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Brian Rabern

University of Edinburgh, School of Philosophy Psychology and Language Sciences, Faculty Member

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I'm a Reader in the school of philosophy, psychology, and language sciences at the University of Edinburgh.
Supervisors: David Chalmers
Address: 3 Charles St., Edinburgh

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Papers by Brian Rabern

Scorekeeping in a chess game

Semantics and Pragmatics, 2022

There is an important analogy between languages and games. Just as a scoresheet records features ... more There is an important analogy between languages and games. Just as a scoresheet records features of the evolution of a game to determine the effect of a move in that game, a conversational score records features of the evolution of a conversation to determine the effect of the linguistic moves that speakers make. Chess is particularly interesting for the study of conversational dynamics because it has language-like notations, and so serves as a simplified study in how the effect of an assertion depends on, as well as evolves, the scoreboard. In this paper, we offer a compositional semantics for chess notation and a simple formal picture for determining the full information conveyed by an entry. We will also discuss an alternative model resembling accounts of centered assertion.

Pure Quotation in Linguistic Context

Journal of Philosophical Logic

A common framing has it that any adequate treatment of quotation has to abandon one of the follow... more A common framing has it that any adequate treatment of quotation has to abandon one of the following three principles: (i) The quoted expression is a syntactic constituent of the quote phrase; (ii) If two expressions are derived by applying the same syntactic rule to a sequence of synonymous expressions, then they are synonymous; (iii) The language contains synonymous but distinct expressions. In the following, a formal syntax and semantics will be provided for a quotational language which adheres to all three principles. The point here is not merely to provide a “possibility proof”, but to reveal the hard constraints on the theory of quotation, and to highlight certain assumptions at the syntax/semantics/post-semantics interfaces.

Against Fregean Quantification⇤

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tars... more There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege’s d...

Semantic Monsters

Proceedings of Sinn und Bedeutung 21

Index, Context, and the Content of Knowledge

The verb ‘knows’ is often treated as an intensional operator, and the logic of knowledge is often... more The verb ‘knows’ is often treated as an intensional operator, and the logic of knowledge is often modelled with a modal operator K—a quantifier over ways that things could be compatible with a subject’s knowledge (or evidence). ‘Knows’ is also often taken to be context-sensitive in an interesting way. What ‘knows’ means seems to be sensitive to the epistemic features of the context, e.g. the epistemic standard in play, the set of relevant alternatives, etc. There are standard model-theoretic semantic frameworks which deal with both intensional operators and contextsensitive expressions. The basic elements of these frameworks were developed by Montague (1968), Scott (1970), and Lewis (1970), and then received more sophisticated renditions and philosophical interpretations in Kaplan (1989a) and Lewis (1980). In this chapter, we provide a brief overview of the various moving parts of these frameworks, the roles of context and index, the need for double indexing, and the relationship be...

The paradox of self-blame*

It is widely accepted both in theory and in practice that there is what has been called a non-hyp... more It is widely accepted both in theory and in practice that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame. In the terminology of the recent literature on these topics, one has standing to blame only if, as a first approximation, one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm – or one like it – is embodied in the common retorts to criticism, “Who are you to blame me?”, and “Look who’s talking!” If I regularly fail to reply to your emails on time, for instance, I’m in no moral position to criticize you for not replying to my emails on time – crucially, even if you are indeed blameworthy for this failure, and, crucially, even if someone else can appropriately make this criticism. Precisely how to formulate and motivate the non-hypocrisy norm on the standing to blame is a complicated affair. But the following is uncontroversial: if there is a standing-norm on blame at all, then there is some suitable non...

The Science of Meaning: Essays on the Metatheory of Natural Language Semantics

The Syntax and Semantics of Wire Diagrams: Two Approaches

In a wire diagram, the variables disappear altogether. The link between a quantifier and the argu... more In a wire diagram, the variables disappear altogether. The link between a quantifier and the argument position into which it binds is instead represented by a “wire” that connects them. It has recently been argued that this wire-diagram notation is superior to the quantifier-variable notation because it can preserve compositionality without positing overly fine-grained meanings. (See: [5], ([2]: 14), ([13]: 215), and ([11], 38).) Consider the fact that the open sentences (1) and (2) differ semantically.

