Liao (2011). Following these studies, a modal indefinite is taken to be an implicature trigger with a bi-dimensional denotation. An exhaustification operator makes use of this bi-dimensional denotation, giving rise to a modal inference and conditioning the distribution of the modal indefinite. Concretely, a wh-indefinite in the form of shenme shu ‘what book’ is an generalized quantifier with a covert quantificational determiner ∃ (cf. Karttunen 1977), as shown in (15a). Following Hamblin (1973) and recent works on Alternative Semantics (e.g., Kratzer and Shimoyama 2002), I take this wh-NP to denote a set of alternative individual books. For instance, in a model with two books a and b, this wh-NP denotes the set {a, b}, as illustrated in (15b). (15) a. b. [DP ∃ [NP what book]] Jwhat bookK = {x | bookw (x)} = {a, b} Combining the existential operator with the wh-NP gives rise to the ordinary denotation of the wh-indefinite, which is a generalized existential quantifier, as shown in (16a). In addition, it has a special, focus-like denotation, which is a set of alternatives to the ordinary denotation (16b). (16) a. b. JDPK = λ Q.λ w.∃x[x ∈ Jwhat bookK ∧ Qw (x)] [ / JDPKA = {λ Q.λ w.∃x[x ∈ D′ ∧ Qw (x)] : D′ ⊂ Jwhat bookK ∧ D′ 6= 0} {λ Q.λ w.∀x[x ∈ Jwhat bookK → Qw (x)]} The alternative set consists of two different kinds of alternatives. The first one is domain alternatives. They are alternatives constructed from non-empty proper subsets of a quantificational domain, as shown in (17a). If the domain contributed by Jwhat bookK has two atomic books, as suggested by (15b), then the set of domain alternatives has two members, each a proper subset of this domain, as exemplified in (17b). (17) a. b. JDPKDA = {λ Q.λ w.∃x[x ∈ D′ ∧ Qw (x)] : D′ ⊂ Jwhat bookK ∧ D′ 6= 0} / {D′ : D′ ⊂ {a, b}} = {{a}, {b}} The second variety is the scalar alternative. Following Chierchia (2013), it is determined by replacing existential quantification in the ordinary denotation with universal quantification.7 7 Alonso-Ovalle (2008) has offered a different mechanism for deriving scalar alternatives, which crucially relies Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 790 J. H. K. Law The number sensitivity of modal indefinites These two types of alternatives have to be operated on by an alternatives-sensitive operator, often abbreviated as O (after only, or Exh (after exhaustification)). Based on Chierchia (2013), I offer the following lexical entry for O: (18) a. b. JO SK = λ w[JSK(w) ∧ ∀q ∈ JSKExh-Alt [q → λ w′ JSK(w′ ) ⊆ q]] JSKExh-Alt = {OIE (p) : p ∈ JSKA } This is often known as a ‘recursive’ exhaustification operator. When applying to a sentence S, it first applies pointwise to the set of alternatives of S, generating a set of pre-exhaustified alternatives, as done in (18b). Note that pre-exhaustification is subject to a condition called ‘Innocent Exclusion’ (Fox 2007, see also Sauerland 2004), which is defined below: (19) a. b. IE-ALTp = ∩{X ⊆ ALT : CONS(p∧¬∩X )∧∀q ∈ ALT [CONS(p∧¬∩X ∧¬q) → q ∈ X ]}, where CONS(p) = p is consistent OIE (p) = p ∧ ∀q ∈ ALT [(q ∈ IE-ALTp ∧ p 6⊆ q) → ¬q] The role of Innocent Exclusion in pre-exhaustification is to avoid excluding alternatives that may lead to contradictory inferences. Each pre-exhaustified alternative that is not entailed by the assertion is negated, helping to generates a strengthened assertion.8 With the mechanism to derive alternatives and the operator that operates on alternatives, this approach derives the ill-formedness of wh-indefinites when they are not in the scope of a modal as a logical contradiction. Since explaining the modal requirement is not the primary concern of this paper, I refer the reader to Liao (2011) and Chierchia (2013) for detailed discussions on this point. How modal variation is achieved can be found in Section 3.3. 3.2. Pluralities Since the seminal work of Link (1983), it has been well accepted into the semantic literature that (i) the domain of individuals (De ) consists of both atomic and plural individuals, (ii) plural individuals are sums of atomic individuals or sums of other plural individuals, and (iii) De is closed under sum formation. For example, a domain with three atomic individuals a, b, and c have the following mereological structure (⊕ is the sum formation operator; each line represents a partial order): on Alternative Semantics. 8 Two notes on the exhaustification operator. First, it is based on Chierchia (2013) but differs from it in having the exhaustification of scalar alternatives and the exhaustification of domain alternatives merged, for the purpose of simplification. Second, it differs from Fox’s (2007) exhaustification operator in being able to lead to contradictions. It is worth noting that whether an exhaustification operator with an innocent exclusion component should be contradiction-free is subject to debate. For instance, while Fox (2007) argues for the desirability of a contradiction-free exhaustification operator, Gajewski (2012) and Chierchia (2013) point out a few merits for allowing an exhaustification operator to derive contradictions. For Chierchia (2013), one of these merits is that it explains why modal indefinites have a restricted distribution in many languages: they are illegitimate precisely when contradictory inferences are induced. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 791 J. H. K. Law The number sensitivity of modal indefinites a⊕b⊕c a⊕b a⊕c b⊕c a b c Following Link (1983), Schwarzschild (1996) and many others, I assume that noun phrases with distinct number morphologies have different denotations. Take noun phrases in English as an example. A singular count noun like book denotes a subset of De , which contains only atomic books. For instance, if a and b in De are books, then the denotation of book is as shown in (20a). By contrast, a bare plural noun like books denotes as its extension a set involving the atomic books as well as their sums, as in (20b). (20) a. b. JbookK = {a, b} JbooksK = {a, b, a ⊕ b} According to Krifka (1989) (see also Quine 1960, Link 1983), these two types of predicates differ in terms of nominal reference. A predicate has cumulative reference iff, when it holds of two distinct individuals, it also holds of their sums (Krifka 1989:78, D12). Obviously, the bare plural books has cumulative reference, since the sum of any two books still belongs to the denotation of books. On the contrary, a predicate has quantized reference iff, when it holds of an individual, it doesn’t hold of any proper subparts thereof (Krifka 1989:78, D14). The singular count noun book has quantized reference, since the sum of a and b is not in the denotation of book. Likewise, in English predicates with numerals like two books are also quantized (despite being plural), because a collection of two units of two books results in four books, rather than two books. Chierchia (1998) argues that Mandarin bare nouns, which lack plural morphology, share the same type of denotation with English bare plurals. In other words, the denotation of shu ‘book’ is comparable to that of books (see also Yang 2001; Jiang 2012), ignoring the implicature associated with the plural morphology (Krifka 1989, Sauerland 2003). This view, which is rather standard in the current literature, meets the empirical requirement that shu may refer to one or more books in Mandarin. Hence, we can conclude that Mandarin bare nouns exhibit cumulative reference. To create quantized predicates, the use of a numeral classifier is needed. In this regard, the function of numeral classifiers is very similar to the function of numerals in English—they both create quantized predicates.9 It is easy to demonstrate that nouns with numeral classifiers are quantized: the sum of two units of yi-ben shu ‘one book’ is not yi-ben shu, but liang-ben shu ‘two books’. 9 In the neo-Carlsonian approach, bare nouns are kind terms and numeral classifiers are lexical predicativizers that help bring a kind term to its predicate use (Krifka 1995, Chierchia 1998, Yang 2001). This view is entirely compatible with the cumulativity-quantization distinction defended here, as long as we bring in the type-shifters that are part and parcel in the neo-Carlsonian approach. However, to avoid complicating the semantic composition, I omit the derivation of bare nouns from kind terms to predicates and assume that bare nouns start out as predicates. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 792 J. H. K. Law The number sensitivity of modal indefinites I argue that the cumulativity-quantization distinction can be extended to wh-indefinites. In particular, bare wh-indefinites are cumulative predicates while non-bare wh-indefinites are quantized predicates. Recall that a wh-phrase provides the quantificational domain for a covert existential quantifier (see Section 3.1). As shown in (21), the existential determiner quantifies over individuals restricted by books, which is cumulative. Assume that there are two atomic books, a and b. The denotation of shenme shu ‘what books’ is a set of alternative books closed under sum formation, as illustrated in (21a). The bi-dimensional denotation of the wh-indefinite is derived as (21b) and (21c). (21) a. b. c. Jwhat booksK = {x | booksw (x)} = {a, b, a ⊕ b} J∃ what booksK = λ Q.λ w.∃x[x ∈ Jwhat booksK ∧ Qw (x)] [ J∃ what booksKA = {λ Q.λ w.∃x[x ∈ D′ ∧ Qw (x)] : D′ ⊂ Jwhat booksK} {λ Q.λ w.∀x[x ∈ Jwhat booksK → Qw (x)]} After putting the bare wh-indefinite in a sentential context, the bi-dimensional meaning in (22) is obtained (the propositional correlates of the individuals are set in boldface). The underlined parts represent the extra contribution of the cumulative nominal predicate after plurality is brought into the picture. (22) a. b. JZilu read what booksK = a ∨ b ∨ a ⊕ b JZilu read what booksKA = {a ∨ b, a, b, a ⊕ b, a ∧ b} Note that the assertion in (22a) has an additional disjunct, contributed by the plural individual in the domain (21a). Since the domain alternatives are derived from the proper subsets of the domain, the addition of the plural individual to the domain has non-trivial effects on the set of domain alternatives. Specifically, there is a weakest alternative, i.e., a ∨ b, which is truth-conditionally equivalent to the assertion a ∨ b ∨ a ⊕ b. In addition, there is a strongest alternative, in this case a ⊕ b, which is truth-conditionally equivalent to the scalar alternative a ∧ b, when lexical distributivity is assumed. Throughout this paper, I assume lexical distributivity and hence the equivalence of the maximal alternative and the scalar alternative. Whenever the maximal alternative is present, I suppress the scalar alternative. Now, I turn to non-bare wh-indefinites, i.e., those with numeral classifiers. Like bare existential wh-phrases, a covert determiner ∃ is still posited for this type of expression. The structure of yi-ben shenme shu ‘one-CL what books’ is (23). (23) [DP ∃ [NP one-CL what books]] Just like (21a), shenme shu ‘what books’ denotes a set of alternative individual books including both atomic and plural individuals. This is repeated in (24a). A numeral classifier serves as a function that can select a subset from a set. The denotation of the numeral classifier under consideration is formulated as in (24b). It takes the set denoted by what books as an argument and returns a set whose only members are those in Jwhat booksK and have one atomic part.10 As shown in (24c), the denotation of NP essentially excludes the maximal individual from 10 Following the notation in Landman (2004), the function ATOM maps an individual to its atomic parts. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 793 J. H. K. Law The number sensitivity of modal indefinites Jwhat booksK, giving rise to a quantized predicate. Finally, the denotation of DP is represented in (24d) and the set of its alternatives is shown in (24e).11 (24) a. b. c. d. e. Jwhat booksK = {x | booksw (x)} = {a, b, a ⊕ b} Jone-CL K = λ D{x | x ∈ D ∧ |ATOM (x)| = 1} JNPK = {x | x ∈ Jwhat booksK ∧ |ATOM (x)| = 1} JDPK = λ Q.λ w.∃x[x ∈ Jwhat booksK ∧ |ATOM (x)| = 1 ∧ Q(x)] [ JDPKA = {λ Q.λ w∃x[x ∈ D′ ∧ |ATOM (x)| = 1 ∧ Qw (x)] : D′ ⊂ Jwhat booksK} {λ Q.λ w∀x[x ∈ Jwhat booksK ∧ |ATOM (x)| = 1 → Qw (x)]} The difference between this example and the case with a bare wh-indefinite is most clearly seen in a sentential context. Consider a sentence with a non-bare wh-indefinite: (25) a. b. JZilu read one-CL what booksK = a ∨ b JZilu read one-CL what booksKA = {a, b, a ∧ b} A noticeable difference is that the maximal individual a ⊕ b is no longer part of the ordinary denotation. Relatedly, it is also absent in the set of alternatives. 3.3. Deontic modals: contradiction and repairing This section answers the first part of the classifier puzzle, namely, why deontic modals militate against bare wh-indefinites. Consider the following ill-formed sentence: (26) *Zilu keyiD kan shenme shu. Zilu may read what book ‘Zilu may read some book(s) (I don’t care which).’ In the Alternatives and Exhaustification approach, the interaction of epistemic modals and modal indefinites is captured by recursively applying the exhaustification operator O (Fox 2007, Liao 2011, Chierchia 2013). Therefore, the LF structure of (27) can be represented as follows: (27) *[IP4 O [IP3 mayD [IP2 [DP ∃ [what books]]1 [IP1 Zilu [VP read t1 ] ] ] ] ] The bi-dimensional denotation of IP2 is equivalent to example (22), i.e., (28). Then, the denotation of IP3 incorporates the contribution of the modal ([⋄] is a shorthand for a deontic possibility modal), as illustrated in (29). (28) 11 I a. b. JIP2K = a ∨ b ∨ a ⊕ b JIP2KA = {a ∨ b, a, b, a ⊕ b, a ∧ b ∧ a ⊕ b} = {a, b, a ∨ b, a ⊕ b} have ignored the potential scalar alternatives associated with the numeral. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 794 J. H. K. Law (29) The number sensitivity of modal indefinites a. b. JIP3K = [⋄](a ∨ b ∨ a ⊕ b) JIP3KA = {[⋄](a ∨ b), [⋄]a, [⋄]b, [⋄](a ⊕ b)} Recall that combining O and IP3 requires the affirmation of the assertion of IP3 and the negation of all the pre-exhaustified alternatives of IP3. The assertion of IP3 is given in (30a) and the set of pre-exhaustified alternatives is given in (30b) and elaborated in (30bi)–(30biv). Note in (30biv) that pre-exhaustifying the maximal alternative returns itself, as this alternative is the strongest member in the set. (30) a. b. JIP3K = [⋄](a ∨ b ∨ a ⊕ b) JIP3KExh-Alt = {O[⋄](a ∨ b), O[⋄]a, O[⋄]b, O[⋄]a ⊕ b} (i) O[⋄](a ∨ b) = [⋄](a ∨ b) ∧ ¬[⋄]a ⊕ b (ii) O[⋄]a = [⋄]a ∧ ¬[⋄]b ∧ ¬[⋄]a ⊕ b (iii) O[⋄]b = [⋄]b ∧ ¬[⋄]a ∧ ¬[⋄]a ⊕ b (iv) O[⋄]a ⊕ b = [⋄]a ⊕ b When O combines with IP3 to give rise to the meaning of IP4, an undesirable inference is generated: (31) JIP4K = [⋄](a ∨ b ∨ a ⊕ b) ∧ [⋄]a → ([⋄]b ∨ ⋄a ⊕ b) ∧ [⋄]b → ([⋄]a ∨ [⋄]a ⊕ b) {z } | {z } | ¬O[⋄]a ∧ [⋄](a ∨ b) → [⋄]a ⊕ b ∧ ¬[⋄]a ⊕ b | {z } | {z } ¬O[⋄](a∨b) ¬O[⋄]b ¬O[⋄]a⊕b It is undesirable as the combination of the underlined conjuncts, derived from the weakest and the strongest alternative, leads to the following inference, which contradicts the assertion: (32) ¬[⋄]a ⊕ b ∧ ([⋄](a ∨ b) → [⋄]a ⊕ b) = ¬[⋄]a ⊕ b ∧ ¬[⋄](a ∨ b) The contradiction can be repaired by adding a numeral classifier to the wh-phrase. In other words, replacing the bare wh-indefinite in (26) with a non-bare one, as shown in (33), can avoid the undesirable result in (32). (33) Zilu keyiD kan yi-ben shenme shu. Zilu may read one-CL what book ‘Zilu may read some book (I don’t care which).’ As exemplified in (24), repeated in (34), the denotation of the wh-phrase remains unchanged, denoting a set of books closed under sum formation, and the numeral classifier is a subset selection function, applying to the wh-denotation and collecting those members with only one atomic part. The resulting denotation (34c) is the set {a, b}, which is not cumulative. After applying the existential closure operator, the bi-dimensional denotation of the DP containing one-CL what books is given in (34d) and (34e). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 795 J. H. K. Law (34) The number sensitivity of modal indefinites a. b. c. d. e. Jwhat booksK = {x | booksw (x)} = {a, b, a ⊕ b} Jone-CL K = λ D{x | x ∈ D ∧ |ATOM (x)| = 1} JNPK = {x | x ∈ Jwhat booksK ∧ |ATOM (x)| = 1} = {a, b} JDPK = λ Q.λ w.∃x[x ∈ Jwhat booksK ∧ |ATOM (x)| = 1 ∧ Q(x)] [ JDPKA = {λ Q.λ w∃x[x ∈ D′ ∧ |ATOM (x)| = 1 ∧ Qw (x)] : D′ ⊂ Jwhat booksK} {λ Q.λ w∀x[x ∈ Jwhat booksK ∧ |ATOM (x)| = 1 → Qw (x)]} Now, let us consider the derivation of (33), whose LF is represented in (35). (35) [IP4 O[IP3 may [IP2 [one-CL what book]1 [IP1 Zilu[VP read t1 ]]]]] After combining DP pointwise with IP1, we can get a bi-dimensional propositional denotation, as in (36a) and (36b). Adding the deontic possibility modal results in (36c) and (36d). (36) a. b. c. d. JIP2K = a ∨ b JIP2KA = {a, b, a ∧ b} JIP3K = [⋄](a ∨ b) JIP3KA = {[⋄]a, [⋄]b, [⋄](a ∧ b)} Recursive exhaustification applies to the IP3, generating and then in turn negating the preexhaustified alternatives in (37a), finally deriving the inference in (37b). (37) a. JIP3KExh-Alt = {O[⋄]a, O[⋄]b, O[⋄](a ∧ b)} Assertion b. Scalar implicature MV implicature z }| { z }| { z }| { JIP4K = [⋄](a ∨ b) ∧ ¬[⋄](a ∧ b) ∧ [⋄] a → [⋄]b ∧ ⋄b → [⋄]a | {z } | {z } | {z } ¬O[⋄](a∧b) ¬O[⋄]a ¬O[⋄]b (37) does not result in any contradiction. In addition, it encodes total modal variation, namely, that both a and b are permitted, as long as they are permitted in different worlds. 3.4. Epistemic modals: partial variation This section is devoted to the account of why epistemic modals are compatible with bare whindefinites as well as non-bare ones. Let us begin with bare wh-indefinites. Consider the following sentence, whose LF is given in (39). (38) Zilu kenengE kan-le shenme shu. Zilu possibly read-ASP what book ‘Zilu possibly read some book(s). (I don’t know which).’ (39) [IP4 O [IP3 possibly [IP2 [DP ∃ [what books]]1 [IP1 Zilu [VP read t1] ] ] ] ] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 796 J. H. K. Law The number sensitivity of modal indefinites If we derived the denotation of IP2 in the same way as IP2 in (27), we would get the same contradiction. However, this undesirable result can be avoided if the modal variation property of epistemic modals is taken into consideration. Specifically, as shown in Section 1, epistemic modals require partial modal variation, whose definition is repeated in (40). (40) Partial (modal) variation: ∃x∃y(⋄φ (x) ∧ ⋄φ (y) ∧ x 6= y) More than one (but not necessarily all) alternatives in the relevant domain qualify as a possible option. Therefore, even though we only consider singleton subdomains generated by wh-indefinites, as defined in (41), partial modal variation is still achieved. (41) a. b. c. Sing. J∃ [what books]]KDA = {λ Q.λ w.∃x[x ∈ D′ ∧ Qw (x)] : D′ ⊂ Jwhat booksK ∧ D′ is a singleton set} Jwhat booksK = {a, b, a⊕b} {D′ } = {{a}, {b}, {a⊕b}} Since the set {a, b} does not count as a singleton subdomain, it plays no role in the derivation of singleton domain alternatives. As a consequence, no weakest alternative is created, despite the presence of domain cumulativity. The denotations of IP2 and IP3 in (39) can be derived as below (⋄ stands for epistemic possibility modals): (42) a. b. c. d. JIP2K = a ∨ b ∨ a ⊕ b JIP2KA = {a, b, a ⊕ b} JIP3K = ⋄(a ∨ b ∨ a ⊕ b) JIP3KA = {⋄a, ⋄b, ⋄a ⊕ b} Recursive exhaustification makes use of the pre-exhaustified alternatives of IP3, as given in (43a). After affirming the assertion of IP3 and negating all the pre-exhaustified alternatives, the modal variation implicature is derived, i.e., MV implicature in (43b). (43) a. JIP3KExh-Alt = {O ⋄ a, O ⋄ b} Assertion b. Scalar implicature MV implicature z }| { z }| { z }| { JIP4K = (⋄(a ∨ b ∨ a ⊕ b) ∧ ¬ ⋄ (a ⊕ b) ∧ ⋄a → (⋄b ∨ ⋄a ⊕ b) ∧ ⋄b → (⋄a ∨ ⋄a ⊕ b) {z } | {z } | Assertion Scalar implicature ¬O1 ⋄a MV implicature ¬O1 ⋄b z }| { z }| { z }| { = ⋄(a ∨ b ∨ a ⊕ b) ∧ ¬ ⋄ (a ⊕ b) ∧ ⋄a ↔ ⋄b As a result, we derive a modal variation effect that holds true of a and b, namely, a subset of the the individuals in the domain. This is essentially how partial modal variation is defined, according to studies like Alonso-Ovalle and Menéndez-Benito (2010), Chierchia (2013) and Fălăus (2014). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 797 J. H. K. Law The number sensitivity of modal indefinites Under the scope of epistemic modals, non-bare wh-indefinites do not lead to a contradiction, either. Take as an example the following sentence, whose LF structure is represented as (45). (44) Zilu kenengE kan-le yi-ben shenme shu. Zilu possibly read-ASP one-CL what book ‘Zilu possibly read some book. (I don’t know which)’ (45) [IP4 O[IP3 possibly [IP2 [one-CL what book]1 [IP1Zilu[VP read t1]]]]] Similar to what we have discussed in the last section, the numeral classifier excludes the maximal individual from the domain given by the wh-phrase, as shown by (24) and repeated in (46a). Hence, the denotations of IP2 are derived as (46b) and (46c) (see also (25)). (46) a. b. c. Jone-CL what booksK = {a, b} JIP2K = a ∨ b JIP2KA = {a, b, a ∧ b} Adding the epistemic modal results in (47), which is the denotation of IP3. Exhaustification makes use of the denotation of IP3 and the set of pre-exhaustified alternatives in (47b). (47) a. b. JIP3K = ⋄(a ∨ b) JIP3KExh-Alt = {O ⋄ a, O ⋄ b, O ⋄ (a ∧ b)} Finally, exhaustification affirms the assertion of IP3 and negates all the pre-exhaustified alternatives not entailed by the assertion, generating the following inference, which is free of contradiction: Assertion (48) Scalar implicature MV implicature z }| { z }| { z }| { JIP4K = ⋄(a ∨ b) ∧ ¬ ⋄ (a ∧ b) ∧ ⋄ |a → ⋄b ∧ ⋄b → ⋄a {z } | {z } | {z } ¬O⋄(a∧b) ¬O⋄a ¬O⋄b 4. Conclusion In this study, I have argued that the interaction between modal flavors and the number morphology of existential wh-indefinites in Mandarin should be understood along the lines of Alternatives and Exhaustification, as long as nominal references are allowed to play a role in structuring the domain of alternatives. In particular, total modal variation, facilitated by deontic modals, is shown to be only compatible with existential wh-indefinites with quantized reference. This is why numeral classifiers are required in existential wh-indefinites in a deontic environment. On the other hand, partial modal variation, allowed by epistemic modals, is shown to be compatible with both existential wh-indefinites with quantized reference and cumulative reference, hence explaining why numeral classifiers are optional with existential wh-indefinites in an epistemic environment. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 798 J. H. K. Law The number sensitivity of modal indefinites References Aloni, M. and M. Franke (2013). On the free choice potential of epistemic and deontic modals. In I. Caponigro and C. Cecchetto (Eds.), From Grammar to Meaning: The Spontaneous Logicality of Language, pp. 108–138. Oxford University Press. Aloni, M. and A. Port (2010). Epistemic indefinites crosslinguistically. In L. Fainleib, N. LaCara, and Y. Park (Eds.), Proceedings of the North East Linguistic Society 41. Alonso-Ovalle, L. (2008). Alternatives in the disjunctive antecedents problem. In C. B. Chang and H. H. J. (Eds.), Proceedings of the 26th West Coast Conference on Formal Linguistics, pp. 42–50. Cascadilla Proceedings Project. Alonso-Ovalle, L. and P. Menéndez-Benito (2010). Modal indefinites. Natural Language Semantics 18(1), 1–31. Chierchia, G. (1998). Reference to kinds across languages. Natural Language Semantics 6(4), 339–405. Chierchia, G. (2006). Broaden your views: Implicatures of domain widening and the “logicality” of language. Linguistic Inquiry 37(4), 535–590. Chierchia, G. (2013). Logic in Grammar: Polarity, Free Choice, and Intervention. Oxford University Press. Dayal, V. (1998). Any as inherently modal. Linguistics and Philosophy 21, 433–476. Fox, D. (2007). Free choice and the theory of scalar implicatures. In U. Sauerland and P. Statava (Eds.), Presupposition and Implicature in Compositional Semantics, pp. 71–120. Palgrave Macmillan. Fălăus, A. (2014). (Partially) free choice of alternatives. Linguistics and Philosophy 37(2), 121–173. Gajewski, J. (2012). Innocent exclusion is not contradiction free. Ms. Hamblin, C. (1973). Questions in Montague grammar. Foundations of Language 10(1), 41–53. Jiang, L. (2012). Nominal Arguments and Language Variation. Ph. D. thesis, Harvard University. Kadmon, N. and F. Landman (1993). Any. Linguistics and Philosophy 16(4), 353–422. Karttunen, L. (1977). Syntax and semantics of questions. Linguistics and Philosophy 1(1), 3–44. Kratzer, A. and J. Shimoyama (2002). Indeterminate pronouns: The view from Japanese. In Y. Otsu (Ed.), Proceedings of the Third Tokyo Conference on Psycholinguistics, pp. 1–25. Hituzi Syobo. Krifka, M. (1989). Nominal reference, temporal constitution and quantification in event semantics. In R. Bartsch, J. Van Benthem, and P. van Emde Boas (Eds.), Semantics and Contextual Expression, pp. 75–115. Foris. Krifka, M. (1995). Common nouns: A contrastive analysis of English and Chinese. In The Generic Book. Krifka, M. (1998). The origins of telicity. In S. Rothstein (Ed.), Events and Grammar, pp. 197–236. Kluwer Academic Publishers. Landman, F. (2004). Indefinites and the Type of Sets. Blackwell Publishing. Li, A. Y.-H. (1992). Indefinite Wh in Mandarin Chinese. Journal of East Asian Linguistics 1(2), 125–155. Liao, H.-C. (2011). Alternatives and Exhaustification: Non-interrogative Uses of Chinese WhProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 799 J. H. K. Law The number sensitivity of modal indefinites words. Ph. D. thesis, Harvard University. Lin, J.-W. (1998). On existential polarity wh-phrases in Chinese. Journal of East Asian Linguistics 7(3), 219–255. Link, G. (1983). The logical analysis of plurals and mass terms: A lattice-theoretical approach. In R. Bauerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use and Interpretation of Language. De Gruyter. Quine, W. V. O. (1960). Word and Object. MIT Press. Sauerland, U. (2003). A new semantics for number. In Proceedings of SALT 13, pp. 258–275. CLC Publications. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy 27(3), 367–391. Schwarzschild, R. (1996). Pluralities. Kluwer Academic Publishers. Yang, R. (2001). Common Nouns, Classifiers, and Quantification in Chinese. Ph. D. thesis, Rutgers University. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 800 Event-related relative measurement1 Haoze LI — New York University Abstract. This paper is concerned with relative measurement, which is expressed by percentage nouns and fractions. It has been observed that in some languages a sentence with relative measurement is ambiguous between two readings. I argue that these two readings involve two types of measurement—individual-related measurement and event-related measurement. I also provide a compositional analysis for the ambiguity of relative measurement. My analysis is able to capture many intriguing contrasts between the two readings of relative measurement, including those related to counting recycled individuals, compatibility with verbal affixes, structural distribution and scope. Keywords: Relative measurement, measure function, event-individual pairs, event semantics 1. Introduction One of the important properties of natural language is its capacity to express measurement. There are two kinds of measurement: absolute measurement, which is expressed by words such as liter and inch, and relative measurement, which is expressed by a class of measure items such as proportional nouns like percent and fractions like thirds. The former type of measurement has received a lot of attention in the semantic literature, while the latter has not until a series of works by Sauerland and Ahn (Sauerland 2014; Ahn and Sauerland 2015a, b, 2017). Unlike absolute measurement, relative measurement concerns the relation between two amounts. For example, in (1), relative measurement is expressed by the relative measure phrase, which consists of the relative measure item 30% and the nominal phrase the locals. This sentence expresses that the local employees at Lenovo made up 30% of all the locals given in the context. (1) Lenovo hired [30% of the locals]. Beyond the basic pattern, Ahn and Sauerland notice that English has another relative measurement construction, as exemplified in (2). Structurally, this sentence differs from (1) in not having the partitive of and the definite determiner, while semantically, it targets a different quantity relation. What this sentence means is that the local employees at Lenovo made up 30% of all the employees at Lenovo. It can be paraphrased as ‘30% of the people hired by Lenovo were locals.’ (2) Lenovo hired 30% locals. In some languages, like Mandarin, these two interpretations arise from a single surface structure, as shown in (3). 1I would like to thank Adina Williams, Anna Szabolcsi, Chris Barker, Dorothy Ahn, Dylan Bumford, Lucas Champollion, Jeff Lin, Jess Law, Qiongpeng Luo, Simon Charlow, Uli Sauerland and Yu’an Yang for their generous comments on various versions of this work. I also thank the audiences at SuB 21. As usual, all inadequacies are mine. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 801 H. Li (3) Event-related relative measurement Lianxiang gu-le 30% de bendiren Lenovo hire-ASP 30% DE locals a. ‘Lenovo hired 30% of the locals.’ (NP-internal) ⇒ |{x : locals(x) ∧ Lenovo-hired(x)}| = 30% × |{y : locals(y)}| b. ‘Lenovo hired 30% locals’ (NP-external) ⇒ |{x : locals(x) ∧ Lenovo-hired(x)}| = 30% × |{y : Lenovo hired(y)}| Here, 30% de bendiren ‘30% locals’ is a noun phrase. In reading (3a), the amount of local employees at Lenovo is measured relative to the set of all locals, which is provided by the NP complement. I call it the ‘NP-internal’ reading. In reading (3b), the amount of local employees at Lenovo is measured relative to the set of all the people hired by Lenovo, which is provided by the NP-external material, i.e., Lianxiang gu-le ‘Lenovo hired.’ I call it the ‘NP-external’ reading. Intuitively, the NP-internal reading in (3a) expresses a quantity relation between two sets of locals—the set of locals hired by Lenovo and the set of all locals; whereas the NP-external reading in (3b) expresses a quantity relation between two sets of event participants—the set of theme participants of some hiring events who are locals and the set of all theme participants of some hiring events. Following this intuition, I argue that the NP-internal reading differs from the NP-external reading essentially in their domains of measurement: the former involves measurement of individuals, while the latter involves measurement of event-individual pairs, whose ontological status is considered to be stages of individuals (Barker 1999, 2010). (For example, if John dances twice, he participates in two non-overlapping dancing events e1 and e2 . The event-individual pairs he1 , Johni and he2 , Johni stand for two stages of John). This claim is based on the observation that although the two readings seem to measure individuals, only the NP-external reading shows event-related properties (Section 2). I propose that there are two kinds of relative measure heads: one implements measurement on a domain of individuals, while another encodes measurement on a domain of event-individual pairs. These two relative measure heads essentially give rise to the NP-internal reading and the NP-external reading (Section 3). I also show that these two readings can be compositionally derived (Section 3.2). My analysis is able to account for a series of contrasts between the NP-internal reading and the NP-external reading, which involve a structural constraint on the NP-external reading (Section 4), the monotonicity condition of measure functions (Section 5) and scope patterns of relative measure phrases (Section 6). Finally, I compare my analysis with the focus mapping approach to relative measurement proposed by Ahn and Sauerland (Sauerland 2014; Ahn and Sauerland 2015a, b) (Section 7). 2. Counting recycled individuals Let’s consider the following scenario. Town A has a population of 10,000, among which 2,000 are children. In the past quarter, a clinic in the town had 5,000 visits by 2,000 different patients. Among the 5,000 visits there were 1,500 visits by 500 different children. In the quarterly business meeting, if the administrator of the clinic states (4), the statement is inaccurate. Instead, if she states (5), the statement is accurate. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 802 H. Li (4) (5) Event-related relative measurement Women zhe yi jidu shouzhi-le quanzheng 30% de ertong. we this one quarter treat-ASP whole.town 30% DE children ‘We treated 30% of the children in the town this quarter.’ (NP-internal) Women zhe yi jidu shouzhi-le 30% de ertong. we this one quarter treat-ASP 30% DE children a. ‘We treated 30% of the children (in the town) this quarter.’ b. ‘We treated 30% children this quarter.’ (NP-internal) (NP-external) Due to the explicit mentioning of the town, which helps to fix the domain of the children, (4) only has an NP-internal reading. It is clear why (4) is false: the number of children treated in the clinic is 500 but the total child population in the town is 2,000, so 30% is not an accurate proportion to report. (5) is ambiguous between an NP-internal reading and an NP-external reading. As we know that the NP-internal reading is false, the truth judgment must come from the NP-external reading. However, only under a specific circumstance may the NP-external reading give rise to a true statement—a single individual can be counted more than once if she makes more than one visit. To see this, note that if we merely count the number of child patients (i.e., 500) relative to the number of total patients (i.e., 2,000), we get 25% instead of 30%. However, if we count the number of child visits (i.e., 1,500) relative to the number of total visits (i.e., 5,000), we get 30%. In short, the truth of (5) tells us that the NP-external reading allows counting recycled individuals. The possibility of counting recycled individuals should remind us of Krifka’s (1990) famous example in (6). This sentence is argued to have two interpretations. The first one is an objectrelated interpretation and the second one is an event-related interpretation, as paraphrased in (6a) and (6b), respectively. If a certain ship passed through the lock twice, it is counted once in the first reading and twice in the second reading. (6) Four thousand ships passed through the lock last night. a. There were 4000 ships such that they passed through the lock. (Object-related) b. There were 4000 events such that in each of them a ship passed through the lock. (Event-related) Since Krifka (1990), various proposals have been defended to account for the ambiguity of (6), such as Moore (1994), Doetjes and Honcoop (1997) and Barker (1999). These proposals share the core idea that recycled individuals are counted by relation to events. The fact that the NPexternal reading allows the counting of recycled individuals suggests that this reading should, too, be event-related. To see that counting recycled individuals is indeed readily compatible with the NP-external reading of relative measurement and hence is not an artifact of Scenario 1, it is worthwhile to consider more examples: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 803 H. Li (7) (8) Event-related relative measurement Women jiudian qunian jiedai-le 30% de gaoguan. we hotel last.year serve-ASP 30% DE high-ranking.officials a. ‘Last year, our hotel served 30% of the high-ranking officials. b. ‘Last year, our hotel served 30% high-ranking officials.’ (NP-internal) (NP-external) Women tushuguan qunian jiechu-le 70% de xiaoshuo. we library last.year lend.out-ASP 70% DE novel a. ‘Last year, our library lent out 70% of the novels.’ b. ‘Last year, our library lent out 70% novels.’ (NP-internal) (NP-external) In these sentences, the identities of the individuals being talked about are irrelevant and easy to ignore in the NP-external reading. In (7), if some high-ranking officials stayed in our hotel twice, each of them could only be counted once in the NP-internal reading, but each of them was counted twice in the NP-external reading. In (8), the same contrast can be observed between the NP-internal reading and the NP-external reading, if some novels were lent out more than once. 3. Proposal In this paper, I propose that relative measurement generally measures the size of one set relative to another, but the members of the sets can be individual objects or event-related stages of individuals. Measuring individuals yields the NP-internal reading, while measuring eventrelated stages results in the NP-external reading. Ontologically, an event-related stage can be understood as an instance of an individual object that participates in a specific event (see also Barker 1999, 2010). Following Barker (1999), I model event-related stages as eventindividual pairs he, xi associating an individual x with an event e. As a first approximation, the two readings of (9) can be represented as (9a) and (9b). (9) Lianxiang gu-le 30% de bendiren. Lenovo hire-ASP 30% DE local a. NP-internal: |{x : locals(x) ∧ Lenovo-hired(x)}| = 30% × |{y : locals(y)}| (The individuals x such that x are locals and hired by Lenovo made up 30% of the locals) b. NP-external: |{he, xi : locals(x) ∧ Lenovo-hired(e, x)}| = 30% × |{he0 , x0 i : Lenovo-hired(e0 , x0 )}| (The event-related stages he, xi such that x are locals and were hired by Lenovo in e made up 30% of the event-related stages he0 , x0 i such that x0 were hired by Lenovo in e0 ) In the following subsections, I lay out the formal details of my proposal, showing how the two readings are compositionally derived. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 804 H. Li Event-related relative measurement 3.1. Two relative measure heads I propose that a relative measure item is decomposed into two parts—a percentage number and a relative measure head (RM). The former simply denotes a number of type d and the latter encodes measurement, which can be individual-related or event-related. I define the individualrelated RM (RMI ) and the event-related RM (RME ) as follows: (10) (11)    P(x0 ) ∧ 0 0 JRMI K = λ nd λ Pet λ Qet .∃x.P(x)∧Q(x)∧card(x) = n×max λ n ∃x card(x0 ) = n0 JRME K = λ n00d λ Pet λ The,he,vtii λ ye λ e00v .MXT(e00 ) ∧ ∃he, xi.e v e00 ∧ T (e, y, x) ∧ P(x) ∧ card0λ zλ e000 .T (e000 ,y,z) (e, x) =   0  e v e00 ∧ R(e0 , y, x0 ) ∧ 0 0 0 n × max λ n ∃he , x i card0λ zλ e000 .T (e000 ,y,z) (e0 , x0 ) = n0 A note on notation: max and MXT stand for a maximal operator on degrees and a maximal operator on events, respectively. The former takes a set of degrees and returns the biggest element in this set, while the latter applies to maximal events consisting of the sum of all smaller events within a given time interval. They are defined as follows: (12) a. b. max(D) := ιn[D(n) ∧ ∀n0 [D(n0 ) → n0 ≤ n]] L MXT(e) := ∃t.e = (λ e0 [τ(e0 ) v t]) (Krifka 1989) In (10), RMI introduces a measure function card (cardinality) on the domain of individuals. In this paper, I use the term measure function to denote a mapping from a class of entities to a degree scale that preserves an ordering relation, such as “be taller than” or “be heavier than.” Examples of typical measure functions are height, weight, and temperature. Following Krifka (1998), we define card as a function mapping individual entities to natural numbers. In (11), RME introduces a measure function card0 on the domain of event-individual pairs. In this study, I follow Doetjes and Honcoop’s (1997) definition of measure functions on eventindividual pairs. Adopting the algebraic semantic approach (Krifka 1989, 1990), Doetjes and Honcoop identify the domain of event-individual pairs as a join semi-lattice on the basis of the join semi-lattice structure of the domain of events. Then, the partial ordering on ordered event-individual pairs can be defined as (13) in terms of the partial ordering of events and the partial ordering of individuals. (13) a. b. he, xi v he0 , x0 i ↔ he, xi ⊕ he0 , x0 i = he0 , x0 i he, xi ⊕ he0 , x0 i = he00 , x00 i ↔ e ⊕ e0 = e00 ∧ x ⊕ x0 = x00 Based on this algebraic structure, they implement Krifka’s (1990) proposal on the measurement of events. The main idea that their implementation relies on is that the measure function card0 on event-individual pairs can be standardized with respect to its corresponding measure function card on individuals. Take children-treating events as an example. If every child is treated once, measuring the he, xi pairs such that x is a child and x is treated in e yields the same value Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 805 H. Li Event-related relative measurement as measuring children that are treated. In this case, different children are involved in different events. As a consequence, if there are n different children, there are the same number of pairs of treating events and children. However, there is a problem: if some children were treated more than once, the equivalence of the pair measurement and the object measurement does not hold. In this case, the relation on treating children has the aspectual property of iterativity as defined below (Krifka 1989; Doetjes and Honcoop 1997): (14) Definition (Iterativity (ITER)) For any event e, object x and relation R, ITER(e, x, R) ↔ R(e, x) ∧ ∃e0 ∃e00 ∃x0 [e0 v e ∧ e00 v e ∧ e0 6= e00 ∧ x0 v x ∧ R(e0 , x0 ) ∧ R(e00 , x0 )] (a relation R is iterative with respect to an event e and an object x just in case there is a part of x which is involved in different parts of e, as specified by R) It does not mean that standardizing one measure function with respect to another cannot work in this case. On the basis of the fact that every iterative event can be partitioned into noniterative subevents, Krifka (1990) proposes that an iterative event e can be correctly counted by dividing e into non-iterative subevents, applying a measure function on events to each noniterative subevent, and adding all the values of the non-iterative subevents together. Following the spirit of this proposal, Doetjes and Honcoop define a measure function on he, xi in terms of its corresponding measure function on objects. Based on their study, I define the measure function on event-individual pairs as (15). (15) Let µ be a measure function and R be an event-individual relation. Then the object induced event-individual pair measure function µR0 can be defined as follows: µR0 = the event-individual pair measure function µ 0 with the smallest domain such that a. Standardization For any event e, individual x and relation R, [¬ITER(e, x, R) ∧ R(e, x)] → [µ 0 (e, x) = n ↔ µ(x) = n] b. Generalization For any events e and e0 , and any individuals x and x0 , [¬he, xi ◦ he0 , x0 i ∧ µ 0 (e, x) = n ∧ µ 0 (e0 , x0 ) = n0 ] → [µ 0 (he, xi ⊕ he0 , x0 i) = n + n0 ] Here, ◦ stands for ‘overlapping’ and he, xi ◦ he0 , x0 i ↔ e ◦ e0 ∧ x ◦ x0 Consider a toy scenario. Three children C1 , C2 and C3 are involved in three treating events e1 , e2 and e3 , respectively. Additionally, C1 is treated a second time, so it is also involved in a fourth treating event e4 . Therefore, the pair he1 ⊕ e2 ⊕ e3 ⊕ e4 , C1 ⊕C2 ⊕C3 i is in the relation of children-treating. Standardization can partition the pair into two parts he1 ⊕ e2 ⊕ e3 , C1 ⊕ C2 ⊕C3 i and he4 ,C1 i. Then, the measure function µ 0 yields the value 3 for he1 ⊕ e2 ⊕ e3 , C1 ⊕ C2 ⊕ C3 i, and the value 1 for he4 ,C1 i. Generalization adds up the two values to 4. The result is as if C1 is counted twice. Thus, µ 0 provides an explicit way to count recycled individuals described in Section 2. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 806 H. Li Event-related relative measurement 3.2. Composition Recall example (3) in the first section, repeated here as (16). According to the proposal discussed in the previous section, the relative measure item 30% consists of a percentage number and a null relative measure head, which can be RMI or RME . (16) Lianxiang gu-le 30% de bendiren Lenovo hire-ASP 30% DE locals a. ‘Lenovo hired 30% of the locals.’ b. ‘Lenovo hired 30% locals.’ (NP-internal) (NP-external) I define the relevant lexical entries in the following table: Item Lianxiang ‘Lenovo’ 30% bendiren ‘locals’ de EC gu ‘hire’ RMI RME Translation Type Lenovo e 30% d λ x.*local(x) et λ x.x hα, αi λV ∃e.V (e) hvt,ti λ xλ yλ e.*hire(e) ∧ *th(e) = x ∧ *ag(e) = y he, he, vtii see (10) hd, het, het,tiii see (11) hd, het, hhe, he,vtii, he,vtiiii In event semantics, a transitive verb is assumed to have three arguments—two individual arguments and one event argument (Krifka 1998; Landman 2000). The individual arguments serve as the agent (ag) and the theme (th) of the event. The event argument is bound by an existential closure operator (EC) at the sentential level. Additionally, I assume that not only plural nouns but also event predicates and thematic roles are closed under sum, which is indicated by the *-operator (Landman 2000; Kratzer 2007; Champollion 2010). In Mandarin, the particle de is often used as a modification marker, but it can also be used in measurement constructions, as in (17). Its status is not clear in these measurement constructions (Cheng and Sybesma 2009; Li and Rothstein 2012; a.o.). In this paper, I simply assume that the particle de is a type-neutral identity function, which passes up the meaning of a constituent that combines with it. (17) san-bang de rou three-pound DE meat ‘three pounds of meat’ suoyou de xuesheng all DE student ‘all of the students’ Let’s consider the NP-external reading first. The object relative measure phrase is composed via Functional Application (FA), as illustrated in (18). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 807 H. Li (18) Event-related relative measurement FA JdeK(JRME K(J30%K))(JlocalsK) ⇒ λ T λ yλ e00 .MXT(e00 ) ∧ ∃he, xi.e v e00 ∧ T (e, y, x) ∧ *local(x) ∧ card0λ zλ e000 .T (e000 ,y,z) (e, x) = #! " 0 v e00 ∧ R(e0 , y, x0 ) ∧ e 30% × max λ n0 ∃he0 , x0 i card0λ zλ e000 .T (e000 ,y,z) (e0 , x0 ) = n0 As a result, the relative measure phrase denotes a function of type hhe, he,vtii, he,vtii. It maps the set characterized by a transitive verb, i.e., a set of he, y, xi sequences, to the set characterized by a verb phrase, i.e., a set of he, yi sequences. (19) a. FA J30% RME de localsK(JhireK) ⇒ λ yλ e00 .MXT(e00 ) ∧ ∃he, xi.e v e00 ∧ JhireK(e, y, x) ∧ *local(x) ∧ card0λ zλ e000 .JhireK(e000 ,y,z) (e, x) = " #! 0 v e00 ∧ JhireK(e0 , y, x0 ) ∧ e 30% × max λ n0 ∃he0 , x0 i card0λ zλ e000 .JhireK(e000 ,y,z) (e0 , x0 ) = n0 b. FA JECK(Jhire 30% RME de localsK(JLenovoK)) ⇒ ∃e00 .MXT(e00 ) ∧ ∃he, xi.e v e00 ∧ JhireK(e, l, x) ∧ *local(x) ∧ card0λ zλ e000 .JhireK(e000 ,l,z) (e, x) = #! " 0 v e00 ∧ JhireK(e0 , l, x0 ) ∧ e 30% × max λ n0 ∃he0 , x0 i card0λ zλ e000 .JhireK(e000 ,l,z) (e0 , x0 ) = n0 (19b) says: there is a maximal event within a specific time interval; the maximal event contains hiring subevents whose agents are Lenovo and whose themes are locals; the measure function card0λ zλ e000 .JhireK(e000 ,l,z) applies to the theme participants of these events, which are stages of individuals participating in these hiring events. The result is equal to 30% times the maximal number of the theme participants of the events of Lenovo’s hiring. Turning to the NP-internal reading, the object relative measure phrase in (16) denotes a generalized quantifier of type het,ti, as illustrated by the following compositional process. (20) FA JdeK(JRMI K(J30%K))(JlocalsK) ⇒    *local(x0 ) ∧ 0 0 λ Q∃x.*local(x) ∧ Q(x) ∧ card(x) = 30% × max λ n ∃x card(x0 ) = n0 Hence, we can compose the relative measure phrase with the rest of the sentence by Quantifier Raising, as shown in (21). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 808 H. Li Event-related relative measurement (21) FA J30% RMI de localsK(λ x.J[EC [Lenovo hire t1 ]]Kg[1/x] ) ⇒  ∃x∃e.*local(x) ∧ JhireK(e, l, x) ∧ card(x) = 30% × max λ n0 ∃x0  *local(x0 ) ∧ card(x0 ) = n0  (21) says: there are locals hired by Lenovo; the measure function card(x) applies to them and the result is equal to 30% times the maximal number of locals. According to my proposal, the NP-external reading involves the measure function on eventindividual pairs. As we have presented in Section 3.1, the measure function counts recycled individuals more than once. By contrast, the NP-internal reading involves the measure function on individuals. Therefore, when an individual participates in an event twice, it can only be counted once. This is the reason for the contrast between the NP-internal reading and the NP-external reading on counting recycled individuals. In addition to counting recycled individuals, the current analysis can account for more contrasts between the NP-internal reading and the NP-external reading, which are listed below: • The NP-external reading is only available when a relative measure phrase occupies the object position, but the NP-internal reading is not subject to this constraint; • When a relative measure phrase has a NP-external reading, the Monotonicity Condition constrains measure functions on event-related domains, whereas when a relative measure phrase has a NP-internal reading, the Monotonicity Condition constrains the individual domain. • A relative measure phrase with a NP-external reading shows weak island sensitivity. For example, it cannot scope over negation or universal quantifiers. However, a relative measure phrase with a NP-internal reading does not have this property. The following sections discuss these contrasts and demonstrate how the current analysis captures them. 4. A structural constraint The first intriguing contrast between the NP-external reading and the NP-internal reading is a structural constraint. Specifically, the NP-external reading may only be observed when a relative measure phrase is used as the object of a transitive verb, but the NP-internal reading is not subject to the same constraint. As shown in (22), a relative measure phrase in the subject position does not give rise to the NP-external reading. (22) 30% de kuaguo gongsi gu-le bendiren. 30% DE international company hire-ASP locals a. ‘30% of the international companies hired locals.’ (NP-internal) b. #‘30% of the units that hired locals were international companies.’ (NP-external) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 809 H. Li Event-related relative measurement According to my analysis, a relative measure phrase with a NP-external reading has the type hhe, he,vtii, he,vtii. Following Krifka (1989) and Landman (2000), I assume that the agent and the theme are syntactic arguments of a transitive verb, i.e., a transitive verb has the type he, he,vtii. Consequently, a relative measure phrase with a NP-external reading must combine with a transitive verb, instead of an element of type he,vti, such as an intransitive verb or a verb phrase. Structurally speaking, therefore, the NP-external reading should only be observed when a relative measure phrase is used as the object of a transitive verb. The same contrast is observed between objects and PP complements, as exemplified by the following examples. (23) Zhengfu [PP gei bendiren] fenpei-le 50% de gongwu. government to locals assign-ASP 50% DE public.housing a. ‘The government assigned 50% of the public housing to locals.’ (NP-internal) b. ‘50% of the housing that government assigned to locals is public housing.’ (NP-external) (24) Zhengfu [PP gei 50% de bendiren] fenpei-le gongwu. government to 50% DE locals assign-ASP public.housing a. ‘The government assigned public housing to 50% of the locals.’ (NP-internal) b. #‘50% of the people that the government assigned public housing to are locals.’ (NP-external) Generally, a preposition is a function taking an individual element of type e and returning a verb phrase modifier of type hhe,vti, he,vtii. We may reason that its type is he, hhe,vti, he,vtiii. Given this type, a relative measure phrase with the NP-external reading cannot combine with a preposition. It should be noted that the type hhe, he,vtii, he,vtii is not specific to relative measure phrases. In Mandarin, many event-related modifiers share the same type. For example, it has been a long-standing puzzle that temporal and spatial measure phrases are often used as NP-internal modifiers (Huang 1992), as shown below: (25) Libai chi-le yi-ge xiaoshi de pingguo. Libai eat-ASP one-CL hour DE apple ‘Libai ate apples for an hour.’ (26) Libai kai-le yibai gongli de che. Libai drive-ASP one.hundred km DE car ‘Libai drove for 100 km.’ There is no doubt that yi-ge xiaoshi ‘one hour’ and yibai gongli ‘100 km’ in these examples measure the temporal duration of the apple-eating event and the distance of the driving event, respectively. Their English counterparts are in the form of for-adverbials, but they syntactically look like nominal modifiers. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 810 H. Li Event-related relative measurement The current proposal on relative measure items with the NP-external reading can be extended to these event-related NP-internal elements. Specifically, they all involve event-related measurement and have a uniform semantic type—het, hhe, he,vtii, he,vtiii. It means that all the NP-internal elements take as arguments an individual predicate and an event-individual relation. The latter enables them to exhibit event-related interpretations. Based on previous studies on temporal and space measure phrases (Moltmann 1991; Krifka 1998; Zwarts 2005; Champollion 2010; a.o.), I suggest the following lexical entries for yi-ge xiaoshi ‘one hour’ and yibai gongli ‘100 km.’ (27) (28) Jone hourK = λ Pet λ Rhe,he,vtii λ yλ e∃x.P(x) ∧ R(e, y, x) ∧ hour0 (e) = 1 J100 kmK = λ Pet λ Rhe,he,vtii λ yλ e∃x.P(x) ∧ R(e, y, x) ∧ km0 (e) = 100 Similar to relative measure items with an external reading, both one hour and 100 km introduce an event-related measure function, i.e., hour0 and km0 . The former is standardized for events by requiring that hour0 (e) = hour(τ(e)), in which the trace function τ maps an event to its running time. The latter must apply to motion events denoted by movement predicates like walk and drive. The measure function km0 is standardized for movement events by defining that km0 (e) = km(σ (e)), in which the trace function σ maps a motion event to the path that the event is linked to. After combining these NP-internal modifiers with the NP complement, the object phrases in (25) and (26) have the same type as the relative measure phrases with the NP-external reading, i.e., hhe, he,vtii, he,vtii. It is predicted that these object phrases cannot be dislocated as topics. This is borne out, as in (29). In these examples, IP should have the type he,vti, and hence cannot combine with the topic phrases. (29) a. *Yi-ge xiaoshi de pingguo, [IP Libai chi-le]. one-CL hour DE apple Libai eat-ASP ‘Libai ate apples for a hour.’ b. *Yibai gongli de che, [IP Libai kai-le]. one.hundred km DE car Libai drive-ASP ‘Libai drove for 100 km.’ In addition, these event-related lexical items are not the only ones that can claim the type hhe, he,vtii, he,vtii. Working in an event-free semantics, Szabolcsi (1989, 1992, 2014) essentially suggests that reflexives and bound pronouns also have the same type (minus the event arguement). In Keenan’s (2016) theory, quantifiers can be regarded as arity-reducers. They apply to an n-place function and return an (n − 1)-place function, and they do so in all their grammatical occurrences. On this view, a relative measure phrase of type hhe, he,vtii, he,vtii is considered a quantifier that applies to a three-place function of type he, he,vtii and returns a two-place function of type he,vti. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 811 H. Li Event-related relative measurement 5. Event maximalization suffixes Mandarin has some verbal suffixes serving to assert that the events denoted by a verb are realized to the maximal degree. Examples of these suffixes include wan and guang, which are understood as ‘completely,’ ‘entirely’ or ‘fully’ in English. Consider the following sentences with such a suffix: (30) Libai chi-wan/guang-le ershi-ke shuijiao. Libai eat-WAN / GUANG-ASP twenty-CL dumpling ‘Libai completely ate twenty dumplings.’ (31) Libai chi-wan/guang-le shuijiao. Libai eat-WAN / GUANG-ASP dumpling ‘Libai completely ate the dumplings.’ The uses of wan/guang in (31) and (30) are to assert that Libai’s eating of dumplings is realized to the maximal degree (see also Filip 2008). (30) says that twenty dumplings were eaten and none of them was left. In (31), the bare noun shuijiao ‘dumplings’ must be understood as a definite noun and refer to the unique and maximal set of dumplings in a given context. The sentence is true if and only if Libai ate all of the dumplings in some time interval. In this paper, I call these suffixes ‘event maximalization suffixes’ (EMS). Interestingly, the occurrence of an EMS blocks the NP-external reading of a relative measure phrase. Consider (32), in which only the NP-internal reading is available. As a minimal pair to this sentence, (33) shows that the NP-external reading returns when the EMS is removed. (32) Libai chi-wan/guang-le yi-duo-ban de shuijiao. Libai eat-WAN / GUANG-ASP one-more-half DE dumplings a. NP-internal: ‘Libai completely ate more than half of the dumplings.’ b. #NP-external: ‘More than half of the food that Libai completely ate were dumplings.’ (33) Libai chi-le yi-duo-ban de shuijiao. Libai eat-ASP one-more-half DE dumplings a. NP-internal: ‘Libai ate more than half of the dumplings.’ b. NP-external: ‘More than half of the food that Libai ate were dumplings.’ This contrast would be mysterious if the NP-external reading and the NP-internal reading both involved measurement of individuals. However, if the NP-external reading involves measurement in an event-related domain, its disappearance in (32) is expected. The unavailability of the NP-external reading is due to the requirement of EMSs that event predicates they combine with must be telic. To my knowledge, there have not been formal studies on this kind of verbal suffixes in Mandarin. Both Moltmann (1997) and Piñón (2005) propose formal analyses for English adverbial completely, which can be seen as the semantic counterpart of EMSs. While it is not impossible to formalize EMSs using ingredients from these approaches to fit in the current picture, doing Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 812 H. Li Event-related relative measurement so adds substantial complexity to the compositional semantics developed so far and would take us too far afield. In this section, I just illustrate the function of EMSs with the help of the picture in (34). (34) The events of eating dumplings This picture demonstrates a set of partially ordered events, i.e., the events of eating dumplings. This set is ordered relative to the cardinality of the dumplings being consumed in the context (see Krifka 1989, 1998, Kennedy 2012). All the five events are in the set denoted by the verb phrase chi shuijiao ‘eat dumplings,’ but only e5 , in which all the dumplings were eaten, is in the set denoted by the verb phrase chi-wan shuijiao ‘completely eat the dumplings.’ In short, the verb phrase with an EMS denotes an event in which its theme participant must be the sum of all the things affected by the event in some time interval. Consequently, the domain denoted by the verb phrase with an EMS has a trivial part-whole structure. As illustrated in the figure, only e5 is in the domain of chi-wan shuijiao ‘completely eat the dumplings.’ None of its proper subparts belongs to the same domain. In slightly more formal terms, this means that a verb phrase with an EMS is quantized, and hence, according to Krifka (1989, 1998), telic. (35) shows that such a verb phrase is incompatible with an NP-internal temporal measure phrase, which is the counterpart of English for-adverbials (see Section 4). By contrast, a verb phrase with an EMS is compatible with (and in fact required by) an in-adverbial, as shown in (36) (see also Xuan 2010). (35) Libai chi-(*wan/guang)-le yi-ge xiaoshi de shuijiao. Libai eat-WAN / GUANG-ASP one-CL hour DE dumpling ‘Libai (*completely) ate (*the) dumplings for one hour.’ (36) Libai yi ge xiaoshi zhilei jiu chi-*(wan/guang)-le shuijiao. Libai one CL hour within just eat-WAN / GUANG-ASP dumpling ‘Libai *(completely) ate *(the) dumplings in one hour.’ According to the literature (Dowty 1979; Krifka 1998; Rothstein 2004; a.o.), a telic predicate can be modified by in-adverbials but resists for-adverbials. The (in)compatibility of a verb phrase with an EMS is hence a telltale sign about the event structure of the VP denotation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 813 H. Li Event-related relative measurement Returning to relative measurement, the NP-external reading of (32) is blocked by the EMS because event-related measurement is not compatible with telic predicates. In this example, the event domain is characterized by the incremental verb with an EMS, i.e., chi-wan. As described before, a verb suffixed by an EMS denotes an event whose theme is maximal with respect to a time interval, and hence it and its sub-parts do not belong to the same domain. In other words, the domain characterized by chi-wan has a trivial part-whole structure. Applying a measure function on this domain leads to violation of a general constraint, namely, that the domain must have a non-trivial part-whole structure. This constraint has been repeatedly verified in various measurement constructions, such as pseudopartitives (Schwarzschild 2002, 2006; Champollion 2017), comparatives (Wellwood 2015) and Japanese split measure phrase constructions (Nakanishi 2007). 6. Scope and weak islands Doetjes and Honcoop (1997) argue that quantification over event-individual pairs is sensitive to weak islands in the sense of Szabolcsi and Zwarts (1992). Specifically, event-related interpretations are not available if quantification over event-individual pairs scopes over negation or universal quantifiers. The same pattern is also observed for the NP-external reading of relative measurement. The NP-external reading and the NP-internal reading of relative measurement show a contrast with respect to scope-taking. When a relative measure phrase has a NP-internal reading, it can take wide or narrow scope relative to negation, as illustrated in (37). (37) Lianxiang meiyou gu 70% de bendiren. Lenovo not hire 70% DE locals a. ‘It is not the case that Lenovo hired 70% of the locals.’ (not > 70%internal ) b. ‘70% of the locals were such that Lenovo didn’t hire them.’ (70%internal > not) By contrast, if a relative measure phrase has a NP-external reading, it cannot take wide scope over negation, as shown in (38). (38) Lianxiang meiyou gu 70% de bendiren. Lenovo not hire 70% DE locals a. ‘It is not the case that 70% of the people hired by Lenovo were locals.’ (not > 70%external ) b. #‘70% of the people that Lenovo didn’t hire were locals.’ (70%external > not) Similar to negation, universal quantification has to take scope over relative measure phrases in order to preserve the NP-external reading, as exemplified by the following example. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 814 H. Li (39) Event-related relative measurement Mei nian cha shui de shihou, zhengfu dou hui shencha 20% de every year review tax DE time government DOU will audit 20% DE kuaguo gongsi. international company a. ‘Every tax year, 20% of the organizations that the government audits are international companies.’ (every > 20%external ) b. #‘20% of the units that the government audits every tax year are international companies.’ (20%external > every) c. ‘Every tax year, the government audits 20% of the international companies.’ (every > 20%internal ) d. ‘There are 20% of international companies x such that the government audits x every tax year.’ (20%internal > every) (39c) and (39d) show that the universal quantifier can take wide scope or narrow scope with respect to the relative measure phrase with the NP-internal reading. However, it cannot take narrow scope when the relative measure phrase has a NP-external reading, as in (39b). In the literature, there are several formal analyses offered to capture weak island effects. Szabolcsi and Zwarts (1992) propose that weak islands can be understood if we pay attention to the Boolean operations that particular quantificational elements are associated with. For example, universal quantification corresponds to ‘meet,’ existential quantification ‘join’ and negation ‘complementation.’ A sentence is not acceptable if a quantificational element in this sentence needs to perform its corresponding Boolean operation on an algebraic structure for which the operation is not defined. Doetjes and Honcoop (1997) follow this analysis and argue that complementation and meet cannot be performed on the domain of event-individual pairs. They assume that the domain of event-individual pairs constitutes a join semi-lattice (see Section 3.1). This essentially follows from the fact that the domain of events has no bottom element. Consequently, the domain of event-individual pairs does not have a bottom element either. In (38b) and (39b), the negation and the universal quantifier performs complementation and meet on the domain of event-individual pairs. Since there is no bottom element in this domain, complementation and meet are undefined. Besides the algebraic semantic approach, Honcoop (1998) and Abrusán (2014) propose two other alternative approaches to weak island effects. The former relies on dynamic semantics, while the latter is based on the semantic and pragmatic properties of questions. The current study remains open to these alternative approaches. The crucial point is that the weak island sensitivity of the NP-external reading provides another piece of evidence for my analysis that this reading is event-related. 7. A previous approach: Focus mapping In this section, I compare my analysis with Ahn and Sauerland’s studies on relative measurement (Sauerland 2014; Ahn and Sauerland 2015a, b). Following the Focus Mapping Hypothesis (Herburger 2000; Beaver and Clark 2008; a.o.), they propose that the NP-external reading of Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 815 H. Li Event-related relative measurement relative measurement is derived by focusing on the NP complement of a relative measure item. For example, in (40), the NP complement is focused. (40) Lianxiang gu-le 30% de [bendiren]F . Lenovo hire-ASP 30% DE local ‘Lenovo hired 30% [locals]F .’ (NP-external) According to the Focus Mapping Hypothesis, focus determines the structure of a quantificational element: focused materials are mapped onto the scope, while non-focused materials are mapped onto the restriction. Therefore, in (40), the quantificational structure induced by the relative measure item 30% can simply be represented as follows: (41) [30% x : Lenovo-hired(x)] locals(x) Although the focus approach is elegant and based on a widely assumed hypothesis, it faces some empirical problems. First, it cannot account for the event-related properties discussed in this paper. Under the focus approach, both the NP-internal reading and the NP-external reading are individual-related. As a result, the contrasts involving counting recycled individuals, the monotonicity constraint and weak island sensitivity cannot be easily captured in this approach. Second, at least in Mandarin, focus is not required to derive the NP-external reading. Consider the question-answer pair in (42). (42) a. b. Lianxiang qunian gu-le duoshao bendiren? Lenovo last.year hire how.many locals ‘How many locals did Lenovo hire last year?’ Lianxiang qunian gu-le [30%]F de bendiren Lenovo last.year hire-ASP 30% DE locals (i) ‘Last year, Lenovo hired 30% of the locals.’ (ii) ‘Last year, Lenovo hired 30% locals.’ (NP-internal) (NP-external) In a question-answer pair, the constituent in the answer corresponding to the wh-word is the focus (Jackendoff 1972; a.o.). Accordingly, in (42a), 30% should be the focus since it directly corresponds to the wh-word of the preceding question. Its NP complement as a piece of repeated information is not focused. However, (42b) is still ambiguous, i.e., the NP-external reading is available even though the NP complement of a relative measure item does not bear focus. 8. Conclusion This paper takes up relative measurement in Mandarin. It is argued that relative measurement may involve event-related measurement or individual-related measurement. Furthermore, an explicit compositional analysis is offered to derive these two readings. The analysis is shown to account for various contrasts between individual-related relative measurement and event-related relative measurement. My analysis also highlights the similarities in NP-internal elements with an external event-related interpretation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 816 H. Li Event-related relative measurement References Abrusán, M. (2014). Weak Island Semantics. Oxford: Oxford University Press. Ahn, D. and U. Sauerland (2015a). The grammar of relative measurement. In S. D’Antonio, M. Moroney, and C. R. Little (Eds.), Proceedings of Semantics and Linguistic Theory 25, Stanford, CA, pp. 125–142. Stanford University. Ahn, D. and U. Sauerland (2015b). Non-conservative quantification with proportional quantifiers: Crosslinguistic data. In T. Bui and D. Ozyildiz (Eds.), Proceedings of NELS 45, Amherst, MA, pp. 1–11. GLSA. Ahn, D. and U. Sauerland (2017). Measure constructions with relative measures: Towards a syntax of non-conservative construals. The Linguistic Review 34, 1–34. Barker, C. (1999). Individuation and quantification. Linguistic Inquiry 30(4), 683–691. Barker, C. (2010). Nominals don’t provide criteria of identity. In M. Rathert and A. Alexiadou (Eds.), The Semantics of Nominalizations across Languages and Frameworks, pp. 9–24. Berlin: Walter de Gruyter. Beaver, D. and B. Clark (2008). Sense and Sensitivity: How Focus Determines Meaning. Oxford: Wiley-Blackwell. Champollion, L. (2010). Parts of a Whole: Distributivity as a Bridge between Aspect and Measurement. Ph. D. thesis, University of Pennsylvania. Champollion, L. (2017). Parts of a Whole: Distributivity as a Bridge between Aspect and Measurement. Oxford: Oxford University Press. Cheng, L. L.-S. and R. Sybesma (2009). De as an underspecified classifier: First explorations. Yuyanxue Luncong [Essays on Linguistics] 39, 123–156. Doetjes, J. and M. Honcoop (1997). The semantics of event-related readings: A case for pairquantification. In A. Szabolcsi (Ed.), Ways of Scope Taking. Dordrecht: Kluwer Academic Publishers. Dowty, D. R. (1979). Word Meaning and Montague Grammar. Dordrecht: Kluwer Academic Publishers. Filip, H. (2008). Events and maximalization. In S. Rothstein (Ed.), Theoretical and Crosslinguistic Approaches to the Semantics of Aspect, pp. 217–256. Amsterdam: John Benjamins. Herburger, E. (2000). What counts: focus and quantification. Cambridge, Massachusetts: MIT Press. Honcoop, M. (1998). Dynamic Excursions on Weak Islands. Ph. D. thesis, University of Leiden. Huang, C.-T. J. (1992). Verb movement and some syntax-semantics mismatches in Chinese. Chinese Languages and Linguistics 2, 587–613. Jackendoff, R. (1972). Semantic Interpretation in Generative Grammar. Cambridge, MA: MIT Press. Keenan, E. (2016). In situ interpretation without type mismatches. Journal of Semantics 33, 87–106. Kennedy, C. (2012). The composition of incremental change. In V. Demonte and L. McNally (Eds.), Telicity, Change, and State: A Cross-categorial View of Event Structure, pp. 103–121. New York: Oxford University Press. Kratzer, A. (2007). On the plurality of verbs. In J. Dölling, T. Heyde-Zybatow, and M. Shafer (Eds.), Event Structures in Linguistic Form and Interpretation, pp. 269–300. Berlin: Mouton de Gruyter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 817 H. Li Event-related relative measurement Krifka, M. (1989). Nominal reference, temporal constitution and quantification in event semantics. In R. Bartsch, J. van Benthem, and P. van Emde Boas (Eds.), Semantics and Contextual Expression, Dordrecht, pp. 75–115. Foris. Krifka, M. (1990). Four thousand ships passed through the lock: Object-induced measure functions on events. Linguistics and Philosophy 13, 487–520. Krifka, M. (1998). The origins of telicity. In S. Rothstein (Ed.), Events and Grammar, pp. 197–236. Dordrecht: Kluwer Academic Publishers. Landman, F. (2000). Events and Plurality: The Jerusalen Lectures. Dordrecht: Kluwer. Li, X. and S. D. Rothstein (2012). Measure readings of Mandarin classifier phrases and the particle de. Language and Linguistics 13, 693–741. Moltmann, F. (1991). Measure adverbials. Linguistics and Philosophy 14, 629–660. Moltmann, F. (1997). Parts and Wholes in Semantics. Oxford: Oxford University Press. Moore, S. (1994). Events, objects and eventual objects. In E. Duncan, D. Farkas, and P. Spaelti (Eds.), Proceedings of the 12th West Coast Conference in Formal Linguistics West, Stanford, CA, pp. 577–590. CSLI. Nakanishi, K. (2007). Measurement in the nominal and verbal domains. Linguistics and Philosophy 30, 235–276. Piñón, C. (2005). Adverbs of completion in an event semantics. In H. J. Verkuyl, H. de Swart, and A. van Hout (Eds.), Perspectives on Aspect, Dordrecht, pp. 149–166. Springer. Rothstein, S. (2004). Structuring Events. Oxford: Blackwell. Sauerland, U. (2014). Surface non-conservativity in German. In C. Pinon (Ed.), Empirical Issues in Syntax and Semantics 8, pp. 125–142. CSSP. Schwarzschild, R. (2002). The grammar of measurement. In B. Jackson (Ed.), Proceedings of SALT XII, Ithaca, NY, pp. 225–245. CLC Publications. Schwarzschild, R. (2006). The role of dimensions in the syntax of noun phrases. Syntax 9, 67–110. Szabolcsi, A. (1989). Bound variables in Syntax: Are there any? In R. Bartsch, J. Van Benthem, and P. van Emde Boas (Eds.), Semantics and Contextual Expression, pp. 295–318. Dordrecht. Szabolcsi, A. (1992). Combinatory grammar and projection from the lexicon. In I. A. Sag and A. Szabolcsi (Eds.), Lexical Matters, pp. 241–268. Stanford, CA: CSLI. Szabolcsi, A. (2014). Quantification and acd: What is the evidence from real-time processing evidence for? a response to hackl et al. (2012). Journal of Semantics 31, 135–145. Szabolcsi, A. and F. Zwarts (1992). Weak islands and an algebraic semantics for scope taking. Natural Language Semantics 1(3), 235–284. Wellwood, A. (2015). On the semantics of comparison across categories. Linguistics and Philosophy 38, 67–101. Xuan, Y. (2010). Xuhua jieguo buyu shi yi zhong wanjie duanyu [grammaticalized resultatives are telic phrases]. Yuyanxue Luncun [Bulletin of Linguistics] 31, 249–277. Zwarts, J. (2005). Prepositional aspect and the algebra of paths. Linguistics and Philosophy 28, 739–779. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 818 Mandarin dou: The common core of distributivity, maximality, and EVEN1 Mingming LIU — Hunan University Abstract. The paper presents a unified analysis of Mandarin dou as an alternative-sensitive (sentential) operator whose semantics equals to Karttunen and Peters (1979)’s EVEN. Different ‘uses’ of dou are analyzed by associating dou with different types of alternative sets: even-dou involves non-entailment-based alternative sets, while distributive-dou entailment-based ones. Keywords: distributivity, maximality, even, Mandarin dou. 1. Introduction Mandarin dou is well discussed in the literature (Lee 1986; Cheng 1995; Shyu 1995; Huang 1996; Lin 1998; Hole 2004; Chen 2008; Xiang 2008; Cheng 2009; Dong 2009; Liao 2011; Xiang 2016, a.o.). This very short paper will not examine every claim previously made concerning dou. Instead, it starts from a simple dou sentence as in (1) and checks it against two influential accounts of dou. It then shows that neither treating dou as a distributivity operator (Lin 1998; Chen 2008) nor taking it to be a maximality operator (Giannakidou and Cheng 2006; Xiang 2008) captures all aspects of (1). It then proposes that dou is an alternative-sensitive operator (cf. Liao 2011; Xiang 2016); specifically, it is EVEN. Different interpretations of a dou sentence are explained by associating dou with alternative sets of different properties: EVEN-dou corresponds to a (propositional) alternative set whose members stand in a likelihood relation, while DISTRIBUTIVE-dou corresponds to an alternative set based on entailment. (1) San.ge xuesheng dou mai.le shi.ben shu. three-CL student DOU buy.ASP ten.CL book a. EVEN-dou: ‘A group of three students together bought 10 books, which is unlikely.’ b. DISTRIBUTIVE-dou: ‘The three students each bought 10 books.’ Let me introduce the basic facts of dou exhibited in (1). (1) is ambiguous between (1a) and (1b) (with stress disambiguating the two).2 Under (1a), dou adds an even-flavor and the sentence is interpreted collectively (the collective-cumulative distinction is irrelevant to our discussion), while in (1b) dou is even-less but triggers a distributive effect (Lin 1998) and a maximality effect (see especially Cheng, 2009: 67), indicated by the each and the in the gloss respectively. 2. Two previous accounts 2.1. Dou as a distributivity operator Lin (1998) takes dou to be Link (1987)’s distributivity operator, as in (2). Being a predicate 1 This paper reports some of the results of Liu (2017). I thank the persons acknowledged there, as well as reviewers and participants (Brian Buccola, Martina Faller, Yael Greenberg, Bernard Schwarz, Eytan Zweig) at SuB 21 for helpful discussion and comments. All errors are my own. 2 Specifically, putting stress on san ‘three’ facilitates (1a) while stressing dou renders (1b). The paper will leave to another occasion an explanation of this fact at the semantics-prosody interface. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 819 M. Liu Mandarin dou modifier, dou turns a mixed predicate such as bought ten books into a strictly distributive one, each bought ten books in this case. (2) JdouLin K = λ Pλ X∀y[y ≤ X ∧ Atom(y) → P(y)] While (2) straightforwardly explains the each in (1b), it fails to capture dou’s maximality/definiteness effect in the same environment — the the in (1b). Importantly, bare numerals such as san.ge xuesheng ‘three students’ in other contexts are not interpreted as definites in Mandarin. This is already evidenced by (1a) which can be felicitously (and truthfully) uttered in a context where there were more than three students in the context but only three bought books, and the three book-buyers together bought ten books. 2.2. Dou as a maximality operator The maximality aspect of dou has been emphasized in Xiang (2008) and Cheng (2009), who follow Giannakidou and Cheng (2006) analyzing dou as a maximality operator as in (3). (3) JdouG&C K = λ P.σ xP(x)3 (3) is essentially what Sharvy (1980) and Link (1983) posit for the meaning of the definite article in English. It thus directly captures the maximality/definiteness effect of dou in (1b) (with three treated as having an adjectival semantics λ Pλ X.|X| = 3 ∧ P(X)).4 However, remember that (1b) also shows the distributive effect. It only has the distributive reading that the three students each bought ten books; it lacks the collective reading that the three students together bought ten books. This is not captured by treating dou as a definite determiner/maximality operator. In sum, neither the distributivity operator analysis nor the maximality operator analysis captures the behavior of dou in (1b). Additionally, neither of the two offers a ready explanation of dou’s even-flavor in (1a). 3 Giannakidou and Cheng (2006) and Cheng (2009) use ι, while following Link (1983) I use σ . I also ignore intensionality. Finally, Giannakidou and Cheng do not specify the semantics of σ explicitly. I adopt the standard L L treatment: σ x.P(x) is defined if P ∈ P, and if defined σ x.P(x) = P, following Sharvy (1980). 4 We also need to tamper with the syntax. Instead of having the structure in (ia), which is required by a distributivity operator analysis of dou and agrees with dou’s adverbial status, we need (ib) to make (3) work (see especially Giannakidou and Cheng 2006: (78)). (i) a. NP dou b. NP dou VP VP Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 820 M. Liu Mandarin dou 3. Dou as EVEN We present a unified analysis of Mandarin dou that captures not only its distributive and maximality effects in (1b), but also its even-flavor in (1a). The central idea is that dou is just EVEN, with the semantics of English even proposed in Karttunen and Peters (1979) (cf. Liao 2011: 217). In (4), π stands for the prejacent of dou, and JπKAlt its alternative semantic value (Rooth, 1985, 1992), a set of propositions in this case. Notice that I assume for simplicity that dou takes sentential scope, which could be achieved either by movement of dou, similar to movement of even (Wilkinson 1996, Karttunen and Peters 1979, Lahiri 1998, Crnič 2014), or by making dou an indicator of a covert even that has sentential scope (Liao, 2011: 215). In the latter view, dou does not have its own meaning. The paper adopts the movement view as in (5), but nothing crucial hinges on this. Finally, I take it that in (1), three is the alternative trigger (evidenced by the prosodic profile of (1a), see footnote 2), and I use F to mark it. (4) Jdou(π)K is defined iff ∀q ∈ JπKAlt [¬(JπK = q) → JπK ≺likely q] if defined, Jdou(π)K = JπK (Karttunen and Peters, 1979) In words: dou is truth conditionally vacuous but presupposes that its prejacent is the most unlikely proposition among its alternatives (we set aside the additive presupposition of even). (5) dou π threeF students bought ten books Treating dou as EVEN naturally accounts for its even-flavor in (1a). (6) below is the alternative set I propose for (1a) (with san.ge xuesheng ‘three students’ interpreted as standard existentials, hinted by the there were . . . in (6)). The prejacent indeed seems to be the most unlikely one among its alternatives. (6)  ...    three were 5 students such that they together bought 10 books, Jπ(1a) KAlt = there were 4 students such that they together bought 10 books,    there were 3 students such that they together bought 10 books (= π)        Two questions arise at this point. First, why is the proposition that there were 2 students such that they together bought 10 books, which presumably is more unlikely than the prejacent, not in (6)? I think the answer has to do with contextual pruning. The same process would explain the felicity of she even made it to the semi-finalsF , even though that she made it to the finals is more unlikely (Kay, 1990). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 821 M. Liu Mandarin dou A second question involves the obligatory collective reading of (1a). Why is the distributive reading not allowed with dou’s even-flavor? The next subsection is devoted to answering this question. 3.1. Even-less dou’s distributive effect Let me first clarify my assumption about distributive readings. I analyze distributive readings by a covert distributivity operator (7) optionally on VP (Link, 1987). (7) JDistK= λ Pλ x∀y[(y ≤ x ∧ Atom(y)) → P(y)] The existence of a covert distributivity operator in Mandarin Chinese is independently justified by (8a), where dou is absent but a distributive reading is possible and strongly preferred for every speaker consulted. In this respect, our judgment agrees with Xiang (2008: 229), but differs from Lin (1998: 201), who claims that (definite) plurals in Mandarin do not have distributive readings, unless dou, according to Lin a distributivity operator, is added. However, it seems that Lin did not take context into consideration. For (8a), even Lin himself (personal communication) agrees that a distributive reading is the preferred one. Below, (8b) and (8c) spell out the LF and semantics of (8a). (8) a. b. c. (Context: I asked who among the kids drew two pictures; you replied:) Zhangsan he Lisi hua le liang fu. Zhangsan and Lisi draw ASP two CL ‘Zhangsan and Lisi each drew two pictures.’ [ TP Zhangsan and Lisi [ VP Dist [ VP drew two pictures ]]] ∀y[(y ≤ z ⊕ l ∧ Atom(y)) → ∃X[|X| = 2 ∧ pics(X) ∧ draw(y, X)]] With Dist, the prejacent of dou in (1)/(5) can be interpreted distributively. Specifically, I propose that (9) is the alternative set associated with dou in (1b), with each representing the distributivity operator Dist. (9) Jπ(1b) KAlt    there were 3 students such that each bought 10 books (= π),  there were 2 students such that each bought 10 books, =   there were 1 students such that each bought 10 books, Note that the propositions in Jπ(1b) KAlt stand in a very interesting relation: dou’s prejacent π logically (asymmetrically) entails all the other alternatives. We have proposed that dou is EVEN, whose semantics requires that the prejacent π be less likely than all π’s alternatives. But entailment is stronger than likelihood: if p entails q, p is at least as unlikely as q (Lahiri, 1998; Crnič, 2014). Thus, the EVEN-presupposition of dou, which essentially is a requirement on the shape of its alternative set, is weaker than what we Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 822 M. Liu Mandarin dou already know about the Jπ(1b) KAlt and is automatically satisfied.5 In this case, the even-flavor is trivial (cf. Liao 2011). In other words, when the alternatives all stand in an entailment relation with the prejacent of dou, dou’s even presupposition can be trivialized.6 Crucially, since the entailment is made possible by the distributive operator (the each in (9)), the correlation between even-less dou and distributive readings is observed. This, I claim, is how dou’s even meaning could disappear in a distributive context in (1b), and the distributive effect of even-less dou is explained. This also explains why (1a) is obligatorily collective. Only by being collective can the alternatives avoid standing in an entailment relation with the prejacent (that 3 students together bought 10 books has nothing to do with that 4 students together bought 10 books), and consequently likelihood and the even-flavor could surface. 3.2. Even-less dou’s maximality effect The maximality/definiteness effect of dou also follows from our proposal. To illustrate, consider contexts where there are exactly three students. In such contexts, any alternative of the form there were n students such that each bought 10 books with n > 3 won’t be included in the actual alternative set. This is because it does not make sense to consider a proposition like that there were 4 students such that each bought 10 books if we already know there could only be three students. Thus, the alternative set has to be the one in (9) and we have already seen how dou is licensed there without triggering an even-flavor. Things change when there were more than three students in the context. Suppose there were four as in (10). In this case, there is a proposition q in the alternative set entailing the prejacent; dou’s presupposition then cannot be satisfied (again, if p entails q, q cannot be more unlikely than p) and the sentence is thus infelicitous in the context. 5 We also need to assume that non-equivalent propositions within Jπ(1b) KAlt have different likelihood, which I take to be satisfied by normal contexts. 6 A few more words on dou’s even-flavor and its disappearance in distributive contexts. When I said dou’s evenflavor is trivialized, I meant its (un)likelihood-flavor is indiscernible — that is, we do not feel any relation based on (un)likelihood between dou’s prejacent and its alternatives, and this is, I argued, due to the existence of a stronger entailment relation among the alternatives, because of distributivity. Some readers may find this intuitively hard to digest, but I believe the reason has to do with our choice of using comparative likelihood as the scale the semantics of even (and thus of dou) is based on (Karttunen and Peters, 1979). Several authors however argue that the scale of even should really be based on “pragmatic entailment”, “better informativeness” (Kay, 1990), “noteworthiness” (Herburger, 2000), or simply a contextually determined scale (Greenberg, 2016). With these theories, the disappearance of likelihood of dou in entailment contexts is more transparent: when entailment is available, dou’s prejacent can be the most noteworthy/informative by logically entailing all the other alternatives; only when entailment is unavailable is likelihood needed to make sense of noteworthiness/better informativeness. I take the above reasoning to be a variant of the idea presented in the main text, but I will stick to the proposal made above, trading popularity (of Karttunen and Peters (1979)’s semantics) for transparency. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 823 M. Liu (10) Mandarin dou Jπn>3 KAlt  there were 4 students such that each bought 10 books (= q),    there were 3 students such that each bought 10 books (= π), = there were 2 students such that each bought 10 books,    there were 1 students such that each bought 10 books,        In other words, to get the even-less dou in (1b), the context has to contain exactly 3 students.7 In this way, we have derived the maximality/definiteness effect of dou in (1b) from its even presupposition. 4. Concluding remarks By examining a single dou sentence, the paper has sketched an analysis of Mandarin dou that captures its even-flavor, its distributive effect, its maximality effect, and the interaction among the three. For a detailed exposition of the analysis, its theoretical implications to the theory of pluralities and the theory of alternatives, and a comparison of the analysis with its close relative Liao (2011), the interested reader is referred to Liu (2017). References Chen, L. (2008). Dou: Distributivity and Beyond. Ph. D. thesis, Rutgers University. Cheng, L. L.-S. (1995). On dou-quantification. Journal of East Asian Linguistics 4(3), 197– 234. Cheng, L. L.-S. (2009). On every type of quantificational expression in Chinese. In M. Rather and A. Giannakidou (Eds.), Quantification, Definiteness, and Nominalization, pp. 53–75. Oxford: Oxford University Press. Crnič, L. (2014). Non-monotonicity in NPI licensing. Natural Language Semantics 22(2), 169–217. Dong, H. (2009). Issues in the Semantics of Mandarin Questions. Ph. D. thesis, Cornell University. Giannakidou, A. and L. L.-S. Cheng (2006). (In)definiteness, polarity, and the role of whmorphology in free choice. Journal of Semantics 23(2), 135–183. Greenberg, Y. (2016). A novel problem for the likelihood-based semantics of even. Semantics and Pragmatics 9(2), 1–28. Herburger, E. (2000). What Counts: Focus and Quantification. Cambridge, MA: MIT Press. Hole, D. (2004). Focus and Background Marking in Mandarin Chinese. London and New York: Routledge Curzon. Huang, S. (1996). Quantification and Predication in Mandarin Chinese: A Case Study of Dou. Ph. D. thesis, University of Pennsylvania. Karttunen, L. and S. Peters (1979). Conventional Implicature. In Syntax and Semantics 11: Presupposition, pp. 1–56. New York: Academic Press. Kay, P. (1990). Even. Linguistics and Philosophy 13, 59–111. Lahiri, U. (1998). Focus and negative polarity in Hindi. Natural Language Semantics 6(1), 7 What happens when there were less than 3 students in the context? In such a context, the alternative set won’t contain the prejacent, which is ruled out by the Focus Interpretation Principle in Rooth (1992), which requires the prejacent to be always in the alternative set. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 824 M. Liu Mandarin dou 57–123. Lee, T. H.-T. (1986). Studies on Quantification in Chinese. Ph. D. thesis, UCLA. Liao, H.-C. (2011). Alternatives and Exhaustification: Non-interrogative Uses of Chinese Whwords. Ph. D. thesis, Harvard University. Lin, J.-W. (1998). Distributivity in Chinese and its implications. Natural Language Semantics 6, 201–243. Link, G. (1983). The logical analysis of plurals and mass terms: A lattice-theoretic approach. In R. Bäuerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use, and Interpretation of Language, Berlin, pp. 302–323. de Gruyter. Link, G. (1987). Generalized quantifiers and plurals. In P. Gärdenfors (Ed.), Generalized Quantifiers, Dordrecht, pp. 151–180. Kluwer. Liu, M. (2017). Varieties of alternatives: Mandarin focus particles. Linguistics and Philosophy 40(1), 61–95. Rooth, M. (1985). Association with Focus. Ph. D. thesis, University of Massachusetts, Amherst. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1(1), 75–116. Sharvy, R. (1980). A more general theory of definite descriptions. The Philosophical Review 89, 607–624. Shyu, S.-I. (1995). The Syntax of Focus and Topic in Mandarin Chinese. Ph. D. thesis, University of Southern California. Wilkinson, K. (1996). The scope of even. Natural Language Semantics 4, 193–215. Xiang, M. (2008). Plurality, maximality and scalar inferences: A case study of Mandarin dou. Journal of East Asian Linguistics 17, 227–245. Xiang, Y. (2016). The Mandarin particle dou: a pre-exhaustification exhaustifier. In C. Piñón (Ed.), Empirical Issues in Syntax and Semantics 11. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 825 826 A solution to Karttunen’s Problem1 Matthew MANDELKERN — Massachusetts Institute of Technology Abstract. There is a difference between the conditions in which one can felicitously assert a ‘must’-claim versus those in which one can use the corresponding non-modal claim. But it is difficult to pin down just what this difference amounts to. And it is even harder to account for this difference, since assertions of pMust ϕq and assertions of ϕ alone seem to have the same basic goal: namely, coming to agreement that [[ϕ]] is true. In this paper I take on this puzzle, known as Karttunen’s Problem. I begin by arguing that a ‘must’-claim is felicitous only if there is a shared argument for its prejacent. I then argue that this generalization, which I call Support, can explain the more familiar generalization that ‘must’-claims are felicitous only if the speaker’s evidence for them is in some sense indirect. Finally, I sketch a pragmatic derivation of Support. Keywords: epistemic modals, indirectness of ‘must’, Karttunen’s Problem, strength of ‘must’. 1. Introduction Compare (1) and (2): (1) It must be raining out. (2) It is raining out. Intuitively, an assertion of (1) and an assertion of (2) have the same basic aim: they are both proposals to accept that it is raining out. Once an assertion of (1) has been accepted, interlocutors are disposed to accept the content of (2): that it is raining out. Thus (1) seems to be as strong as (2). But it does not seem to be stronger than (2): it is very strange to assert (1) after (2) is already accepted, as witnessed by the oddness of (3): (3) ??It’s raining; and moreover, it must be raining. This suggests that assertions of (1) and (2) carry the same basic information. Yet the conditions under which they can be felicitously asserted differ in subtle ways. Suppose that Jane is in a windowless room, and sees her colleagues come in with wet umbrellas. Then she can assert either (1) or (2). But now suppose that Jane is looking out a window at the rain. She can still assert (2), but an assertion of (1)—‘It must be raining out’—would be decidedly odd. 1I am grateful to audiences at MIT, the 2015 University of Chicago Workshop on Modality and Subjectivity, the New York Philosophy of Language Workshop, Arché, and Hampshire College; to reviewers for Sinn und Bedeutung 21; and to Justin Bledin, David Boylan, Agnes Callard, Nilanjan Das, Brendan de Kenessey, Janice Dowell, Daniel Drucker, Vera Flocke, Irene Heim, Matthias Jenny, Angelika Kratzer, Daniel Lassiter, Rose Lenehan, Sarah Murray, Dilip Ninan, Jacopo Romoli, Bernhard Salow, Ginger Schultheis, Brett Sherman, Alex Silk, Daniel Skibra, Eric Swanson, and Roger White for very helpful comments and discussion. Special thanks to Kai von Fintel, Justin Khoo, Robert Stalnaker, and Stephen Yablo. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 827 M. Mandelkern A solution to Karttunen’s problem Generally there exists a systematic difference between the conditions in which one can felicitously assert a ‘must’-claim with complement ϕ, versus the conditions in which one can felicitously assert ϕ alone.2 This puzzle, known as Karttunen’s Problem,3 gets to the heart of a number of broad foundational questions concerning the meaning of epistemic modals and the structure of conversation, and will be the topic of this paper. The argument of the paper comes in three parts. In §2, I get clear on the data: what exactly the difference in felicity conditions between sentences like (1) and (2) amounts to. The main claim in the literature, which I call Indirectness, is that a ‘must’-claim is felicitous only if the speaker’s evidence for its prejacent is indirect, whereas its bare prejacent can be asserted whether the speaker’s evidence is direct or indirect. I argue that, while Indirectness is correct, there is another, equally important, generalization which plays a key role in solving Karttunen’s Problem: namely, that a ‘must’-claim is felicitous only if the speaker ensures there is a salient argument in support of the claim’s prejacent. I call this constraint Support. In §3, I show that once we have Support clearly in sight, we can derive Indirectness through general pragmatic reasoning. In §4, I give a Gricean account of why Support arises in the first place. This solution to Karttunen’s Problem predicts that assertions of pMust ϕq and ϕ have the same basic update effect, while explaining why the former, but not the latter, requires that the speaker share an argument for [[ϕ]], and that her evidence for [[ϕ]] be indirect. 2. The data The main extant claim regarding the difference between an assertion of pMust ϕq versus an assertion of ϕ alone is that it amounts to an Indirectness constraint:4 Indirectness: A claim of pMust ϕq is felicitous only if the speaker’s evidence for [[ϕ]] is indirect; a claim of non-modal ϕ can be felicitous whether the speaker’s evidence for [[ϕ]] is direct or indirect. Indirectness is motivated by considering pairs of sentences like (4a) and (4b): (4) a. b. It must be raining. It’s raining. First suppose that the speaker of (4a) is looking out at the rain. Then her assertion is distinctly odd; whereas if she said (4b), it would be unmarked. By contrast, if she has a piece of indirect evidence for rain—say, wet umbrellas—then either is felicitous. Indirectness is the most natural generalization to draw from data like these. Indirectness partly characterizes the difference in felicity between pMust ϕq and ϕ, but does it exhaust that difference? Most of the literature on Karttunen’s Problem has indeed focused exclusively on Indirectness. But a different, mostly neglected, thread has pointed to a further 2A ‘must’-claim is a claim containing an unembedded strong epistemic necessity modal. von Fintel and Gillies (2010), who credit Karttunen (1972) with bringing the issue to attention. 4 Karttunen (1972), Veltman (1985), Kratzer (1991), von Fintel and Gillies (2010), Kratzer (2012), Matthewson (2015), Lassiter (2016), Giannakidou and Mari (2016), Sherman (2016). 3 Following Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 828 M. Mandelkern A solution to Karttunen’s problem contrast in felicity conditions between pMust ϕq and ϕ: in making a ‘must’-claim, the speaker must ensure that an argument for its prejacent is salient to all the interlocutors.5 Support: A claim of pMust ϕq is felicitous only if there is an argument for [[ϕ]] salient to all the interlocutors; a claim of non-modal ϕ can be felicitous whether or not there is a salient argument for [[ϕ]]. The data that motivate Support are less clearcut than those that motivate Indirectness. This is unsurprising: evaluating Support requires evaluating discourses as a whole, rather than single utterances, and it can be difficult to determine, in a given context, whether an argument has been made salient. In the remainder of this section, I will provide new data to argue that Support is indeed required to account for the difference in felicity conditions between pMust ϕq and ϕ. Consider the following case: (5) Patch the rabbit sometimes gets into the box where her hay is stored. On his way out, Mark hears a snuffling from the box. At work, Bernhard asks him how Patch is. a. [Mark:] She’s great. She must have gotten into the hay box this morning. b. [Bernhard:] Cute! Suppose the conversation ends here, and assume that Bernhard doesn’t know anything about Patch’s set-up at Mark’s house, or anything else which might help him figure out why Mark thinks that Patch was in the box of hay. There is something distinctly odd about this exchange. Intuitively, what Mark has said needs elaboration; either Mark should have proffered reasons to think that Patch was in the hay box, or Bernhard should have asked him for reasons, perhaps with, ‘Why do you say that?’ Here is a more felicitous version of (5); assume the same setup: (6) a. b. [Mark:] She’s great. I heard a snuffling from the box of hay on my way out—she must have gotten into the box. [Bernhard:] Cute! Now suppose the conversation ends here. This exchange has none of the peculiarity of (5). Likewise, a non-modal variant of (5) is perfectly fine: (7) a. b. [Mark:] She’s great. She got into the box of hay this morning. [Bernhard:] Cute! The infelicity of (5) thus seems to be due to the fact that a ‘must’-claim is made while no argument for its prejacent is given. Cases like this provide our first piece of evidence for Support. To get another case of this kind on the table, consider (8), adapted from Murray (2014): 5 See especially Stone 1994. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 829 M. Mandelkern (8) A solution to Karttunen’s problem On her way to a meeting in a windowless building, Sarah sees Jim enter with a wet umbrella. Sarah enters the meeting. Thomas, who didn’t see the umbrella, asks ‘What’s the weather like?’ Sarah responds: a. It must be raining out. b. It’s raining out. c. It must be raining out; I just saw Jim come in with a soaking wet umbrella. d. It’s raining out; I just saw Jim come in with a soaking wet umbrella. Thomas replies: ‘Oh, too bad. Ok, let’s talk about the agenda for this meeting.’ If the conversation ends here, then (8a)—the variant with a ‘must’ and no argument—is odd, while the other variants are fine—again, just as Support predicts. Comparing ‘must’ with other words that might at first glance seem to work in a similar way can help bring out the plausibility of Support. Consider (9), adapted from a television spy drama: (9) a. b. The suspect is fleeing south. We’ve sent agents ahead to Mattapan. Why Mattapan? (i) Apparently the Russians have a safe-house there. (ii) The Russians must have a safe-house there. If the conversation ends here, then (9bii) is peculiar in a way that (9bi) isn’t. ‘Apparently’, like ‘must’, is constrained by a form of Indirectness; but ‘apparently’, unlike ‘must’, is acceptable here without an argument. Support predicts precisely this contrast (assuming that no corollary governs ‘apparently’). Finally, I note that the patterns reported here are robust across strong epistemic necessity modals, in English and in all the other languages I have checked.6 I thus conclude that we should adopt Support as part of our characterization of the difference in felicity conditions between a ‘must’-claim and its bare prejacent. Before moving on, let me say more about what Support amounts to. First, what does an argument amount to? I will think of an argument for [[ϕ]] in a particular context as a set of propositions which the speaker is commonly recognized to believe provides reason to believe [[ϕ]]—either by deductively entailing its conclusion; by inductively supporting the conclusion; or by showing how the conclusion follows from what is already accepted. Second, what does ‘salience’ amount to? I won’t say much about this, but a few features are worth noting. First, an argument need not itself be commonly accepted (i.e. common ground (Stalnaker, 1970)). One can felicitously assert an argument conjoined with a ‘must’-claim, even if the argument has not yet been (and never is) accepted by all the speakers (if Bernhard doesn’t believe me that I heard a snuffling from the box of hay, this does not render (6) infelicitous). The sense in which an argument Γ must be salient is rather that it must be common ground that the speaker takes Γ to provide reason to believe the prejacent of her ‘must’-claim, and that she 6 Bengali, French, German, Hindi, Japanese, Russian, Spanish, Swiss German, and Turkish. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 830 M. Mandelkern A solution to Karttunen’s problem is proposing to add Γ to the common ground. I will refer to an argument with this status as ‘salient’ or ‘shared’ or ‘publicly available’. An important point about salience is that an argument can be salient without being made explicit. If Bernhard and Mark can both hear snuffling from the box of hay, then Mark can say ‘Patch must be in the hay box’, without any further argument. Here, the premise that merits Mark’s conclusion—that Mark can hear snuffling from the box—is sufficiently salient, rendering the ‘must’-claim acceptable. Similarly, arguments can sometimes be accommodated, provided it is clear enough from the context what the speaker has in mind. Another noteworthy feature of salience is that the argument in question need not be salient at the time of the assertion; it can be provided shortly after the assertion, as in (10):7 (10) a. b. c. [Mark:] Patch must have gotten into the box of hay. [Bernhard:] Why do you say that? [Mark:] I heard her snuffling around when I was leaving. 3. Explaining Indirectness via Support Support, in addition to Indirectness, is thus necessary to characterize the difference in felicity conditions between a ‘must’-claim and its bare prejacent.8 How should we explain these differences? There are three possible strategies: account for Indirectness and Support separately; account for Support in terms of Indirectness, and give an independent account of Indirectness; or account for Indirectness in terms of Support, and give an independent account of Support. I will briefly arguing against the first two strategies and then pursue the third. 3.1. Against the first two strategies Considerations of theoretical parsimony tell against the first strategy. What about the second? This strategy is prima facie attractive, since there are a number of extant attempts to give an independent account of Indirectness; it is natural to try to recruit them to explain Support. But there are two significant problems with this approach. The first is that I do not believe that extant accounts of Indirectness are satisfying. I will not make this case here, however, because a second, simpler point suffices to show that the second strategy is wrong-headed: there does not seem to be any way to reduce Support to Indirectness. A natural first thought is that this reduction would go by way of a general pragmatic constraint that requires a speaker to share her evidence for a claim if that evidence is indirect. But there is no such pragmatic constraint, as we saw in cases above where non-modal claims were felicitous without shared evidence. A closely related thought is that there is a general pragmatic constraint which requires a speaker to share her evidence if she explicitly indicates the source of her 7 As 8I for other constructions that require something to be made salient, like anaphora resolution. will not take a stand on the further question of whether they are jointly sufficient. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 831 M. Mandelkern A solution to Karttunen’s problem evidence.9 But, again, as the example above with ‘apparently’ shows—and as cross-linguistic work on evidentials suggests (see Murray (2014))—there is no such constraint: one can use ‘apparently’ or evidential marking without sharing what your evidence is. A natural second thought is that Support reduces to a requirement to assure your interlocutors that Indirectness is satisfied. But this approach is not plausible, for a few reasons. First, the cases given above that are felt to be infelicitous without an argument—Patch in her box, Sarah in her windowless office building, the Russian safe-house—there is simply no reason to worry that the speaker’s evidence might not be indirect. Second, it is not generally true that whenever a formulation is constrained by a form of Indirectness, the speaker must habitually share her evidence in order to reassure her interlocutors that it satisfies the constraint in question: again, we saw this in (9) with ‘apparently’, which is governed by an Indirectness constraint, but which doesn’t require a shared argument.10 Finally, from a more theoretical standpoint, it is hard to see why an Indirectness constraint would ever directly yield an obligation to share one’s evidence: we are fairly charitable in assuming that speakers are complying with felicity conditions. For instance, if Indirectness were encoded as a presupposition, then, on a standard approach to presuppositions, it will be required that it be common ground that the speaker’s evidence for the prejacent is indirect. But in general interlocutors are perfectly happy to accommodate presuppositions,11 leaving it puzzling why Indirectness would lead to a requirement for a speaker to share her evidence. 3.2. Deriving Support from Indirectness I thus do not see a promising way for the second strategy to go. By contrast, I will argue now that the third strategy—deriving Indirectness from Support, and then giving an independent explanation of the latter—provides a satisfying solution to Karttunen’s Problem. In brief, the idea is as follows. I argue that an assertion of pMust ϕq is a bid to update the common ground with [[ϕ]]. Support then says that it is a proposal to do so on the basis of an argument Γ. General principles forbidding redundant assertions entail that [[ϕ]] should not follow from Γ in a way that is mutually recognized to be obvious. Finally, speakers are generally obligated to give their best argument for [[ϕ]] if they’re giving an argument for [[ϕ]] at all. It follows that, in order for an assertion of pMust ϕq to be felicitous, [[ϕ]] should not follow in a mutually obvious way from the best argument a speaker of pMust ϕq can have for [[ϕ]]; in other words, a form of Indirectness. The first step in our derivation is the assumption that an assertion of pMust ϕq is pragmatically strong in the sense that it is just as strong as an assertion of ϕ. Following Stalnaker (1978), I assume that an assertion of ϕ is a proposal to update the common ground with [[ϕ]]. Then we can spell out Pragmatic Strength as saying that an assertion of pMust ϕq is, inter alia, a proposal to update the common ground with [[ϕ]]: 9 Thanks to Justin Bledin for discussion. again, Murray (2014) likewise observes that grammatical evidential markers for indirectness do not give rise to any obligation to share one’s evidence. 11 See e.g. Lewis (1979), Stalnaker (2002) and many others. 10 And, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 832 M. Mandelkern A solution to Karttunen’s problem Pragmatic Strength: An assertion of pMust ϕq is as strong as an assertion of ϕ, in the sense that once the common ground is updated with [[Must ϕ]], it is updated with [[ϕ]]. Pragmatic Strength says that conversants do not typically leave open the possibility of [[¬ϕ]] after accepting pMust ϕq. To see its plausibility, note the weirdness of (11b) and (11c) as responses to (11a): (11) a. b. c. The gardener must be the murderer. I concur. Moreover, the gardener is the murderer. I concur. Let’s bring him and the butler in to see if we can pin down which of them is the murderer. Pragmatic Strength provides the most natural explanation of the infelicity of (11b) and (11c). The second step is to note that in general, when a speaker tries to get her interlocutors to accept [[ϕ]] on the basis of an argument, the argument must be non-redundant in a relevant sense. Compare the two variants in each of (12) and (13): (12) a. I put Patch in her box this morning, and no one has let her out. So she’s in her box. b. ??I see Patch in her box. So she’s in her box. (13) a. Clinton has amassed a majority of pledged delegates and superdelegates. So a woman will clinch the Democratic nomination! b. ??Clinton will clinch the Democratic nomination. So a woman will clinch the Democratic nomination! Without further justification for their repetitiveness, there is something pedantic or redundant about (12b) and (13b). By contrast, (12a) and (13a) are fine. The difference seems to be that in (12a) and (13a), there is enough epistemic space left between the argument in the first sentence and its conclusion in the second that its conclusion is not felt to be redundant. This intuition can be regimented as a norm against redundant assertions, along the following lines: Non-Redundancy: A proposal to update the common ground with [[ϕ]] on the basis of an argument Γ is infelicitous if [[ϕ]] follows from Γ in a way that is mutually recognized to be obvious. Non-Redundancy nicely captures the contrast between (12a) and (12b). The first is acceptable, since having put Patch in her box in the morning, together with no one else having let her out, does not, in an intuitive sense, obviously entail that Patch is in the box. The second is not, since it does follow in a mutually obvious way from seeing Patch in her box that she is in her box. Likewise for (13).12 12 Note that Non-Redundancy does not forbid post hoc support for an assertion with a redundant argument; it is perfectly fine to justify oneself, if challenged, with ‘Because I saw it’. What Non-Redundancy forbids is making Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 833 M. Mandelkern A solution to Karttunen’s problem The last step in our derivation says that a speaker must give the best argument for [[ϕ]] that she has, if she’s giving an argument for [[ϕ]] at all. To see the plausibility of this constraint, consider (14): (14) John was at the Red Sox game and knows on this basis who won. He also read about the game in the Boston Globe. a. [Max:] Who won the game? b. [John:] ?? The Red Sox, according to the Globe. If John intends (14b) to answer Max’s question, then there is something strange about it; we expect John to give his strongest evidence for the claim that the Red Sox won. In general, speakers are required to share the best piece of evidence they have for a claim, if they are sharing evidence at all. This follows naturally from a broadly Gricean vantage point on conversational dynamics. In (14b), John is violating Grice’s Maxim of Quantity by failing to ‘make his contribution as informative as is required (for the current purposes of the exchange)’ (Grice, 1989). More precisely, the general lesson of cases like this is a corollary of the Maxim of Quantity which I call Strongest Evidence:13 Strongest Evidence: When a speaker aims to update the common ground with [[ϕ]] on the basis of an argument Γ, she is obligated to do so by providing the strongest argument—the best piece of evidence—which she has for that claim. We can now put these pieces together to derive Indirectness from Support. Support says that an assertion of pMust ϕq is felicitous only if there is a shared argument for [[ϕ]]. Pragmatic Strength says that an assertion of pMust ϕq is a proposal to update the common ground with [[ϕ]]. I will make the plausible further assumption that an assertion of pMust ϕq is thus a proposal to update the common ground with [[ϕ]] on the basis of a shared argument for [[ϕ]] (this is an assumption that will fall out of the derivation of Support below). According to NonRedundancy, [[ϕ]] must not follow from that argument in a mutually obvious way. According to Strongest Evidence, that argument must constitute the best evidence the speaker has for [[ϕ]]. It follows that in order for a speaker to be able to felicitously assert pMust ϕq, [[ϕ]] cannot follow in a mutually obvious way from the speaker’s best piece of evidence for [[ϕ]]. In other words, the speaker’s best evidence for [[ϕ]] must be indirect, in the sense of indirectness relevant to evaluating whether an argument is felt to be redundant. Put differently: Suppose a speaker has direct evidence (in the sense relevant to judgments about redundancy) for [[ϕ]]. If she were to assert pMust ϕq, then due to Strongest Evidence and Support, she would have to give that evidence as an argument on the basis of which she is proposing her interlocutors accept [[ϕ]]; but then she would be bound to violate Non-Redundancy. So if she has direct evidence for [[ϕ]], she cannot assert pMust ϕq. an initial bid to update the common ground with something on the basis of an argument from which it follows in a mutually obvious way. 13 See Faller (2012) for more careful discussion of how this kind of reasoning would go. To spell out Strongest Evidence in more detail, we need to be able to access a scale of evidential strength, according to which, say, direct perceptual evidence counts as stronger than any kind of testimonial evidence. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 834 M. Mandelkern A solution to Karttunen’s problem In sum, in asserting pMust ϕq, the speaker has to ensure there is a shared argument which represents her best evidence for [[ϕ]], and yet is not so strong that it makes the ‘must’-claim sound redundant. Thus [[ϕ]] can’t follow in a mutually obvious way from her best evidence for [[ϕ]]. No parallel constraint follows for non-modal claims—since Support requires only that ‘must’-claims be supported by an argument—and thus Support, plus Pragmatic Strength, Non-Redundancy, and Strongest Evidence, entail a form of Indirectness. 3.3. Predictions The present proposal derives Indirectness from general principles about redundant assertions, and thus makes a striking empirical prediction: namely, that S’s evidence Γ for [[ϕ]] counts as indirect in the sense relevant to Indirectness just in case an assertion of ϕ following sequential assertions of the elements of Γ does not strike us as redundant. In addition to providing a new explanation for Indirectness, this also provides a new characterization of the notion of indirectness involved, an answer which I will now argue provides a better characterization of the data than the natural alternative, according to which ‘must’ lexically encodes a requirement that the speaker’s evidence be indirect in a sense that lines up with intuitions about whether evidence is direct or indirect, and with categories which are encoded by grammatical evidentials (I’ll call this ‘an evidential approach’). I will highlight a few points. First, the present approach predicts that ‘must’-claims based on reliable testimony like (15) will not be acceptable: (15) ??The website says the movie is at 7:30. So the movie must at 7:30. Our approach predicts this, since reliable testimony for [[ϕ]] is typically felt to be a redundant argument for [[ϕ]], as shown by examples like (16):14 (16) a. What time is the movie? b. ??The cinema website says that it’s at 7:30. So the movie’s at 7:30. By contrast, this is surprising on an evidential approach, since testimony is, intuitively, indirect evidence (it is natural to say that you know that the movie is at 7:30, but that you know indirectly, via the website). An evidential approach thus must simply stipulate that testimony ‘counts as direct’ for the purposes of evaluating ‘must’. The second prediction worth highlighting is that, on the present approach, what counts as redundant in a given context—and thus judgments about the felicity of ‘must’—depends on what counts as mutually obvious in that context. Thus, e.g., while (15) is infelicitous out of the blue, it may be felicitous in a context in which the inference from website listings to fact is not generally accepted, as in (17): 14 Why sequences like this are treated as redundant is, of course, an important question for theories of redundancy to address, but one I will not answer here. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 835 M. Mandelkern (17) A solution to Karttunen’s problem Google says that the movie is at 7:30. Websites listing movie times are generally extremely unreliable. Google is extremely reliable, though, so the movie is indeed at 7:30. Given the felicity of (17), we predict that a ‘must’-claim will be felicitous here as well; and indeed, (18) is felicitous: (18) Google says that the movie is at 7:30. Websites listing movie times are generally extremely unreliable. Google is extremely reliable, though, so the movie must indeed be at 7:30. More generally, we rightly predict that judgments about the felicity of ‘must’-claims depend on what counts as mutually obvious in context. It is not as clear how an evidential approach would predict this, since it does not seem like what counts intuitively as direct versus indirect evidence varies from context to context: our evidence for the time of the movie is equally indirect, in an intuitive sense, in (18) as in (16). Third, we can explain why ‘must’-claims that conclude a complicated argument are generally acceptable, even if the premises of the argument entail its conclusion. Examples of this kind, in particular those involving mathematical or logical claims, are the most puzzling examples for an evidential approach to ‘must’. ‘Must’ is often warranted in mathematical or logical contexts, like (19).15 (19) If the set of validities were decidable, then the halting problem would be decidable. The halting problem is not decidable. So the set of validities must be undecidable. It is not clear what the evidential approach would predict about (19). It is not clear that there is an intuitive sense on which our evidence that the set of validities is undecidable is indirect. Perhaps the evidential approach would claim that evidence for mathematical claims is always indirect in the relevant sense. But in addition to being somewhat stipulative, this response runs into trouble when it comes to examples like (20): (20) ??24 plus 24 must be 48. If all evidence from mathematics is indirect, then the evidential approach will wrongly predict that ‘must’ is warranted in (20) and sentences like it. In any case, it is not clear how the evidential approach can distinguish between cases like (19) versus (20). By contrast, our approach can. The conclusion of (19) does not follow in a way that is mutually obvious from the premises, whereas the conclusion of (20) does. 15 Is the ‘must’ here epistemic? Some have argued that this ‘logical’ ‘must’ is not genuinely epistemic (e.g. Giannakidou and Mari (2016), Goodhue (2016)). Two things militate against this option. First, it is inelegant to multiply modal flavors further than we need to. Second, even if we say that the logical ‘must’ is not epistemic, we still need a theory of its distribution, since it is not always warranted, even when its complement is a logical consequence of the common ground (as examples like (20) show); simply saying that this ‘must’ is logical, not epistemic, thus does not yet explain its behavior. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 836 M. Mandelkern A solution to Karttunen’s problem These points confirm the key claim of the present approach to Indirectness: what matters for determining whether a ‘must’ is warranted is not whether the speaker’s evidence for it is indirect in a sense which lines up with our intuitions about sources of evidence, or with categories encoded by grammatical evidentials, but rather whether the speaker’s evidence for it makes the prejacent mutually obvious. I conclude by discussing a different prediction of the present account. I have proposed that Indirectness arises due to conversational norms. It is a hallmark of pragmatic phenomena like this that they can be cancelled, since the underlying conversational norms are generally defeasible. We thus predict that Indirectness will be cancelled when one of the underlying norms is not in play. This prediction, again, is borne out, in particular in contexts in which Strongest Evidence is not in play because it is overridden by considerations which prevent the speaker from sharing her strongest evidence for [[ϕ]]. For instance, suppose that Mary is at Tom’s party. She goes out to the street to smoke, where she runs into Ben. She knows Ben wasn’t invited to the party, and doesn’t want him to know that she was invited. Ben can hear music coming from Tom’s place, and asks Mary what’s going on at Tom’s. Mary wants to communicate that he’s having a party, but she doesn’t want to share her strongest evidence for this—and doesn’t seem to be under any obligation to do so, since she is trying not to hurt Ben’s feelings. In this context, she can felicitously assert (21): (21) Given the music, it must be some kind of party. (21) may be misleading, but it is perfectly felicitous, despite the fact that Mary’s evidence is direct. The prediction of our pragmatic account is thus borne out: Indirectness can be violated when one of the underlying pragmatic norms can itself be appropriately ignored.16 4. Support Support plus independently motivated pragmatic principles thus provide a satisfying explanation of Indirectness. I turn now to the question of how to account for Support. I briefly criticize extant proposals before giving my own account. 4.1. Extant proposals Support says that ‘must’ requires that an argument for its prejacent be made salient. A natural first thought about how to account for Support is to treat ‘must’ as containing something like an implicit indexical which refers to an argument: ‘must’ means roughly ‘it follows from this argument that. . .’, where the implicit ‘this’ requires a salient referent. Stone (1994) suggests an account along just these lines: on his approach, ‘must’ has a lexical argument place which must be saturated by an argument made salient by context. In other words, ‘must’ denotes a two 16 It is less clear to me whether similar cases can be constructed in which it is Non-Redundancy which is suspended, since Non-Redundancy already has an element of context-sensitivity built in (since what counts as ‘mutually obvious’—in the objectionable sense relevant here—is itself context-dependent). But if we can find contexts in which it is suspended, then we predict that in those contexts as well, Indirectness will be suspended. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 837 M. Mandelkern A solution to Karttunen’s problem place operator, taking an argument and a proposition p, which says that the argument provides decisive reason to believe p. But a solution along these lines, natural though it is, does not work. The issue stems from the fact that no parallel to Support shows up for unembedded epistemic possibility modals. Consider (22): (22) Julie’s cat has been sneezing a lot lately. Ben asks her how the cat is doing. Julie says: a. Not so great. I need to take him to the vet, he might have an upper respiratory infection. b. Not so great. I need to take him to the vet, he has an upper respiratory infection. c. Not so great. I need to take him to the vet, he must have an upper respiratory infection. Suppose the conversation ends here. As Support predicts, (22c) is infelicitous as it stands, without an argument. By contrast (22a)—like the non-modal variant in (22b)—is perfectly fine here. This suggests that ‘might’ is not subject to a Support-like constraint. If we took Stone’s approach, however, then, provided we assume that ‘must’ and ‘might’ are duals, we would predict that ‘might’ has an anaphoric requirement for an argument, just as ‘must’ does: if ‘might’ means ‘not must not’, then the argument requirement of ‘must’ will project through negation, and thus ‘might’ will require a salient argument, too. We could avoid this by giving up the assumption that ‘must’ and ‘might’ are duals, and that ‘might’ does not have a lexical argument place for an argument. But, crucially, going this way leads to a serious new puzzle. Assuming we treat ‘cannot’ as equivalent to ‘not might’, then we will predict that unembedded ‘cannot’ does not have an anaphoric requirement for an argument any more than unembedded ‘might’ does. But this is wrong: the same examples we used to motivate Support for ‘must’ above can be used to motivate it for unembedded ‘cannot’ (modulo obvious changes). Thus, for instance, consider (23): (23) Emma notices that her neighbor Phil hasn’t taken in his mail in some time, and concludes that he is out of town. Another neighbor asks if Phil is around. Emma responds: a. No, he can’t be. b. No, he’s not. c. No, he can’t be: no one has taken his mail in for a week. d. No, he’s not: no one has taken his mail in for a week. The exchange ends here. (23a) is marked as compared with the other variants in (23). As with the examples involving ‘must’, then, ‘can’t’ seems to require that an argument be made salient, in this case not for its prejacent but for its negation. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 838 M. Mandelkern A solution to Karttunen’s problem Thus a lexical derivation of Support along the lines Stone suggests faces a dilemma: either treat ‘must’ and ‘might/can’ as duals, and wrongly predict that the latter have a Support-like requirement; or do not treat them as duals, and wrongly predict that ‘cannot’ lacks a Supportlike requirement. This approach thus strikes me as a non-starter. Similar criticisms extend to the account suggested in Swanson (2015), who builds on Kratzer (1981) in adopting a premise semantics for epistemic modals, with the added requirement that those premises be publicly available. This approach faces the same dilemma. If we treat ‘might/can’ as the duals of ‘must’, then this explanation will overgenerate: it will wrongly predict that they are likewise subject to Support, since they will likewise require a set of premises to be made public. Alternately, we could abandon duality, but then we cannot explain Support for ‘cannot’. The present objection can also be extended to a treatment of Support as a presupposition.17 Presuppositions project through negation; thus a presuppositional approach would either treat ‘might/can’ as duals of ‘must’, and thus wrongly predict that ‘might/can’ obey Support; or would abandon duality, and once again fail to predict Support for ‘cannot’. 4.2. Support as a manner implicature We can avoid these problems by deriving Support as a pragmatic implicature along the following lines. The derivation depends in part on adopting a semantics for ‘must’ defended in Stalnaker (2014) and Mandelkern (2016).18 I will not try to motivate the semantics here in general terms, but here’s a sketch. The idea is that ‘must’ is a universal quantifier over the set of worlds compatible with what is common ground after the ‘must’-claim in question has been made and negotiated (either accepted or rejected; call this the prospective common ground). pMust ϕq thus means, roughly, pWe will commonly believe [[ϕ]] after this claim is made and assessedq; ‘might’ is treated as the dual of ‘must’, and thus pMight ϕq will mean p[[ϕ]] is compatible with what we commonly believe, after this claim is made and assessedq.19 The basic idea is the familiar one that ‘might’ and ‘must’ are used to coordinate on what structural properties the context set has. I adopt the present semantics for ‘must’ partly because I think it is plausible, and partly because it lends itself naturally to the present derivation. A similar derivation of Support may well be possible with a different underlying semantics for ‘must’; the crucial features of the semantics for present purposes are, first, that it is pragmatically strong; and, second, that it makes salient the question of the interlocutors’ collective doxastic relationship to its prejacent. Any semantics for ‘must’ with these two features will suffice for present purposes. On the present approach, pMust ϕq and ϕ alone have the same basic update effect: namely, adding [[ϕ]] to the common ground. pMust ϕq is thus in competition with a different assertion which has the same basic update effect but which is structurally simpler: namely, an assertion 17 A suggestion due to Eric Swanson (p.c.). approach and Stalnaker’s differ in some ways, but the differences do not matter for our purposes. 19 This gloss is only rough, because these constructions embed differently. See Mandelkern (2016) for further discussion. The basic idea for embeddings is that the domain of quantification for embedded ‘must’ is determined by its local context. I will prescind from deciding whether to go in for a factive or a non-factive notion of common ground in spelling out this semantics. 18 My Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 839 M. Mandelkern A solution to Karttunen’s problem of ϕ alone.20 Because ϕ is structurally simpler,21 choosing an assertion like pMust ϕq instead requires some explanation. Because the two options have the same update effect, the interlocutors cannot reason that the speaker chose one of them because she didn’t know the other, or knew the other was false (as in scalar reasoning). There is, however, an important difference between pMust ϕq versus ϕ alone: namely, that the former makes salient the question of the interlocutors’ collective doxastic relation to [[ϕ]], while the latter does not: it is only about [[ϕ]]. There are a variety of ways to make this intuition precise; it doesn’t matter for our purposes how we choose between them.22 For our purposes, we can just treat the question raised by an assertion of any sentence ψ as the two cell partition {ψ, ψ̄}. Then the question made salient by an assertion of [[ϕ]] is just the question whether [[ϕ]] is true; whereas the question made salient by an assertion of pMust ϕq is the question whether we will come to commonly accept [[ϕ]]. Given that pMust ϕq has a simpler alternative with the same basic update effect (namely ϕ), if a speaker chooses to use this more complex expressions, then we will seek an explanation of this fact. Given that the chief difference between pMust ϕq and ϕ is in the question made salient by each, we will therefore reason that, in choosing the more complex option, she wishes to raise to salience the question of the group’s collective doxastic relation to [[ϕ]], and thus the group’s reasons for accepting [[ϕ]]. What kind of reason for accepting [[ϕ]] would be worth highlighting in this way? Whenever a speaker proposes to update the common ground with [[ϕ]], this provides ceteris paribus reason for her interlocutors to accept [[ϕ]]: namely, the speaker’s authority. A reason of this kind, therefore, is totally humdrum, and thus not worth highlighting. The use of an assertion like pMust ϕq rather than an assertion of ϕ alone thus can be justified only if the speaker wishes to highlight a substantial argument for [[ϕ]]—i.e., an argument over and above the speaker’s authority—on the basis of which the speaker wishes her interlocutors to accept [[ϕ]]. In other words (the interlocutors will reason), the speaker wishes them to accept [[ϕ]] on the basis of an argument that is commonly available to them. The speaker must, therefore, ensure that such an argument is salient—either by providing it, or being assured that her interlocutors can recover it from the common ground, possibly by accommodation. In short: Support arises as a manner implicature, thanks to the fact that the speaker chose to propose to accept [[ϕ]] by way of an assertion which makes reference to the interlocutors’ doxastic relation to [[ϕ]]. This approach has a number of attractions. First, it derives Support from a simple, independently motivated modal semantics, rather than lexical stipulation, and thus explains why Support arises for anything that has the meaning of ‘must’. Second, it avoids the problem raised 20 See Degen et al. (2015) for a different manner-implicature based approach to explaining the behavior of ‘must’. Like the present approach, that approach relies on the assumption that pMust ϕq is a costly alternative to ϕ whose use must be somehow explained. In contrast with the present approach, that approach attempts to derive Indirectness directly, rather than by way of Support, and without adverting to the different QUDs raised by modal vs. non-modal variants. 21 I will not spell out assumptions about how we calculate which alternatives are relevant. It seems fairly plausible that however we do so, ϕ will count as a relevant alternative to pMust ϕq (and p¬ϕq as a relevant alternative to pCan’t ϕq); this follows e.g. on the account given in Katzir (2007), according to which alternatives are calculated by the deletion or replacement of nodes at LF. 22 See Lewis (1988), Roberts (2012) and citations therein. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 840 M. Mandelkern A solution to Karttunen’s problem above for extant approaches. If we treat ‘might/can’ as duals of ‘must’, we will predict that the corollary of Support will be blocked for ‘might/can’, but will still be derived for ‘cannot’. First, the derivation of a Support constraint for ‘might/can’ will be blocked because a crucial step in our derivation of Support was that pMust ϕq has a structurally simpler alternative with the same basic update effect; this obviously does not hold for pMight ϕq, which has a very different update effect than ϕ. And, second, assuming that ‘can’ and ‘might’ mean the same thing, and that ‘not’ scopes over ‘can’ in ‘cannot’, the derivation given above will extend immediately to unembedded ‘cannot’, predicting in particular that Support and Indirectness arise for the negation of the prejacent of ‘cannot’, just as they do for the prejacent of ‘must’. Note that for the same reason that this derivation of Support is blocked for ‘might’, the corresponding derivation of Support will likewise be blocked for weak epistemic necessity modals like ‘ought’ and ‘should’, as well as probability modals, since assertions of pought/should/probably ϕq and ϕ do not have the same basic update effect. These predictions again seem correct: (24) a. b. When do you want to meet? Let’s say Thursday; (i) I should be free then. (ii) I ought to be free then. (iii) I’ll probably be free then. (iv) I must be free then. If the conversation ends here, responses (24bi), (24bii), and (24biii) are all acceptable; by contrast, (24biv) is a strange way to end the conversation, and seems to require that some argument be given (‘. . .my secretary always leaves my Thursdays open’). The prediction of the present account, then—that modals which are not Pragmatically Strong, like ‘might/ought/should/probably’, do not carry a Support constraint—thus seems correct.23 The present proposal makes a prediction which is worth highlighting: any construction which has the features which played a role in the present derivation is predicted to give rise to a Support-like constraint. That is, any construction which has ϕ as a structurally simpler relevant alternative; which has the same basic update effect as an assertion of ϕ; and which highlights the speakers’ collective doxastic relation to [[ϕ]], is, ceteris paribus, predicted to give rise to Support (and thus also Indirectness). Further research should examine other expressions that share these three features to see if this prediction is borne out.24 23 And the Indirectness inference for ‘might/ought/should/probably’ is easy to explain on pragmatic grounds without a detour through Support. 24 pIt’s agreed that ϕq, pLet’s agree that ϕq, pWe should believe ϕq, and pIt is clear that ϕq all seem to have these properties, and do indeed appear to be governed by corollaries of Support and Indirectness (see Barker 2009 on the last of these). This suggests that, even if the pragmatic derivation I have given here is mistaken in some of its details, the explanation for both Indirectness and Support is pragmatic, and stems from the properties I have pointed to. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 841 M. Mandelkern A solution to Karttunen’s problem 5. Conclusion The argument of this paper has come in three parts. I began by arguing that, to fully characterize the differences in felicity conditions between an assertion of pMust ϕq and an assertion of ϕ, we need not only Indirectness but also Support. Next, I argued that we can derive Indirectness from Support together with general pragmatic principles about assertions, and I argued that this derivation of Indirectness makes attractive predictions about when a ‘must’-claim is unacceptable. Finally, I made a proposal about how to derive Support as a manner implicature from a certain semantics for epistemic modals which treats them as quantifiers over the set of worlds compatible with the common ground. The three parts of this argument are, to a degree, independent. If each of these moves is successful, however, then taken together, they constitute a solution to Karttunen’s Problem: characterizing and explaining the differences in felicity conditions between an assertion of pMust ϕq and an assertion of ϕ. In short: because of its more complex form and the question it makes salient, pMust ϕq, unlike ϕ alone, requires that an argument be given for [[ϕ]]; and from the requirement, in turn, we can conclude that the speaker’s evidence for [[ϕ]] is relevantly indirect. In conclusion, I highlight a few broad upshots of my approach to Karttunen’s Problem. The first is about the relation between ‘must’ and evidentiality. I have argued that ‘must’ does not grammaticalize a certain constraint on the type of evidence, in any intuitive sense, which the speaker must have for its prejacent. Rather, the felt indirectness of ‘must’-claims is accounted for pragmatically, and it is accounted for not directly in terms of judgments about type of evidence but rather in terms of judgments about redundancy. The second is about the meaning of ‘must’. My derivation of Support rests on a certain semantics for ‘must’. If the derivation is successful, then it provides an argument for adopting that semantics, and presents a challenge for advocates of different semantics for ‘must’: to show how those approaches can explain Support. The third regards the theory of redundancy. I have argued that the norms that governs redundancy in assertions play a crucial role in explaining our interpretation of modal language. My sketch of what those norms are like, however, leaves unanswered substantial questions, in particular about what counts as a ‘mutually obvious’ inference—questions which I hope to explore in future work. A theory of redundancy—in essence, a theory of how our minds structure and access information—will play a central role in understanding the way that information is structured in discourse, and judgments about ‘must’-claims provide a rich source of data for this theory. I close with an abstract point about the architecture of semantic and pragmatic theories. My proposal rests on the assumption that an assertion of pMust ϕq and an assertion of ϕ have the same basic update effect, but different semantic values. Indeed, on the semantics I have sketched, pMust ϕq and ϕ informationally entail one another—in the sense that a context updated with either one entails the other—but they do not semantically entail one another. The possibility of this divergence between update effect and meaning proved essential for simultaProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 842 M. Mandelkern A solution to Karttunen’s problem neously capturing the intuition that an update with pMust ϕq is pragmatically strong, and the intuition that it cannot always be asserted where ϕ alone can be. Not everyone thinks that we should distinguish between semantic content and pragmatic update effect at all; in particular, at a high level, certain threads in dynamic semantics aims to identify these. If the present approach to Karttunen’s Problem is the right one, however, then distinguishing semantic content from pragmatic update effect in our theorizing about natural language turns out to be crucial. References Barker, C. (2009). Clarity and the grammar of skepticism. Mind and Language 24(3), 253–73. Degen, J., J. T. Kao, G. Scontras, and N. D. Goodman (2015). A cost- and information-based account of epistemic must. 28th Annual CUNY Conference on Human Sentence Processing. Faller, M. (2012). Evidential scalar implicatures. Linguistics and Philosophy 35, 285–312. von Fintel, K. and A. Gillies (2010). Must...stay...strong! Natural Language Semantics 18(4), 351–383. Giannakidou, A. and A. Mari (2016). Epistemic future and epistemic MUST: Nonveridicality, evidence, and partial knowledge. In Mood, Aspect and Modality: What is a Linguistic Category? University of Chicago. Goodhue, D. (2016). Epistemic must is not evidential, it’s epistemic. In Proceedings of the North East Linguistic Society (NELS), Volume 46. Grice, P. (1989). Studies in the Way of Words. Harvard. Karttunen, L. (1972). Possible and must. In J. Kimball (Ed.), Syntax and Semantics, Volume 1, pp. 1–20. New York: Academic Press. Katzir, R. (2007). Structurally-defined alternatives. Linguistics and Philosophy 30, 669–690. Kratzer, A. (1981). The notional category of modality. In H. Eikmeyer and H. Rieser (Eds.), Words, Worlds, and Contexts: New Approaches in Word Semantics. de Gruyter. Kratzer, A. (1991). Modality. In A. von Stechow and D. Wunderlich (Eds.), Semantics: An International Handbook of Contemporary Research, pp. 639–650. Berlin: de Gruyter. Kratzer, A. (2012). Modals and Conditionals. Oxford: Oxford University Press. Lassiter, D. (2016). Must, knowledge, and (in)directness. Natural Language Semantics 24, 117–163. Lewis, D. (1979). Scorekeeping in a language game. Journal of Philosophical Logic 8(1), 339–359. Lewis, D. (1988). Relevant implication. Theoria 54(3), 161–74. Mandelkern, M. (2016). How to do things with modals. Manuscript. Matthewson, L. (2015). Evidential restrictions on epistemic modals. In L. Alonso-Ovalle and P. Menendez-Benito (Eds.), Epistemic Indefinites. New York: Oxford University Press. Murray, S. (2014). Varieties of update. Semantics and Pragmatics 7(2), 1–53. Roberts, C. (1998/2012). Information structure in discourse: Towards an integrated formal theory of pragmatics. Semantics and Pragmatics 5, 1–69. Sherman, B. (2016). Open questions and epistemic necessity. Manuscript. Stalnaker, R. (1970). Pragmatics. Synthese 22, 272–289. Stalnaker, R. (1978). Assertion. In P. Cole (Ed.), Syntax and semantics, Volume 9, pp. 315–322. New York: Academic Press. Stalnaker, R. (2002). Common ground. Linguistics and Philosophy 25, 701–721. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 843 M. Mandelkern A solution to Karttunen’s problem Stalnaker, R. (2014). Context. Oxford University Press. Stone, M. (1994). The reference argument of epistemic must. In Proceedings of IWCS 1, pp. 181–190. Swanson, E. (2015). The application of constraint semantics to the language of subjective uncertainty. Journal of Philosophical Logic 45(121), 121–146. Veltman, F. (1985). Logics for Conditionals. Ph. D. thesis, University of Amsterdam. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 844 Expletive negation and the decomposition of only1 Daniel MARGULIS — Massachusetts Institute of Technology Abstract. This paper is focused on the seemingly superfluous sentential negation showing up in Hebrew until-clauses. I discuss a scalar implicature arising from until-clauses which surprisingly becomes uncancellable when this negation is present. I argue that this inference becomes obligatory due to the presence of an only-like exhaustivity operator, which gets (partially) spelled out as negation since it is composed of negation and an exceptive. Moreover, this negation is shown to share more properties with only. Keywords: Expletive negation, exhaustification, scalar implicatures, until. 1. Introduction A seemingly superfluous negation participates in a multitude of constructions, among which are certain temporal clauses. This paper is focused on the superfluous sentential negation showing up in Hebrew until-clauses.2,3 I refer to sentential negation which does not make a straightforward contribution to meaning as E XPLETIVE N EGATION or E X N in short. The assumption that sentential negative morphemes are interpreted as negative operators is what makes E X N puzzling.4 In this paper I discuss a scalar implicature arising from until-clauses which surprisingly becomes uncancellable when E X N is present. I argue that this inference becomes obligatory due to the presence of an only-like exhaustivity operator, which gets (partially) spelled out as negation. According to the proposal put forward in the paper, negation is capable of realizing an only-like operator because such an operator is actually composed of negation and an exceptive, as has already been proposed for overt only in von Fintel and Iatridou (2007). 1 For helpful comments and insightful discussion I thank Kai von Fintel, Danny Fox, Martin Hackl, Irene Heim, Sabine Iatridou, Ezer Rasin, and Roger Schwarzschild. I would also like to thank Moshe E. Bar-Lev, Itai Bassi, Gennaro Chierchia, Cleo Condoravdi, Luka Crnič, Veneeta Dayal, Michel DeGraff, Aron Hirsch, Roni Katzir, Giorgio Magri, David Pesetsky, Maribel Romero, and Milena Sisovics. Earlier versions of this paper were presented at the Hebrew University, Tel Aviv University, the Göttingen Negation workshop (September 2015), SNEWS 2015 at Harvard, and WCCFL 32 in Salt Lake City. 2 The phenomenon is also attested at least in Bangla (Ishani Guha, p.c.), French (Sophie Moracchini, p.c.), German (Krifka, 2010), Italian (Tovena, 1996), and Russian (Abels, 2005). 3 Other occurrences of puzzling negation which will not be discussed in this paper include negative concord (Zeijlstra, 2004, 2008: among many others), preposed negation in biased polar questions (Ladd, 1981; Büring and Gunlogson, 2000; Romero and Han, 2004; Han and Romero, 2004), rhetorical and tag questions, exclamatives (Portner and Zanuttini, 2000), complements of certain attitude predicates (Abels, 2005; Yoon, 2012; Makri, 2015), comparatives, and complements of almost (Kaufmann and Xu, 2013). 4 The puzzle remains as long as one assumes a correspondence between the negative morpheme and an interpreted negative operator. In the simple case the negative morpheme itself carries the negative semantics. A sentential negative morpheme could also give rise to an interpreted negative operator when it is in a dependency with an abstract negation, as in Zeijlstra’s (2004; 2008) work on negative concord. In both cases, a superfluous negative morpheme is perplexing. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 845 D. Margulis Expletive negation and the decomposition of only Such an analysis predicts that E X N and only should share more properties. I show that this prediction is borne out: E X N is odd when there are no alternatives to exclude, it is incompatible with overt only and with downward entailing (DE) environments, it triggers optional stress and preposing of the until-clause, and cannot license negative concord. The paper is structured as follows: §2 presents the data on E X N and its interpretive effect. §3 consists of the analysis in which only is decomposed into negation and an exceptive, and shows how it can capture the semantics and syntax of E X N. §4 discusses further predictions of the proposal and shows that they are borne out. §5 concludes and briefly mentions questions that are left open. 2. Data 2.1. E X N in until-clauses A Hebrew until-clause can host the sentential negation lo, superficially without affecting interpretation, as demonstrated by the following examples.5 (1) adam hu xaf mi-peSa ad Se (lo) huxexa aSmat-o man he free from-crime until that NEG was proven guilt-his ‘A man is innocent until proven guilty.’ (2) ze lo nigmar ad Se ze (lo) nigmar it NEG finished until that it NEG finished ‘It ain’t over till it’s over.’ (3) joni jaSan ad Se ha-Sxenim (lo) hidliku muzika Y. slept until that the-neighbors NEG lit music ‘Yoni was asleep until the neighbors turned some music on.’ (4) ha-Svita timaSex ad Se (lo) jePanu driSot ha-ovdim the-strike will continue until that NEG will be answered demands the-workers ‘The strike will continue until the workers’ demands are met.’ (5) miri lo nirdemet ad Se (lo) korPim l-a sipur M. NEG falls asleep until that NEG read.PL to-her story ‘Miri doesn’t fall asleep until you read her a story.’ Note that (1)–(5) can in principle have an additional reading in which negation is interpreted as usual. For example, (1) can have the (odd) reading ‘A man is innocent until not proven guilty’.6 5 Examples 6 As (1) and (3) are modified versions of Eilam’s (2007) examples (3) and (5). Eilam (2007) observed, this reading is the only one available if the negative morpheme lo is stressed. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 846 D. Margulis Expletive negation and the decomposition of only 2.2. The Interruption Implication 2.2.1. Optional interruption without E X N In this subsection I discuss English examples, but it should be noted that the facts are the same for Hebrew until-clauses when they do not contain E X N. The next subsection contains discussion of Hebrew E X N cases. Sentences containing until generally give rise to an inference – which I call THE INTERRUP TION IMPLICATION – according to which the matrix eventuality came to an end upon the onset time of the until-phrase/clause. From (6) for example, one infers that Mary stopped playing the piano at five or at the time of John’s opening the door. (6) Mary played the piano until five / until John opened the door. ¬[Mary played the piano after five / after John opened the door]. The interruption implication has two properties of a scalar implicature: (i) it is cancellable, and (ii) it does not arise when the until-clause is embedded in a downward-entailing environment. None of (7a)–(7d) gives rise to the interruption implication. (7) In all the following 6 ¬[Mary played the piano after John opened the door]: a. Mary played the piano until John opened the door. Moreover, she was still playing the piano (when and) after he opened it. b. Mary played the piano until John opened the door and perhaps even afterwards. c. Mary played the piano at least until John opened the door. d. Q: Is Mary still playing the piano? A: Well, I’m not sure but (what I know is that) she definitely played the piano until John opened the door. Scalar implicatures are known to disappear in downward-entailing environments. Compare (8a) to (8b), which embeds a minimally modified version of (8a) in the restrictor of a universal quantifier, a downward-entailing environment. If the not all inference in (8a) were part of the meaning of some, we should expect (8b) to quantify over students who did only some of the reading. However, it follows from (8b) that students who did all of the reading got an A just like those who did some but not all of it. (8) a. b. Mary did some of the reading. ! Mary did only some of the reading. (= M. did some but not all of it.) Every student who did some of the reading got an A. ! 6 Every student who did only some of the reading got an A. Similarly, the interruption implication in (9a) is not preserved in (9b). Those students who played the piano not only until John opened the door, but even until some later time, are entitled to a prize to no lesser degree than those who played the piano only until John opened the door. This is a reason not take the interruption implication to be part of the lexical semantics of until. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 847 D. Margulis (9) Expletive negation and the decomposition of only a. b. Mary played the piano until John opened the door. ! Mary played the piano only until John opened the door (and no later). Every student who played the piano until John opened the door will get a prize. ! 6 Every student who played the piano only until opened the door (and no later) will get a prize. The cancellability of the interruption implication and its disappearance in downward entailing environments puts it in the same group of inferences as scalar implicatures. Now let us see how E X N affects the availability of the interruption implication. 2.2.2. Obligatory interruption with E X N The facts are the same for Hebrew until-clauses, but only without E X N. E X N makes the interruption implication obligatory: it cannot be cancelled nor can an until-clause containing E X N be embedded in a downward-entailing environment. (10) (11) (12) joni jaSan le-faxot ad Se azavti Y. slept to-less until that 1.left ‘Yoni slept at least until I left.’ *joni jaSan le-faxot ad Se lo azavti Y. slept to-less until that NEG 1.left (cf. (10) and (7c)) joni jaSan ad Se lo azavti, #ve-ulaj afilu ad zman mePuxar joter Y. slept until that NEG 1.left, and-maybe even until time late more ‘Yoni slept until I left #and perhaps even until some later time.’ (cf. (7b)) Example (13a), but not (13b), can be used in the exchange in (14), which requires at least partial ignorance regarding Yoni’s awakening time (cf. (7d)). (13) a. joni jaSan ad Se azavti Y. slept until that 1.left ‘Yoni was asleep until I left.’ (14) Q: Is Yoni still asleep? A: Well, I’m not sure but (13a). A’: #Well, I’m not sure but (13b). b. joni jaSan ad Se lo azavti Y. slept until that NEG 1.left ‘Yoni was asleep until I left.’ In the previous section we have seen scalar implicatures disappear in downward-entailing (DE) environments. Later I will propose that E X N is related to a grammatical mechanism generally responsible for scalar implicatures. If they disappear in DE environments because this mechanism cannot take place in such environments, we expect a clash between DE environments and E X N. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 848 D. Margulis Expletive negation and the decomposition of only Consistent with the obligatoriness of the interruption implication with E X N, an until-clause containing E X N cannot be embedded in a DE environment such as the restrictor of a universal quantifier (15b) or the antecedent of a conditional (16b). Examples (15c) and (16c) show that E X N is allowed in related upward-entailing environments: the restrictor of one and the consequent of a conditional. (15) a. kol mitmoded Se jaPatsor et ha-neSima ad Se ha-paamon every contestant that 3.stop.FUT ACC the-breath until that the-bell jetsaltsel jekabel pras 3.ring.FUT 3.receive.FUT prize ‘Every contestant who holds their breath until the bell rings will get a prize.’ b. ??kol mitmoded Se jaPatsor et ha-neSima ad Se ha-paamon lo every contestant that 3.stop.FUT ACC the-breath until that the-bell NEG jetsaltsel jekabel pras (nixumim) 3.ring.FUT 3.receive.FUT prize (consolations) ‘Every contestant who holds their breath until the bell rings will get a (consolation) prize.’ c. mitmoded exad Se jaPatsor et ha-neSima ad Se ha-paamon lo contestant one that 3.stop.FUT ACC the-breath until that the-bell NEG jetsaltsel jekabel pras 3.ring.FUT 3.receive.FUT prize ‘One contestant who holds their breath until the bell rings will get a prize.’ (16) a. im miri taPatsor et ha-neSima ad Se ha-paamon jetsaltsel, hi if M. 3.stop.FUT ACC the-breath until that the-bell 3.ring.FUT she tekabel pras 3.receive.FUT prize ‘If Miri holds her breath until the bell rings, she will get a prize.’ b. ??im miri taPatsor et ha-neSima ad Se ha-paamon lo jetsaltsel, hi if M. 3.stop.FUT ACC the-breath until that the-bell NEG 3.ring. FUT she tekabel pras 3.receive.FUT prize ‘If Miri holds her breath until the bell rings, she will get a prize.’ c. im miri rotsa le-kabel pras, hi taPatsor et ha-neSima ad Se if M. wants to-receive prize, she 3.stop.FUT ACC the-breath until that ha-paamon lo jetsaltsel the-bell NEG 3.ring. FUT ‘If Miri wants to get a prize, she will hold her breath until the bell rings.’ To summarize the data in this section, the interruption implication, an otherwise optional scalar implicature, becomes obligatory with E X N. Moreover, E X N cannot be embedded in DE environments. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 849 D. Margulis Expletive negation and the decomposition of only 3. Analysis 3.1. The core of the proposal: only An intuition which can provide insight into the contribution of E X N is that adding E X N to an until-clause parallels the addition of only: Mary played until John E X N opened the door ≈ Mary played only until John opened the door. Fleshing out this intuition will get us closer to an LF and allow us to predict the obligatoriness of the interruption implication with E X N. (17) Hypothesis: until-clauses hosting E X N contain an only-like exclusive particle. If an only-like exclusive particle is involved, we need to determine the set of alternatives it operates on. Suppose that ϕ until t has the set of alternatives in (18), for any t− ,t,t+ such that t− < t < t+ : (18) Alt(ϕ until t) = {. . . , ϕ until t− , ϕ until t, ϕ until t+ , . . . } That is, the alternatives of ϕ until t differ from it only in the time until which ϕ holds. This way we can generate a set of alternatives that exhausts the entire (contextually restricted) temporal domain.7 Crucially, this set of alternatives is ordered by entailment, as shown in (19). For example, ϕ until five asymmetrically (Strawson-)entails that ϕ until four. (19) (λ w. ϕ until t+ in w) ⊂ (λ w. ϕ until t in w) ⊂ (λ w. ϕ until t− in w) To see that the hypothesis in (17) makes the correct predictions, let us assume for now that (20) holds. In the next section I modify (20) and explicate the affinity between E X N and only. (20) Assumption (to be modified): E X N is semantically vacuous but triggers obligatory strengthening in the sense of Fox (2007); Chierchia et al. (2012); Chierchia (2013). That is, E X N requires the alternatives of the clause in which it occurs to not be ignored but be taken into consideration by an exhaustivity operator. Such an operator is a covert counterpart of only, a simplified version of which is defined in (21). E XHAUST asserts the truth of its prejacent and the falsity of any alternative which is not entailed by the prejacent.8 Assuming for simplicity that the only alternatives are the ones in (18), strengthening results as in (22). (21) (22) JE XHAUSTK = λ Ast,t .λ pst .λ ws . p (w) = 1 ∧ ∀q ∈ A [(p 6⊆ q) → q (w) = 0] ≈ JOnlyK JE XHAUST(Alt) (ϕ until t)Kw = 1 iff ϕ until t in w ∧ for any t+ > t, ¬ [ϕ until t+ ] in w 7I am assuming that until’s complement has to denote a time, either inherently (‘until five’) or by definitizing a temporal property (‘until John opened the door’). For more details see §3.3.1. 8 The denotation in (21) omits Fox’s (2007) qualification that the excluded alternatives be INNOCENTLY EX CLUDABLE. This is so since in the case of (18), the alternatives are already totally ordered, and in particular all non-weaker alternatives are innocently excludable. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 850 D. Margulis Expletive negation and the decomposition of only This is so because both ϕ until t and ϕ until t− are entailed by ϕ until t, but ϕ until t+ is not. Thus, ϕ until t ends up meaning ϕ until t and no later than t, giving us the interruption implication.9 Moreover, the incompatibility of E X N with DE-environments (§2.2.2) is predicted by the analysis when taken together with any grammatical theory of scalar implicatures which explains their disappearance in such environments by lack of exhaustification. In other words, since I propose to relate E X N with E XHAUST, all that is needed to predict E X N’s incompatibility with DE-environments is a reason for E XHAUST to be incompatible with such environments. Since such incompatibility is in fact attested, I submit that once we have an explanation for this phenomenon the incompatibility of E X N with DE-environments would be predicted without further stipulations.10 3.2. Decomposing only Why should the assumption in (20) hold? It would be peculiar for a negative morpheme to be ambiguous between actual negation and E X N, especially across so many languages (see fn. 2). So how should one think of the association between E X N and only? If one entertains the possibility that E XHAUST is syntactically complex, containing a negative piece, one could better understand E X N as a plain compositional negation. (23) Revised hypothesis a. Until-clauses hosting E X N contain an only-like operator. (= (17)) b. The negative morpheme is a reflex of a negative component of that operator. 3.2.1. Sufficiency Modal Constructions One decomposition of only is proposed by von Fintel and Iatridou (2007), who discuss S UFFI CIENCY M ODAL C ONSTRUCTIONS such as in (24): (24) To get good cheese, you only have to go to the North End. They observe that crosslinguistically, one also finds a second pattern: To get good cheese, you 9 For convenience I will continue referring to the interruption implication as a scalar implicature, even though under the grammatical view adopted here scalar implicatures are analysed as entailments. 10 It should be noted that unlike E XHAUST and E X N, overt only is allowed in DE environments: (i) (ii) If the rhino eats only artichokes, it might be sick. Every rhino who ate only artichokes was examined by the vet. Additionally, the prejacent is treated differently by the two operators: E XHAUST asserts it, while only presupposes it. An idea suggested to me by Danny Fox (p.c.) would be that while only and E XHAUST are built of the same parts, E XHAUST involves local accommodation, thus turning the presupposed prejacent into an asserted one. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 851 D. Margulis Expletive negation and the decomposition of only do not have but go to the North End. The following are two examples adapted from von Fintel and Iatridou’s (2)–(3): (25) (26) . . . dhen echis para na pas sto North End NEG have.2 SG EXCEPT NA go.2 SG to.the North End ‘. . . you only have to go to the North End’ . . . tu n’as qu’à aller au North End you NE-have QUE-to go to.the North End ‘. . . you only have to go to the North End’ (Greek) (French) Another observation made by von Fintel and Iatridou is that for a (goal-oriented necessity) modal to be able to participate in a sufficiency modal construction, it has to be a non-PPI modal. That is, it has to be able to scope under negation. Von Fintel and Iatridou propose to treat only crosslinguistically – even in languages where there are no overt negation-and-exceptive sufficiency constructions – as composed of a negation and an exceptive. Together with the assumption that the exceptive is (or hosts) an NPI, they allow the modal to take scope between the two components: (27) To get good cheese, you do not have to do anything other than going to the N. End. 3.3. Proposal: E X N is an exponent of only To briefly sum up, the data involves a negative morpheme along with an obligatory interruption implication, which I submit results from an only-like exhaustivity operator (§3.1). The decomposition of only into a negative part and an exceptive part as proposed by von Fintel and Iatridou (2007) paves the way to understanding E X N as a regular compositional negation: if E X N is the negative component of the exhaustivity operator, as I propose, we can predict the data while maintaining a single meaning for the negative morpheme. To achieve this I will assume that both pieces are syntactically present: negation is overt, while the exceptive is covert. A sentence of the form A until E X N B is thus paraphrasable as A until not anything other than B. As before, assuming that what anything other than ranges over is times (18), we would not be able to exclude any earlier time due to entailment, but would be able (and required) to exclude later times, thus predicting the interruption implication. In the following two sections I go through the details of the proposal. 3.3.1. Assumptions The following structure is what I take to be the LF for Mary played the piano until John E X N opened the door. I return to the decomposition of E XHAUSTP after discussing my assumptions below. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 852 D. Margulis Expletive negation and the decomposition of only (28) E XHAUSTP 3 ∃ closure E XHAUST Alt MAX John open the door Mary play the piano until t3 The movement step in (28) is a case of Focus-movement, a kind of sideways movement discussed in Wagner (2007) and Erlewine and Kotek (2017), among others. The associate of the focus-sensitive operator E XHAUST moves to it, as the associate of only would in Wagner’s (2007) analysis. I will assume that clauses denote temporal properties (i.e., characteristic functions of sets of time intervals).11 I follow Condoravdi (2010) in: (i) taking until to uniformly compose with a time, even when its surface complement is a clause, and (ii) assuming that a maximality operator MAX (i.e., a definite determiner of type hit, ii) applies to until’s clausal complement to yield the desired time argument: the (smallest) maximal interval instantiating the complement. Until will be analyzed as denoting a relation between times: JuntilK ∈ Dhi,iti . It composes with its first argument, be it a time-denoting DP or a clause, resulting in a temporal property (i.e., of type hi,ti). This temporal property then composes intersectively (i.e., by Predicate Modification) with the matrix clause. To capture the entailment that the main clause was true at all times up to the time of the untilphrase, I take it that until’s quantificational force is universal. Just like other quantifiers, until has a contextually restricted domain (von Fintel, 1994). The domain of time intervals Di is contextually restricted to its subset Ci . This would prevent Mary played the piano until five from entailing that she played the piano since the beginning of time. 11 These functions of type hi,ti could in principle be extended to other kinds of intensions in various ways (e.g., by assuming that type s is of world-time pairs and that clauses are of type hs,ti, or that clauses are of type hi, sti or hs, iti). Since this extension is immaterial to the analysis, I ignore worlds altogether. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 853 D. Margulis Expletive negation and the decomposition of only Alternatives are derived by substituting until’s complement with other times in Ci . Thanks to keeping Ci constant, until 5 ends up asymmetrically (Strawson-)entailing until 4 (as far as Strawson-entailment is concerned, this is a variant of Condoravdi, 2010). I implement von Fintel and Iatridou’s (2007) view of the exceptive phrase as being an NPI and having existential force by taking the exceptive phrase to contain, in addition to the exceptive head, an existential quantifier restricted to a contextually salient domain. In the relevant cases the domain is the contextually restricted temporal domain Ci . Given these assumptions, the decomposition of E XHAUST P in (28) is as follows: (29) NEG [∃ [Ci [EXCEPT [MAX [John open the door]]]]] Note that there is a tension between the semantics and the surface syntax regarding the position of negation. For interpretation, we need it scoping as high as possible to negate not only the until-clause but also the matrix clause. On the other hand, negation shows up inside the untilclause in the surface string (see more on this in §3.3.3). To allow a suitable configuration, I will assume the following structure, with a negation of type hitt, itti.12,13 (30) E XHAUSTP 3 NEG ∃ closure ∃ Ci EXCEPT Mary play the piano until MAX t3 John open the door 12 Other cases of high-type negation include determiner negation such as no NP, not every NP, as well as the ones in impossible and unhappy. 13 The semantics is compatible with negation occupying a lower position, adjoined to the the existential quantifier in (29), or a higher position, c-commanding both the matrix clause and the until-clause. The former would be similar to determiner negation in fn. 12, while the latter would be plain propositional negation. The proposal ends up not taking either of these paths due to the surface position of negation, as discussed in §3.3.3. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 854 D. Margulis Expletive negation and the decomposition of only 3.3.2. Denotations and calculations Below I specify the denotations of the components and their composition. The discussion considers nominal complements as well as clausal complements of until. (31) (32) JPK := JMary played the pianoK = λti . Mary play the piano at t a. b. JuntilK = λti0 .λti00 . ∀t ∈ Ci [(t < t 0 ) → (t ⊆ t 00 )]. In words, until relates two times, returning truth iff all times preceding the first are contained within the second. Juntil fiveK = λti00 . ∀t ∈ Ci [(t < 5pm) → (t ⊆ t 00 )]. That is, the (characteristic function of the) set in Ci of all times which contain all times preceding 5pm. (33) Entailment between alternatives (cf. (19)): λti00 . ∀t ∈ Ci [(t < 5pm) → (t ⊆ t 00 )] ⊂ λti00 . ∀t ∈ Ci [(t < 4pm) → (t ⊆ t 00 )] That is, the set of times containing everything in Ci which precedes 5pm is a proper subset of the set containing everything in Ci preceding 4pm. This is so because if all times up to five are in an interval, then all times up to four are also in that interval, so any interval in the former set will be in the latter set. The latter set additionally contains at least an interval whose right edge is four, which is not a member of the former set. Thus we have captured the downward entailment property of until. (34) Without interruption: JP until fiveK = λti . JPK (t) = 1 ∧ ∀t 0 ∈ Ci [(t 0 < 5pm) → (t 0 ⊆ t)] That is, the (characteristic function of the) set in Ci of all times at which Mary played the piano and which also contain all times prior to five.14 (35) a. b. c. d. (36) Without interruption:   JP until MAX OK = λti00 . JPK (t 00 ) = 1 ∧ ∀t ∈ Ci t < tO j → (t ⊆ t 00 ) That is, the (characteristic function of the) set in Ci of all times at which Mary played the piano and which also contain all times prior to John’s door-opening. (37) With interruption: J(30)K = 1 iff ¬∃t 00 ∈ Ci [t 00 6= tO j ∧ ∃t 0 [JPK(t 0 ) = 1 ∧ ∀t ∈ Ci [t < t 00 → t ⊆ t 0 ]]] That is, (30) is true iff there doesn’t exist a time other than John’s door-opening time until which Mary plays the piano. 14 I JOK := JJohn opened the doorK = λti . John open the door at t JMary played the piano until John opened the doorK = JP [until [MAX [O]]]K tO j := JMAX[O]K = the smallest t s.t. ∀t 0 [JOK(t 0 ) = 1 → t 0 ⊆ t], if defined Juntil [MAX (O)]K = λti00 . ∀t ∈ Ci [(t < tO j → (t ⊆ t 00 )] That is, the (characteristic function of the) set of all times which contain all times in Ci preceding John’s door-opening. am assuming that existential closure applies later and eliminates the final lambda-binder. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 855 D. Margulis Expletive negation and the decomposition of only 3.3.3. Linearization In the Hebrew examples in §2, E X N appears on T(ense) of the embedded until-clause, whereas the analysis locates the negation responsible for it in the main clause. What can explain this? It is important to note that even non-expletive occurrences of lo raise a linearization question, if we follow Zeijlstra (2004, 2008) in assuming that abstract negation is the semantic negation in strict negative concord languages such as Hebrew. I propose a PF rule for Hebrew negation which captures both E X N and other (‘ordinary’) occurrences of Hebrew negation: (38) An (abstract) negation NEG is spelled out as lo on the closest T it c-commands. This predicts both the distribution of ordinary negation and that of E X N, if we take NEG, as part of E XHAUST, to be locally above the until-clause. This will put it high enough for the embedded T to bear agreement, but too low for the matrix T. Exactly this kind of configuration is predicted by the LF in (30) because the complement of until, including its T head, moves to E XHAUST.15 4. Predictions We have seen how the idea that E X N is an exponent of only predicts the obligatoriness of the interruption implication and the incompatibility of E X N with DE-environments. Furthermore, the current analysis predicts E X N to share more properties with only. This prediction is borne out in (i) E X N’s oddness when there are no alternatives to exclude, (ii) its incompatibility with overt only, (iii) its ability to trigger stressing and preposing of the until-clause, and (iv) the lack of negative concord licensing by E X N. I examine these predictions below. 4.1. #E X N when there are no alternatives to exclude World knowledge makes (39b) odd, while felicitous without E X N. This is so because the prejacent is stronger than all other alternatives, rendering E X N – and only in the English translation – vacuous.16 (39) a. ani ohav ot-ax ad Se jigamer ha-zman / jitpotsets ha-olam I love.FUT ACC-you until that end.FUT the-time / explode.FUT the-world ‘I will love you until the end of time / until the world explodes.’ b. #ani ohav ot-ax ad Se lo jigamer ha-zman / jitpotsets ha-olam I love.FUT ACC-you until that NEG end.FUT the-time / explode.FUT the-world ‘#I will love you only until the end of time / only until the world explodes.’ 15 Michel DeGraff (p.c.) suggests another way to capture the surface position of negation while allowing it to take wide scope: movement. Negation would have to start inside the until-clause, where it is pronounced, and move out of it at LF to take matrix scope. This seems to be in line with the observation that E X N tends to be accompanied by subjunctive mood in the until-clause in various languages. 16 Just as in the English translation, (39b)’s oddness can be ameliorated by taking the speaker to have some alternatives (i.e., later times) in mind. This supports the claim that there must be some alternatives to exclude. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 856 D. Margulis Expletive negation and the decomposition of only 4.2. E X N is incompatible with overt only Just like adding only to an existing only is ungrammatical, arguably because the second only would be vacuous, E X N cannot be accompanied by an overt only with the same associate:17,18 (40) a. *joni jaSan rak ad Se ha-Sxenim lo hidliku muzika Y. slept only until that the-neighbors NEG lit music b. joni jaSan rak ad Se ha-Sxenim hidliku muzika Y. slept only until that the-neighbors lit music ‘Yoni was asleep only until the neighbors turned some music on.’ 4.3. Preposing and stress The relevant background on Hebrew is that contrastive focus can cause preposing of the focused phrase, as illustrated below. Both (42a) and (42b) are licit corrections to (41).19 (41) hu axal tapuax-adama he ate apple-earth ‘He ate a potato.’ (42) a. hu axal artichoke he ate ‘He ate an ARTICHOKE.’ ARTI S OK b. hu axal ARTISOK he ate artichoke ‘He ate an ARTICHOKE.’ Many of the speakers I have consulted prefer (some require) preposing the until-clause when it contains E X N and stressing ad ‘until’.20 For example, take (4), repeated here as (43a). Its version (43b), with preposing of the until-clause and stress on until is judged by the informants I have consulted as preferable compared to (43a) if E X N is present. (43) a. b. ha-Svita timaSex ad Se (lo) jeanu driSot ha-ovdim the-strike will continue until that NEG will be answered demands the-workers ‘The strike will continue until the workers’ demands are met.’ A : D Se (lo) jeanu driSot ha-ovdim ha-Svita timaSex until that NEG will be answered demands the-workers the-strike will continue ‘U NTIL the workers’ demands are met the strike will continue.’ 17 As long as E X N has sentential scope, an overt only with narrow focus is allowed, for example, associating with a DP. 18 (40a) is grammatical – though odd – under a non-expletive interpretation of negation. 19 Cf. English negative inversion, where association with focus causes optional overt movement: (i) Only in the living room did Kim agree to hang the photo. 20 Rubinstein and Doron (2015) make a similar observation regarding E X N and stress in constituent unconditionals, which is placed on a wh-item. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 857 D. Margulis Expletive negation and the decomposition of only Stress and preposing, two hallmarks of association with focus, would be better understood if E X N were, as I propose here, a component of a focus-sensitive operator. Those speakers who require stress and preposing must have obligatory overt focus-movement. 4.4. No negative concord with E X N As noted in §2, negation in until-clauses can in principle also have an ‘ordinary’ negative interpretation. When a Negative Concord Item (NCI, a.k.a. n-word) is c-commanded by the negation lo, this becomes the only available interpretation. In other words, E X N cannot license negative concord.21 In both (44) and (45) the first example contains the negation lo and has both interpretations available, whereas the second example contains a NCI replacing the embedded subject and causing lo to not be expletive. (44) a. b. (45) a. b. ha-saxkan himSix b-a-stsena ad Se joni (lo) baxa the-actor continued in-the-scene until that Y. NEG cried –‘The actor continued with the scene until Yoni cried.’ –‘The actor continued with the scene until Yoni was no longer crying.’ ha-saxkan himSix b-a-stsena ad Se af exad lo baxa (joter) the-actor continued in-the-scene until that no one NEG cried (more) Only: ‘The actor continued with the scene until nobody was crying (anymore).’ (Not: ‘The actor continued with the scene until somebody cried.’) miri amda al ha-bama ad Se joni (lo) maxa kapaim M. stood on the-stage until that Y. NEG clapped palms –‘Miri stood on the stage until Yoni applauded.’ –‘Miri stood on the stage until Yoni did not applaud (anymore).’ miri amda al ha-bama ad Se af exad lo maxa kapaim (joter) M. stood on the-stage until that no one NEG clapped palms (more) Only: ‘Miri stood on the stage until nobody was applauding (anymore).’ (Not: ‘Miri stood on the stage until somebody applauded.’) Lack of negative concord under E X N follows from the independent generalization that exceptives are intervenors for negative concord, as (46) demonstrates. If E X N comes with a covert excpetive, as proposed here, negative concord is predicted not to be licensed. The only available reading in (44b) and (45b) arises from the need to parse these sentences without an exceptive, which would otherwise block negative concord. 21 One might wonder whether NPIs are licensed by E X N. Modulo the archaic flavor of NPIs in Modern Hebrew, (i) in fact shows that the NPI davar ‘a thing’ cannot be licensed by E X N, similarly to NCIs in (44) and (45) above. I thank Luka Crnič for raising this question. (i) servu le-Saxrer-o mi-maPatsar-minhali ad Se lo axal davar 3.refused. PL to-release-him from-arrest-administrative until that NEG 3.ate.SG thing Only: ‘They refused to release him from administrative detention until he did not eat anything (=until he went on a hunger strike).’ (Not: ‘They refused to release him from administrative detention until he ate something.’) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 858 D. Margulis (46) Expletive negation and the decomposition of only miri lo ra’ata af exad M. NEG saw no one ‘Miri didn’t see anybody.’ b. *miri lo ra’ata ela af exad M. NEG saw but no one c. *miri lo ra’ata milvad af exad M. NEG saw except no one a. 5. Conclusion 5.1. Summary We have seen that expletive negation suspiciously mimics only and its covert counterpart E XHAUST: (i) It renders the interruption implication, which is an otherwise optional scalar implicature, uncancellable; (ii) E X N is incompatible with DE environments just like E XHAUST is; (iii) E X N is odd if there are no alternatives to exclude; (iv) It is incompatible with overt only; (v) It triggers optional stress on until and preposing of the until-clause, both of which are hallmarks of association with focus, and (vi) E X N cannot license negative concord. I have proposed that E X N is in fact an ordinary compositional negation, being part of a negationand-exceptive construction responsible for all the only-like phenomena, whereas the exceptive is covert. This follows von Fintel and Iatridou’s (2007) proposal to decompose overt only into a negation and an exceptive. The analysis predicts the obligatoriness of the interruption implication as an entailment of the decomposed only. E X N’s incompatibility with DE environments results from an independent property of covert only, observable when scalar implicatures disappear in such environments. The vacuity of E X N when there are no alternatives to exclude or when there is a distinct, overt only explains why E X N is odd in such cases. Preposing and stress associated with E X N are compatible with E X N being part of a focus-sensitive operator, and E X N’s incapability to license negative concord is expected since exceptives block negative concord. The crosslinguistic picture arising from this proposal is one where a negation-and-exceptive construction can be pronounced as a single item (e.g., English only), as two items (e.g., French ne. . . que), as an overt negation with a covert exceptive (E X N), as an overt exceptive with a covert negation (e.g., archaic English but as in the building had but a single window), or not pronounced at all (E XHAUST). 5.2. Next steps There are multiple questions pertaining to E X N and to the specific proposal advanced in this paper which are left unanswered: Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 859 D. Margulis Expletive negation and the decomposition of only 1. Covert exceptives What governs the pronunciation of exceptive heads? That is, when can an exceptive be covert? This is needed to prevent all occurrences of only and of E XHAUST from being expressible as negation. 2. Punctual until Can the analysis be extended to punctual until in examples like (47), where an interruption-like inference is obligatory?22 (47) The dog didn’t bark until Kim sneezed. ( The dog barked when Kim sneezed) 3. Causality E X N has an interpretive effect which is additional to the interruption implication and is not predicted by what I have proposed in this paper. Until-clauses containing E X N are felt to convey causality of sorts, as though the eventuality described by the until-clause leads to the interruption of the eventuality described by the main clause in a non-coincidental way.23 4. Free Relatives A question related to questions 1 and 3 above pertains to E X N in Free Relative clauses, as attested in Hebrew, Yiddish, Russian, Polish, Udmurt, Georgian (Eilam, 2007; Rubinstein and Doron, 2015; Rubinstein et al., 2015; Haspelmath and König, 1998), and Bangla (Ishani Guha, p.c.). As Eilam (2007) shows, the contribution of E X N in such cases is reminiscent of that of -ever in English Free Relatives, along with ignorance and indifference inferences. It is not clear that an exclusive inference parallel to the interruption implication is present in such cases. At the same time, a source of hope for a unified account comes from the observation that some Free Relatives can host an overt only, as illustrated in (48).24 (48) a. ha-kelev jaPakov axarej-xa le-Pan Se-rak telex the-dog 3 MSG.follow.FUT after-2 MSG to-where that-only go.2 MSG ‘The dog will follow you wherever you go.’ 22 I thank Maribel Romero for raising this question. A related phenomenon, which to the best of my knowledge was not mentioned before, is the unavailability of de re readings with E X N. The E X N-less sentence in (i) can be true even if Miri is willing to be here until some time, say noon, and unbeknownst to her, Yoni is going to return at noon. When E X N is added in (ii) it can only be the case that Miri is willingly waiting for Yoni. In other words, in (i) she is willing to be here until some time that the speaker describes as Yoni’s return time, but in (ii) she is willing to be here until some time that she describes as Yoni’s return time. 23 (i) (ii) miri muxana li-hiyot po ad Se yoni yaxzor M. ready to-be here until that Y. return.FUT ‘Miri is willing to be here until Yoni returns.’ miri muxana li-hiyot po ad Se yoni lo yaxzor M. ready to-be here until that Y. NEG return.FUT ‘Miri is willing to be here until Yoni returns.’ 24 Another (de re; de dicto) (*de re; de dicto) telling observation is that similarly to the facts on until in fn. 23, Free Relatives hosting E X N are obligatorily read de dicto. That is, they are of the wh-ever kind, with ignorance and indifference inferences, and not plain extensional definite descriptions. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 860 D. Margulis Expletive negation and the decomposition of only b. ha-kelev jaPakov axarej-xa le-Pan Se-lo telex the-dog 3 MSG.follow.FUT after-2 MSG to-where that-NEG go.2 MSG ‘The dog will follow you wherever you go.’ 5. Negative concord Why are exceptives intervenors for negative concord? I hope that future research will shed light on these issues. References Abels, K. (2005). Expletive negation in Russian: A conspiracy theory. Journal of Slavic linguistics 13(1), 5–74. Büring, D. and C. Gunlogson (2000). Aren’t positive and negative polar questions the same? Paper presented at LSA Annual Meeting, Chicago. Chierchia, G. (2013). Logic in Grammar: Polarity, Free Choice, and Intervention. Oxford University Press. Chierchia, G., D. Fox, and B. Spector (2012). The grammatical view of scalar implicatures and the relationship between semantics and pragmatics. In C. Maienborn, K. von Heusinger, and P. Portner (Eds.), Handbook of Semantics, Volume 3. Mouton de Gruyter. Condoravdi, C. (2010). NPI licensing in temporal clauses. Natural Language & Linguistic Theory 28(4), 877–910. Eilam, A. (2007). The crosslinguistic realization of -ever: Evidence from modern Hebrew. In Proceedings of the 43rd Annual Meeting of the Chicago Linguistic Society, pp. 39–53. Erlewine, M. Y. and H. Kotek (2017). Focus association by movement: Evidence from binding and parasitic gaps. In To appear in Proceedings of Sinn und Bedeutung 21. von Fintel, K. (1994). Restrictions on Quantifier Domains. Ph. D. thesis, University of Massachusetts, Amherst. von Fintel, K. and S. Iatridou (2007). Anatomy of a modal construction. Linguistic Inquiry 38(3), 445–483. Fox, D. (2007). Free choice and the theory of scalar implicatures. In U. Sauerland and P. Stateva (Eds.), Presupposition and implicature in compositional semantics, pp. 71–120. Palgrave Macmillan. Han, C.-H. and M. Romero (2004). Disjunction, focus, and scope. Linguistic Inquiry 35(2), 179–217. Haspelmath, M. and E. König (1998). Concessive conditionals in the languages of Europe. In J. van der Auwera and D. P. Ó Baoill (Eds.), Adverbial Constructions in the Languages of Europe, Volume 3. Mouton de Gruyter. Kaufmann, M. and T. Xu (2013). Almost or almost not? The interaction between cha(yi)dian ‘almost’ and negation in Mandarin Chinese. In Proceedings of the 49th Annual Meeting of the Chicago Linguistic Society. Krifka, M. (2010). How to interpret “expletive” negation under bevor in German. In T. Hanneforth and G. Fanselow (Eds.), Language and Logos: Studies in Theoretical and Computational Linguistics, pp. 214–236. Akademie Verlag. Ladd, D. R. (1981). A first look at the semantics and pragmatics of negative questions and tag questions. In Proceedings of Chicago Linguistic Society 17, pp. 164–171. Makri, M.-M. (2015). Expletive negation in attitude contexts. In Proceedings of ConSOLE Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 861 D. Margulis Expletive negation and the decomposition of only XXIII, pp. 427–448. Portner, P. and R. Zanuttini (2000). The force of negation in wh exclamatives and interrogatives. In L. R. Horn and Y. Kato (Eds.), Studies in Negation and Polarity: Syntactic and Semantic Perspectives, pp. 201–239. Oxford University Press. Romero, M. and C.-H. Han (2004). On negative yes/no questions. Linguistics and Philosophy 27(5), 609–658. Rubinstein, A. and E. Doron (2015). Expletive negation in constituent unconditionals. Presented at Negation and Polarity Workshop, The Hebrew University of Jerusalem. Rubinstein, A., I. Sichel, and A. Tsirkin-Sadan (2015). Superfluous negation in modern Hebrew and its origins. Journal of Jewish Languages 3(1–2), 165–182. Tovena, L. M. (1996). An expletive negation which is not so redundant. In K. Zagona (Ed.), Grammatical Theory and Romance Languages. Selected Papers from the 25th Linguistic Symposium on Romance Languages (LSRL XXV), 4, pp. 263–274. John Benjamins. Wagner, M. (2007). Association by movement: Evidence from NPI-licensing. Natural Language Semantics 14(4), 297–324. Yoon, S. (2012). Parametric variation in subordinate evaluative negation: Korean/Japanese versus others. Journal of East Asian Linguistics 22(2), 133–166. Zeijlstra, H. H. (2004). Sentential Negation and Negative Concord. LOT/ACLC. Zeijlstra, H. H. (2008). Negative concord is syntactic agreement. Ms., University of Amsterdam. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 862 Predicting polar question embedding1 Clemens MAYR — Leibniz-Zentrum Allgemeine Sprachwissenschaft Abstract. This paper shows that it is fully predictable whether a polar interrogative clause can appear under a declarative embedding predicate. The idea in a nutshell is as follows: whenever a predicate appears to not embed polar interrogatives, the interpretative component independently derives a trivial meaning for the sentence. Such trivial meanings manifest themselves in unacceptability. A crucial property of this proposal is that interrogative embedding is polaritysensitive, which is shown to be empirically supported. As a consequence, one must not stipulate in the lexical entry of a given predicate whether or not it embeds polar interrogative clauses. Keywords: question embedding, logic in grammar, polarity, embedding predicates. 1. Introduction Know can embed both declarative and polar interrogative clauses, as shown in (1). From this one might expect that any proposition-taking predicate (PTP) shows this behavior.2 As is wellknown, this is, however, not the case. For instance, the closely related PTP believe does not embed polar interrogative clauses, as shown in (2). This is somewhat unexpected. The lexical meaning of believe is the one of know modulo additional meaning components.3 (1) a. b. John knows that Mary smokes. John knows whether Mary smokes. (2) a. John believes that Mary smokes. b. *John believes whether Mary smokes. Following Lahiri (2002), I refer to PTPs embedding both declarative and interrogative clauses as responsive and those only embedding the former as non-rogative. The question posed by (1) and (2) can then be stated as in (3). (3) The responsiveness puzzle: Under what conditions is a PTP responsive? The standard answer to this question, going back to Grimshaw (1979), is that predicates are lexically specified as to which type of complement clause they combine with. The assumption underlying such approaches is that whether a PTP embeds a given clause type is completely arbitrary and not predictable from independent principles. In other words, there simply are no special properties inherent to know that make it responsive, as implied by (3). 1I thank Gennaro Chierchia, Franzi Conradts, Andreas Haida, Irene Heim, Hazel Pearson, Nadirah PorterKasbati, Floris Roelofsen, Uli Sauerland, Viola Schmitt, Kerstin Schwabe, Benjamin Spector, and Hubert Truckenbrodt for comments and suggestions. I also thank audiences at ZAS, the universities of Belfast, Siena, Tübingen, and Vienna, and Sinn und Bedeutung 21. The work reported here has been supported by DFG grant STE 2555/2-1. 2 Since the standard assumption is that declarative clauses denote propositions, I refer to predicates embedding them as proposition-taking ones. 3 See for instance Gettier (1963). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 863 C. Mayr Predicting polar question embedding This paper takes (3) seriously and argues against Grimshaw’s 1979 conviction. Based on the observation that certain PTPs embed polar interrogative clauses only in particular contexts, I suggest that a lexical stipulation approach is untenable. PTPs are generally not specified with respect to whether they embed interrogative clauses or not. Rather, I argue that the distribution of embedded interrogative clauses is fully predictable on semantic grounds alone. The strong thesis followed in this paper is that whenever a PTP is seemingly unable to embed a polar interrogative, this is due to the interpretative component necessarily generating a trivial meaning for the sentence as a whole. Trivial meanings are tautologies and contradictions, which make themselves felt as unacceptability of the sentence (see Gajewski 2002; Chierchia 2006, 2013; Fox and Hackl 2006; Abrusán 2014 a.o.). Two factors play a role in determining whether a meaning is trivial or not: (i) the particular lexical semantics of the PTP, and (ii) the polarity of the sentence as a whole. The apparent impossibility of interrogative embedding under believe in (2b), for instance, is due the sentence denoting the tautology. (1b), on the other hand, does not have such a trivial denotation, and thus no degradedness is felt. I show in the following that this simple approach can deal with numerous types of PTPs. As will be seen, the key insight here is that interrogative embedding necessitates an existential semantics (Spector and Egré 2015, see also Lahiri 2002; Theiler et al. 2016 a.o.). Confining myself to the embedding of polar interrogatives, which is done for reasons of space, moreover allows me to work with completely standard meanings for the PTPs discussed. For wh-interrogatives, however, the lexical semantics would have to be somewhat complicated. I refer the reader to Mayr (2017) for discussion of wh-interrogatives.4 The structure of the paper is as follows. In section 2, I discuss the issue that interrogative embedding poses for a theory of grammar in more detail. Section 3 introduces the proposed system. Section 4 shows its application to the know-believe distinction. Section 5 discusses further classes of PTPs. Section 6 concludes the paper. 2. Problems of interrogative embedding 2.1. Arguments for lexical stipulation Know when embedding a declarative clause, as in (1a), licenses the inference that that clause is true. That is, know is veridical.5 Believe, as in (2a), does not do so, i.e., it is non-veridical. An old intuition is therefore that a responsive PTP must be veridical (Hintikka, 1975; Berman, 1991; Ginzburg, 1995a, b; Egré, 2008). Indeed, many veridical PTPs, as in (4), embed interrogative clauses. And many non-veridical ones do not, as in (5). Here and below X and 6 X indicate that the example has or does not have the proposition that X as an inference. 4 Given what has just been said, I will not discuss the issue of emotive factive PTPs in this paper. These allow for embedding of wh-interrogatives but not of polar interrogatives (see Guerzoni 2007; Sæbø 2007; Nicolae 2013; Romero 2015; Roelofsen et al. ta; Mayr 2017 a.o.). (i) a. b. *John is amazed / happy / surprised whether Mary smokes. John is amazed / happy / surprised which girls smoke. 5 More precisely, know is, of course, not only veridical but also factive. A PTP is factive if the inference that the complement declarative clause is true remains under entailment-cancelling operators. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 864 C. Mayr (4) Predicting polar question embedding a. b. (5) John deduced / discovered / established / figured out / found out / forgot / learned / recalled / remembered that Mary smokes. Mary smokes John deduced / discovered / established / figured out / found out / forgot / learned / recalled / remembered whether Mary smokes. a. John alleged / asserted / claimed / conjectured / desired / expected / feared / hoped / inferred / wanted / wished that Mary smokes. 6 Mary smokes b. *John alleged / asserted / claimed / conjectured / desired / expected / feared / hoped / inferred / wanted / wished whether Mary smokes. This conclusion is, however, called into question by the fact that there are PTPs which embed interrogative clauses yet are non-veridical, as (6) shows (see Grimshaw 1979; Lahiri 2002; Uegaki 2015). (6) a. b. John announced / confirmed / declared / heard / predicted / reported / told us that Mary smokes. 6 Mary smokes John announced / confirmed / declared / heard / predicted / reported / told us whether Mary smokes. Apart from veridicality, no other semantically discernible property has been found that would separate the responsive PTPs from the non-rogative ones. That is, neither the former nor the latter seem to form a coherent lexical class. It has thus been claimed that it is not predictable given formal semantic properties of a given PTP whether it is responsive or not (Grimshaw, 1979; Uegaki, 2015). In particular, Grimshaw has advanced the view that predicates are specified lexically for so-called s-selectional properties (see also Chomsky 1965; Baker 1968). That is, each PTP is at least specified for whether the embedded clause can be +-declarative and +-interrogative. The idea here is that such s-selectional specification does not follow from anything more basic. 2.2. Problems for lexical stipulation According to the lexical specification hypothesis each PTP comes with a feature setting specifying whether an interrogative is a possible complement or not. The surrounding linguistic context should not be able to alter this setting. The data in (7) show that the PTP be certain contradicts this prediction. On its own be certain can embed declarative clauses as in (7a) but not polar interrogatives as in (7b). With negation as in (7c), however, embedding of a polar interrogative markedly improves (see for instance Eckardt 2007; Egré 2008). (7) a. John is certain that Mary smokes. b. *John is certain whether Mary smokes. c. John isn’t certain whether Mary smokes. 6 Mary smokes Transitive say, in contrast to its ditransitive use, and be convinced exhibit a behavior parallel to be certain, as is shown by (8). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 865 C. Mayr (8) Predicting polar question embedding a. John said / is convinced that Mary smokes. b. *John said / is convinced whether Mary smokes. c. John didn’t say / isn’t convinced whether Mary smokes. 