Ancient Logic

Questa tesi intende presentare l’implicazione connessiva da due punti di vista: uno logico (parte I) e uno storico (parte II). Nell’introduzione si darà un rapido sguardo ai paradossi dell’implicazione materiale e si indicheranno alcuni tentativi di soluzione: in particolare, si presenteranno i vari approcci connessivi, con particolare attenzione per quello di Graham Priest. Nel capitolo 1 della parte I, si presenterà sintassi e semantica della logica connessiva PrC, così come è esposta in Priest [47], servendosi dei modelli kripkeani. Si mostreranno anche alcune proprietà peculiari della nozione di conseguenza logica connessiva: essa è transitiva e chiusa sotto modus ponens ma non è riflessiva, né monotona né chiusa sotto sostituzione uniforme. I principi connessivi sono validi in tale semantica, però delle tesi di Boezio sono valide solo le versioni deboli, ovvero quelle che hanno per connettivo principale un’implicazione materiale. Verrà poi definita una nuova semantica per PrC, equivalente alla precedente, ma la cui relazione di accessibilità è esplicitata ed è una relazione di equivalenza. Inoltre, si mostrerà come sia possibile, tramite una funzione di traduzione e la sua inversa, tradurre, salva veritate, formule di PrC in formule della logica modale S5 e viceversa. Nel capitolo 2, verrà rapidamente descritto un calcolo di sequenti etichettati per S5 e si accennerà alle proprietà del suddetto calcolo. In seguito, si definirà un calcolo etichettato per PrC (rispetto alla semantica con relazione di equivalenza), chiamato G3.PrC: se ne presenteranno le regole e si dimostreranno i due risultati fondamentali di validità e completezza per G3.PrC. Nella parte II, analizzeremo il passo degli Analitici Primi nel quale alcuni logici rintracciano alcune delle più famose formule connessive. Dopo un commento del passo e una rapida panoramica su alcune delle più autorevoli esegesi del brano, si esporrà una nuova interpretazione del testo, che si basa sui capitoli degli Analitici che fanno da contesto al passaggio in questione: lo Stagirita vorrebbe dimostrare che una conclusione vera non può seguire per necessità da premesse false. Si motiveranno, sulla base della filosofia aristotelica, le due tesi che fungono da base alla nuova interpretazione proposta: (i) le regole logiche cui Aristotele fa riferimento sono semantiche (in termini moderni: lo Stagirita starebbe parlando della nozione di conseguenza logica); (ii) con le due lettere A e B, Aristotele intende le due premesse di un sillogismo (A) e la conclusione (B) e non due enunciati qualsiasi (non sarebbero, dunque, variabili enunciative tout court). Infine, si analizzeranno le tre figure sillogistiche per saggiare la validità del ragionamento aristotelico nella nuova esegesi data, mostrando come, sebbene insorgano alcune difficoltà, sia possibile affermare che la nuova interpretazione valida l’argomento dello Stagirita.

The goal of this paper is to present a new reconstruction of Aristotle’s assertoric logic as he develops it in Prior Analytics, Book A1-7. This reconstruction will be much closer to Aristotle’s original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by Ben-Yami (2004; 2014) called ‘QUARC’. This system is apt for a more adequate reconstruction since it does not need first-order variables (‘x’, ‘y’, . . . ) on which the usual quantifiers act – a feature also not to be found in Aristotle. Further, in the classical reconstruction, there is also need for binary connectives (‘^’, ‘!’) that don’t have a counterpart in Aristotle. QUARC, again, does not need them either to represent the Aristotelian sentence types. However, the full QUARC is also not called for so that I develop a subsystem thereof (‘QUARC_AR') which closely resembles Aristotle’s way of developing his logic. I show that we can proof all of Aristotle’s claims within this systems and, lastly, relate it back to classical logic.