Structural fixed-point theorems

The semantic paradoxes are often associated with self-reference or referential circularity. Howev... more The semantic paradoxes are often associated with self-reference or referential circularity. However, Yablo has shown in [2] that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In [1] we laid the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes. The remaining task is to classify the so-called dangerous directed graphs. In appendix A of [1], we sketched a reformulation of the problem in terms of fixed points of certain functions. Here we expand on this reformulation, removing all syntactic considerations to get a purely mathematical problem. It is definitely possible that the problem’s solution depends on the axioms of set theory we choose—this would be an interesting outcome. For sets A and B, we write A for all functions from B to A. W...

Binding bound variables in epistemic contexts

Inquiry, 2018

Frege and saving substitution

Philosophical Studies, 2020

Goodman and Lederman (Philos Stud 177(4):947–952, 2020) argue that the traditional Fregean strate... more Goodman and Lederman (Philos Stud 177(4):947–952, 2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires.

A Bridge from Semantic Value to Content

Philosophical Topics, 2017

Introduction to the Science of Meaning

Oxford Scholarship Online, 2018

This Introduction aims to acquaint the reader with some of the main views on the foundations of n... more This Introduction aims to acquaint the reader with some of the main views on the foundations of natural language semantics, to discuss the type of phenomena semanticists study, and to give some basic technical background in compositional model-theoretic semantics necessary to understand the chapters in this collection. Topics discussed include truth conditions, compositionality, context-sensitivity, dynamic semantics, the relation of formal semantic theories to the theoretical apparatus of reference and propositions current in much philosophy of language, what semantic theories aim to explain, realism, the metaphysics of language and different views of the relation between languages and speakers, and the epistemology of semantics.

Future Contingents and the Logic of Temporal Omniscience*

Noûs, 2019

At least since Aristotle's famous 'sea-battle' passages in On Interpretation 9, some substantial ... more At least since Aristotle's famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to what we might call the doctrine of the open future. This doctrine maintains that future contingent statements-roughly, statements saying of causally undetermined events that they will happen-are not true. 1 But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking backwards) it was the case that it would happen. How can it be that, looking forwards, it isn't true that there will be a sea-battle, while also being true that, looking backwards, it was the case that there would be a sea-battle? This tension forms, in large part, what might be called the problem of future contingents. Some theorists respond to this tension by insisting that one of the intuitions here must simply be denied. For example, so-called Peircians give up the backward-looking intuition, while so-called Ockamists give up the forward-looking intuition (see Prior 1967: 113-135). But a dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition-including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et.al (2001) and MacFarlane (2003, 2014)-have argued that the apparent tension between the intuitions is in fact merely apparent. 2 In short, such philosophers seek to maintain both of the following two theses:

Monsters and the Theoretical Role of Context

Philosophy and Phenomenological Research, 2017

Against the Russellian Open Future

Mind, 2016

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the for... more Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form ‘will()’, that is based on the classic Russellian analysis of definite descriptions. Todd’s analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of ‘will’ both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form ‘will()’.

Does Semantic Relationism Solve Frege’s Puzzle?

Journal of Philosophical Logic, 2016

In a series of recent works, Kit Fine (2003, 2007) has sketched a novel solution to Frege's puzzl... more In a series of recent works, Kit Fine (2003, 2007) has sketched a novel solution to Frege's puzzle. Radically departing from previous solutions, Fine argues that Frege's puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine's proposed solution to Frege's puzzle. We argue that Fine has mis-diagnosed his own solution-his attempted solution does not deny compositionality. The correct characterization of Fine's solution fits him more comfortably among familiar solutions to the puzzle. Keywords Frege's puzzle • proper names • Compositionality • Semantic relationism • variables In a series of recent works, Kit Fine (2003, 2007) has sketched a novel solution to Frege's puzzle. The novelty is itself surprising and exciting given the minimal This work was supported in part by project FFI2012-37658 (Spanish Government).

The Antinomy of the Variable: A Tarskian Resolution

Journal of Philosophy, 2016

Propositions and Multiple Indexing

Thought: A Journal of Philosophy, 2012

It is argued that propositions cannot be the compositional semantic values of sentences (in conte... more It is argued that propositions cannot be the compositional semantic values of sentences (in context) simply due to issues stemming from the compositional semantics of modal operators (or modal quantifiers). In particular, the fact that the arguments for double indexing generalize to multiple indexing exposes a fundamental tension in the default philosophical conception of semantic theory. This provides further motivation for making a distinction between two sentential semantic contents-what Dummett (1973) called "ingredient sense" and "assertoric content".