6 Mary smokes Be certain and the other PTPs just discussed are non-veridical. Interestingly, be clear is veridical, and yet it shows the same behavior as be certain. In other words, (non)-veridicality is once again not a good indicator as to whether interrogative embedding is possible at all. (9) a. It is clear that Mary smokes. b. *It is clear whether Mary smokes. c. It isn’t clear whether Mary smokes. Mary smokes The distribution of polar interrogative clauses as complements of the PTPs above is reminiscent of negative polarity items (NPIs) like any (Adger and Quer, 2001), as in (10). (10) a. *John saw any girl. b. John didn’t see any girl. Contexts other than negation which allow for NPIs improve the embedding of polar interrogatives under be certain as well. Typical such contexts are downward monotonic environments (see Fauconnier 1979; Ladusaw 1979; Linebarger 1987; Krifka 1995; Giannakidou 1999; Chierchia 2004, among many others): antecedents but not consequents of conditionals, negative quantifiers, and restrictors but not scopes of universal quantifiers. Indefinites thus never allow for NPIs. The following demonstrate that polar interrogatives under be certain show an NPI-like behavior: (11) a. If John is certain whether Mary smokes, he knows her well. b. *If John knows Mary well, he is certain whether she smokes. (12) a. b. (13) a. Every student who is certain whether Mary smokes knows her well. b. ?Every student who knows Mary well is certain whether she smokes. (14) a. *Some student who is certain whether Mary smokes knows her well. b. *Some student who knows Mary well is certain whether she smokes. No student who is certain whether Mary smokes does not know her. No student who does not know Mary is certain whether she smokes. 2.3. Intermediate conclusion Summarizing, I note two things: (i) the prediction of the lexical specification account that linguistic context cannot affect clausal embedding appears to be wrong. (ii) The way linguistic context affects clausal embedding is systematic and tracks the licensing of NPIs to a consider- Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 866 C. Mayr Predicting polar question embedding able extent. In light of this I conclude that the lexical specification hypothesis is untenable.6 Now, how could the embedding of polar interrogative clauses be similar to the distribution of NPIs? One of the main contending views regarding NPIs goes as follows: first, any girl in (10) denotes an existential quantifier over girls. Second, the sentence has alternatives about particular girls such as John saw Mary for (10a) and John didn’t see Mary for (10b). Third, each sentence in (10) undergoes exhaustification with respect to its alternatives resulting in the conjunction of the sentence—its prejacent—with the negation of the alternatives. This leads to a contradiction without but not with negation, accounting for the pattern in (10) (see Heim 1984; Kadmon and Landman 1993; Krifka 1995; Chierchia 2006, 2013; Crnič 2014, among many others). In the following I show that something similar is happening in the case of the embedding of polar interrogatives. 3. A polarity system for polar interrogative embedding In the case of polar interrogative clauses, it is the semantics for interrogative embedding necessitating existential quantification (Spector and Egré, 2015). The alternatives are contributed by the embedded interrogative (Klinedinst and Rothschild, 2011). The exhaustification process relative to these alternatives accounts for the patterns discussed in the preceding section. Assume for be certain Hintikka’s 1969 universal semantics for propositional attitudes: (15) [[be certain]] = λ pst .λ xe .λ ws .∀w0 [w0 ∈ Doxx,w → p(w0 ) = 1] Be certain applied to a proposition p asserts that p is true in all of the subject’s doxastic alternatives. This means p is true in all the worlds doxastically accessible to the subject from the world of evaluation w. Consider now the sentences in (16) again. Assume that the denotation of the embedded interrogative is as in (17). This is an existential quantifier ranging over a set of propositions, i.e., over a question denotation in the sense of Hamblin (1973) and Karttunen (1977). The set contains the positive and the negative answer to the polar interrogative. In the following, I abbreviate this set as Q0 —that is, {λ w. Mary smokes in w, λ w.Mary doesn’t smoke in w} = Q0 . (16) a. John isn’t certain whether Mary smokes. b. *John is certain whether Mary smokes. (17) [[whether Mary smokes]] = λ Qhst,ti .λ ws .∃p[p ∈ {λ w0 .M smokes in w0 , λ w0 .M doesn’t smoke in w0 } ∧ Q(p) = 1] = λ Qhst,ti .λ ws .∃p[p ∈ Q0 ∧ Q(p) = 1] Now, since the denotation of be certain requires a proposition as argument, it cannot apply to 6 To this one might add the observation that the embedding patterns appear to be cross-linguistically stable. From the perspective of a lexical stipulation based account this is unexpected. Languages should be allowed to differ widely with respect to which PTP embeds which clause-type. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 867 C. Mayr Predicting polar question embedding (17). Assume therefore, following Lahiri (2002), that the embedded interrogative must take scope over the entire clause, which gives the LFs in (18a) and (18b) for (16a) and (16b), respectively. The operator Exh is discussed below. (18) a. b. [ S01 ExhAlt [ S1 not [[ whether Mary smokes ] λ p[ John is certain p ]]]] [ S02 ExhAlt [ S2 [ whether Mary smokes ] λ p[ John is certain p ]]] For (18a), on the one hand, the denotation of S1 —its literal meaning—corresponds thus to (19). This says that there is no proposition in Q0 which is true in all of John’s doxastic alternatives. (18b), on the other hand, has as its literal meaning (19b) saying that there is a proposition in Q0 that is true in all of John’s doxastic alternatives. (19) a. b. [[S1 ]]g = λ w.¬∃p[p ∈ Q0 ∧ ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1]] [[S2 ]]g = λ w.∃p[p ∈ Q0 ∧ ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1]] Consider next the alternatives to the literal meanings in (19a) and (19b). I stipulate them to constitute sets of propositions satisfying the following requirement: each member corresponds to the denotation one would get by replacing the embedded interrogative in (17) with one of its answers in the set Q0 . Since the answers are propositions be certain can be applied directly.7 (20) a. b. Alt([[S1 ]]g ) = {λ w.¬∀w0 [w0 ∈ DoxJ,w → Mary smokes in w0 ], λ w.¬∀w0 [w0 ∈ DoxJ,w → Mary doesn’t smoke in w0 ]} g Alt([[S2 ]] ) = {λ w.∀w0 [w0 ∈ DoxJ,w → Mary smokes in w0 ], λ w.∀w0 [w0 ∈ DoxJ,w → Mary doesn’t smoke in w0 ]} Finally, each literal meaning derived in (19) is strengthened relative to its alternatives in (20). This is done with the help of the Exh-operator defined in (21) (see Groenendijk and Stokhof 1984; Krifka 1995; van Rooij and Schulz 2004; Chierchia 2006, 2013; Fox 2007; Spector 2007, among many others). Exh takes a proposition p—the prejacent S1 or S2 — asserts it and states that all propositions which are not Strawson-entailed by p are false. In the following ⇒ indicates regular entailment, and ⇒S Strawson-entailment. In the particular case at hand and more generally whenever a sentence is presuppositionless, Strawson-entailment reduces to regular entailment. For more discussion, see section 4.2.8 [[ExhAlt ]] = λ ws .p(w) = 1 ∧ ∀q ∈ Alt[p ;S q → q(w) = 0] (21) The denotation of the prejacent S1 of Exh in (18a), i.e., (19a), entails each of its alternatives in (20a). If John is ignorant with respect to whether Mary smokes, then it follows both that John is not certain that Mary smokes and that he is not certain that Mary does not smoke. As 7 This can be derived more formally by having the existential quantifier ranging over Q0 be restricted to exactly one of the answers in Q0 . Such an implementation would use Chierchia’s 2006 notion of domain alternatives. 8 Entailment and Strawson-entailment (von Fintel, 1999) are defined as follows: (i) a. b. For any p, q ∈ Dst , p entails q, p ⇒ q, iff for all w ∈ Ds such that p(w) = 1, q(w) = 1. For any p, q ∈ Dst , p Strawson-entails q, p ⇒S q, iff for any presupposition r of q and all w ∈ Ds such that p(w) = r(w) = 1, q(w) = 1. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 868 C. Mayr Predicting polar question embedding a consequence Exh does not negate any of the alternatives, and the strengthened interpretation of (16a) is equivalent to its literal one without Exh: (22) [[S01 ]]g = λ w.¬∃p[p ∈ Q0 ∧ ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1]] (22) corresponds to the intuitive interpretation of the sentence. In particular, consider the sentence in the context in (23). Here it is unacceptable because the truth-conditions in (22) require John to not believe any of the propositions in Q0 , which contradicts the context. Notice that (23) provides direct evidence for the assumption that there is existential quantification over answers involved (Spector and Egré, 2015). If the truth-conditions were about a particular answer, the sentence should be acceptable. (23) Context: Mary smokes, but John believes she does not smoke. #John isn’t certain whether Mary smokes. Consider next the denotation of the prejacent S2 of Exh in (18b) given in (19b). Each of its alternatives in (20b) entails it. For instance, if John believes that Mary smokes, then there is a proposition in Q0 that John believes. Consequently, Exh negates each of the alternatives and conjoins them with the denotation of the prejacent yielding (24). (24) [[S02 ]]g = λ w.∃p[p ∈ Q0 ∧ ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1]] ∧ ¬∀w0 [w0 ∈ DoxJ,w → Mary smokes in w0 ] ∧ ¬∀w0 [w0 ∈ DoxJ,w → Mary doesn’t smoke in w0 ] => (24) is equivalent to saying that John either believes that Mary smokes or that he believes that she does not smoke but that he neither believes that she smokes nor that he believes that she does not smoke. This is a contradiction. Following Gajewski (2002), Fox and Hackl (2006), Chierchia (2006, 2013), Abrusán (2014) a.o., I assume that such trivial meanings lead to judgements of degradedness. This assumption regarding triviality thus derives the pattern in (16). In particular, the system sketched here explains why be certain and other PTPs are only sometimes responsive. Moreover, the crucial reason why negation did not result in a contradiction and allowed for embedding of polar interrogatives was that it reverses the entailment patterns between the literal interpretation and the alternatives. As a consequence it follows that any entailment reversing environment, such as the downward monotonic contexts discussed in section 2.2 above, are predicted to not result in contradictions either. 4. The know-believe distinction Let me now return to the responsiveness puzzle and in particular the difference between know and believe. As already discussed, the former embeds polar interrogatives whereas the latter does not do so. Moreover, we need to add to this the observation that negation does not seem to affect either of these properties. The picture as it presents itself is thus as in (25) and (26). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 869 C. Mayr Predicting polar question embedding (25) a. b. John knows whether Mary smokes. John doesn’t know whether Mary smokes. (26) a. *John believes whether Mary smokes. b. *John doesn’t believe whether Mary smokes. Now, both know and believe have lexical properties differentiating them from each other, but setting them also apart from be certain. Know, on the one hand, is factive, whereas the other two PTPs are not: (27) a. b. c. John (doesn’t) know(s) that Mary smokes. John (doesn’t) believe(s) that Mary smokes. John is(n’t) certain that Mary smokes. 6 6 Mary smokes Mary smokes Mary smokes Believe, on the other hand, is a neg-raising predicate (Horn, 1978). When negated it appears that the negation takes scope below believe giving rise to a stronger than expected inference, as shown in (28b). Neither know nor be certain is neg-raising, as (28a) and (28c) show. (28) a. b. John doesn’t know that Mary smokes. 6 John doesn’t believe that Mary smokes. c. John isn’t certain that Mary smokes. 6 John knows that Mary doesn’t smoke John believes that Mary doesn’t smoke John is certain that Mary doesn’t smoke In the following, I show how the lexical properties of neg-raising and factivity interact with the system sketched in the preceding section thereby deriving the patterns in (25) and (26). 4.1. Neg-raising Following Bartsch (1973), Löbner (2003) and Gajewski (2007) a.o., I assume that neg-raising PTPs presuppose that the subject is opinionated about the truth of the complement clause. That is, believe has a denotation parallel to be certain but presupposes that the subject either believe the propositional argument to be true or believe it to be false:9 (29) [[believe]] = λ pst .λ xe .λ ws : ∀w0 [w0 ∈ Doxx,w → p(w0 ) = 1] ∨ ∀w0 [w0 ∈ Doxx,w → p(w0 ) = 0] . ∀w0 [w0 ∈ Doxx,w → p(w0 ) = 1] In the positive case of (27b) the presupposition in (29) is harmless as it is entailed by and in fact equivalent to the assertive component. In the negative case, however, the presupposition entails the assertion. The consequence of this is that even though the assertion has weak wide-scope negation, the presupposition strengthens the intuited inference to a meaning saying that John believes that Mary does not smoke. 9I adopt here and in the following Heim and Kratzer’s 1998 notation for presuppositions, according to which λ χ : φ . ψ is a function that is only defined for objects χ such that φ holds. In addition presuppositions are underlined. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 870 C. Mayr Predicting polar question embedding Consider now the degraded (30) repeated from above. Its truth-conditions before exhaustification are as in (31). What is the presupposition of (31)? Taking the first of the propositions in Q0 and setting it for p in (31) gives the presupposition that John either believes that Mary smokes or that she does not smoke. Taking the second proposition in Q0 , however, yields exactly the same. As a consequence, the presupposition of (31) is that John either believes that Mary smokes or that she does not smoke. Given the existential quantification in the assertive component of (31), the assertion is equivalent to the presupposition. This means that whenever (31) has a defined truth-value, it is true. It is a tautology. Therefore (30) has a trivial literal meaning and is degraded even without exhaustification. (30) (31) *John believes whether Mary smokes. [[(30)]]g = λ w.∃p ∈ Q0 : ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1] ∨ ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 0] . ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1] Given this it is easy to see why (32) is also degraded. (32) *John doesn’t believe whether Mary smokes. The truth-conditions are as in (33). The presupposition requires again that John either believes that Mary smokes or that she does not smoke. The assertive component now states that John does not believe any of the propositions in Q0 . Thus whenever (33) is defined, it is false. (31) is therefore degraded because it also has a trivial literal meaning. (33) [[(32)]]g = λ w.¬∃p ∈ Q0 : ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1] ∨ ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 0] . ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1] This treatment of believe predicts, of course, that other neg-raising PTPs are similarly nonrogative regardless of the polarity of the surrounding linguistic context. This is indeed the case as (34) and (35) show. (34) a. John doesn’t expect / reckon / think / assume / presume / reckon that Mary drinks. John P-s that Mary doesn’t drink b. *John (doesn’t) expect(s) / reckon(s) / think(s) / assume(s) / presume(s) / reckon(s) whether Mary drinks. (35) a. It isn’t advisable / desirable / likely / probable that Mary drinks. It is P that Mary doesn’t drink b. *It is(n’t) advisable / desirable / likely / probable whether Mary drinks. The idea that neg-raising PTPs lead to trivial meanings when embedding an interrrogative goes back to Zuber (1982), though it is implemented differently there (see also Theiler et al. 2016). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 871 C. Mayr Predicting polar question embedding 4.2. Factivity Assume the standard lexical entry for know in (36). (36) applied to a proposition p and an individual x states that x believes p and presupposes that p is true. (36) [[know]] = λ pst .λ xe .λ ws : p(w) = 1 . ∀w0 [w0 ∈ Doxx,w → p(w0 ) = 1] As a consequence the literal meaning of (37) is as in (38). (37) John knows whether Mary smokes. (38) [[(37)]]g = λ w.∃p ∈ Q0 : p(w) = 1 . ∀w0 [w0 ∈ DoxJ,w → p(w0 ) = 1] The literal meaning in (38) is non-trivial. It asserts that there is a proposition p in Q0 that John believes. It presupposes that p is true in w. Thus in a world in which Mary smokes (38) says that John believes that Mary smokes, and in a world in which she does not smoke (38) says that she does not do so. That is, the factivity of know ensures that the subject stand in the knowrelation to the true answer, whatever it is. Given the discussion in section 3, the alternatives to (38) used for strengthening by Exh are as in (39). (39) Alt([[S]]g ) = {λ w : Mary smokes in w . ∀w0 [w0 ∈ DoxJ,w → Mary smokes in w0 ], λ w : ¬Mary smokes in w . ∀w0 [w0 ∈ DoxJ,w → ¬Mary smokes in w0 ]} Now recall that Exh negates only those alternatives that are not Strawson-weaker than its prejacent, i.e., those alternatives that are not Strawson-entailed by the prejacent. As defined in footnote 8 following von Fintel (1999), for a proposition p to Strawson-entail a proposition q the presuppositions of q must be assumed to be true. When we want to see whether (38) Strawson-entails the first alternative in (39), we must therefore assume that Mary smokes in some particular world wo as in (40a), as this is the presupposition of the alternative. Now, (38) is true in wo if (40b) holds. Since the two propositions in Q0 contradict each other, the proposition in Q0 that John knows in wo must be that Mary smokes given (40a). Thus (40a) together with (40b) guarantees that Mary smokes is the true answer to Q0 in wo and that John believes that Mary smokes is true. Therefore, (38) Strawson-entails the first alternative in (39), as stated in (40c). By the same logic (38) also Strawson-entails the second alternative in (39). In fact, it is Strawson-equivalent to both its alternatives. (40) a. b. c. Mary smokes in wo . For some p ∈ Q0 , John knows p in wo . (40a) & (40b) ⇒S John knows in wo that Mary smokes. As a consequence, Exh does not negate any of the alternatives, and the strengthened meaning of (37) is equivalent to its literal meaning in (38). Since this meaning is non-trivial, we have explained why (37) is acceptable. We also immediately explain why its negation in (41) is equally acceptable. Since it is the factive presupposition of know that makes the alternatives Strawson-equivalent to the literal meaning, it follows that further embedding under negation Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 872 C. Mayr Predicting polar question embedding will not affect the result just obtained. (41) John doesn’t know whether Mary smokes. The first consequence of this treatment for know is that factive PTPs in general should be responsive. This is by and large borne out. All the veridical PTPs in (42), repeated from (4), are actually factive, thus explaining (42b). (42) a. b. John deduced / discovered / established / figured out / found out / forgot / learned / recalled / remembered that Mary smokes. Mary smokes John deduced / discovered / established / figured out / found out / forgot / learned / recalled / remembered whether Mary smokes. Second, veridical PTPs that are not factive, such as be clear, are not predicted to license interrogative embedding across-the-board. Here a downward monotonic environment is necessary for embedding to be possible: (43) (44) a. b. It is clear that Mary smokes. It isn’t clear that Mary smokes. 6 Mary smokes Mary smokes a. *It is clear whether Mary smokes. b. It isn’t clear whether Mary smokes. Third, it should be stressed that the polarity system proposed in section 3 makes the fact that be certain embeds interrogatives only under negation the flip-side of the fact that know always does so. Finally, note that the use of Strawson-entailment rather than of regular entailment is crucial for the account. One might therefore ask why this particular type of entailment should be used. I do not have an answer to this. However, NPI-licensing in general is subject to Strawsonentailment. As is well-known, it is the Strawson-donward-monotonic property of only that lets it license NPIs (von Fintel, 1999). 5. Other non-veridical predicates 5.1. Ambiguous predicates and being about the true answer Recall now the PTPs in (45). In section 2.1 they were shown to be problematic for accounts relating interrogative embedding to veridicality directly. The reason for this is that the PTPs are non-veridical. (45) a. b. John announced / confirmed / declared / heard / predicted / reported / told us that Mary smokes. 6 Mary smokes John announced / confirmed / declared / heard / predicted / reported / told us whether Mary smokes. John P-ed the true answer to “Does Mary smoke?” Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 873 C. Mayr Predicting polar question embedding As seen in section 4.2, the present system does not rely on a connection between veridicality and responsiveness. Still, as it stands it does not predict the pattern in (45) either. Now, notice that the PTPs are veridical with respect to the embedded interrogative: (45b) licenses the inference that the subject stand in the relation denoted by the PTP to the true answer to the embedded interrogative. Following Spector and Egré (2015), I assume that the PTPs in (45) come in both a factive and a non-factive version. Consider tell for concreteness. In (45a), on the one hand, its non-factive version in (46) is, or at least can be chosen. Thereby no veridicality inference is felt. (46) [[tell1 ]] = λ pst .λ ye .λ xe .λ ws . ∀w0 [w0 is compatible with what x tells y in w → p(w0 ) = 1] The reason why, on the other hand, in (46b) the factive version in (47) must be chosen is now straightforwardly explained on the present account: using the non-factive version of tell in (46) would result in a trivial strengthened meaning and thereby degradedness. That is, it would lead to a contradiction after exhaustification completely parallel to what we have seen with be certain in section 3. On its factive interpretation, however, tell works just like know. Factivity blocks the contradiction otherwise derived by exhaustification, as seen in section 4.2. (47) [[tell2 ]] = λ pst .λ ye .λ xe .λ ws : p(w) = 1 . ∀w0 [w0 is compatible with what x tells y in w → p(w0 ) = 1] Recall moreover from section 4.2 that the factivity presupposition of know guarantees that the subject stand in the know-relation to the true answer to the embedded interrogative, whatever it is. The limited veridicality inference in (45b) with respect to the true answer thus follows on the present account: only (47) can be used here, and this necessitates a relation between the subject and the true answer. As far as I am aware, the present account is the first to be in a position to explain why seemingly non-veridical PTPs must be about the true answer when embedding an interrogative clause as in (45b). This makes a testable prediction. Whenever one of the PTPs from (45) embeds an interrogative clause and moreover occurs in an environment where contradiction by exhaustification is avoided independently, the non-factive interpretation should be usable. That is, not even limited veridicality as in (45b) should ensue. Consider (48). The sentence is odd in the context given. Now notice that on the factive interpretation of tell in (47) the sentence should be acceptable, as it would assert that John did not tell us the true answer to Does Mary smoke?. Since the context satisfies this, we conclude that the sentence does not have such truth-conditions. Without a factive presupposition, the sentence states that John did not tell us any possible answer to the question Does Mary smoke?. These truth-conditions are not fulfilled by the context accounting for the degradedness. (48) Context: John told us that Mary smokes, which is in fact false. #John didn’t tell us whether Mary smokes. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 874 C. Mayr Predicting polar question embedding The degradedness in (48) more precisely suggests that the factive version of tell and similarly ambiguous PTPs becomes usable only when the non-factive one would lead to a contradiction via exhaustification. This is unlike what Spector and Egré (2015) suggest. They argue that such PTPs can always have the non-factive interpretation when embedding interrogative clauses. They cite (49) as evidence for this, minimally modified to show a polar interrogative here. (49) seemingly does not require the subject to stay in a relation to the true answer. (49) Every day, the meteorologists tell the population / predict / announce whether it will rain the following day, but they are often wrong. I suggest that the fact that (49) is not degraded is entirely expected on the present account. The surfacing of the non-factive interpretations of the PTPs involved is, in particular, due to the fact that they are embedded under the universal temporal quantifier every day. First, (49) becomes less acceptable when every day is absent: (50) #The meteorologists tell the population / predict / announce whether it will rain the following day, but they are often wrong. Second, note that other universal quantifiers also license the use of the non-factive interpretation of the PTP: (51) The meteorologists are required to tell the population / predict / announce whether it will rain the following day, even if they don’t know. It is well-known that universal quantifiers obviate contradictions which would otherwise arise through exhaustification when occurring unembeddedly (e.g. Fox and Hackl 2006; Fox 2007; Chierchia 2013; Abrusán 2014). Let me show how this works for (51). Its LF with non-factive tell would be something like (52). (52) [ S0 ExhAlt [ S required [[ whether it will rain ] λ p[ the meteorologists to tell1 the population p ]]]] The literal meaning of S states that in every deontically accessible world the meteorologists tell the population a possible answer to the question Will it rain?. This neither entails that in every such world the meteorologists tell the population that it will rain nor that in every world they tell them that it will not rain. That is, the literal meaning does not entail its alternatives. Therefore Exh negates them giving the strengthened meaning in (53). (53) [[S0 ]]g = 1 iff ∀w0 .∃p[p ∈ Q0 ∧ the meteorologists tell the population p in w0 ] ∧ ¬∀w0 [the meteorologists tell the population in w0 it will rain] ∧ ¬∀w0 [the meteorologists tell the population in w0 it will not rain] Crucially, (53) is not trivial. (53) states that the meteorologists are required to tell the population some answer but that they are neither required to tell them that it will rain nor that they are required to tell them that it will not rain. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 875 C. Mayr Predicting polar question embedding This raises the question why (54) with an existential modal is similarly acceptable, even though existential modals generally do not obviate contradictions via exhaustification. (54) The meteorologists are allowed to tell the population / predict / announce whether it will rain the following day, even if they don’t know. I suggest that in cases like (54) it is actually the factive version of the PTP that is used, as in the LF in (55), with Exh embedded under the modal. (55) [ S0 allowed [ S ExhAlt [[ whether it will rain ] λ p[ the meteorologists to tell2 the population p ]]]] This delivers the interpretation of S0 in (56). First, notice that the alternatives to the prejacent of Exh are Strawson-equivalent to the prejacent. That is, Exh does not negate any of them, as in the case of know discussed in section 4.2. Second, the factive presupposition of tell is interpreted with respect to the world bound by the existential modal. As a consequence (56) says that in some deontically accessible world the meteorologists tell the population the true answer to the interrogative in that world. This does not entail anything about the true answer in the actual world. Now, if know in (54) moreover introduces a presupposition about the actual world, this does not lead to a contradiction with (56). In other words, with embedded exhaustification and the factive use of tell, (54) does not come out as degraded. (56) [[S0 ]]g = 1 iff ∃w0 .∃p ∈ Q0 : p(w0 ) = 1 . the meteorologists tell the population p in w0 5.2. Predicates with an order-based semantics Recall now the following desiderative PTPs from (5). (57a) has the inference that John prefers Mary smoking to her not smoking. This is generally accounted for by attributing an order-based semantics to the PTPs. (57) a. John desired / wanted / wished that Mary smokes. 6 Mary smokes John prefers Mary to smoke b. *John desired / wanted / wished whether Mary smokes. Since the PTPs in (57) are all non-veridical, we might expect interrogative embedding to improve under negation, similarly to be certain. But this is not the case as (58) shows. The PTPs in (58) are thus closer to believe. (58) *John didn’t desire / want / wish whether Mary smokes. Indeed, such desiderative PTPs are neg-raising. Consider (59). If want were not neg-raising, (59) should be compatible with John not having a preference as to whether Mary smokes or not given the inference observed for (57a). However, (59) rather implies that John prefers Mary to not smoke. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 876 C. Mayr Predicting polar question embedding (59) John doesn’t want that Mary smokes. John prefers Mary to not smoke This suggests that the account offered for believe in 4.1 should be extendable to desiderative PTPs. Notice, however, that such PTPs are non-monotonic (see e.g. Asher 1987; Heim 1992; Villalta 2008; Lassiter 2011; Rubinstein 2012; Anand and Hacquard 2013 a.o.). (60a) does not entail (60b). (60) a. b. John desired / wanted / wished that Mary and Sue smoke. John desired / wanted / wished that Mary smokes. To account for this non-monotonicity property, I adopt Heim’s 1992 similarity-based account of desiderative predicates. The entry for want, for instance, is as in (61). (61) applied to a proposition p asserts that for all of the subject’s doxastic alternatives w0 the worlds most similar to w0 in which p is true are more desirable to the subject in w than the worlds most similar to w0 in which p is false.10 Applied to (60a), for instance, (61) says that John believes that if Mary and Sue smoke he is in a more desirable world than if they do not smoke. The counterfactual component in (61) blocks entailment in both directions in (60). Crucially, (61) has the opinionatedness presupposition familiar from believe built in. [[want]] = λ pst .λ xe .λ ws .[∀w0 ∈ Doxx,w .Simw0 (p) >x,w Simw0 (¬p)] ∨ [∀w0 ∈ Doxx,w .Simw0 (¬p) >x,w Simw0 (p)] . ∀w0 ∈ Doxx,w .Simw0 (p) >x,w Simw0 (¬p) (61) Consider now the ungrammatical (57b) with want. Its literal meaning is as in (62). Given the existential quantification over answers, the assertive component says that John prefers Mary smoking to her not smoking or he prefers the reverse. [[(57b)]] = λ w.∃p ∈ Q0 : [∀w0 ∈ DoxJ,w .Simw0 (p) >J,w Simw0 (¬p)] ∨ [∀w0 ∈ DoxJ,w .Simw0 (¬p) >J,w Simw0 (p)] . ∀w0 ∈ DoxJ,w .Simw0 (p) >J,w Simw0 (¬p) (62) Now, since the two possible answers are the negations of each other, they make the same contribution to the presuppositional component. Each says that John either prefers Mary to smoke or he prefers the reverse. Thus the presupposition of (62) is equivalent to the assertion. Therefore the literal meaning of (57b) is trivial. Now, the negation in (58) has the same presupposition as (62). But the assertive component now requires that John have no preference among the possible answers. This contradicts the presupposition and thus (58) also has a trivial literal meaning. In other words, the order-based semantics of desiderative PTPs does not interfere with their neg-raising property, and they come out as non-rogative, as desired. This treatment 10 The similarity relation among worlds and the notion of desirability employed in (60) are defined as in (i) and (ii), following again Heim (1992: 195ff.). (i) (ii) Simw (p) := {w00 ∈ W : w00 ∈ p and w00 resembles w no less than any other world in p} a. For any w, w0 , w00 ∈ W , w0 >α,w w00 iff w0 is more desirable to α in w than w00 . b. For any w ∈ W, X ⊆ W,Y ⊆ W , X >α,w Y iff w0 >α,w w00 for all w0 ∈ X, w00 ∈ Y . Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 877 C. Mayr Predicting polar question embedding can be extended to other neg-raising PTPs in (5) with an order-based semantics, such as expect, fear and hope. 6. Conclusion and outlook In this paper I argued that embedding of polar interrogative clauses under PTPs involves an existential semantics, as suggested more generally by Spector and Egré (2015). This allowed me to account for the surprising context-dependence of the embedding of such clauses under be certain and other PTPs. Specifically, I proposed an exhaustification-based polarity system (Krifka, 1995; Chierchia, 2006, 2013) which leads to a contradiction for polar interrogatives with unnegated be certain. This system moreover has the immediate consequence that polar interrogatives can be embedded under factive PTPs even when not negated. The reason is that factivity avoids contradiction by exhaustification. This proposal also explains why seemingly non-veridical PTPs like tell show a limited kind of veridicality when embedding polar interrogatives. The reason is, again, that otherwise a contradiction would ensue. Finally, the existential semantics for embedding of polar interrogatives predicts that neg-raising PTPs—even those with an order-based semantics—always give rise to trivial meanings. That is, the system predicts such PTPs to never embed polar interrogatives. The most important issue for future research now is to investigate how the proposed system can be extended to wh-interrogatives. First, the existential semantics assumed in this paper does not directly work with wh-interrogatives. It would give rise to too weak mention-some interpretations. Second and connected to this, the factivity presupposition assumed in the present paper does not automatically yield Strawson-equivalence in the case of wh-interrogatives embedded under factive PTPs. I.e., they should not be licensed contrary to fact. The consequence of this is that the lexical semantics for the PTPs themselves must be altered somewhat. For discussion of how this can be done, I refer the reader to Mayr (2017). 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Wiegand (Eds.), Semantics and Linguistic Theory (SALT) 25, pp. 225– 245. Ithaca, NY: CLC Publications. Rubinstein, A. (2012). Roots of Modality. Ph. D. thesis, University of Massachusetts at Amherst. Sæbø, K. J. (2007). A whether forecast. In B. T. ten Cate and H. Zeevat (Eds.), TbiLLC 2005, pp. 189–199. Berlin, Heidelberg: Springer. Spector, B. (2007). Scalar implicatures: Exhaustivity and Gricean reasoning. In M. Aloni, A. Butler, and P. Dekker (Eds.), Questions in Dynamic Semantics, pp. 225–249. Oxford, Amsterdam: Elsevier. Spector, B. and P. Egré (2015). A uniform semantics for embedded interrogatives: An answer, not necessarily the answer. Synthese 192, 1729–1784. Theiler, N., F. Roelofsen, and M. Aloni (2016). A uniform semantics for declarative and interrogative complements. ms. ILLC. Uegaki, W. (2015). Content nouns and the semantics of question-embedding. Journal of Semantics 33, 1–38. van Rooij, R. and K. Schulz (2004). Exhaustive interpretation of complex sentences. Journal of Logic, Language and Information 13, 491–519. Villalta, E. (2008). Mood and gradability: An investigation of the subjunctive mood in Spanish. Linguistics and Philosophy 31(4), 467–522. von Fintel, K. (1999). NPI licensing, Strawson entailment, and context dependency. Journal of Semantics 16, 97–148. Zuber, R. (1982). Semantic restrictions on certain complementizers. In S. Hattori and K. Inoue (Eds.), Proceedings of the 13th International Congress of Linguists, Tokyo. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 880 Modal subordination of propositional anaphora: On the role of tense and the modal particle ook in contextual counterfactuals in Dutch1 A. Marlijn MEIJER — Humboldt-Universität zu Berlin Sophie REPP — Humboldt-Universität zu Berlin Abstract. This paper examines a variant of modal subordination that involves reference to propositions that have been introduced in the scope of a negative operator. In the dialogues under consideration, this kind of reference is most reliably established if the modal particle (MP) ook and past perfect morphology are present in the response, which contains the anaphor (Meijer 2016). We provide experimental evidence that supports this empirical claim and provide a theoretical explanation for the data. We assume that the discourses at issue involve contextual counterfactuals (CFs) whose antecedent may be positive or negative and provides the antecedent for the anaphor. CFs with a negative antecedent ‘doubt’ the truth of the previous utterance, whereas CFs with a positive antecedent do not. As a consequence, the MP, which presupposes that the epistemic modal base already entailed the previously uttered proposition, is incompatible with the former but not the latter type of CF (Meijer 2016). For the tense marking we propose that the effects are due to the local interpretation of the non-fake tense in the consequent of the CF (cf. Ippolito 2013). Keywords: modal subordination, modal particles, propositional anaphora, counterfactuality 1. The phenomenon Propositions can be targeted by demonstrative pronouns like English that, see (1), where the proposition denoted by a declarative clause is the referent that is picked up by that in the subsequent sentence. We may say that the first clause introduces a propositional discourse referent (e.g. Asher 1986, 1993; Geurts 1998). That referent is targeted by that. Krifka (2013) suggests that clauses with sentential negation introduce two propositional discourse referents: the negative proposition that is denoted by the entire clause, and the positive proposition that is denoted by the syntactic object below the negation. Evidence for this claim comes from data like (2). (2B) and (2B’) are possible discourse continuations of the negative assertion (2A). Both contain the pronoun that. In (2B), that refers to the negative proposition ¬φ , two plus two is not five. In (2B’), that refers to the positive proposition φ , two plus two is five. Note that (2B’) contains the modal verb would, whereas (2B) does not contain a modal verb. (1) (2) 1 [John was out last night]φ . Mary knew thatφ . A: Two plus two isn’t five. ≡ ¬φ B: Everyone knows that¬φ . (Krifka 2013) B’: Thatφ would be a contradiction. We would like to thank Maribel Romero, Manfred Krifka and the audiences at Sinn und Bedeutung 21 and ConSOLE XXIV for discussion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 881 A. M. Meijer & S. Repp Modal subordination of propositional anaphora Reference to antecedents that are in the scope of negation or of intensional operators was first described for nominal anaphora by Roberts (1989), see (3a-b) and (4a-b). In the first utterance of these discourses, there is an indefinite that introduces a discourse referent in the scope of an intensional operator (a book in (3a)), or in the scope of negation (a car in (4a)). In the second utterance, (3b) and (4b), which both contain a modal verb (will/would), a pronoun refers back to the discourse referent that was introduced in the first utterance. (3b’) and (4b’) are minimal variants of (3b) and (4b) without a modal verb. These variants are not felicitous continuations of (3a) and (4a). Thus, in order to establish reference to a discourse referent below an intensional operator or negation in the previous utterance, a modal must be used. (3) a. b. If John bought [a book]i , he will be home reading it by now. (Roberts 1989:683) Iti ’ll be a murder mystery. b’. # Iti is a murder mystery. (4) a. b. John doesn’t have [a car]i . Iti would be in the garage. (Roberts 1997:239) b’. # Iti is in the garage. The propositions denoted by the clauses in (3b) and (4b) are said to be modally subordinated to the propositions in (3a) and (4a) (Roberts 1989, 1997). The modal base of the modal in the second utterance is restricted: in (3) by the proposition in the antecedent of the conditional; in (4), by the accommodated counterfactual proposition John bought a car. In the restricted domain of the modal, the familiarity presupposition for the use of the respective pronoun is fulfilled because a book and a car are given in that domain. Roberts (1997) highlights that domain restriction across utterances can be compared with domain restriction in conditionals, where the antecedent restricts the domain of the consequent. So for instance (4b) can be paraphrased as if John had a car, it would be in the garage. Going back to Krifka’s example for anaphoric reference to a proposition under negation, the presence of would is not surprising from the perspective of modal subordination involving nominal anaphora. The example is an instance of modal subordination involving a propositional anaphor. However, interestingly, the presence of a modal does not always seem to be necessary to refer to a propositional discourse referent in the scope of negation, see (5). In the continuations (5B/B’), there is no modal verb. Both continuations are felicitous although they differ with respect to the reference of that, which seems to be due to the presence vs. absence of a negation. If there is a negation, as in (5B), that refers to the positive proposition φ , you won the jackpot. If there is no negation, that refers to the negative proposition ¬φ , you did not win the jackpot. Goodhue and Wagner (resubm.) suggest that these different interpretations are due to our world knowledge. Winning the jackpot is unlikely whereas not winning it is likely. (5) A: You didn’t win the jackpot. ≡ ¬φ (Goodhue and Wagner resubm.) B: I didn’t expect thatφ . B’: I expected that¬φ . Although a modal does not always seem to be necessary to refer to a proposition under negation, in certain contexts the presence of a modal does not seem to be sufficient. Consider the Dutch Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 882 A. M. Meijer & S. Repp Modal subordination of propositional anaphora discourses in (6) (Meijer 2016). (6A) is a negative assertion. (6B) is a felicitous continuation, in which the speaker uses a predicate of personal taste to express their opinion about what was stated in the assertion. As the difference between (6B/B’) indicates, reference to the positive proposition with the demonstrative pronoun dat ‘that’ only is possible if in addition to a modal verb (here zouden ‘would’), the MP ook (literally ‘also’) as well as a past participle (geweest ‘been’) are present (Meijer 2016). In (6B), which contains ook and the past participle geweest, dat refers to the positive proposition φ , Jan worked yesterday. (6B’) is infelicitous on the reading that involves reference to the non-negated proposition (Meijer 2016). It is worth pointing out here that (6B’) is coherent if dat is interpreted as referring to ¬φ . (7) illustrates that German seems to behave similarly regarding the anaphoric possibilities of the pronoun das ‘that’ in the presence vs. absence of the MP auch (lit. ‘also’) and the past participle gewesen ‘been’.2 In this paper, we will use the terms φ -reference vs. ¬φ -reference, in order to distinguish the two interpretations of dat, viz. as referring to φ vs. ¬φ . (6) A: B: (7) A: B: Jan heeft gisteren niet gewerkt. ≡ ¬φ Jan has yesterday not worked ‘Jan didn’t work yesterday.’ Dasφ /#¬φ zou ook raar zijn geweest. MOD OOK strange be been that ‘That would have been strange.’ B’: Dat#φ /¬φ zou raar zijn. MOD strange be that ‘That would be strange.’ Hans hat gestern nicht gearbeitet. ≡ ¬φ Hans has yesterday not worked Dasφ /#¬φ wäre auch komisch gewesen. B’: Das#φ /¬φ wäre komisch. BE . SBJV AUCH strange been BE . SBJV strange that that Note that similar to Roberts’ cases of modal subordination involving nominal anaphora, (6B) and (7B) express conditional readings. Meijer (2016) calls such utterances contextual counterfactuals. Speaker B seems to accommodate an antecedent for a counterfactual (CF) conditional whose consequent is uttered overtly: if Jan had worked yesterday, that would have been strange. The antecedent of the CF provides the referent φ which is picked up by dat/das in the consequent. Turning to (6B’) and (7B’), we could assume that the accommodated CF plausibly is if Jan hadn’t worked yesterday, that would be strange. Again, the antecedent of the CF provides the referent that is picked up by dat/das in the consequent, in this case this is ¬φ . However, there is an important difference between the CFs that are accommodated in the (B)- vs. (B’)versions. In the (B)-versions, the second speaker accepts what the first speaker said as true: In the actual world Jan did not work. It is in the CF worlds that Jan worked. In the (B’)-version, in contrast, the second speaker doubts what the first speaker said, i.e. it is not established as common ground that Jan did not work. Rather, the second speaker implicates that Jan did work. 2 Some native speakers of German report that (7B’) is not coherent for them even on a ¬φ -reading. It seems that the midclause insertion of the conjunction aber ‘but’ improves (7B’) as in Das wäre aber komisch. We assume that the improvement is due to aber overtly marking the contrast with the previous utterance – after all, speaker B’ calls into doubt the utterance by the first speaker. See below for elaboration. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 883 A. M. Meijer & S. Repp Modal subordination of propositional anaphora It is important to note at this stage that discourses involving predicates of personal taste only seem to enable φ -reference if the predicate of personal taste is one of surprise or wonderment. Consider the response in (8B), which is minimally different from the one in (6B’): the predicate normaal ‘usual’ replaces the predicate raar ‘strange’. A proposition whose truth one finds normal, i.e. expects to be true cannot be surprisingly or unexpectedly true. The discourse in (8) is incoherent – with any kind of reference. The same observation holds for German (not illustrated). We will not explore the role of the type of predicate of personal taste in this paper and restrict our discussion to predicates of surprise/wonderment (for details see Meijer 2016).3 (8) A: Jan heeft gisteren niet gewerkt. Jan has yesterday not worked ‘Jan didn’t work yesterday.’ B: #Datφ /¬φ zou ook normaal zijn geweest. MOD OOK usual be been that ‘That would have been normal.’ In the present paper, we will explore the marking that is required to establish φ -reference in discourses involving responses with predicates of personal taste like (6B) and (7B) in more detail. The other cases of reference to a positive proposition in the scope of negation mentioned above are beyond the scope of this paper and must be left for future research. Also, we will be mainly focusing on Dutch. The goal of the paper is twofold. First, we will present quantitative evidence supporting Meijer’s claims about the influence of the presence of the MP ook and the past participle geweest on establishing φ -/¬φ -reference in responses like (6) (section 2). This quantitative verification is important because the judgments are somewhat subtle and sometimes puzzle native speakers. We will also see, however, that the empirical results offer some intricacies that merit some detailed discussion. Second, we will theoretically evaluate the experimental findings. For ook (section 4), we will largely Meijer’s suggestion that the particle signals that the knowledge that is available to the speaker, already entailed the truth of the proposition that was asserted by the previous speaker before that assertion was made. Therefore, the accommodation of a CF that calls into question the truth of the utterance of the previous speaker – which is what seems to be happening with ¬φ -reference – is incompatible with using the particle ook in that CF. With respect to the tense marking, Meijer suggests in her discussion of the occurrence of the past participle and zouden, that this combined marking fits a cross-linguistic pattern of establishing counterfactuality with multiple tense markers. However, she does not provide an explanation of the temporal marking in relation to the two anaphoric possibilities. Prima facie there is no obvious reason why the presence of a past participle in the consequent should result in φ -reference whereas the absence of that participle should re3 There are instances of φ -reference which do not require the presence of ook. Consider (i) (Berry Claus, p.c.), where ook is not required for dat to refer to the proposition Jan has won the final match. In fact, if ook were present, (iB) would be slightly odd. Note that (i) is not a contextual CF, and cannot be paraphrased as one. (i) A: B: Jan heeft de laatste wedstrijd niet gewonnen. ≡ ¬φ Jan has the final match not won ‘Jan hasn’t won the final match.’ Datφ zou nodig zijn geweest om deel te nemen aan de finale. that MOD required be been to part to take on the finale ‘That would have been required for taking part in the final.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 884 A. M. Meijer & S. Repp Modal subordination of propositional anaphora sult in ¬φ -reference. In section 4 we will propose an explanation for the tense marking in the contextual CFs in (6), building on the proposal for tense in CFs by Ippolito (2013). 2. Experiment For the quantitative verification of the empirical observations made in Meijer (2016), we conducted a semantic forced choice experiment. The experiment tested discourses which consisted of a negative assertion uttered by one speaker, and a response by another speaker that involved a predicate of personal taste. There were four types of discourses, which differed in whether or not the response contained the MP ook and/or the past participle geweest. (9) is a sample item. (9) Willem en Elisabeth laten hun grote tuin herinrichten. Hiervoor hebben ze een tuinman ingehuurd. Ze spreken over de herinrichting van de tuin. ‘Willem and Elisabeth are having their large garden redecorated. They hired a gardener to do this. They are talking about the redecoration of their garden.’ W: De tuinman heeft het gras nog niet gezaaid. The gardener has the grass still not sown. ‘The gardener hasn’t sown the lawn yet.’ E1: [−TENSE,−OOK] Dat zou raar zijn. that would odd be E2: [−TENSE,+OOK] Dat zou ook raar zijn. that would OOK odd be E3: [+TENSE,−OOK] Dat zou raar zijn geweest. that would odd be been E4: [+TENSE,+OOK] Dat zou ook raar zijn geweest. that would OOK odd be been The participants in the experiment were asked to choose between one of two possible interpretations for Elisabeth’s responses in (10E1-E4), such that the anaphoric pronoun dat was interpreted as referring to the negative proposition ¬φ , the gardener has not sown the lawn yet, or to the positive proposition φ , the gardener has sown the lawn (already),4 which arguably were introduced in the utterance by Willem. As discussed in the previous section, Meijer (2016) observed that dat receives a φ -interpretation in the response in discourses like (9) if both ook and the past participle geweest are present. Therefore we expect that in condition E4, participants should choose the interpretation where dat refers to φ . In condition E1, in contrast, dat should not refer to φ because the response neither contains ook nor geweest. So participants should choose the φ -interpretation much less often for E1 than for E4. As for E2 and E3, Meijer 4 The antecedent clause, uttered by the first speaker, contained the negative polarity item nog ‘yet’. This item cannot be part of the positive proposition, and most likely is replaced by the positive polarity counterpart al ‘already’ during the referential process (in a way to be explored by future research). This replacement does not seem to cause problems for anaphoric reference to positive/negative propositions: the materials used here have been adapted from earlier acceptability judgment studies on anaphoric reference involving response particles reported in Meijer, Claus, Repp and Krifka (2015) and in Claus, Meijer, Repp and Krifka (accepted), where the replacement did not seem to lead to degradedness. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 885 A. M. Meijer & S. Repp Modal subordination of propositional anaphora (2016) observes that if only geweest or only ook are present in the response, that response is not fully coherent on the reading involving φ -reference. For the forced choice between the φ and the ¬φ -interpretation, this might either mean that participants choose randomly between these two interpretations, or that they still show a preference for one over the other. On the basis of the concrete meaning contributions that we propose for the past perfect morphology (section 3) and that Meijer proposes for ook (section 4), we expect for both E2 and for E3 a higher proportion of φ -references than for E1. For E2, there should be a very high proportion of φ -references – possibly as high as for E4 – because, as we will see below, ¬φ -reference results in a presupposition failure for ook. For E3, the proportion of φ -references might be a bit lower because the past tense morphology is ambiguous, see section 3 for details. 2.1. Method 24 native speakers of Dutch were recruited through Prolific Academics (https://www.prolific.ac) and received payment for their participation. The experiment had a 2x2 within-subjects design with the factors OOK (+/−ook) and TENSE (+/−past participle). There were 24 experimental items and 24 fillers from another experiment. Items were allocated to participants and conditions in a Latin square design. Each item was constructed as illustrated in (9). There was a scene-setting passage that introduced the interlocutors and the topic of the conversation. One of the interlocutors made a negative assertion, the other responded such that the response was one of the four conditions illustrated in (9). The predicates of personal taste used in the materials all expressed surprise. There were twelve such predicates: gek ‘crazy’, raar ‘odd’, vreemd ‘strange’, uitzonderlijk ‘extraordinary’, merkwaardig ‘remarkable’, opvallend ‘notable’, eigenaardig ‘peculiar’, verbazingwekkend ‘surprising’, bizar ‘bizarre’, opmerkelijk ‘remarkable’, maf ‘crazy’ and apart ‘unusual’. Each predicate was used twice. After having read the dialogue in (9), participants were given a choice between two paraphrases which were meant to reveal the φ - vs. ¬φ -interpretation of the response, see (10). The tense marking in the clause preceding the paraphrases matched the tense marking in the response, i.e. for conditions E1 and E2 the marking was zou plus infinitive, and for conditions E3 and E4 it was zou plus hebben ‘have’ plus past participle. The antecedent paraphrases always had past perfect tense marking. We will discuss this tense marking in section 3. (10) Elisabeth zou het raar {vindenE1/2 /hebben gevondenE3/4 }, ‘Elisabeth would {findE1/2 / have foundE3/4 } it weird,’ ○ als the tuinman het gras nog niet had gezaaid. ¬φ if the gardener the grass yet not had sown ‘if the gardener had not sown the lawn yet.’ ○ als the tuinman het gras al had gezaaid. φ if the gardener the grass already had sown ‘if the gardener had sown the lawn already.’ For half of the participants, the first proposition was ¬φ ; for the other half, it was φ . After participants had chosen one of the paraphrases, the item disappeared from the screen. A verifiProceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 886 A. M. Meijer & S. Repp Modal subordination of propositional anaphora cation task followed. Participants read an assertion about the previous test item and judged its truth. Participants that scored at chance level on this task were excluded from the analysis. 2.2. Results Figure 1 and Table 1 show the mean proportions of choice of the positive proposition, i.e. of φ -reference, for the four conditions in the experiment. Descriptively, we may say that the individual effects of the ook and geweest was similar (each producing around 70% φ -references), and that the most reliable way of establishing φ -reference was a combination of the two markers. If no marker was present, φ -reference was chosen not very often. The statistical analysis was carried out with linear mixed-effects models with a binomial logit function. The fixed factors were TENSE and OOK with contrast coding −1 for −OOK and −TENSE, and +1 for + OOK and + TENSE. Participants and items were random factors. The best models (forward selection) contained random participant slopes for OOK and random intercepts for items. The analysis revealed a main effect of TENSE (b = 2.96, SE = 0.40, t = 7.4, p < .001) and of OOK (b = 2.78, SE = 0.50, t = 5.6, p < .001). φ -reference was chosen more often when the past participle was present, and it was chosen more often when the MP was present. There also was an interaction of the two factors (b = −1.32, SE = 0.56, t = −24, p = .019). The effect of the participle was smaller when ook was present than when it was not present. condition [−TENSE, −OOK] [−TENSE, +OOK] [+TENSE, −OOK] [+TENSE, +OOK] proportion .278 .688 .708 .861 sd .449 .465 .456 .347 Table 1. The propositions of choice of the non-negative conditional clause and the standard deviation. Figure 1. The mean proportion of choice of the non-negative conditional clause. The experiment has shown that for φ -reference, speakers prefer the presence of both the past participle geweest and the MP ook. However, even if only one of these markers is present φ -reference is more likely than if none of these markers is present. In the following we will propose how these results can be accounted for. 3. Tense in contextual counterfactuals The literature on CFs distinguishes between two major types of CFs: those with simple past morphology, and those with past perfect morphology, see (11a) and (b), respectively. The difference is also sometimes characterized as (11a) containing one layer of past morphology – in the antecedent (be + PAST) and in the consequent (WOLL + PAST) –, and (11b) containing Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 887 A. M. Meijer & S. Repp Modal subordination of propositional anaphora two layers of past morpholgy – additional have in antecedent and consequent (Iatridou 2000).5 (12) shows that the same marking is present in Dutch. The finite verb zou in the consequent is the 3rd person past tense of the auxiliary zullen ‘will.INFINITIVE’.6 Now crucially, both in English and in Dutch, the ‘actual tense’ in these examples, i.e. their temporal interpretation, seems to be different from what the morphological marking suggests. (11a) and (12a) seem to convey that it is not true that John is here at present and Jane is happy at present, whereas (11b) and (12b) seem to convey that it is not true at some relevant moment in the past that John was here and Jane was happy. So (11a) and (12a) are about worlds ‘contrary to the present’ whereas (11b) and (12b) are about worlds ‘contrary to the past’ (Iatridou 2000). It seems that there is one past too many both in the antecedent and in the consequent of the CFs. This ‘additional’ layer of past has been called fake past or fake tense (Iatridou 2000 and subsequent literature). The ‘remaining’ tense is the one that fits the actual temporal interpretation, i.e. present tense in (11a) and (12a) and past tense in (11b) and (12b). (11) a. b. If John were here Jane would be happy. If John had been here Jane would have been happy. (12) a. Als Jan hier was, zou Anne gelukkig zijn. if Jan here be.PAST will.PAST Anne happy be Als Jan hier was geweest, zou Anne gelukkig zijn geweest. if Jan here be.PAST been will.PAST Anne happy be been b. The above observations have spurred various analyses where the fake past is assumed to trigger a CF reading either via a past interpretation or via a modal interpretation (see Schultz 2014 for a brief overview). Proposals also differ with respect to whether the fake tense outscopes the entire conditional or not. We will explore two past-as-past approaches with wide-scope fake tense here, viz. Arregui (2007) and Ippolito (2013), because these approaches address some complications that we will talk about instantly and that are relevant for the discussion of our experimental results. Terminology-wise, we will dub the tense outscoping the conditional wide-scope past/tense, and the tense that seems to be interpreted in the conditional clauses, i.e. present tense in (11a) and (12a) and past tense in (11b) and (12b), the local tense. Now, an important challenge for the analysis of the local tense is the observation that the intuitions about the temporal interpretation in the above examples, although apparently clear, are 5 We will not distinguish between present CFs and future less vivid (FLV) conditional sentences (cf. Iatridou 2000) here. The latter contain a telic rather than stative predicate in the antecedent, which has consequences for the interpretation of the present (future-oriented or not). We will see later that the type of predicate in general seems to play an important role in the temporal interpretation of CFs but we cannot discuss this issue in this paper. 6 Zullen is traditionally characterized as a future auxiliary. Broekhuis and Verkuyl (2014) argue that zullen is purely modal and therefore is different from English WOLL. This debate is not immediately relevant for the present discussion. Furthermore, note that it is also possible to form a past perfect consequent without zouden in Dutch. In (i) the consequent contains the same morphology as the antecedent. We gloss over this here. (i) Als Jan hier was geweest, dan was An gelukkig geweest. if Jan here was been then was An happy been Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 888 A. M. Meijer & S. Repp Modal subordination of propositional anaphora deceptive. As was observed in Dudman (1984) and subsequent literature (e.g. Ogihara 1999; Arregui 2007, 2009; Ippolito 2003, 2013), CFs with simple past marking cannot only be about the present but also about the future, and CFs with past perfect marking cannot only be about the past but also about the present and the future, see (13) from Dudman (1984). The data are equivalent in Dutch, which for reasons of space we cannot show here. (13) a. b. c. If Grannie missed the last bus tomorrow, she would walk home. If Her Majesty had been here now, she would have been revolted. If Grannie had missed the last bus on Friday (next Friday), she would have walked home. (She is actually dead) Importantly for our discussion of φ -reference, there are restrictions on the use of the morphological tense marking for certain temporal interpretations. Observe that the set of examples we have looked at so far does not include a CF with simple past marking that has a past interpretation. The following examples illustrate that even with an elaborate context, a simple past marking in antecedent and consequent (14b), only in the consequent (14c), or only in the antecedent (14d), is unacceptable if a past interpretation of both antecedent and consequent is intended (compare (14a)). (14b) and (14c), where the antecedent is marked with simple past, are generally unacceptable with a past interpretation of the antecedent. (14d) is ‘only’ infelicitous with the indicated past interpretation of the consequent. If we replace last week in the consequent of (14d) with now and imagine that Paul’s failure to turn up has created long-term sadness in Jane, (13d) is felicitous. Thus, it is clearly possible to combine a past perfect antecedent with a simple past consequent if the latter contains a non-past interpretation. Again, the data are parallel in Dutch. (14) Paul had announced for last week that he would be in London. His old friend Jane was looking forward to seeing him. However, Paul didn’t turn up, and Jane wasn’t happy. a. If John had visited London last week Jane would have been happy (last week). b. *If Paul visited London last week Jane would be happy (last week). c. *If Paul visited London last week Jane would have been happy (last week). d. #If Paul had visited London last week Jane would be happy (last week). The restrictions on the tense morpohology in an otherwise apparently fairly flexible tense marking system in CFs has received different kinds of analyses in the literature. As mentioned above, both Arregui (2007) and Ippolito (2013) assume that a layer of fake tense outscopes the conditional. The proposals differ with respect to the local tense in the conditional clauses (as well as with respect to the number of wide-scope past operators, see below). We will briefly describe the two proposals here. Arregui (2007) sees the crucial difference between simple past vs. past perfect morphology as an aspectual rather than a tense difference. She suggests that simple past antecedents with eventive predicates contain a perfective operator, whereas antecedents with the past perfect (or those with a stative predicate) come with a perfect operator. The perfective operator introduces Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 889 A. M. Meijer & S. Repp Modal subordination of propositional anaphora a deictic event pronoun. The deictic nature of that pronoun creates the presupposition that the respective event is true in the actual world, i.e. that it has happened.7 For instance, in contexts like (14), the presupposition Paul visited London is clearly violated: Paul was not in London. So a simple past antecedent is expected to be infelicitous. A past perfect antecedent, in contrast, is felicitous because the perfect operator does not come with a deictic event pronoun. Turning to Ippolito (2013), we need to go in a bit more detail in order to be able to discuss our findings within her theory further below. Similarly to Arregui (2004, 2009), Ippolito assumes that a CF reading arises from the presence of a past operator that takes scope over the entire conditional. This past operator binds the time argument of the accessibility function of the modal WOLL. This function returns the set of worlds that have the same history as the evaluation world up to a time t, the accessibility time. At t, the truth of e.g. John having visited London has not been decided yet and what is called in the philosophical literature branching into different futures occurs only afterwards. The wide-scope past operator shifts the accessibility time to the past, which means that the worlds started branching into different futures at a time in the past. In addition to the accessibility time, there is another time that is important in Ippolito’s account. This is the reference time, which is the time when presuppositions of the antecedent and the consequent are evaluated: the presuppositions must be entailed by the worlds that are historically accessible from the reference time. Since the set of possible worlds can only become smaller over time, and because the reference time cannot precede the accessibility time, the presuppositions eventually must be satisfied at the reference time. The default reference time is the utterance time. For illustration Ippolito discusses the following example. For someone to be in love they must be alive (cf. Musan 1997 for existence presuppositions of this kind). So, a presupposition of the antecedent in If John were in love with Mary, he would ask her to marry him is that John is alive in worlds that are historically accessible from the utterance time, and thus by extension at the utterance time. As a consequence, the utterance of this conditional after a statement like John is dead is infelicitous. However, if the same conditional appears with past perfect marking it is felicitous in this context. According to Ippolito, this effect is due to the past perfect introducing a second past tense operator that scopes over the entire conditional. The function of this operator is to shift the reference time to the past. As a consequence, the presuppositions of antecedent/consequent are evaluated for worlds that are historically accessible from a reference time that is before the utterance time. With respect to the example we just discussed, this means that the being-alive presupposition must be entailed by historically accessible worlds at that past reference time. Since there is a time in the past where worlds with a living John are still accessible the CF If John had been in love with Mary, he would have asked to marry him is felicitous if John is dead at the utterance time. Now, in addition to the two wide-scope past operators, Ippolito assumes that the antecedent and the consequent each have ‘local’ deictic tense, which is always evaluated with respect to the utterance time. Such local deictic tenses are also assumed e.g. by Romero (2014). What is special about Ippolito’s account is that the present perfect – due to a deficit in English morphology – may either signal the presence of the two wide-scope operators that we discussed, or the presence of the two wide-scope operators plus the presence of local past tense. The mor7 See Arregui (2007: 247ff.) for cases where the speaker does not or cannot know whether the event has happened / will have happened. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 890 A. M. Meijer & S. Repp Modal subordination of propositional anaphora phological deficit is that standard English does not have the morphology to express three layers of past. Therefore, Ippolito proposes the following structures for CFs: (15) Simple past (a) and past perfect (b&c) CFs (Ippolito 2013: 96ff.) a. [PAST1 [ WOLL [ PRESENTdeictic φ ] [PRESENTdeictic ψ]]] b. [PAST1 [PAST2 [ WOLL [ PRESENTdeictic φ ] [PRESENTdeictic ψ]]] c. [PAST1 [PAST2 [ WOLL [ PASTdeictic φ ] [PASTdeictic ψ]]]] In (15a) and (b), there is a deictic present tense in the antecedent and in the consequent of the conditional. This structure is not compatible with the examples in (14) above, because these all involve the adverb last week. The present tense indicates that we are evaluating an event that would have taken place now which is inconsistent with last week. Therefore, we must assume that the examples in (14) have the structure in (15c). A question that arises is how we can account for the felicitous minimal variant of (14d) in which we replaced last week in the consequent with now. According to Ippolito’s structures in (15b) and (c), there would still be two past tense operators outscoping the entire conditional, because the antecedent occurs in the past perfect. Yet, intuitively, using a past perfect rather than a simple past in the consequent alters the interpretation of the conditional. At this point, we do not see how Ippolito’s account can be altered, such that it can account for such ‘mixed’ CFs. With this much in hand, let us now turn to our cases of φ -reference / ¬φ -reference in the experiment presented in section 2. Recall that the utterance of the first speaker in our discourses is a negative assertion stating that a certain event (e.g. one of the gardener sowing the lawn) has not taken place. We are assuming that this assertion is one about the past, which is the default interpretation of the present perfect in Dutch (Broekhuis and Verkuyl 2014).8 Next, recall that we are assuming that the second speaker, who uses a contextual CF to evaluate the utterance of the first speaker, plausibly accommodates either the past perfect CF in (16Bφ ) or the one in (16B¬φ ). (16) A: B: The gardener hasn’t sown the lawn yet. Dat zou (ook) raar zijn (geweest), . . . that will.PAST OOK odd be been φ . . . als de tuinman het gras al had gezaaid. . . . if the gardener the grass already have.PAST sow.PERF ¬φ . . . als de tuinman het gras nog niet had gezaaid. . . . if the gardener the grass not yet have.PAST sow.PERF ‘It would {be / have been} strange if the gardener had(n’t) sown the lawn {yet / already}’ 8 There are differences between the Dutch present perfect and the English simple past but note that the Dutch present perfect can be used in sentences that contain a temporal modifier like yesterday, which is not possible with the English present perfect: *John has gone to the cinema yesterday vs. John went to the cinema yesterday. A thorough discussion of this issue is beyond the scope of this paper; we refer the reader to De Vuyst (1985). Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 891 A. M. Meijer & S. Repp Modal subordination of propositional anaphora Starting with the tense in the antecedent, recall from the introductory section that when accommodating a CF like the one in (16Bφ ) the second speaker accepts what the first speaker said as true. In the actual world, the gardener hasn’t sown the lawn, in the CF worlds he has sown the lawn. In Ippolito’s terms, the CF worlds are historically accessible only from a reference time in the past, at which it was still possible for the gardener to sow the lawn. Therefore, there must be two past operators scoping over the conditional. As a consequence, the conditional antecedent in (16Bφ ) must be marked with the past perfect. This is the tense morphology that we used in the paraphrases in the experiment for φ -reference. On Arregui’s account we expect past perfect marking as well because that marking comes with no presupposition concerning the actual existence of the event at issue – which is what is required in the above context: the context says that the event did not take place. Further below – when we discuss the tense marking in the consequent, which we argue can be captured best in Ippolito’s account – we will suggest that the local deictic tense in the antecedent of (16Bφ ) is past tense as well. As for (16B¬φ ), we said in the introductory section that the second speaker doubts what the first speaker said, viz. that the gardener hasn’t sown the lawn. The second speaker implicates that the gardener has sown the lawn. What is interesting about this kind of CF is that intuitively, the present perfect marking in the antecedent of the conditional also seems to be allowed. That is the sentence that is uttered by the first speaker can form the antecedent of the contextual CF. In English, this would look as follows: A: John did not work. B: If John didn’t work. . . . Note that the preferred interpretation of the antecedent seems to be that of an antecedent in an indicative conditional. Thus, such a marking somehow reduces the ‘degree’ of counterfactuality of the sentence. An antecedent with past perfect marking seems to be better suited to express stronger counterfactuality (cf. Iatridou 2000; Ippolito 2013). For the present purposes we need to lay that issue aside. In the experiment, we chose past perfect marking for the antecedent of the paraphrases that we gave to the participants both for φ -reference and for ¬φ -reference because this choice enabled us to compare minimal pairs in the investigation of the tense marking in the consequent. Turning to the tense in the consequent, the experiment revealed that morphological marking with the past perfect increased the chances that the demonstrative pronoun in the response was interpreted as having φ -reference. As we saw above, the consequent of a CF with a past perfect antecedent in principle can occur with simple past marking or with past perfect marking, if the antecedent is overt. So in principle the choice of tense for the consequent is open.9 9 Also observe that the choice between present perfect and past perfect does not seem to influence nominal reference under modal subordination, at least in examples like (iA). The indefinite een dier ‘an animal’, which occurs under negation in the first utterance, is felicitously picked up by the pronoun het ‘it’ in the second utterance, independently of the morphological marking in that utterance, which corresponds to the consequent in an accommodated CF. (i) Context: Paul gaat af en toe vroeg in de ochtend jagen. Rond het middaguur vraagt Anna, die Paul die dag nog niet gezien heeft, zich af of hij vanochtend heeft gejaagd. ‘Every now and then Paul goes hunting early in the morning. Around noon, Anna, who hasn’t seen Paul today yet, is wondering if he was out hunting this morning.’ A: Paul heeft geen dieri geschoten. Heti zou daar in de hoek {liggen /hebben gelegen}. Paul has NEG+a animal shot it would there in the corner lie /have lain ‘Paul has not shot an animal. It would {be/have been} lying in the corner over there.’ Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 892 A. M. Meijer & S. Repp Modal subordination of propositional anaphora Let us see how the accounts by Arregui (2007) and Ippolito (2013) can be applied to our findings about the consequent. Arregui (2007) designed her proposal for the antecedent in CFs but observes in a footnote (p. 224, n. 2) that the tense restrictions that she discusses for antecedents are essentially the same for consequents. She suggests that the latter also fit the proposal she makes but does not discuss any details. As we briefly mentioned above, a crucial question within Arregui’s aspectual account is whether the consequent is eventive or stative. For eventives, the tense matters because they combine with the deictic event pronoun that is introduced by the perfective aspect. For statives, the tense does not matter because there is no event pronoun. The evaluating consequents in our examples, see (20), are stative. So tense should not matter. However, our experimental results seem to suggest it does. This is problematic for Arregui’s account and we do not see a straightforward way of fixing the problem. As we saw above, Ippolito (2013) assumes that there local tense in the antecedent and in the consequent of conditionals that receives a deictic interpretation. However, she also points out that it is not quite clear how the tense marking in the consequent can be related to the wide scope past operator(s), whose presence is signaled by the past perfect morphology in the antecedent, and which, as we saw above, we must assume is present in our discourses. Ippolito discusses a potential sequence-of-tense analysis (also cf. Romero 2014) for past perfect marking in the antecedent and the consequent. However, as we mentioned above, she does not consider ‘mixed’ CFs, i.e. CFs with a past perfect antecedent and with a simple past consequent in English (which would correspond to the present perfect in Dutch). To explain the results that we obtained in the experiment within Ippolito’s proposal we will capitalize on the idea that the local tenses are interpreted deictically. Let us start with the preferred preference of the past participle for φ -reference. Recall that our contextual CFs are responses to a negated assertion about the past. This assertion thus introduces a salient time in the past. It is a plausible to assume that a subsequent contextual CF will say something about this salient time. Thus, we assume that the consequent conveys that the speaker thinks that the worlds that are picked up by the propositional anaphor contain spatio-temporal regions that are specified for that salient time in the past, are strange – or rather were strange, because they are in the past. It is not very plausible to assume that the strangeness only applies at the time of speaking, which is what the absence of the past participle would signal. Turning to the ¬φ -reference, it seems that we may say exactly the same: the contextual CF is a response to a negative assertion about the past. As a consequence we might expect the presence of a past participle. However, recall that the CFs that are arguably accommodated in the two cases are different. In the case of ¬φ -reference, the speaker doubts the truth of the previous utterance. So, the evaluative comment refers to the truth of the utterance just made rather than to past CF worlds on whose counterfactuality both speakers agree as in the case of φ -reference. Since the truth of the utterance is at issue at the utterance time, the consequent preferably is marked without the past participle. Linking these suggestions to Ippolito’s structures for CFs in (15), we might say that φ -reference has the structure in (15c). Both the antecedent and the consequent contain a local deictic past, with the entire conditional being in the scope of the two past operators that we argued for Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 893 A. M. Meijer & S. Repp Modal subordination of propositional anaphora above. ¬φ -reference cannot straightforwardly be matched to Ippolito’s structures because there seem to be different tenses in antecedent and consequent. Also, recall that the details of the interpretation of such doubting CFs still pose a number of questions that need to be addressed in future research. With respect to the experimental results, the above suggestions explain why the presence of the past participle increases the proportions of φ -reference. Still, recall that in condition E3, which contained a past participle but not the MP, there still was a non-negligible proportion of ¬φ -choices. We may assume that speakers adopted a structure like (15b) when they made this choice. According to Ippolito past perfect marking is compatible with a local present tense interpretation: the past perfect may signal the presence of only the two wide scope past operators. An alternative, or additional explanation for the results for E3 might be that the contextual CFs with φ -reference have a kind of default marking, which includes the MP ook. The experimental results suggest that this might indeed be the case because φ -choices were most frequent if both the participle and the particle were present (condition E4). Hence, if one of the ‘typical’ markers is missing, slight incoherence might arise, which most likely influences the way participants interpreted the response. This issue needs to be investigated in future research in an acceptability study. Finally, recall that the proportion of φ -choices was nonnegligible when the past participle (and the MP ook) was absent (condition E1). Again, it is possible that some speakers do not find such utterances coherent (as is the case for German, see footnote 2). As a consequence they might have found it difficult to determine the meaning of the response. This issue also needs to be investigated in an acceptability study. 4. The MP ook In this section we will discuss the finding that the presence of the MP ook increased the proportion of φ -references. We will generally follow the proposal by Meijer (2016) but deviate in some of the details. Meijer builds her analysis – which she provides for ook and its German cousin auch – on previous accounts of the German particle because descriptions of Dutch ook are scarce. We will employ the same strategy in our initial characterization of the particle but then focus on ook.10 (17) shows an example of the MP ook. Speaker A notes that Peter 10 Note that ook (as well as auch) is ambiguous between a MP and an additive focus particle reading. As a focus particle ook comes in two variants: unstressed and stressed. If it is unstressed it associates with a focus in its c-command domain, see (i). If it is stressed it associates with a focus that is outside its c-command domain, see (ii). Both variants come with the presupposition that there is an alternative in the context for which the predicate that holds for the focus constituent also holds for the alternative. Thus, in (i) and (ii) there must be someone in addition to Marie that Peter called. There are subtle differences between the two versions of the particle, see e.g. Krifka (1998) and Reis and Rosengren (1997) for analyses of stressed German auch. (i) Peter heeft ook M ARIE gebeld. Peter has OOK Marie called ‘Peter has also called Mary.’ (ii) Peter heeft M ARIE OOK gebeld. Peter has Marie OOK called ‘Peter has also called Mary.’ Focus particle(s) and the MP can be distinguished from each other by their prosody (the MP cannot be stressed) and their syntactic distribution. Most importantly for the present purposes, the focus particles but not the MP come with the above-mentioned presupposition. Our experimental materials (recall (9) in section 2) were such that that presupposition was not satisfied in the context. Neither did the scene-setting passage provide a focus alternative to dat (which would have been required for the stressed variant of ook), nor did it provide a focus Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 894 A. M. Meijer & S. Repp Modal subordination of propositional anaphora looks bad. Speaker B’s response is to be read as conveying that Peter’s looking bad was not unexpected to him, since Peter has been ill for a long time (cf. Karagjosova 2003 for auch). (17) A: Peter ziet er slecht uit. Peter looks there bad out ‘Peter looks bad.’ B: Hij is ook lang ziek geweest. he is OOK long ill been ‘Well, he has been ill for a long time.’ Auch has been claimed to indicate that a previously asserted proposition was expected to be true already (Thurmair 1989, Karagjosova 2003). As a consequence, with an auch-utterance, a speaker confirms the proposition asserted prior to the auch-utterance. Karajogosova (2003) notes that auch-utterances can be ‘corrective’, in the sense that speakers can use them to indicate to their interlocutor that the previous utterance did not even contain new information. Furthermore, she suggests that auch signals that the speaker has made some sort of inference, based on what s/he already knew (for instance, from Peter being ill for a long time, we can infer that he looks bad). She notes that auch-utterances often can be translated with becauseconstructions (e.g. Peter looks bad because he has been ill for a long time for (17B)). However, note that it is not actually possible to paraphrase contextual CFs using because, as the use of auch does not seem to be causal here. In line with this intuition, Bergmann and Repp (2015) provide experimental evidence suggesting that auch is not causal in the same way that the e.g. German markers denn ‘because’ and eben ‘obviously’ are. A recall experiment showed that denn and eben helped recalling information. This effect was not found for auch. Yet, the recall of information has been claimed to be aided by the presence of causal markers (e.g. Caron, Micko and Thüring 1988). Meijer (2016) largely follows the theories by Thurmair (1989) and Karagjosva (2003), but offers a formal analysis of auch and ook as epistemic markers. Roughly, Meijer suggests that auch/ook presupposes that the proposition asserted in the previous utterance (proposition φ−1 ) was already entailed by the epistemic modal base before it was asserted, as shown in (18). The epistemic modal base f (w) contains the propositions that describe the knowledge that has been established in a world w (Kratzer 1981). (18) ⟦ook(φ )⟧c,w = φ ; defined if ∩ f (w) ⊆ φ−1 before φ−1 was uttered Applying (18) to (17), we can say that the knowledge available to B enabled him to infer that Peter was looking bad, before A asserted this. Specifically, B’s world knowledge that if one is ill for a long time, one looks bad and the knowledge that Peter has been ill for a long time most likely are decisive here. Note that the dialog in (17) is still fine if A knows nothing about Peter’s medical history, but does know that he looks bad. The fact that for A, the proposition that Peter looks bad does not have to be inferable in the way that ook signals that it is for B, alternative to (to be) strange (which would have been required for the unstressed variant of ook). Furthermore, it is difficult to accommodate the presupposition of additive focus particles (Kripke 2009). Hence, we assume that it is highly unlikely that the participants in the experiment interpreted the word ook as a focus particle. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 895 A. M. Meijer & S. Repp Modal subordination of propositional anaphora shows us that it need not be the context set that is the contextually salient body of knowledge, but it could also be the knowledge of the speaker.11 However, in what Karagjosova calls the ‘corrective’ use of auch, it seems that the particle indicates that the speaker who is making the auch-utterance indicates to his/her interlocutor that s/he should have known already that this proposition was inferable. In such scenarios, it might be the context set that is the relevant body of information. Meijer’s (2016) specific proposal for auch and ook is slightly different from what we are assuming here. It is couched in the framework by von Fintel and Gillies (2010) on must, where a distinction is made between two sets of propositions that are relevant for epistemic/evidential modality. The first set is the kernel. This set consists of propositions that the speaker takes to be true (propositions denoting world knowledge, direct observations and trustworthy knowledge). The second set is the intersection of the kernel: the modal base it determines. For must, roughly, the authors argue that it presupposes that its prejacent is entailed by the modal base that the kernel determines but that it is not in the Kernel. Meijer (2016) tentatively suggests that the MPs signal that the prejacent was entailed by the modal base, but remains agnostic about the presupposition auch/ook bear with respect to the kernel. For ook, Meijer points out that the kernel does not seem to play a role, since (17B) is felicitous, even if both speakers have seen that Peter looks bad and are aware of their mutual knowledge. For some speakers of German, the use of auch in such scenarios is marked, which suggests that for these speakers, the prejacent of auch cannot be in the kernel. Meijer (2016) therefore remains agnostic with respect to the role of the kernel in uses of auch. Since the kernel does not seem relevant for ook, we will stick to (18) and leave research into the use of auch in scenarios in which the prejacent is in the kernel for future research.12 Let us return to the use of ook in contextual CFs and to our experimental results. From the above suggestion for ook, it follows that if ook is used in response to a negative assertion the utterance that ook occurs in is interpreted as affirming this negative assertion. Such an affirmation is present in the CFs with φ -reference but not in the CFs with ¬φ -reference. Recall that in the latter the second speaker doubts what the first speaker said, viz. that ¬φ is true. Hence, we predict that ook should not be felicitous with ¬φ -reference. With respect to our experiment, this means that conditions with ook (E2, E4) should elicit a low proportion of ¬φ -choices. This is what we found. However, recall that there still was a non-negligible proportion proportion of choices for ¬φ for contextual CFs that contain ook, but not geweest (E2). As we pointed out above, the most common, or preferred, way of establishing φ -reference in contextual CFs is by including both the MP and the past participle. As we mentioned in the discussion on geweest, it could be that the lack of one of these markers made the response incoherent for some of the participants. Future research should investigate this matter in an acceptability judgment study. 11 We are aware that some authors have argued against such an analysis of modal verbs (e.g. von Fintel and Gillies 2008) and we do not wish to enter this debate on modality. However, for the use of ook the data strongly suggest that it is the knowledge of the speaker that is relevant for a felicitous use of the MP. 12 It seems that (18) holds too for those speakers of German who think that the German equivalent of (17) is fine even if both speakers are aware of their mutual knowledge of A’s assertion before A made this assertion. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 896 A. M. Meijer & S. Repp Modal subordination of propositional anaphora 5. Conclusion In this paper we have argued that two important factors for establishing reference to a proposition in the scope of a negation in a previous utterance are the tense marking and the presence or absence of the MP ook (cf. Meijer 2016). We have provided experimental evidence for a certain class of evaluative utterances that supports this empirical claim. With Meijer (2016) we have assumed that these evaluative utterances are contextual CFs for which an antecedent is accommodated on the basis of the previous utterance. The antecedent that is accommodated either contains a negation or not, and it serves as the antecedent for the propositional anaphor in the consequent, i.e. decides whether the anaphor refers to the proposition in the scope of the negation φ or the negated proposition ¬φ . With Meijer (2016) we have argued that ook presupposes that the previous utterance could be inferred from previous knowledge and thus must be true. Since this presupposition is only satisfied in CFs with φ -reference, the presence of ook is only compatible with such a reading. Furthermore, we have argued that φ -reference is preferably marked with a past participle in the consequent because a local deictic past tense – which plausibly is the temporal interpretation of the consequent – requires past perfect tense morphology (Ippolito 2013). ¬φ -reference in contrast, is compatible with a local deictic present tense in the consequent. References Arregui, A. (2004). On the Accessibility of Possible Worlds: The Role of Tense and Aspect. Ph. D. thesis, University of Massachusetts, Amherst. Arregui, A. (2007). When aspect matters: The case of would-conditionals. Natural Language Semantics 15(3), 221–264. Arregui, A. (2009). On similarity in counterfactuals. Linguistics and Philosophy 32(3), 245– 278. Asher, N. (1986). Belief in Discourse Representation Theory. Journal of Philosophical Logic 15(2), 127–189. Asher, N. (1993). Reference to Abstract Objects in Discourse. Dordrecht: Kluwer. Bergmann, B. and S. Repp (2015). Causality and the influence of different modal particles on the mental representation of discourses. Poster presented at AMLaP 21. Malta, September. Broekhuis, H. and H. J. Verkuyl (2014). Binary tense and modality. Natural Language and Linguistic Theory 32(3), 973–1009. Caron, J., H. C. Micko, and M. Thüring (1988). Conjunctions and the recall of composite sentences. Journal of Memory and Language 27(3), 309–323. Claus, B., A. M. Meijer, S. Repp, and M. Krifka (accepted). Puzzling response particles: An experimental study on the German answering system. Semantics and Pragmatics. De Vuyst, J. (1985). The present perfect in Dutch and English. Journal of Semantics 4(2), 137–163. Dudman, V. H. (1984). Conditional interpretations of if -sentences. Australian Journal of Linguistics 4, 143–204. Fintel, K. and A. S. Gillies (2008). CIA leaks. Philosophical review 117(1), 77–98. Fintel, K. and A. S. Gillies (2010). Must. . . stay. . . strong! Natural Language Semantics 18(4), 351–383. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 897 A. M. Meijer & S. Repp Modal subordination of propositional anaphora Geurts, B. (1998). Presuppositions and anaphors in attitude contexts. Linguistics and Philosophy 21(6), 545–601. Goodhue, D. and M. Wagner (resubmitted for review). Intonation, yes and no. lingbuzz/003082. Iatridou, S. (2000). The grammatical ingredients of counterfactuality. Linguistic Inquiry 31(2), 231–270. Ippolito, M. (2003). Presuppositions and implicatures in counterfactuals. Natural Language Semantics 11(2), 145–186. Ippolito, M. (2013). Subjunctive Conditionals: A Linguistic Analysis. Cambridge, MA: MIT Press. Karagjosova, E. (2003). Modal particles and the common ground. In P. Kühnlein, H. Rieser, and H. Zeevat (Eds.), Perspectives on Dialogue in the New Millennium, pp. 335–349. Amsterdam: John Benjamins. Kratzer, A. (1981). The notional category of modality. In H.-J. Eikmeyer and H. Rieser (Eds.), Words, Worlds, and Contexts, pp. 38–74. Berlin: De Gruyter. Krifka, M. (1998). Additive particles under stress. In D. Strolovitch and A. Lawson (Eds.), Proceedings of Semantics and Linguistic Theory 8, pp. 111–128. Krifka, M. (2013). Response particles as propositional anaphors. In T. Snider (Ed.), Proceedings of Semantics and Linguistic Theory 23, pp. 1–18. Kripke, S. (2009). Presupposition and anaphora: Remarks on the formulation of the projection problem. Linguistic Inquiry 40(3), 367–386. Meijer, A. M. (2016). Referring to a proposition ‘inside’ a negated one: The modal particles auch and ook in contextual counterfactuals. In K. Bellamy, E. Karvovskaya, and G. Saad (Eds.), ConSOLE XXIV: Proceedings of the 24th Conference of the Student Organization of Linguistics in Europe (6–8 January 2016, York), Leiden, pp. 19–42. Leiden University Center for Linguistics. Meijer, A. M., B. Claus, S. Repp, and M. Krifka (2015). Particle responses to negated assertions: Preference patterns for German ja and nein. In T. Brochhagen, F. Roelofsen, and N. Theiler (Eds.), 20th Amsterdam Colloquium, pp. 286–295. Musan, R. (1997). Tense, predicates, and lifetime effects. Natural Language Semantics 5(3), 271–301. Ogihara, T. (1999). Double-access sentences generalized. In T. Matthews and D. Strolovitch (Eds.), Proceedings of Semantics and Linguistic Theory 9, pp. 224–236. Reis, M. and I. Rosengren (1997). A modular approach to the grammar of additive particles: The case of German auch. Journal of Semantics 14(3), 237–309. Roberts, C. (1989). Modal subordination and pronominal anaphora in discourse. Linguistics and Philosophy 12(6), 683–721. Roberts, C. (1997). Anaphora in intensional contexts. In S. Lappin (Ed.), The Handbook of Contemporary Semantic Theory. Oxford: Basil Blackwell. Romero, M. (2014). ‘Fake tense’ in counterfactuals: A temporal remoteness approach. In L. Crnič and U. Sauerland (Eds.), The Art and Craft of Semantics: A Festschrift for Irene Heim, Volume 2, pp. 47–63. Cambridge, MA: MITWPL. Schulz, K. (2014). Fake tense in conditional sentences: A modal approach. Natural Language Semantics 22(2), 117–144. Thurmair, M. (1989). Modalpartikeln und ihre Kombinationen. Tübingen: Walter de Gruyter. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 898 The proper treatment of the wide scope or reading of the English either . . . or . . . construction1 Mioko MIYAMA — University of Tokyo Abstract. The main concern of this paper is the availability of the wide scope or reading in the English either . . . or . . . construction and its interaction with the behavior of either. I propose that a hybrid analysis consisting of an ellipsis analysis (Schwarz, 1999), which directly arises from the requirement of or that it connect disjuncts of the same type, and a choice function analysis of either (cf. Winter (2001); Schlenker (2006) for a choice function analysis of or) explains the whole data set. I also discuss a prediction the present analysis makes and some remaining issues, including a data issue in which the judgments made by my informants differ from the ones observed in a previous study. Keywords: disjunction, wide scope or reading, choice function, ellipsis. 1. Introduction This paper focuses on the English either . . . or . . . construction, in which either can be overt or covert as presented in Larson (1985): (1) a. b. Mary is looking for a maid or a cook. Mary is looking for either a maid or a cook. (Larson, 1985: 218) The proposal of this paper is that a hybrid analysis consisting of a choice function analysis of either (cf.Winter (2001); Schlenker (2006) for a choice function analysis of or) and an ellipsis analysis (Schwarz, 1999) straightforwardly explains the basic data concerning the (un)availability of the wide scope or reading. The rest of the paper is organized as follows. In Section 2, I review the basic data set of the availability of the wide scope or reading and its interaction with either. The main proposal is given in Section 3, where it is shown that neither a pure ellipsis analysis nor a pure choice function analysis explains the data set in Section 2. I propose that a hybrid analysis which combines the ellipsis analysis and a choice function analysis of either, a modified version of the choice function analysis of disjunction, covers the whole data set introduced in Section 2. Section 4 concludes the paper and discusses some potential problems related to the predictions that the present analysis makes. 1I am grateful to Akira Watanabe and Noriko Imanishi for giving me helpful comments and suggestions. I also express my deep gratitude to Barbara Partee, who gave me important advices and suggestions to the very first version of this paper, without which the research would never have taken shape, and to Christopher Tancredi, who has also given me numerous invaluable comments to the later versions of this paper, without which the research would never have developed into the present version. I also thank the audience at Sinn und Bedeutung 21, especially Mats Rooth, for discussion and judgments. All remaining errors are my own. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 899 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction 2. The basic data set As noted in Partee and Rooth (1983) as a problematic case and discussed in Rooth and Partee (1982) in more detail, when disjunction is combined with certain kinds of elements in a sentence, the sentence is (at least) three-ways ambiguous: (2) The department is looking for a phonologist or a phonetician. (Partee and Rooth, 1983: 374) a. Jlook forK(Ja phonologist or a phoneticianK) (d) (narrow scope or de dicto reading) b. ∃x : Ja phonologist or a phoneticianK(x), Jlook forK (x) (d) (de re reading) c. Jlook forK(Ja phonologistK) (d) ∨ Jlook forK(Ja phoneticianK) (d) (wide scope or de dicto reading) There is a de re reading in (2b) according to which there is a specific person x who is either a phonologist or a phonetician, and the department is looking for him. (Since this reading does not affect the discussion in this paper, I disregard this reading hereafter.) The narrow scope or de dicto reading (the NS reading) is in (2a), and under this reading the department would be satisfied by finding either a phonologist or a phonetician. The “problematic” de dicto reading, which I am interested in, is described in (2c). On this reading, the department do not yet necessarily have a specific candidate in mind. They do already have in mind which of the two specialists they are going to look for, but the speaker forgot which it was. The reading becomes clearer when continued with “. . . but I don’t know which.” Thus the overall meaning is as if the disjunction is connecting two propositions, taking widest scope, even though the indefinite in each disjunct takes narrow scope. This is called the “wide scope or” reading (the WS reading) in Rooth and Partee (1982). Larson (1985) observes that the possible readings of a sentence change when either comes into the structure. He states a generalization: (3) Larson’s (1985) generalization (Winter, 2000: 395): a. In or coordinations without either, as well as in either . . . or . . . coordinations with either undisplaced, the scope of or is confined to those positions where either can potentially appear. b. When either is displaced it specifies the scope of or to be at that displaced position. Thus, while when either is adjacent to the Disjunction Phrase both NS and WS readings are available (4), when either floats to a higher position the NS reading disappears (5). (4) (5) a. b. a. b. Mary is looking for a maid or a cook. Mary is looking for either a maid or a cook. (i) Jlook forK(Ja maid or a cookK)(m) (ii) Jlook forK(Ja maidK)(m) ∨ Jlook forK(Ja cookK)(m) (NS reading) (WS reading) Mary is either looking for a maid or a cook. Mary either is looking for a maid or a cook. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 900 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction c. Either Mary is looking for a maid or a cook. (i) ?*Jlook forK(Ja maid or a cookK) (m) (ii) Jlook forK(Ja maidK)(m) ∨ Jlook forK(Ja cookK) (m) (NS reading) (WS reading) Winter (2000) and Schlenker (2006) report data which at first glance look like an exception to Larson’s (1985) generalization in (3), where disjunction can take wide scope over an island as in (6) and (9) but either cannot appear out of the island as in (8) and (11).2 Note that either can appear inside the island and the disjunction can take either the narrow or wide scope as shown in (7) and (10). (6) If Bill praises Mary or Sue then John will be happy. (Winter, 2000: 403) a. If Bill praises Mary then John will be happy and if Bill praises Sue then John will be happy. (NS) b. If Bill praises Mary then John will be happy or if Bill praises Sue then John will be happy. (WS) (7) a. b. (8) *Either if Bill praises Mary or Sue then John will be happy. (9) Students taking the exam have a choice of two options: Greek or Latin. a. Not a single student who picked some/a certain option (I don’t remember which) passed the exam. (baseline; island-escaping indefinites) b. #Not a single student who picked at least one option (I don’t remember which) passed the exam. (baseline; non-island-escaping indefinites) c. Not a single student who picked Greek or Latin (I don’t remember which) passed the exam. (10) If Bill praises either Mary or Sue then John will be happy. ( OK NS / OK W S) If Bill either praises Mary or Sue then John will be happy. ( OK NS / OK W S) (Winter, 2000: 403) a. Not a single student who picked either Greek or Latin (I don’t remember which) passed the exam. b. ?Not a single student who either picked Greek or Latin (I don’t remember which) passed the exam. 2 Larson, 1985: 245 reports that the scope of or actually is sensitive to CNP islands and Wh islands when either is not present as in (i) and (ii) (according to his claim, movement of the null operator in the position of either is sensitive to islands). Thus there seems to be a discrepancy in judgment. (i) (ii) John maintains the claim that Bill should resign or retire. a. John maintains [SHOULD (resign (b)) ∨ SHOULD (retire (b))] b. *John maintains [SHOULD (resign (b))] ∨ John maintains [SHOULD (retire (b))] John knows who should resign or retire. a. John knows p, where p is true & ∃x [p = SHOULD (resign (x)) ∨ SHOULD (retire (x))] b. ??[ John knows p] ∨ [John knows q], where p is true & ∃x [p = SHOULD (resign (x))], and where q is true & ∃x [q = SHOULD (retire (x))] Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 901 M. Miyama (11) The proper treatment of the wide scope or reading of the English either . . . or . . . construction *Either not a single student who picked Greek or Latin passed the exam. (Schlenker, 2006: 306) The fact that sentences with either inside an island do have WS readings ((7), (10)) conforms to the generalization in (3a), since sentences with either in its base position can have the scope of or higher than the surface position of either. In contrast, it goes against the generalization in (3b), since floated either does not mark the exact scope of or but allows the scope of or to be in a higher position. In this section we have seen Larson’s (1985) generalization in (3), in which it is stated that (i) in sentences with no either or with either in its base position, or can take both the narrow scope and the wide scope, while (ii) in sentences with floated either, only the WS reading is available. We have also seen data reported by Winter (2000) and Schlenker (2006), in which or can take scope over an island but either cannot overtly appear outside the island. In the next section, we will see that a hybrid analysis, which combines Schwarz’s (1999) ellipsis analysis and a version of a choice function analysis that slightly modifies a choice function analysis for disjunction suggested in previous studies, explains the data in this section neatly. 3. Proposal: A hybrid analaysis In this section, I introduce two previous analyses on the either . . . or . . . construction: the ellipsis analysis (Schwarz, 1999) and the choice function analysis of or (Winter, 2001; Schlenker, 2006). It is shown that although both analyses have advantages, they also have problems. I propose that the hybrid analysis which combines the two analyses with some modification covers the data set introduced in Section 2: (i) the ellipsis treatment of disjunction, which comes from the semantic requirement on or that it has to take two disjuncts of the same semantic type, explains the obligatory WS reading of the “floated either” sentences in (5), and (ii) the choice function analysis of either, which is a modified version of the choice function analysis of or, explains the ambiguity of sentences with no either or with either in its base position (4). 3.1. The ellipsis analysis The ellipsis analysis of Schwarz (1999) claims that “unbalanced disjunction” as in (12), in which in the surface form the disjuncts are not the same size under the assumption that the overt position of either marks the left edge of the first disjunct, is derived by ellipsis. The analysis correctly predicts that when either floats only the WS reading is available, since the underlying form involves balanced disjunction and directly corresponds to the WS reading. (12) a. b. John either ate rice or beans. John either [ VP ate rice] or [ VP ate beans] Either John ate rice or beans. Either [ IP John ate rice] or [ IP John ate beans] (Schwarz, 1999: 351-352) The ellipsis analysis can also explain the fact that the size of the second disjunct can be smaller Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 902 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction than the first one (13a) while the size of the first disjunct cannot be smaller than the second one (13b). (13) a. b. either [Xt or Yτ ] (where τ is any semantic type) Mary is either looking for a maid or a cook. Mary either is looking for a maid or a cook. Either Mary is looking for a maid or a cook. either [Xt or Yτ ] (where τ 6= t) #Mary is either a maid or looking for a cook. ∗John either Mary or saw Sue. The ellipsis analysis is able to handle this fact since ellipsis is sensitive to the linear order of the elements under consideration. Specifically, ellipsis is applied to the second (non-initial) element, under identity of the deleted element with the initial element. Thus when the size of the second disjunct is smaller than the first one (13a), it is possible to assume that there is some elided material for the second disjunct, while when the size of the first disjunct is smaller than the second one (13b), we cannot claim that the first disjunct has undergone ellipsis, since ellipsis cannot be applied to the initial element. We successfully account for the difference in the acceptability between (13a) and (13b).3 Next, let me closely examine the nature of the ellipsis operation that is involved in deriving unbalanced disjunction. Specifically, I will examine whether the proposal can explain data beyond the simplest ones like (12), namely sentences such as (13). (14) John either cited a theory that Partee or Rooth invented. (14) is an example of unbalanced disjunction which involves a Complex NP Island. According to the ellipsis analysis, its structure is as in (15), based on the assumption that unbalanced disjunction has a balanced structure in its underlying form. The surface form in (14) is derived by (i) eliding the embedded verb in the first disjunct and (ii) eliding everything but the embedded subject and verb in the second disjunct, as shown in (15). In the rest of this subsection, I investigate whether such a derivation is really possible. John either [cited a theory that Partee invented] or [cited a theory that Rooth invented]. (15) 3 Note that the ellipsis analysis have difficulty in accounting for the data of “R-either” in Den Dikken (2006), in which either seems to be “buried” inside the first disjunct. (i) John either ate rice or he ate beans. (Den Dikken, 2006: 690) Larson (1985), who proposes a movement analysis of either, claims that sentences like (iia) involve an unbalanced disjunction of VP and CP as in (iib). The matrix subject moves out from the first disjunct and either, originally inside the DisjP, optionally moves leftwards. (ii) a. b. Mary either is driving to the airport or she is taking a cab. Maryj eitheri is [ DisjP ti or [ VP tj driving to the airport] [ CP she is taking a cab]]. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 903 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction Going back to the original argument of the ellipsis analysis proposed by Schwarz (1999), Schwarz (1999) claims that the ellipsis operation involved in the derivation of unbalanced disjunction (17) is in fact Gapping (16). (16) Tom has a pistol and Dick has a sword. (17) a. b. John either ate rice or ate beans. Either John ate rice or John ate beans. (Schwarz, 1999: 351-352) As supporting evidence, he observes that Gapping and unbalanced disjunction behave similarly. For one thing, Gapping always targets the finite verb of the second conjunct, and sometimes extra material too, including subjects as in (18). This parallels the unbalanced disjunction data in (17). (18) On Monday I bought a car and on Tuesday I bought a motorcycle. (Schwarz, 1999: 354) For another, it is possible for Gapping to leave only one expression as in (19). This behavior also parallels (17). (19) John bought a book yesterday, and a newspaper. (Schwarz, 1999: 354) An important characteristic that Gapping and unbalanced disjunction have in common is that neither of them allows “dangling remnants,” where the first and second conjuncts/disjuncts are not parallel. In both (20) and (21), the second conjunct/disjunct has some extra material that the first conjunct/disjunct does not, and this leads to the degraded status of the sentences. (20) *Some talked about politics and others talked with me about music. (Schwarz, 1999: 356) (21) a. ?Either [he invited you] or [he invited me to a party]. b. ??Either [this pissed Bill] or [this pissed Sue off]. (Schwarz, 1999: 357) According to Schwarz (1999), the reason why the sentences in (21) are less degraded than (20) is because what is prohibited from being left as a “dangling remnant” can be Right Node Raised from both the first disjunct and the second disjunct. Right Node Raising must take place in a disjunct-final position as in (21), thus having no ameliorating effect on (20) since the “dangling remnant” there is in a medial position. Now let us return to (14) and see whether the derivation (15) is a possible one. (14) (15) John either cited a theory that Partee or Rooth invented. John either [cited a theory that Partee invented] or [cited a theory that Rooth invented]. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 904 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction As stated earlier, the surface form in (14) is derived by (i) eliding the embedded verb in the first disjunct and (ii) eliding everything but the embedded subject and verb in the second disjunct, as shown in (15). The second step, namely the deletion of elements in the second disjunct, can be explained with Gapping, given that Gapping can potentially leave only one element as in (19) and, in addition, the least embedded verb can potentially be the only material elided. In fact, as laid out in Johnson (2006) in detail, Gapping cannot target an embedded verb excluding the matrix verb as in (22), following the No Embedding Constraint (23). (22) *Alfonse stole the emeralds, and I think that Mugsy stole the pearls. (Johnson, 2006: 412) (23) The No Embedding Constraint (Johnson, 2006: 412) Let A and B be conjoined or disjoined phrases, and β be the string elided in B whose antecedent is α in A. Then α and β must contain the highest verb in A and B. The first step of deriving (14), namely eliding the embedded verb in the first disjunct, is also accounted for by claiming that the embedded verb, which is the rightmost element in the first disjunct, undergoes Right Node Raising. The claim is consistent with the observation that Right Node Raising has to target the conjunct/disjunct-final element as in (21). Furthermore, the data conform to the classic claim that Right Node Raising has to target constituents (cf. Postal (1974); Bresnan (1974) among others), which is shown by the contrast between (24a) and (24b). As can be observed from the difference in acceptability between (24a,b) and (25c), the elided material in the first disjunct in unbalanced disjunction also has to form a constituent as in (24a,b) and the sentence is degraded when it is not a constituent as in (25c). (24) a. b. He tried to persuade them, but he couldn’t convince them, that he was right. *He tried to persuade, but he couldn’t convince, {them / the students} that he was right. (Bresnan, 1974: 615) (25) a. John either thinks that Mary talked yesterday with Sue or thinks that Mary talked today with Sue. John either thinks that Mary talked yesterday about music or today about music. ??John either thinks that Mary talked yesterday with Sue about music or today with Sue about music. b. c. Now it has been shown that the ellipsis analysis of unbalanced disjunction, claimed to involve Gapping and Right Node Raising according to Schwarz (1999), successfully derives sentences like (14) with the underlying structure (15). I thus adopt the ellipsis analysis to account for the unbalanced disjunction examples. Further, to ensure that either occurs with or, I claim that either is syntactically required to take a DisjP as its argument and or inside the DisjP has to take two disjuncts of the same type/size (cf. Law of coordination of likes), thus motivating the ellipsis treatment when the surface form is unbalanced. However, even though the ellipsis analysis explains very well the unbalanced disjunction data, it has a crucial problem that it does not have much to say about the availability of the WS Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 905 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction reading for sentences with either in its base position, adjacent to the DisjP. Recall that such sentences are ambiguous, having both NS and WS readings, as we have seen in (4) in Section 2. (26) a. b. Mary is looking for a maid or a cook. Mary is looking for either a maid or a cook. (i) Jlook forK(Ja maid or a cookK) (m) (ii) Jlook forK(Ja maidK)(m) ∨ Jlook forK(Ja cookK) (m) (NS reading) (WS reading) In such “balanced disjunction” examples, there is no motivation to posit ellipsis in the derivation of the sentences, and thus in the ideal case, ellipsis would not be involved in the derivation of these sentences. Thus the ellipsis analysis predicts that only the NS reading is possible. The ellipsis analysis on its own leaves unexplained the problem of the ambiguity of the sentence when either is in its base position.4 It is precisely this problem that the choice function analysis readily explains. I next turn to the details of the choice function analysis. 3.2. The choice function analysis of disjunction In this section, I review the choice function analysis of disjunction suggested in Winter (2001) and Schlenker (2006). It is shown that the analysis can explain the ambiguity that sentences with either in its base position and the fact that the WS reading is available in sentences with the disjunction in an island. Winter (2001) suggests a (Skolem) choice function analysis for disjunction and claims that through existential closure over the choice function variable that the disjunction introduces, we obtain the WS reading as in (27).5 This is basically applying the choice function analysis that he proposes for indefinites to disjunction. (27) If Bill praises Mary or Sue then John will be happy. ∃ f [CH( f ) ∧ [h i d (min(M ∪ S))(λ x.praise0 (x)(b0 ) → happy0 ( j0 ))]] = ∃ f [CH( f ) ∧ [h i d ({{m0 } , {s0 }})(λ x.praise0 (x)(b0 ) → happy0 ( j0 ))]] = ∃A ∈ {{m0 } , {s0 }}[(λ P.A ⊆ P)(λ x.praise0 (x)(b0 ) → happy0 ( j0 ))] = [praise0 (m0 )(b0 ) → happy0 ( j0 )] ∨ [praise0 (s0 )(b0 ) → happy0 ( j0 )] (Winter, 2001: 159) 4 The fact that the ellipsis analysis predicts that either marks the exact scope of or becomes problematic again when we see data other than the basic ones in Section 4. 5 M and S are the quantifiers corresponding to the proper names Mary and Sue respectively (and thus can be connected by Generalized Disjunction as in (27)) and the notations m0 and s0 are the lexical denotations of Mary and Sue respectively. The operator min (for the operation Minimum Sort) takes Q, a set of objects of type τ (which is a boolean type) and gives back the set of minimal sets of Q, where a set A is a minimal set of Q iff A is in Q and every proper subset of A is not in Q. (i) d min = λ Qτt .λ Aτ .Q(A) ∧ ∀B ∈ Q [B ⊆ A → B = A] (Winter, 2001: 53) d h f i is a distributive version of a choice function. The operator h i lifts a choice function with the following definition. (ii) h i d = λ g(ett)(et) .λ Aett .λ Bet . A 6= 0/ ∧ g(A) ⊆ B Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 906 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction Importantly, the choice function analysis has the obvious advantage that, since existential closure is not confined within islands, it successfully predicts the availability of the WS reading in sentences with no either or with either in its base position ((4), (6), (9)), even if the disjunction is inside an island. Furthermore, since existential closure can be applied to any node whose semantic type is t, the choice function analysis can account for the ambiguity that the sentences have; namely having both the NS and WS reading. Thus the choice function analysis neatly explains the ambiguity of sentences with no either or with either in its base position, which was a problem for the ellipsis analysis alone as we have seen in Section 3.1. However, the choice function analysis has at least two problems. First, it has difficulty in deriving the WS reading for sentences with floated either since the analysis in itself does not have the machinery to derive the reading. In such sentences, the surface form is unbalanced disjunction, while the WS reading involves two propositional disjuncts as we can see from (5) repeated below. (28) a. b. c. Mary is either looking for a maid or a cook. Mary either is looking for a maid or a cook. Either Mary is looking for a maid or a cook. (i) ?*Jlook forK(Ja maid or a cookK) (m) (ii) Jlook forK(Ja maidK)(m) ∨ Jlook forK(Ja cookK) (m) (NS reading) (WS reading) Second, the choice function analysis of disjunction has a problem in the mechanism used to determine the position of the choice function variable, and it becomes visible when we closely inspect the unbalanced disjunction example (28a). The problem is, the choice function analysis of disjunction actually does not rule out the possibility of the choice function variable being introduced at a position lower than is actually allowed. Since, according to the choice function analysis of disjunction, the only thing that the disjunction does is to require that the two disjuncts be of the same size and to introduce a choice function variable just outside the DisjP, there is no way to determine the size of the DisjP and the position where the choice function variable is introduced just from the role of the disjunction. Thus, for example, the choice function analysis of disjunction wrongly predicts that we can place the choice function variable just above [a maid or a cook] in (28a). The requirements of the disjunction are fulfilled in this situation, conjoining two disjuncts of the same size and placing the choice function variable above the DisjP. This results in the narrow scope reading of the disjunction, which the sentence does not have. Thus a pure choice function analysis also have problems. In Subsection 3.3, I propose that we need to combine the choice function analysis with the ellipsis analysis in order to solve the first problem, and in addition, we need to modify the choice function analysis so that either, not or, introduces the choice function variable in order to solve the second problem. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 907 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction 3.3. The hybrid analysis In previous subsections, I have shown that the ellipsis analysis and the choice function analysis of disjunction both have advantages and problems. The ellipsis analysis is able to account for the obligatory WS reading of floated either examples, but it cannot explain the availability of the WS reading in sentences with either in its base position. The choice function analysis of disjunction can explain the ambiguity of sentences with either in its base position, but lacks the machinery to derive the WS reading in floated either examples and overgenerates the NS reading. Now we can see that the problem of the ellipsis analysis and the first problem of the choice function analysis of disjunction are solved if we combine the two analyses. The first version of the hybrid analysis, “the ellipsis analysis + the choice function analysis of disjunction,” is given in (29). Below I give an overview of how the analysis can explain the basic data set. In sentences with no either or with either in its base position (30), where there is an ambiguity between narrow scope and wide scope or, no ellipsis is involved in the derivation of “balanced disjunction.” Thus there are multiple possible positions for Existential Closure which correspond to the multiple possible scope positions of or. (29) The ellipsis analysis + the choice function analysis of or a. Either syntactically requires a DisjP as its argument b. Or semantically requires two disjuncts of the same semantic type c. Or introduces a choice function variable (30) Ambiguous between NS and WS or a. Mary is looking for a maid or a cook. b. Mary is looking for either a maid or a cook. ⇒ No ellipsis / Multiple possible positions of Existential Closure [∃ f ] Mary is looking for [∃ f ] PRO to FIND f({a maid, a cook}) (cf. Larson et al. (1997)) In sentences with floated either as in (31), where the WS reading is forced, either marks the left edge of the first disjunct and ellipsis is involved in the derivation. Since the choice function variable is introduced with the disjunction, Existential Closure is restricted to a position above the DisjP. Thus we can account for the fact that only the WS reading is available in the sentences. (31) Unambiguous: only WS or a. Mary is either looking for a maid or a cook. b. Mary either is looking for a maid or a cook. c. Either Mary is looking for a maid or a cook. ⇒ Involve ellipsis / Existential Closure possible only above DisjP a. Mary is either looking for a maid or looking for a cook. ∃f. Mary is f({looking f or a maid, looking f or a cook}) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 908 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction b. Mary either is looking for a maid or is looking for a cook. ∃f. Mary f({is looking f or a maid, is looking f or a cook}) c. Either Mary is looking for a maid or Mary is looking for a cook. ∃f. f({Mary is looking f or a maid, Mary is looking f or a cook}) The first version of the hybrid analysis seems to explain well the data set in Section 2. However, the second problem of the choice function analysis of disjunction, namely the analysis predicts that a NS reading is available for the “floated either” examples, remains. This problem arises because we have assigned the role of introducing the choice function variable to the disjunction. This is the point where the analysis needs refinement. What, then, has the role of introducing the choice function variable? The obvious alternative candidate is either, and this indeed seems to be the right choice to make. Observe that, in all of the examples we have seen in (30) and (31), the position where the choice function variable is placed actually coincides with the overt position of either. Thus I propose that the item that has the role of introducing the choice function variable is either, rather than or, and argue for a choice function analysis of either. As for the semantic role of or, I assume that or forms a set consisting of the disjuncts (cf. Alonso-Ovalle (2006)) that serves as the argument of the choice function variable. I adopt the claim made by Mitrović and Sauerland (2014) for the syntactic structure and the semantic computation inside coordination. Mitrović and Sauerland (2014) give a decomposed structure (32) for the Japanese phrase involving conjunction Bill mo Mary mo ‘’Bill and Mary.’ JP µP (32) XP µ0 J0 J0 Bill mo coordinator (silent) µP YP µ0 Mary mo According to Mitrović and Sauerland (2014), languages can be classified into languages with an overt µ head such as Japanese mo, which can be used as a quantificational particle or a focus particle, and languages with an overt J(unction) head such as English and, which can be used when the coordinated items are individuals and when the coordinated items are propositions. The semantics of the two heads is as in (33). (33) a. b. Jµ 0 K(R<et> )(S<et> ) = R ⊆ S JJ0 K(Q1<ett> )(Q2<ett> ) = Q1 ∩ Q2 With the help of the type-shifting operation from e to et at the XP/YP level, the individuals Bill and Mary are shifted to their characteristic properties and can combine with µ 0 . The overall denotation of JP in (32) is thus the set {Bill, Mary}. Although the semantic difference between conjunction and disjunction needs to be clarified, I claim that the denotation of a DisjP is the Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 909 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction set of the disjuncts and adopt the claim of Mitrović and Sauerland (2014) that the denotation can be derived compositionally. Other elements of the hybrid analysis, namely (29a) and (29b), are carried over, so the final version of the hybrid analysis is as in (34). I also claim that even in sentences where either is covert, the presence of or indicates that a phonetically null version of either is present in the structure, thus ensuring that the possible readings are the same as for sentences with overt either.6 (34) The ellipsis analysis + the choice function analysis of either a. Either syntactically requires a DisjP as its argument (= (29a)) b. Or semantically requires two disjuncts of the same semantic type (= (29b)) c. Either introduces a choice function variable d. Or semantically forms a set of the disjuncts that serves as the argument of the choice function variable Below I show how interpretations are assigned for sentences with either in its base position (36) and with floated either (37). By claiming that either syntactically selects a DisjP and semantically introduces a choice function variable as in (35), we carry on the advantage of the choice function analysis and at the same time avoid the trouble of wrongly predicting a NS reading for the sentences in (31). (35) JeitherK = f: f ∈ Dcf (where f is a choice function Chf(f) iff for all P in dom(f): f(P) ⊆ P) (36) Mary i is looking for [ TP PRO i TO FIND [ XP either [ DisjP a maid or a cook]]]. a. JXPK = JeitherKJDisjPK = f ({a maid, a cook}) b. JTPK = λ w.∃ f . Chf(f) & Mary to find f({a maid, a cook}) in w c. J(36)K = λ w0 . Mary is looking for [λ w.∃ f . Chf(f) & Mary to find f({a maid, a cook}) in w] in w0 Mary i is [ XP either [ DisjP looking for PRO i TO FIND a maid or looking for PRO i TO FIND a cook]]. a. JXPK = JeitherKJDisjPK = f ({λ x.λ w0 . x is looking for [λ w. Mary to find a maid in w] in w0 , λ x.λ w0 . x is looking for [λ w. Mary to find a cook in w] in w0 }) (37) 6A point that needs explanation if we are to argue for the presence of covert either/Op is that in a question, the possible readings differ as to whether there is overt either or not. When there is no overt either, the sentence is ambiguous between an Alternative Question (AltQ) reading and a Yes/No Question (YNQ) reading as in (ia), while sentences with overt either only have the YNQ reading as in (ib) and (ic) (although there seems to be some speaker variation). I leave this problem for future research. (i) a. b. c. Did Mary look for a maid or a cook? (AltQ / YNQ) Did Mary look for either a maid or a cook? (*AltQ / YNQ) Did Mary either look for a maid or a cook? (*AltQ / YNQ) Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 910 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction b. J(37)K = ∃f. Chf(f) & f({λ x.λ w0 . x is looking for [λ w. Mary to find a maid in w] in w0 , λ x.λ w0 . x is looking for [λ w. Mary to find a cook in w] in w0 }) In this section, I have shown that the hybrid analysis, which combines the choice function analysis of either with the ellipsis analysis, fully accounts for the basic data set in Section 2. In the next section, I discuss the predictions that the hybrid analysis makes and some data that are problematic at first sight. 4. Conclusion and further issues In this paper I have investigated the availability of the WS reading in the either . . . or . . . construction and its interaction with the behavior of either. It has been shown that the WS reading should be treated semantically, rather than syntactically. The rest of this section is devoted to discussion of a prediction that the choice function analysis of either + the ellipsis analysis makes and of some data beyond the basic data set that we have limited ourselves to up to this point. The data apparently go against the prediction, but it is shown that the data are indeed not problematic, pointing out judgment issues that have been overlooked previously. A prediction that the present analysis makes is that either marks the “minimal possible scope” of or. I have claimed that either introduces a choice function variable and the scope of the variable is determined by the position of Existential Closure. Existential Closure should thus be able to occur at any type t position above either. First consider (6)-(8), repeated in (38)-(40) below. (38) If Bill praises Mary or Sue then John will be happy. (Winter, 2000: 403) a. If Bill praises Mary then John will be happy and if Bill praises Sue then John will be happy. (NS) b. If Bill praises Mary then John will be happy or if Bill praises Sue then John will be happy. (WS) (39) a. b. (40) *Either if Bill praises Mary or Sue then John will be happy. If Bill praises either Mary or Sue then John will be happy. ( OK NS / OK W S) If Bill either praises Mary or Sue then John will be happy. ( OK NS / OK W S) (Winter, 2000: 403) As shown in (38) and (39), when a DisjP is inside an if-clause, which is an island, both the NS and WS readings are available, and the possible readings are the same in sentences with either inside the if-clause. As I have stated above, this is straightforwardly accounted for by the proposed analysis, since Existential Closure is not restricted within islands, and ellipsis that takes place inside the if-clause does not cause any problem. In contrast, (40) at first sight seems to go against the prediction that the choice function analysis makes. This is because, according to the analysis, there is no reason for the sentence to become unacceptable. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 911 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction It may be possible to posit a restriction on ellipsis to avoid this difficulty, for example claiming that ellipsis is island-sensitive, but I would like to point out that there might be a problem in the data itself. Specifically, some native speakers that I have consulted (although the number is still small) suggested that (40) might be degraded for a syntactic reason rather than a semantic one. In particular, they felt that either coming next to if itself is bad, which indicates that the cause of the degradedness lies in this particular island. Indeed, at least one native speaker who reports that (40) has a syntactic problem judged (41) as grammatical, in which either is overtly outside other islands, such as a complex NP island (41a) and a wh-island (41b). Although the judgment has to be confirmed by a larger number of native speakers, this suggests that the overt position of either is not constrained by syntactic islands, and if this is the case, the data in (40) is not a problem for the present analysis. (41) a. b. John maintains either the claim that Bill should resign or retire. John knows either who should resign or retire. However, the problem of the degraded status of (40) remains. Why is it unacceptable even though the full version of the sentence (42) is acceptable? (42) Either if Bill praises Mary or if Bill praises Sue then John will be happy. I have no concrete answer to this question, but I would like to suggest that the unacceptability does not come from island sensitivity but from a syntactic restriction on ellipsis inside questions. This is because there seems to be a connection between (40)&(42), disjoined wh questions (43) and disjoined Yes/No Questions (44). In all examples the elided versions are bad. Given that there are studies which claim that some conditionals are a kind of question (e.g. Starr (2014)), it might be the case that what makes (40), (43b), and (44b) unacceptable is the same restriction on ellipsis operative inside questions. (43) a. I need an answer to one of the two questions: Who came or who left? b. *I need an answer to one of the two questions: Who came or left? (44) a. I need an answer to one of the two questions: Did John come or did he leave? b. *I need an answer to one of the two questions: Did John come or leave? Another point that apparently goes against the prediction of the present analysis that either marks the “minimal possible scope” of or is Larson’s (1985) generalization that we have seen earlier in this paper in (45b). (45) Larson’s (1985) generalization (Winter, 2000: 395): a. In or coordinations without either, as well as in either . . . or . . . coordinations with either undisplaced, the scope of or is confined to those positions where either can potentially appear. b. When either is displaced it specifies the scope of or to be at that displaced position. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 912 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction Observe that the generalization in (45) states an imbalance in the semantic role of either: on the one hand, in sentences with no either or with either in its base position, either marks the minimal possible scope of or (45a), but on the other hand, in sentences with floated either, either marks the exact scope of or (45b). This imbalance between the positions of either would be a difficult problem to explain. However, some native speakers I have consulted do not agree with the “exact scope marking” nature of floated either but judge that floated either also marks the minimal possible scope of or. Let us see the examples from Larson (1985). The sentences in (46) have embedded non-finite clauses. In sentences with no either (46a) or with either in its base position (46b), there are three possible readings: (A) or taking narrowest scope, below look for, (B) or taking scope at the embedded clause level, and (C) or taking widest scope at the main clause level. Larson’s (1985) judgment for (46c) and (46d) is that the position of floated either coincides with the scope of or, as given in the second line of the table. The judgment of some native speakers I have consulted, given in the third line of the table, differs crucially from Larson’s (1985) in the judgment of (46c). Specifically, they judge that both the (B) reading (the exact scope reading) and the widest scope reading of or are available. This shows that they judge that floated either marks not the exact scope of or but the minimal possible scope of or. Thus their judgment does not accord with (45). (46) Non-finite clauses (Larson, 1985: 221) a. Sherlock pretended [to be looking for a burglar or a thief]. b. Sherlock pretended [to be looking for either a burglar or a thief]. A. S. pretend to look for ((a burglar) or (a thief)) B. S. pretend [S. look for (a burglar) or S. look for (a thief)] C. S. pretend to look for (a burglar) or S. pretend to look for (a thief). c. Sherlock pretended [to either be looking for a burglar or a thief]. d. Sherlock either pretended [to be looking for a burglar or a thief]. (44a,b) Larson (1985) Other native speakers (44c) (44d) *A, OK B, *C *A, *B, OK C OK A, OK B, OK C *A, OK B, OK C *A, *B, OK C OK A, OK B, OK C If this intuition turns out to be correct, it makes it easier to account for the scope of or and its interaction with either, since we do not have to say, for example, that base-generated either has to move covertly to mark the scope of or while floated either overtly marks the scope of or, which Larson (1985) actually proposes. What is more, the uniform “minimal possible scope marking” nature of either, if it is real, fits very well with the choice function analysis argued for in this paper, confirming the prediction that the analysis makes, namely that either should mark the minimal possible scope of or. Thus there might be supporting evidence to further extend the analysis to data outside the basic data set. Note that the ellipsis analysis on its own predicts that either would mark the exact scope of or, lending further support not to adopt a pure ellipsis analysis but to combine it with the choice function analysis of either. Before closing the section, let me briefly state another prediction of the present analysis related to the one discussed in this section: either marks the minimal scope of or, and what is more, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 913 M. Miyama The proper treatment of the wide scope or reading of the English either . . . or . . . construction the scope of or must be unbounded. This is because, as far as I understand, there is no way to keep Existential Closure from taking place when the semantic type of the node is type t. The prediction that the scope of or must be unbounded is a falsifiable one, and I leave further investigation into this question for future research. This section has discussed the predictions that the hybrid analysis makes, pointing out judgment issues that have been overlooked previously and opening up the possibility that the hybrid analysis can cover data outside the basic ones. References Alonso-Ovalle, L. (2006). Disjunction in Alternative Semantics. Ph. D. thesis, University of Massachusetts, Amherst. Bresnan, J. (1974). The position of certain clause-particles in phrase structure. Linguistic Inquiry 5, 614–619. Den Dikken, M. (2006). Either-float and the syntax of co-or-dination. Natural Language and Linguistic Theory 24, 689–749. Johnson, K. (2006). Gapping. In M. Everaert, H. V. Riemsdijk, R. Goedemans, and B. Hollebrandse (Eds.), The Blackwell Companion to Syntax, pp. 407–435. Oxford: Blackwell. Larson, R., M. den Dikken, and P. Ludlow (1997). Intensional transitive verbs and abstract clausal complementation. http://semlab5.sbs.sunysb.edu/ rlarson/itv.pdf. Larson, R. K. (1985). On the syntax of disjunction scope. Natural Language and Linguistic Theory 3, 217–264. Mitrović, M. and U. Sauerland (2014). Decomposing coordination. In Proceedings of the Northeast Linguistic Society 44, pp. 39–52. Partee, B. and M. Rooth (1983). Generalized conjunction and type ambiguity. In R. Bäuerle, C. Schwarze, and A. von Stechow (Eds.), Meaning, Use, and Interpretation of Language, pp. 360–383. Berlin: Walter de Gruyter. Postal, P. (1974). On Raising: One Rule of English Grammar and Its Theoretical Implications. Cambridge, MA: MIT Press. Rooth, M. and B. Partee (1982). Conjunction, type ambiguity, and wide scope ‘or’. In Proceedings of the 1st West Coast Conference on Formal Linguistics, pp. 353–362. Schlenker, P. (2006). Scopal independence: A note on branching and wide scope readings of indefinites and disjunctions. Journal of Semantics 23, 281–314. Schwarz, B. (1999). On the syntax of either . . . or. Natural Language and Linguistic Theory 17, 339–370. Starr, W. B. (2014). What ‘if’? Philosopher’s Imprint 14(10), 1–27. Winter, Y. (2000). On some scopal asymmetries of coordination. In H. Bennis, M. Everaert, and E. Reuland (Eds.), Interface Strategies: Proceedings of the Colloquium, pp. 387–405. Amsterdam: KNAW, Royal Netherlands Academy of Arts and Sciences. Winter, Y. (2001). Flexibility Principles in Boolean Semantics: The Interpretation of Coordination, Plurality, and Scope in Natural Language. Cambridge, MA: MIT Press. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 914 Hillary Clinton is not Mitt Romney rich: Nouns modifying degree and dimension of adjectives1 Charlie O’HARA — University of Southern California Abstract. In loose English speech, speakers can be observed to use nouns to modify adjectives. This paper explores the four readings which this construction can attain, associated with four types of parameters typically associated with adjectives: degrees, judges, comparison classes, and dimensions. A formal analysis is put forth that derives all four phenomena by recentering pragmatic halos around the modifying noun. Keywords: adjectives, degree, dimensions, comparison class, equative, alternatives. 1. Introduction Consider the sentence in (1). (1) Hillary Clinton is rich, but not Mitt Romney rich. Mitt Romney rich is indicative of a construction that seems unique to varieties of English, where a noun phrase modifies the meaning of the following adjective. Mitt Romney rich can be ambiguous between several different readings. (2) a. b. c. How rich is Hillary Clinton? Does Hillary Clinton care about poor people? Mitt Romney’s only inviting rich people to his birthday party, did he invite Hillary Clinton? As an answer to the first question, (1) obtains the DEGREE READING: Mitt Romney rich means something similar to as rich as Mitt Romney. The second question obtains a DIMENSION READING , Mitt Romney rich means something like rich in the way Mitt Romney is. The third reading is a JUDGE READING, similar to is considered rich by Mitt Romney. A fourth reading is more difficult to obtain with the sentence in (1), but is more apparent in (3). (3) They are rich, of course [. . . ], but not New York City rich. Here we obtain a C OMPARISON C LASS rich for someone in NYC. READING , New York City rich means something like, 1 Thanks to Roumyana Pancheva, Barry Schein and Lauren Winans for patience, feedback and much helpful discussion on this project. I also would like to thank audiences at SuB21 and WCCFL34 for helpful questions, in particular Curt Anderson, Peet Klecha, Stephanie Solt, Ai Taniguchi, Alexis Wellwood, and Eva Wittenberg. Thanks to everyone who has been sending me examples they find in the wild of these constructions, for reminding me why I was interested in this project. All the ways this paper are good belong to them, all the ways it is bad belong to me. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 915 C. O’Hara Hillary Clinton is not Mitt Romney rich These four readings correspond to four aspects of adjectives that can be context dependent; the scale of the adjective (see Solt, 2016; Sassoon, 2010; Kennedy, 2013), the judge argument (Lasersohn, 2005; Stephenson, 2007; Kennedy, 2013; Bylinina, 2014), the standard degree, and the comparison class on which that standard is set. In section 2, I will discuss the data in question, exploring properties of each reading. In section 3, I will propose an analysis using pragmatic halos to account for all the types with a uniform semantics. Finally, in section 4 I conclude. 2. Basic data Here, I call these constructions reference modifiers (RMs), in two senses. Bolinger (1967) previously used referent vs. reference modification to distinguish between attributive adjectives that modify what the noun refers to (huge in (4a)), and those that modify the noun itself (Asian in (4b))—this distinction is basically the distinction between intersective and nonintersective interpretations of adjectives (Partee, 1995). (4) a. b. Those are huge elephants. Those are Asian elephants. ([[huge elephant]]=huge∩elephant) ([[Asian elephant]]6=Asian∩elephant) Whether all RMs of the form referred to in this in paper modify reference rather than referent is a question that cannot be answered without a theory of the semantics of the modifier itself, but we can note that some readings (particularly dimension readings) can be interpreted in clearly non-intersective ways. Osama Bin Laden famous can refer to a scale of how derived from or related to acts of terror one’s fame is, a scale that cannot be a referent of an unmodified famous. In the sentence (5), the studios are still able to hire individuals that are more famous than the actor, but not those who are more Osama Bin Laden famous. (5) After the scandal, the actor was too Osama Bin Laden famous to hire. 6→ too famous to hire. More simply, I call these RMs because the majority of these constructions modify by referencing an individual or a prototype that must be known to the interlocutors; often a figure or event from pop culture. Now we turn to some of the basic facts of RMs. 2.1. Modifier-adjective positive requirement Only certain readings of RMs require that what the modifier is referring to be in the positive extension of the adjective. Roughly, if in some context a RM Modifier Adjective (Modifier=Mitt Romney, Adjective=rich) is grammatical, Modifier is Adjective must be true in that context. This is unsuprisingly untrue for the JUDGE READING (6), as expected, because judge RMs denote the positive extension of an adjective as judged by the referent of the modifier; the example in (6) gets the judge reading particularly well because this is the only reading where Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 916 C. O’Hara Hillary Clinton is not Mitt Romney rich the referent of the modifier can be incompatible with the scale discussed.2 (6) The salsa isn’t spicy, but it is my dad spicy. The Comparison Class reading does require compatibility with the adjective, but is fully grammatical even if the prototypical member of the comparison class referred to by the modifier does not satisfy the adjective in its positive form. Consider (7): one would be hard pressed to find a context where mansions were cheap, but we are able to get a comparison class reading where the house in question is cheap for a mansion. This reading, like for-phrases (Kennedy, 2007; Bale, 2008; Solt, 2011), does require that the subject is a member of the comparison class. (7) It isn’t cheap, but it is mansion cheap and if you want a mansion that’s as good as you’re gonna get. The degree reading does require that the positive sentence to be true to be grammatical, consider (8). This sentence does not work unless we are in some context where snails are considered fast. (8) #The animal was snail fast. Further, I argue that the dimension reading requires this as well.3 The sentence in (9) can obtain a meaning where the person in question is shorter than the speaker’s threshold for tall but is a politically imposing figure, much like Napoleon (perhaps tall in spirit). While we may not consider Napoleon tall, in order to get this sort of reading, it is crucial that under some wordplay and metaphorical meaning Napoleon is “politically tall”. For a non-tall individual with less culturally relevant jokes made comparing their physical height and their success or imposingness, this does not seem to work. Though James Madison is considered the father of the American Constitution, I have much more difficulty creating James Madison tall, as he was a short man. (9) They’re not tall but they’re Napoleon tall. The different sorts of relationships required between the modifiers and the adjectives are summed up in the table in (10). (10) Required relationship between referent of modifier and scale of adjective Reading Judge CC Degree Dimension Compatible 7 3 3 3 Positive 7 7 3 3 2 Of course, a context could exist where we have considered the flavor of our family members, in which case other readings of this sentence would be possible. 3 However, it seems as if a subtype of dimension readings do not require it. In order to understand tall in the way Napoleon is tall, Napoleon must be tall in some way, but I’m sick, but I’m blood pressure healthy clearly does not require blood-pressure to be healthy but is grabbing a dimension directly. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 917 C. O’Hara Hillary Clinton is not Mitt Romney rich 2.2. Degree RMs The degree reading of an RM (11a) can often be paraphrased as an equative (11b). (11) a. b. Mary is Usain Bolt fast. Mary is as fast as Usain Bolt. However, these constructions differ in two important ways: a degree RM is more imprecise than an exactly reading of the equative; and the degree RM can create indirect comparisons using implicit comparison classes. 2.2.1. Implicit comparison classes Unlike the equative, the degree RM can make indirect comparisons—comparing positions of the individuals on their relative scales—without any overt reference to comparison classes. While the typical equative (and comparative by parallel) construction involve comparison of individuals based upon their degrees on the same scale, sentences like (12) seem to compare individuals based on their degrees on distinct (but often related scales). (12) a. b. c. Marie Curie is smarter than Marilyn Monroe is beautiful. (Modified from Bale, 2011) John is taller for a man than Mary is for a woman. (Bale, 2011) Mary is as fast for a middle schooler as Usain Bolt is for an Olympian. Several recent proposals attempt to explain these indirect equatives (Bale, 2006, 2008, 2011; Sassoon and van Rooij, 2016). Bale (2008) shows that these do differ from metalinguistic comparisons (13) (Embick, 2007; Morzycki, 2011) due to several distributional realities, notably, metalinguistic comparatives have a strong preference (if not a requirement) for the more morpheme over the -er morpheme. (13) Seymour is more intelligent than devious. (Bale, 2011) Degree RMs, like (11b) are able to be true in the case that the indirect comparison seen in (12c) is true, which is not true for the equative without explicit comparison classes, (11b). While the equative can express such a meaning in an exaggerative context, in O’Hara (to appear) I argue that the Degree RM is not achieving these kinds of readings through exaggeration in the same way, as evidenced by the contrast in (14): the literal meaning of Usain Bolt fast is the meaning that was used in the first sentence, so well not literally contradicts the prior sentence. (14) Mary is {as fast as Usain Bolt/#Usain Bolt fast}. Well not literally. . . In these comparison class indirect equatives, somehow the relative position of an individual within their own comparison class is being compared. Therefore, the realities of how we find an individual’s relative position in their comparison class is rather important. Bale (2008) handles this by deriving a scale from a linear order of equivalence classes fromed by a relation Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 918 C. O’Hara Hillary Clinton is not Mitt Romney rich like x is as ADJ as y. Bale defines a universal scale where the equivalence classes of individuals from a given comparison class are evenly spaced. Thus, if our comparison class for Mary involves six middle school runners, of whom Mary is the fastest, and no two runners are of equal speed; Mary is associated to the maximal possible universal scale degree (d 6 ), the next runner is associated with d 5 and so on, with the slowest 6 6 runner being associated with degree d 1 . Since Usain Bolt is the fastest man in the world, 6 regardless of the size of the comparison class he is being considered in, Usain is going to be associated to the maximal degree, d nn . Therefore, Mary and Usain Bolt have the same degree on the universal scale, d1 . However, this approach fails to capture a few intuitions present in indirect comparisons, as noted by Wellwood (2014). Consider Katie Ledecky, American Olympian who finished the 800m freestyle at the 2016 Olympics over a pool length ahead of her opponents. If Mary won her middle school race, but not so significantly, (15) is not as true. (15) F Mary is as fast for a middle schooler as Katie Ledecky is for an Olympian. Therefore, it seems not only the linear order of the equivalence classes must be preserved when comparing disparate scales, but also the distance between degrees. Sassoon and van Rooij (2016) handle this by formulating the scale fast for a middle schooler as the ratio from an individual’s speed’s deviation from the norm for middle schoolers, and the standard deviation for a middle schooler, (16).4 (16) norm(µfast ,[[mdschl]])) [[fast for a middle schooler]]= λ x : [[mdschl]](x). (µfast (x)− std(µ ,[[mdschl]]) fast This formulation allows a finer comparison of diverse scales, allowing us to get the correct truth conditions for (15). Under such an interpretation, since Katie Ledecky surpasses the norm for her comparison class by a number of standard deviations, but in our context Mary surpassed the norm by less standard deviations for her comparison class. However, an additional issue could arise: Say Katie Ledecky surpassed the norm of her comparison class by exactly 5 standard deviations, and each standard deviation is relatively large, resulting in a change of race time by about a second. It is possible that Mary could also surpass the norm of her class by 5 standard deviations, but the standard of deviation for her class could be orders of magnitude smaller than Katie Ledecky’s. In this case, we note that Katie Ledecky notably finishes before everyone else, but Mary finishes her race in a photo finish with all of the other members of her race, though Katie Ledecky would have the same degree of fast for an Olympian as Mary has for fast for a middle schooler. This seems potentially problematic, but it seems possible that the difference between these two situations is whether or not the deviation from the norm is observable to the speakers. Standard deviation (a purely mathematical/statistical measure) might not be sufficient. 4 Solt (2011) uses median absolute deviation in a similar way while trying to define the positive construction. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 919 C. O’Hara Hillary Clinton is not Mitt Romney rich Unlike the equative, the degree RM does not require an overt comparison class (through a forphrase) to get these indirect, relative readings. I argue the difference here derives from the different ways the degree of the standard (i.e. that which the subject is being compared to, recently Katie Ledecky) is derived. The denotation of the equative involves the calculation of the maximal degree on some scale denoted by the adjective (potentially relativized by comparison classes) which the standard surpasses (17). In (17), SFAST,C represents some relevant scale related to fast for some comparison class C. (17) [[as fast as Katie Ledecky]]=λ x.max(λ d.SFAST,C (d, x)) = 5 max(λ d 0 .SFAST,C0 (d 0 , KL)) However, since by the very nature of an equative (or a comparative) we are comparing the individuals in question, there is a great preference to use a comparison class that includes both individuals; making an indirect comparison unlikely without overt morphology. Degree RMs do not have clauses so rather than deriving the degree in the way an equative does, the RM simply selects some degree that is somehow associated to the standard and the adjective. The most salient degrees for a given individual will likely be in their most common comparison class; for Katie Ledecky, it is with the swimmers she raced against at the Olympics, so Mary as a middle schooler will not be part of the comparison class, and will therefore select a different comparison class that is contextually appropriate for her. 2.2.2. Imprecision The equative is said to have two readings, the strong exactly-as reading, and the weak at least as reading. The degree RM seems to quantifiy over a different set of degrees than either of these readings. (18) a. S TRONG E QUATIVE (exactly) as fast as Usain Bolt Usain Bolt b. W EAK E QUATIVE (at least) as fast as Usain Bolt Usain Bolt c. D EGREE RM Usain Bolt fast Usain Bolt The lower bound is apparent in sentences like (19); there must be some degrees of speeds slower than Usain Bolt’s speed that still qualify as Usain Bolt fast. (19) a. How fast is Andre de Grasse? 5 Here I denote an exactly reading of an equative, following Rett (2008) that this is basic; this relation would be ≥ if an at least as reading is taken as basic (Schwarzschild, 2008). Neither are crucial for this point. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 920 C. O’Hara Hillary Clinton is not Mitt Romney rich b. Andre de Grasse is Usain Bolt fast, but he’s not as fast as Usain Bolt. Here, speakers may paraphrase Usain Bolt fast as being in the same speed tier as Usain Bolt, allowing for Andre de Grasse to have a lower speed than Usain Bolt, but still be Usain Bolt fast. This is actually a fact of the semantic relationship of Usain Bolt fast to as fast as Usain Bolt, rather than a pragmatic force trying to derive meaning from the sentence. If there was not a difference in in semantics between the two phrases, (20) should be able to capture the same meaning, which it cannot. (20) #Andre de Grasse is as fast as Usain Bolt, but he’s not Usain Bolt fast. Further, we can see that there is in fact an upper bound on RMs unlike the at least as reading of the equative. Yao Ming, the former NBA player, is 7’6” tall. Given the same context, there are certain heights, such that someone is not Yao Ming tall but they are as tall as Yao Ming. (21) a. b. c. Speaker A: My friend Cody is super tall! Speaker B: Are they as tall as Yao Ming? Speaker A: Yes, in fact they’re 15 ft tall! (22) a. b. c. Speaker A: My friend Cody is super tall! Speaker B: Are they Yao Ming tall? Speaker A: ??Yes, in fact they’re 15 ft tall! This arises from the same sense speakers have that the RM, Yao Ming tall refers to a tier of heights around Yao Ming’s height. The RM gets a reading closer to about as tall as Yao Ming or around Yao Ming’s height. The fact that this paraphrases to about suggests that the RM has a less precise reading than the equative when being evaluated upon the same scale. This is not a surprising result; the RM is a more marked construction than the equative (it is typologicially rare, and rare within (particularly formal) English; the ambiguity of the many possible readings also makes the processing of RMs difficult), and marked constructions tend to have marked meanings, which in this case is the weaker, less precise meaning (Horn, 1984). 2.2.3. Distribution of Degree RMs A final noteworthy property of Degree RMs is their distribution with overt degree morphology. Like the equative, this construction is unable to appear below other degree quantifiers (23) (23) a. #Mary is very/too/sorta Usain Bolt fast. b. #Mary is more/as Usain Bolt fast than/as Jill. On the other hand, degree RMs are available above gradable degree phrases, like more and too phrases. (24) a. Man be glad you’re not Yao Ming—You’re too tall for this room, but you’re not (Yao Ming/way) too tall for this room. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 921 C. O’Hara Hillary Clinton is not Mitt Romney rich b. You’re taller than Kevin, but you’re not Yao Ming taller than Kevin, so the picture doesn’t look too funny. These distributional facts show that Degree RMs have the same distribution as degree quantifiers like the comparative, providing evidence that this construction is also a degree quantifier. 2.2.4. Summary of Degree RMs This section has shown evidence that degree RMs are able to quantify over degrees in a way that is somewhat different than the equative, or any other degree quantifier. Crucially, Degree RMs are able to capture indirect comparisons without any overt comparison class phrase. When Degree RMs do represent direct comparisons, they tend to be interpreted less precisely. 2.3. Judge RMs While the degree of gradable adjectives is the most studied argument, it is not the only one available to adjectives. The degree which certain items receive on many adjectival predicates is dependent upon the judge or the individual doing the evaluation. Predicates of Personal Taste (Lasersohn, 2005) like fun are the most clear case—it’s more surprising if two people ranked all the rides at an amusement park in order of funness exactly the same than if they disagree somewhere. This can be observed via faultless disagreement (Kölbel, 2003). In (25), the speakers do not contradict each other, because they are differing on the contextually determined judge of funness, rather than anything greater. (25) a. b. The roller coaster is more fun than the merry-go-round. No, the merry-go-round is more fun than the roller coaster. This does not remain true, if the judge is overt, marked by either a for or a to phrase. (26) a. The roller coaster is more fun for/to me than the merry-go-round. b. #No, the merry-go-round is more fun for/to you than the roller coaster. Thus, predicates of personal taste require a judge in order to be evaluated—whether this judge is supplied by a judge index of evaluation (Lasersohn, 2005) or as a thematic argument (Stojanovic, 2007; Bylinina, 2014), is not important for our purposes. This judge can be targeted by a Judge RM. (27) The roller coaster is more me fun than the merry-go-round. Subjectivity is not limited to predicates of personal taste; adjectives not associated with objective physical scales, called evaluative by Bierwisch (1989), can be equally subjective. These adjectives include smart, healthy, lazy. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 922 C. O’Hara (28) Hillary Clinton is not Mitt Romney rich Given Paulo is recovering a full body cast post-accident; and Daniel smokes 20 cigarettes a day and mostly eats fast food. a. Paulo is healthier than Daniel. b. No, Daniel is healthier than Paulo. Sassoon (2013); Bylinina (2014) argue that the source for this subjectivity can come from the multidimensionality of healthy; healthy quantifies over a variety of scales (blood pressure, mobility, amount of aortic plaque, etc.), and which scales receive which priority/weight is dependent on the context and the speaker. Unlike predicates of personal taste, for and to phrases cannot overtly supply a judge argument here, without prosodic breaks setting off the phrase.6 However, verbs like find can supply the judge here. (29) a. b. I find Paulo healthier than Daniel. Paulo is healthier, to me, than Daniel. A Judge RM is able to capture these subjective versions of these evaluative adjectives as well. (30) a. I don’t care what the doctor says, Paulo is more me healthy than Daniel. Finally, even simple objective unidimensional adjectives like tall or rich appear to be judgedependent in the positive. (31) a. b. Hillary Clinton is rich. No, Hillary Clinton is not. This seems to simply be an issue of where the standard degree supplied by the null POS morpheme, lies relative to Hillary Clinton’s degree of wealth. Since this is based on the contextual standard degree, this sort of judge dependence is available in the positive, very constructions, and sorta constructions, but not in more objective constructions, like the comparative. Again, speakers differ on whether overt to-phrases can supply the judge here, but verbs like find definitely can. (32) a. b. I find Hillary Clinton rich. Hillary Clinton is rich to me. The Judge RMs are again able to supply the judge for these sort of constructions, given appropriate context. (33) Given Mitt Romney is inviting only people he considers rich to a party. a. Hillary Clinton did not get an invite. She’s rich, but not Mitt Romney rich. 6 Speakers may differ in acceptability of these phrases in these contexts; Bylinina (2014) seems to suggest that these comma intonation for-phrases are only possible sentence initially; however, several consultants and myself allow them in a variety of positions; and even sometimes without such a clear intonation contrast from with predicates of personal taste. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 923 C. O’Hara Hillary Clinton is not Mitt Romney rich Exactly how the judge-dependence for each of these types of constructions may differ (see Bylinina, 2014), but the Judge RMs seem to be able to capture these readings regardless. 2.4. Comparison Class RMs Particularly in the positive construction, comparison classes are also a critical part of evaluating adjectives. Identifying the standard necessarily involves identifying the set which the individual is being compared to. (34) The rock climbing wall in Maggie Daley Park is tall. Whether the rock climbing wall in Maggie Daley Park in Chicago is considered tall, depends on what it is being compared to. At 40 ft tall, it is one of the tallest things in Maggie Daley Park, it is taller than the average rock climbing wall, but it is also not very tall in comparison to things in downtown Chicago. Depending on which class we use—things in MDP, rock climbing walls, or things in downtown Chicago—the height at which things are considered tall is different, perhaps 20ft, 35ft, and 600ft. This comparison class can be made explicit using a for-phrase. (35) The rock climbing wall in MDP is tall for {a thing in the park/a rock climbing wall/a thing in Chicago} These comparison classes can also be overtly noted using a Comparison Class RM. (36) The rock climbing wall isn’t thing in Chicago tall, but it is rock climbing wall tall. As discussed in Section 2.2.1, comparison classes are available in degree constructions other than the positive as well. In indirect comparatives, overt comparison classes can be used to compare relative difference from the norm for each class as in (37). Comparison Class RMs may also be available, though they feel degraded (and might be metalinguistic) here (38). (37) Usain Bolt is faster for an Olympian than Mary is for a child. (38) (?)Usain Bolt is more Olympian fast than Mary is child fast. 2.5. Dimension RMs Where the other three types of RMs interact with adjectives in ways that resemble relatively well-studied concepts, the degree, judge, and comparison class; the dimension RMs interact with a less well-understood aspect of adjectives: the scale upon which they are evaluated. Morzycki (2012) argues that there many adjectives encode several different dimensions in their lexical encoding. In (39), big seems to be being evaluated over distinct senses. (39) a. The US is bigger than Canada Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde (Population) 924 C. O’Hara Hillary Clinton is not Mitt Romney rich b. Canada is bigger than the US (Area) dimensions(big) = {size-by-population, size-by-area, size-by-importance, . . . } (40) Somehow, the dimensions the adjective is evaluated upon must be selected by context, Morzycki suggests that degree quantifiers like POS existentially quantify over these dimensions: something is big in the case that some dimension of big exists so that the thing surpasses the standard on that dimension.7 This set of dimensions clearly must be able to be contextually restricted: when speaking about land, the population dimension is not selectable. As discussed in the section on Judge RMs, Sassoon (2007, 2013) discusses a variety of adjectives that seem to quantify over the dimensions in a different way than big. In order to be healthy, one must be healthy on all relevant dimensions; i.e. blood pressure, mobility, etc. Thus many adjectives have multiple dimensions available to them. Specific dimensions can be picked out overtly using a with regard to phrase. (41) a. b. Japan is bigger with regard to population than Canada. Tara is healthier with regard to blood pressure than I. RMs are capable of accomplishing the same thing. (42) a. b. Japan is more population big than Canada. Tara is more blood pressure healthy than I. Both of the above constructions are able to shift the dimension of an adjective by referencing the dimension in question directly; but the dimension can also be restricted in a different way by like or in the way phrases, or Dimension RMs. (43) a. b. c. Nigeria is big like Japan, not big like Canada. Nigeria is big in the way Japan is, not the way Canada is. Nigeria is Japan big, not Canada big. Given appropriate context, big like Japan means the same thing as big with regard to population. However, these constructions seem to be capable of picking out any dimension of the adjective which the modifying individual has a salient (usually large) degree on. In fact, it is possible in this way to refer to dimensions that are not necessarily quantified over by the adjective typically. For an example, consider that Yao Ming and Andre the Giant were both 7 Some difficulties might arise for such an account. I have checked with several other speakers, who seem to share the intuition that while (39a) seems to work, (i) is less licit out of the blue, contra to what would be expected if big here was simply selecting the size-by-population dimension. (i) ?Japan is bigger than Canada. This suggests somehow the area dimension has some sort of primacy, only allowing the population dimension out of the blue if the area dimension is ambiguous or at least close. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 925 C. O’Hara Hillary Clinton is not Mitt Romney rich exceptionally tall men, but Yao Ming is skinner and Andre the Giant is broader. If presented with a giraffe and an elephant of the same height, speakers have little difficulty identifying who is Yao Ming tall and who is Andre the Giant tall. (or tall like Yao Ming, or tall in the way Yao Ming is) (44) a. b. The giraffe is Yao Ming tall. The elephant is Andre the Giant tall. Tall is typically thought of as a prototypically monodimensional measurable adjective. The scale over which it is evaluated is typically the same in all contexts: height. In this context, Yao Ming tall paraphrases to something like tall in a slender way. We can see that this slenderness dimension is not quantifiable over by tall; we are unable to access it using a with regard to phrase (45). (45) # The giraffe is tall with regard to slenderness. Yet, there are strong restrictions to which sorts of dimensions can be selected here. The dimension must be properties of the Yao Ming’s tallness, not simply properties of Yao Ming. Yao Ming is rich and successful, and even given an equally tall but poorer person: Lonnie, Yao Ming tall cannot mean tall and rich, and Lonnie tall cannot mean tall and poor. The distinction here comes from other evidence about what dimensions are part of the lexical encoding of tall. While plain tall does not allow paraphrases of tall in a slender way in the same way healthy can be paraphrased as healthy with regards to blood pressure, evidence that tall encodes some information about slenderness, rather than wealth is available from prototypical uses of tall. First consider two cups of the same height, one slender and one as wide as it is tall. If the tall cup is referred to, speakers identify the slender cup as the tall cup. While slenderness is not typically part of the scale quantified over when identifying tall, it can be made accessible here. Wealth is not available in this way; given two people of the same height, one clearly rich, and one clearly poor, speakers will be left confused by reference to the tall person. The second evidence comes from slack regulators and other constructions which strengthen utterances, or make them more prototypical. One of these (which we will return to later, as it seems somewhat related to RMs), referred to as lexical cloning, contrastive focus reduplication, or identical constituent compounding, where a word or phrase is copied in order often achieving a more prototypical meaning (Ghomeshi et al., 2004). Given a building that is 300 ft tall, but 2000 ft long and wide, we can imagine the sentence in (46a). The same sort of result can be seen with typical intensifying slack regulators like exactly, precisely and really. (46) a. b. I guess that building is tall, but it’s not TALL tall. That building is not really/exactly/precisely tall. The prototypical tall thing’s (or perhaps building here) height exceeds its other dimensions, Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 926 C. O’Hara Hillary Clinton is not Mitt Romney rich allowing for a slenderness dimension to be accessed here. Thus it seems, somewhere in the lexical encoding these additional dimensions are available. It seems notable here that though prototypically tall things are slender, the polarity of this slenderness dimension is not fixed in the ways the dimensions of big and healthy are. Tall in a slender way and tall in a broad way are both valid, but big in a populous way and healthy in a physically fit way seem less strange than their counterparts big in a unpopulous way and healthy in a physically unfit way. If these counterparts do exist, they refer to something like healthy even though very unhealthy in this one dimension, suggesting individuals must be very healthy on the remaining dimensions to make up for that. It is possible that even tall in a broad way is defined this way, as tall even though not slender, evidence from this arises from the fact that it is easier to generate tall in a slender or skinny way from a reference that is tall in a skinny way than to generate tall in a broad way without defining it in opposition to tall in a slender way: telephone pole tall is easy to understand, in comparison to Great Wall of China tall. These dimension RMs are able to appear below degree morphology, and seem incompatible above degree morphology. (47) a. The giraffe is more Yao Ming tall than the elephant. b. #The giraffe is Yao Ming taller than the elephant. A worthwhile question is whether or not Yao Ming tall is truthfully gradable, or if this is a metalinguistic comparative in (47a). Exactly how to probe this distinction seems difficult: most of the diagnostics that differentiate metalinguistic and true comparatives (Morzycki, 2011) do not occur here. McCawley (1998) notes that only metalinguistic comparatives allow displacement of the comparative morpheme, which does not seem to be possible here.8 (48) a. b. Your problems are legal more than financial. The giraffe is Yao Ming tall more than the elephant. 2.6. Data summary All four types of RMs can appear with a variety of adjectives, more widely than might be expected: Degree RMs can appear with typically gradable predicates like tall, but they are also available for adjectives with minimal or maximal standards (Kennedy and McNally, 2005) like coked-up businessman awake or arrow straight. Judge RMs can appear with predicates of personal taste, but also multidimensional adjectives, and almost all adjectives in a positive construction. Comparison Class RMs are equally able to appear seemingly with any gradable adjective. Finally, dimension RMs appear with conventionally multidimensional adjectives like 8 However, it may be that this property of comparing predicates rather than subjects, identifying metalinguistic comparatives that compare individuals seems more difficult, and I’m not certain works here; seeming to get a different frequency sense in (ib). (i) a. b. The coffee there is more coldbrew than when I make it. (?)The coffee there is coldbrew more than when I make it. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 927 C. O’Hara Hillary Clinton is not Mitt Romney rich healthy, ambiguous adjectives like big but also a variety of adjectives that have been typically thought of as simple and unidimensional like tall. 3. Analysis In this section, I propose a uniform semantics for RMs that can handle all of these meanings. Each type of RM restricts the meaning of the predicate to a meaning more closely associated with the reference. Here we will see this can be captured by recentering the pragmatic halo (Lasersohn, 1999) denoted by the predicate. Morzycki (2011); Anderson (2016) capture compositional semantic imprecision using pragmatic halos consisting of alternatives (Hamblin, 1973; Kratzer and Shimoyama, 2002). Under this Hamblinized approach, the denotation of an adjective like tall is as in (49) (49) 0 JtallKd ,C = { f<d,et> : f ≈d 0 ,C λ dλ x.tall(d)(x)} Here, following Morzycki (2011), the ≈d,C relation is a similarity relation, stating that iff α ≈d,C β , given the similarity scale given in context C, α is similar to β at least to the degree d. Here, the degree of similarity is the contextual degree of precision. Morzycki (2011) and Anderson (2016) make use of this degree (using a typeshift PREC) to capture metalinguistic comparatives (which are argued to be evaluated on the dimension of precision) and precision intensifiers and attenuators. Here rather than manipulating the degree of precision, RMs select one of these alternatives that is best associated with the reference and recenters the halo. Take American Football Player healthy, a dimension RM which seems to select a scale of evaluation of healthy that unfortunately prioritizes physical fitness over limiting brain damage. Under Sassoon (2007)’s representation, healthy typically denotes universal quantification over the dimensions of health. However, within our pragmatic halo, alternatives that ignore specific dimensions will be available (much like how, as shown by Anderson (2016), everyone is here can be uttered by a professor when a few students are missing (p. 23)). (50) a. b. 0 JhealthyKd ,C =  { f<d,et> : f ≈d 0 ,C λ d.λ x.∀g ∈ dimension(healthy) : [g(d)(x)]}  λ d.λ x.∀g ∈ dim(healthy) : [g(d)(x)],       λ d.λ x.∀g ∈ (dim(healthy) − brain health) : [g(d)(x)], .8,C JhealthyK =   λ d.λ x.∀g ∈ (dim(healthy) − cholesterol) : [g(d)(x)],     etc. Given this loose denotation for healthy, the RM must simply select the appropriate dimension. This is accomplished using a null operator RM which selects an element of the predicate its modifying that is associated (∝) with the reference.9 (51) a. b. 0 JRM Kd ,C = λ xρ λ Sτ : ∃s ∈ S[s ∝d,C x].s 0 JNFL player RM Kd ,C = λ Sτ : ∃s ∈ S[s ∝d,C NFL player].s 9 Often this association is the ability of the reference to directly satisfy the predicate, RMs, this is not possible. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde but particularly with judge 928 C. O’Hara Hillary Clinton is not Mitt Romney rich c. 0 JNFL player healthyKd ,C = { f<d,et> : f ≈d 0 ,C λ d.λ x.∀g ∈ (dim(healthy)− BrainHealth) : [g(d)(x)]} One of the reasons selecting a dimension on more unidimensional adjectives like tall seems harder is due to the structure of the pragmatic halos for tall. Whereas healthy at its most precise universally quantifies across all dimensions of healthiness, the additional dimensions of tall are less critically related. The alternative selected by Yao Ming tall, of tall in a slender way, is only available in very imprecise readings uses of tall. Even given the cups having the same height, (52) The skinny glass is sorta taller than the fatter one. Anderson (2016) argues that sorta expands the pragmatic halo of the predicate it modifies, selecting a degree of precision close to but lower than the standard degree of precision. Thus, the degree of precision must be lower to allow the RM to select any nontrivial dimensions. Earlier we saw that these dimensions are stored in the adjective and are also accessed in the most precise and prototypical readings. I claim that these additional dimensions are available as presuppositions to the most precise meaning of tall. If something is not saliently skinny enough, we cannot call it tall, but even on high level of precision, wide things are not less tall than things which have lower degrees of height than them. (53) a. #The Pentagon is tall tall. b. The telephone pole is tall tall. c. #The telephone pole is more tall tall than the Pentagon It is not surprising that dimensions referenced in the presupposition of the lexical entry of an adjective are somehow similar to the most precise form of the lexical entry, but it also makes sense that these are less similar than subsets of dimensions like what we explored with healthy. The purpose of the ∝ associated relation appears when we attempt to capture comparison class and judge RMs. Consider fun, which as a predicate of personal taste contains a judge argument somewhere in its denotation. I will presume a relativist approach here, but noncritically. (54) a. 0 JfunKd ,C,J = { f<d,et> : f ≈d 0 ,C λ d.λ x.funJ (d)(x)} The pragmatic halo here will include functions which are not exactly fun—like exciting—but will more importantly include fun scales that are ordered by different judges. The association function in the RM can note the association of a judge to the function to which they are the judge. (55) a.   λ d.λ x.fun (d)(x),   J       λ d.λ x.exciting (d)(x),   J .8,C,J λ d.λ x.funme (d)(x), JfunK =    λ d.λ x.funyou (d)(x),        etc. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 929 C. O’Hara Hillary Clinton is not Mitt Romney rich b. 0 Jme funKd ,C,J = { f<d,et> : f ≈d 0 ,C λ d.λ x.funme (d)(x)} Reference to the judge is made again in the positive construction when setting the standard. Assuming a denotation as follows for the POS morpheme, if the RM attaches above the POS morpheme, it can select the correct form. (56) a. b. c. 0 JPOSKd ,C,J = λ G<d,et>  λ x.∃d[G(x)(d) ∧ d! > normJ (G)]  λ x.∃d[tall(d)(x) ∧ d! > norm (tall)],   J       λ x.∃d[tall(d)(x) ∧ d! > norm (tall)],   me .8,C,J λ x.∃d[tall(d)(x) ∧ d! > normyou (tall)], JPOS tallK =    λ x.∃d[tall(d)(x) ∧ d! > normMitt Romney (tall)],       etc. 0 JMitt Romney POS tallKd ,C,J = {g<e,t> : g ≈d 0 ,C λ x.∃d[tall(d)(x) ∧ d! > normMitt Romney (tall)]} This predicts that Mitt Romney rich is ungradable, and therefore incompatible with degree morphology. This is caused by putting the judge dependence in the positive morpheme: if that assumption is false, judge dependence must be lower and possible with RMs everywhere it is possible with overt for and to phrases. It is difficult to probe for data that tests this in particular because on these adjectives judge-dependence does not change the ordering of the degrees but only the location of the norm, making more Mitt Romney rich and more rich coextensive. Comparison classes work the same way; reference to comparison classes is part of the positive morpheme, (or perhaps somewhere lower in order to capture indirect comparisons, see Sassoon and van Rooij, 2016). Regardless, some alternatives will be something like “has a degree on this scale surpassing the standard for comparison class C on this scale”, and the comparison class RM simply selects the alternative with the appropriate comparison class. Degree RMs are less obvious. Consider the denotation of a gradable predicate, like fast. This is made up of a set of alternatives, which are each sets of predicates given different degrees (57b). (57) a. b.  λ d.λ x.fast(d)(x), = etc.  λ x.fast(5mph)(x), λ d.λ x.fast(d)(x) = λ x.fast(6mph)(x),   etc JfastK.8,C,J  Here, the RM selects an element from this set rather than the set of alternatives. A degree that is associated with an individual like Usain Bolt may be his most famous speed (27.7 mph), or using a less measured set of degrees, it could be something like a very high degree. This ambiguity between the exact speed and the relative speed is what allows the ambiguity between direct and indirect comparisons discussed previously. The set of alternatives for Usain Bolt fast include a variety of degree near but not equal to Usain Bolt’s degree of speed. (58) a. 0 JUsain Bolt fastKd ,C,J = { f<e,t> : f ≈d 0 ,C λ x.fast(27.7mph)(x)} Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 930 C. O’Hara Hillary Clinton is not Mitt Romney rich 4. Conclusion Thus, RMs can be formulated as recentering pragmatic halos, capturing all the four readings discussed in this paper. This approach is able to capture these constructions, but also should be extendible to a variety of similar seeming constructions with different categories of predicates. The lexical cloning construction (salad salad or tall tall, Ghomeshi et al., 2004) would be a subtype of this: the alternative most associated with the predicate itself would be the most precise alternative, and this semantically vacuous recentering of the halo could cause a change in the degree of precision. Other related forms are: Judge RMs on the precision variable (59a), dimension RMs on nouns (59b) or verbs (59c). Further work must be done to investigate the full range of RMs in English. (59) a. b. c. Given Sam is known to be imprecise: Is everybody there, or is it just Sam everybody? The biggest bird is like an ostrich bird not a eagle bird so it can’t fly. My son can swim, but he can only baby swim, so he’s not going out on a boat. References Anderson, C. (2016). Intensification and Attenuation Across Categories. Ph. D. thesis, Michigan State University. Bale, A. C. (2006). The Universal Scale and the Semantics of Comparison. Ph. D. thesis, McGill University. Bale, A. C. (2008). A universal scale of comparison. Linguistics and Philosophy 31(1), 1–55. Bale, A. C. (2011). Scales and comparison classes. Natural Language Semantics 19(2), 169– 190. Bierwisch, M. (1989). The semantics of gradation. In M. Bierwisch and E. Lang (Eds.), Dimensional Adjectives. Springer-Verlag. Bolinger, D. (1967). Adjectives in English: Attribution and predication. Lingua 18(1), 1–34. Bylinina, L. (2014). The Grammar of Standards and Comparison Classes in Degree Constructions. Ph. D. thesis, Utrecht Institute of Linguistics. Embick, D. (2007). Blocking effects and analytic/synthetic alternations. Natural Language and Linguistic Theory 25(1), 1–37. Ghomeshi, J., R. Jackendoff, N. Rosen, and K. Russell (2004). Contrastive focus reduplication in English (the salad-salad paper). Natural Language and Linguistic Theory 22(2), 307–357. Hamblin, C. (1973). Questions in Montague English. Foundations of Language 10(1), 41–53. Horn, L. (1984). Towards a new taxonomy of pragmatic inference: Q-based and R-based implicature. In D. Schiffrin (Ed.), Meaning, Form, and Use in Context: Linguistic Applications. Georgetown University Press. Kennedy, C. (2013). Two sources of subjectivity: Qualitative assessment and dimensional uncertainty. Inquiry 56(2–3), 258–277. Kennedy, C. (2007). Vaguness and grammar: The semantics of relative and absolute gradable adjectives. Linguistics and Philosophy 30(1), 1–45. Kennedy, C. and L. McNally (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language 81(2), 345–381. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 931 C. O’Hara Hillary Clinton is not Mitt Romney rich Kölbel, M. (2003). Faultless disagreement. Proceedings of the Aristotelian Society 104(1), 55–73. Kratzer, A. and J. Shimoyama (2002). Indeterminate pronouns: The view from Japanese. In Y. Otsu (Ed.), Third Tokyo Conference on Psycholinguistics, pp. 1–25. Lasersohn, P. (1999). Pragmatic halos. Language 75(3), 522–551. Lasersohn, P. (2005). Context dependence, disagreement, and predicates of personal taste. Linguistics and Philosophy 28(6), 643–686. McCawley, J. D. (1998). The Syntactic Phenomena of English. University of Chicago Press. Morzycki, M. (2011). Metalinguistic comparison in an alternative semantics for imprecision. Natural Language Semantics 19(1), 39–86. Morzycki, M. (2012). The several faces of adnominal degree modification. In J. Choi, E. A. Hogue, J. Punske, D. Tat, J. Schertz, and A. Trueman (Eds.), Proceedings of WCCFL29, Somerville, Mass. Cascadilla Press. O’Hara, C. (to appear). Nouns attributively modifying adjectives in English. In WCCFL 34. Partee, B. H. (1995). Lexical semantics and compositionality. In L. Gleitman and M. Liberman (Eds.), An Invitation to Cognitive Science Volume 1: Language. MIT Press. Rett, J. (2008). Degree Modificiation in Natural Language. Ph. D. thesis, Rutgers University. Sassoon, G. (2007). Vagueness, Gradability, and Typicality: A Comprehensive Semantic Analysis. Ph. D. thesis, Tel Aviv University. Sassoon, G. (2010). Measurement theory in linguistics. Synthese 174(1), 151–180. Sassoon, G. (2013). A typology of multidimensional adjectives. Journal of Semantics 30(3), 335–380. Sassoon, G. and R. van Rooij (2016). The semantics and pragmatics of for phrases. Ms. Schwarzschild, R. (2008). The semantics of the comparative and degree constructions. Language and Linguistics Compass 2(2), 308–331. Solt, S. (2011). Notes on the comparison class. In R. Nouwen, R. van Rooij, U. Sauerland, and H.-C. Schmitz (Eds.), Vagueness in Communication (ViC2009), Revised Selected Papers (LNAI 6517), pp. 189–206. Solt, S. (2016). Ordering subjectivity and the absolute/relative distinction. In N. Bade, P. Berezovskaya, and A. Scoller (Eds.), Proceedings of SuB20, pp. 676–693. Stephenson, T. (2007). Judge dependence, epistemic modals, and predicates of personal taste. Linguistics and Philosophy 30(4), 487–525. Stojanovic, I. (2007). Talking about taste: Disagreement, implicit arguments and relative truth. Linguistics and Philosophy 30(6), 691–706. Wellwood, A. (2014). Measuring Predicates. Ph. D. thesis, University of Maryland, College Park. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 932 One many, many readings1 Doris PENKA — University of Konstanz Abstract. This paper pursues a unified analysis of the different readings that the so-called quantifier many gives rise to. Adopting a degree-based semantics account, many is decomposed into a gradable cardinality predicate and the positive operator POS. The different readings are argued to result from different scope of POS and association with focus. This improves on alternative accounts, which either employ more than one lexical entry for many or do not specify a compositional implementation. Keywords: quantifier decomposition, degree semantics, positive operator 1. Introduction It is well known that the quantifier many gives rise to several readings. Partee (1989) distinguishes the so-called cardinal and proportional reading of many. Under the cardinal reading, a sentence with many is true iff the number of individuals that fall in the intersection of the restrictor and the nuclear scope counts as large in the given context. Sentence (1) under the cardinal reading, for instance, is true in a scenario where the number of students who took Intro to Semantics is considered large, e.g. compared to other courses or compared to previous years. (1) Many students took Intro to Semantics. Under the proportional reading, sentence (1) can be paraphrased as ‘A high proportion of all the students took Intro to Semantics’ and comes out as true if the ratio of the number of students taking Intro to Semantics to the total number of students counts as high in the given context. Under the proportional reading, the truth of a sentence does not only depend on the number of individuals in the intersection, but also on the number of individuals in the denotation of the NP. In contrast to the cardinal reading, we also learn something about the students who did not take Intro to Semantics, namely that their number is small. Besides the cardinal and proportional reading, Westerståhl (1985) noted an additional reading of many. This reading is illustrated by his celebrated sentence (2), which is intuitively considered true in the scenario in (3) (describing the actual state of affairs at the time Westerståhl’s paper was written), but false both under the cardinal and proportional reading – neither the absolute number 14 can be considered large nor the ratio of 14 to millions of Scandinavians. (2) Many Scandinavians have won the Nobel Prize in literature. (3) Of a total of 81 Nobel Prize winners in literature, 14 come from Scandinavia. 1 I would like to thank audiences at Sinn und Bedeutung 21 and at the University of Konstanz for valuable comments and suggestions. I am grateful in particular to Maribel Romero, Bernhard Schwarz, Anthea Schöller and Sven Lauer for helpful discussion. The research reported here was undertaken while being a research fellow of the Zukunftskolleg at the University of Konstanz. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 933 D. Penka One many, many readings Intuitively, sentence (2) is true in the scenario in (3) because 14 out of a total of 81 Nobel Prize winners in literature is considered a high proportion. In this case the relevant proportion is determined not with respect to the NP denotation, but with respect to the denotation of the VP. Since this reading can be paraphrased as ‘Many of the Nobel Prize winners in literature are Scandinavians’, with the arguments of many reversed in comparison to the sentence (2), this reading has become known as the reverse reading. One way of coping with this three-way ambiguity would be to employ three different lexical entries for many, each corresponding to one of the readings discussed above. In the framework of Generalized Quantifier Theory (GQT), we would then have the following determiners:2 (4) a. [[manyCARD]] = lP.lQ. | P Ç Q | > n, where n is a large number CARDINAL b. [[ manyPROP]] = lP.lQ. | P Ç Q | : | P | > k, where k is a large fraction PROPORTIONAL c. [[manyREV]] = lP.lQ. | P Ç Q | : | Q | > k, where k is a large fraction REVERSE The lexical entry for manyREV in (4c) is particularly noteworthy, as pointed out by Westerståhl (1985). Since it makes reference to the cardinality of the VP denotation, it violates the Conservativity Universal (Barwise and Cooper, 1981; Keenan and Stavi, 1986). According to this semantic universal, determiners in natural languages are conservative, which means that the extension of the second argument of a determiner counts only insofar as it overlaps with the extension of the first argument, corresponding to the restrictor. But for reverse many in (4c), the entire extension of the second argument enters into the truth conditions. Even leaving aside the issue of non-conservativity raised by the lexical entry for reverse many, there are obvious reasons to be dissatisfied with the meaning rules in (4). Employing a separate lexical entry for each reading is not very insightful and a more parsimonious way of dealing with the ambiguity that many gives rise to would be welcome. The aim of the present paper is to explore a unified analysis in which the different readings are derived from a single lexical entry of many. Recent advancements in semantic theory give reasonable hope to such an endeavor. There is a growing body of work that decomposes the expressions GQT labels as quantifiers into smaller meaningful parts and derives the interpretations these expressions give rise to in a fully compositional way (Hackl, 2000, 2009 among many others). The analysis developed in the present paper builds in particular on Romero (2015, 2016), who shows that the reverse reading can be explained under the assumption that the so-called quantifier many is the positive form of a gradable determiner many, which is analysed in a degree-based semantic framework in analogy to gradable adjectives. While the present paper follows Romero in adopting a degree semantics account and her analysis of the positive operator, the goal of the investigation is to take the analysis a step further and derive all three readings from a single lexical entry in a compositional manner. The key idea is that many itself is a gradable cardinality predicate that combines with the positive operator POS, 2 Cardinal many has also been treated as a cardinality predicate rather than as a genuine quantifier (Hoeksema, 1983; Partee, 1989, among others). Motivation for this comes from the observation that cardinal many patterns with indefinites and other so called weak determiners in terms of distribution in existential there-sentences and in subject position of individual-level predicates (Milsark, 1977); see section 4.2. We will use a version of this cardinality predicate analysis that makes the parallel between many and gradable adjectives transparent. Proceedings of Sinn und Bedeutung 21 Edited by Robert Truswell, Chris Cummins, Caroline Heycock, Brian Rabern, and Hannah Rohde 934 D. Penka One many, many readings and the different readings result from different scope of POS (cardinal vs. proportional readings) and (free) association with focus (regular vs. reverse readings). The paper is organized as follows: Section 2 lays out the ingredients that go into the analysis: on the one hand many as gradable cardinality predicate, on the other the semantics of degree operators, in particular of the positive operator. The analysis is presented in Section 3, showing how the different readings can be derived using these ingredients. Section 4 takes a closer look at reverse readings. In Section 5 it is shown how distributional restrictions on the different readings can be explained in terms of the proposed analysis. Section 6 concludes. 2. Ingredients of the analysis In the analysis I propose, what has been labeled quantifier many is analysed as the positive form of a gradable cardinality predicate. There are thus two ingredients that go into the analysis, each having been motivated and proposed independently. The first is the assumption that many is not a determiner, but rather a gradable cardinality predicate. The second is the semantics of degree operators, specifically the semantics of the positive operator. 2.1. Many as a gradable cardinality predicate Since many shows an obvious analogy to gradable adjectives – it can be put in the comparative form more as well as in the superlative most – it has also been proposed that it should be analysed in analogy to gradable adjectives (Schwarz, 2006; Hackl, 2009, among many others). In this type of analysis, many is a cardinality predicate with the semantics in (5).3 (5) [[many]] = ld.lx. |x| ≥ d The lexical entry in (5) follows the usual semantics assumed for gradable adjectives (e.g., Heim, 2001) and is formulated in analogy to that of gradable adjectives like high in (6). Note in particular that this semantics for gradable adjectives is downward monotonic, in the sense that a specific individual is not only associated with a single degree, but with a set of degrees: high is a relation between an individual x and all degrees up to x’s exact height, i.e. all degrees contained in the interval (0, HEIGHT(x)]. (6) [[high]] = ld.lx. HEIGHT(x) ≥ d The dimension that many targets is that of cardinality. In a mereological framework of plural semantics (Link, 1983), many relates a plural individual with the number of atomic parts it consists of, i.e. |x| is the cardinality of {y: atom(y) & y ≤ x}.4 Under this view, many is a predicate rather than a determiner. Quantificational force, the