Scorekeeping in a chess game

Semantics and Pragmatics, 2022

There is an important analogy between languages and games. Just as a scoresheet records features ... more There is an important analogy between languages and games. Just as a scoresheet records features of the evolution of a game to determine the effect of a move in that game, a conversational score records features of the evolution of a conversation to determine the effect of the linguistic moves that speakers make. Chess is particularly interesting for the study of conversational dynamics because it has language-like notations, and so serves as a simplified study in how the effect of an assertion depends on, as well as evolves, the scoreboard. In this paper, we offer a compositional semantics for chess notation and a simple formal picture for determining the full information conveyed by an entry. We will also discuss an alternative model resembling accounts of centered assertion.

Pure Quotation in Linguistic Context

Journal of Philosophical Logic

A common framing has it that any adequate treatment of quotation has to abandon one of the follow... more A common framing has it that any adequate treatment of quotation has to abandon one of the following three principles: (i) The quoted expression is a syntactic constituent of the quote phrase; (ii) If two expressions are derived by applying the same syntactic rule to a sequence of synonymous expressions, then they are synonymous; (iii) The language contains synonymous but distinct expressions. In the following, a formal syntax and semantics will be provided for a quotational language which adheres to all three principles. The point here is not merely to provide a “possibility proof”, but to reveal the hard constraints on the theory of quotation, and to highlight certain assumptions at the syntax/semantics/post-semantics interfaces.

Against Fregean Quantification⇤

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tars... more There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege’s d...

Semantic Monsters

Proceedings of Sinn und Bedeutung 21

Index, Context, and the Content of Knowledge

The verb ‘knows’ is often treated as an intensional operator, and the logic of knowledge is often... more The verb ‘knows’ is often treated as an intensional operator, and the logic of knowledge is often modelled with a modal operator K—a quantifier over ways that things could be compatible with a subject’s knowledge (or evidence). ‘Knows’ is also often taken to be context-sensitive in an interesting way. What ‘knows’ means seems to be sensitive to the epistemic features of the context, e.g. the epistemic standard in play, the set of relevant alternatives, etc. There are standard model-theoretic semantic frameworks which deal with both intensional operators and contextsensitive expressions. The basic elements of these frameworks were developed by Montague (1968), Scott (1970), and Lewis (1970), and then received more sophisticated renditions and philosophical interpretations in Kaplan (1989a) and Lewis (1980). In this chapter, we provide a brief overview of the various moving parts of these frameworks, the roles of context and index, the need for double indexing, and the relationship be...

The paradox of self-blame*

It is widely accepted both in theory and in practice that there is what has been called a non-hyp... more It is widely accepted both in theory and in practice that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame. In the terminology of the recent literature on these topics, one has standing to blame only if, as a first approximation, one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm – or one like it – is embodied in the common retorts to criticism, “Who are you to blame me?”, and “Look who’s talking!” If I regularly fail to reply to your emails on time, for instance, I’m in no moral position to criticize you for not replying to my emails on time – crucially, even if you are indeed blameworthy for this failure, and, crucially, even if someone else can appropriately make this criticism. Precisely how to formulate and motivate the non-hypocrisy norm on the standing to blame is a complicated affair. But the following is uncontroversial: if there is a standing-norm on blame at all, then there is some suitable non...

The Science of Meaning: Essays on the Metatheory of Natural Language Semantics

The Syntax and Semantics of Wire Diagrams: Two Approaches

In a wire diagram, the variables disappear altogether. The link between a quantifier and the argu... more In a wire diagram, the variables disappear altogether. The link between a quantifier and the argument position into which it binds is instead represented by a “wire” that connects them. It has recently been argued that this wire-diagram notation is superior to the quantifier-variable notation because it can preserve compositionality without positing overly fine-grained meanings. (See: [5], ([2]: 14), ([13]: 215), and ([11], 38).) Consider the fact that the open sentences (1) and (2) differ semantically.

Structural fixed-point theorems

The semantic paradoxes are often associated with self-reference or referential circularity. Howev... more The semantic paradoxes are often associated with self-reference or referential circularity. However, Yablo has shown in [2] that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In [1] we laid the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes. The remaining task is to classify the so-called dangerous directed graphs. In appendix A of [1], we sketched a reformulation of the problem in terms of fixed points of certain functions. Here we expand on this reformulation, removing all syntactic considerations to get a purely mathematical problem. It is definitely possible that the problem’s solution depends on the axioms of set theory we choose—this would be an interesting outcome. For sets A and B, we write A for all functions from B to A. W...

Binding bound variables in epistemic contexts

Inquiry, 2018

Frege and saving substitution

Philosophical Studies, 2020

Goodman and Lederman (Philos Stud 177(4):947–952, 2020) argue that the traditional Fregean strate... more Goodman and Lederman (Philos Stud 177(4):947–952, 2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires.

A Bridge from Semantic Value to Content

Philosophical Topics, 2017

Introduction to the Science of Meaning

Oxford Scholarship Online, 2018

This Introduction aims to acquaint the reader with some of the main views on the foundations of n... more This Introduction aims to acquaint the reader with some of the main views on the foundations of natural language semantics, to discuss the type of phenomena semanticists study, and to give some basic technical background in compositional model-theoretic semantics necessary to understand the chapters in this collection. Topics discussed include truth conditions, compositionality, context-sensitivity, dynamic semantics, the relation of formal semantic theories to the theoretical apparatus of reference and propositions current in much philosophy of language, what semantic theories aim to explain, realism, the metaphysics of language and different views of the relation between languages and speakers, and the epistemology of semantics.

Future Contingents and the Logic of Temporal Omniscience*

Noûs, 2019

At least since Aristotle's famous 'sea-battle' passages in On Interpretation 9, some substantial ... more At least since Aristotle's famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to what we might call the doctrine of the open future. This doctrine maintains that future contingent statements-roughly, statements saying of causally undetermined events that they will happen-are not true. 1 But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking backwards) it was the case that it would happen. How can it be that, looking forwards, it isn't true that there will be a sea-battle, while also being true that, looking backwards, it was the case that there would be a sea-battle? This tension forms, in large part, what might be called the problem of future contingents. Some theorists respond to this tension by insisting that one of the intuitions here must simply be denied. For example, so-called Peircians give up the backward-looking intuition, while so-called Ockamists give up the forward-looking intuition (see Prior 1967: 113-135). But a dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition-including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et.al (2001) and MacFarlane (2003, 2014)-have argued that the apparent tension between the intuitions is in fact merely apparent. 2 In short, such philosophers seek to maintain both of the following two theses:

Monsters and the Theoretical Role of Context

Philosophy and Phenomenological Research, 2017

Against the Russellian Open Future

Mind, 2016

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the for... more Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form ‘will()’, that is based on the classic Russellian analysis of definite descriptions. Todd’s analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of ‘will’ both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form ‘will()’.

Does Semantic Relationism Solve Frege’s Puzzle?

Journal of Philosophical Logic, 2016

In a series of recent works, Kit Fine (2003, 2007) has sketched a novel solution to Frege's puzzl... more In a series of recent works, Kit Fine (2003, 2007) has sketched a novel solution to Frege's puzzle. Radically departing from previous solutions, Fine argues that Frege's puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine's proposed solution to Frege's puzzle. We argue that Fine has mis-diagnosed his own solution-his attempted solution does not deny compositionality. The correct characterization of Fine's solution fits him more comfortably among familiar solutions to the puzzle. Keywords Frege's puzzle • proper names • Compositionality • Semantic relationism • variables In a series of recent works, Kit Fine (2003, 2007) has sketched a novel solution to Frege's puzzle. The novelty is itself surprising and exciting given the minimal This work was supported in part by project FFI2012-37658 (Spanish Government).

The Antinomy of the Variable: A Tarskian Resolution

Journal of Philosophy, 2016

Propositions and Multiple Indexing

Thought: A Journal of Philosophy, 2012

It is argued that propositions cannot be the compositional semantic values of sentences (in conte... more It is argued that propositions cannot be the compositional semantic values of sentences (in context) simply due to issues stemming from the compositional semantics of modal operators (or modal quantifiers). In particular, the fact that the arguments for double indexing generalize to multiple indexing exposes a fundamental tension in the default philosophical conception of semantic theory. This provides further motivation for making a distinction between two sentential semantic contents-what Dummett (1973) called "ingredient sense" and "assertoric content".

The compositionality argument for temporalism

Arché Tense in Semantics and Philosophy of Language Workshop, June 5, 2014.