ABSTRACT: In this essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed evidence that there are numerous (over a hundred) and extensive parallels in both formulation and content between the Stoics and Frege, so plentiful that one would be hard pressed to brush them off as a coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope.
The published version of this paper is open access. See https://ics.sas.ac.uk/publications/themes-plato-aristotle-and-hellenistic-philosophy?fbclid=IwAR0FmeF913u6_OeYi4zIJ-fi5a3ZRRuLNn-FMk-vGzsgo2JPwfT9vHsoIzs

ABSTRACT: In this essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed evidence that there are numerous (over a hundred) and extensive parallels in both formulation and content between the Stoics and Frege, so plentiful that one would be hard pressed to brush them off as a coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope.
(The whole volume in which the paper is published is open access. Google the title and choose the link from ics-dot-sas-dot-ac-dot-uk for download.)

Boethius fasst im sechsten Jahrhundert den Plan, sämtliche Werke Aristoteles’ und Platons ins Lateinische zu übersetzen und mit Kommentaren zu versehen. Die Motivation für dieses Projekt liegt in seiner Einsicht in die bildungstheoretischen Grundlagen des Platonismus und des Aristotelismus begründet, die ihm auch als Maßstab für seine ethischen Erkenntnisse und sein pädagogisch orientiertes Schaffen dienen. Darüber hinaus liefert seine Sorge um die Anschlussfähigkeit dieser Bildungstradition an die gesellschaftlichen Bedingungen im lateinischsprachigen Raum seiner Zeit den entscheidenden Impuls.
Ziel dieses Buches ist es, Boethius’ Übersetzungsprojekt in die verschiedenen Ebenen der mit diesem Projekt verbundenen Wissenstransfers aufzuschlüsseln und sowohl die Inhalte als auch die Bedingungen dieser Transfers aufzuzeigen. Die Übersetzungen im engeren Sinne sind hierbei nur ein Teil des Wissenstransfers. Denn mit Blick auf die Sorge um eine gelingende Vermittlung der Inhalte für die verschiedenen Niveaustufen seines Zielpublikums stellen die Kommentierungen und die Maßnahmen der didaktischen Vermittlung einen integralen Bestandteil seines Übersetzungsprojekts und damit weitere Wissenstransferebenen dar. Die Vorgehensweisen bei diesen verschiedenen Aspekten der Übersetzung wiederum finden ihre Grundlage in den sprachphilosophischen und seelentheoretischen Einsichten, die für Boethius’ Konzeption einer gelingenden Vermittlung verantwortlich sind. Die Theorie der Sprache, die Boethius in seiner Bearbeitung der aristotelischen Schrift Peri hermêneias (bzw. De interpretatione) ins Lateinische überträgt, bildet damit zugleich die Grundlage für die Praxis seiner Übertragung.

The aim of this paper is to provide some acquaintance with the exegetical history of ἐξαίφνης inside the Platonic Tradition, from Plato to Marsilio Ficino, by way of Middle Platonism and Greek Neoplatonism.
(Since this is only a draft, several modifications should be made later, notably in order to improve the English.)
Some part has been presented in Los Angeles: “Damascius’ Theodicy: Psychic Input of Disorder and Evil into the World”, 16th Annual ISNS (International Society for Neoplatonic Studies) Conference, Loyola Marymount University, 14th June 2018

Dalla tarda antichità all'età moderna la logica antica è stata la sillogistica aristotelica e la sillogistica aristotelica è stata la logica. Come scriveva Kant in un celebre passo della Prefazione alla seconda edizione della Critica della Ragione Pura (1787):

My purpose in this paper is to investigate some ancient conceptions of the composition and structure of sentences, focusing on Plato and Aristotle, with short forays into other authors and ages. I shall concern myself mainly with two mutually connected issues. First, both Plato and Aristotle hold that a minimal simple sentence consists of two expressions of different kinds, which they call onoma and rhema; I shall try to make clear the nature and purport of this distinction, which is controversial. Secondly (but partly at the same time), I shall try to trace the emergence and early development, from Plato to the Stoics, of the idea that a simple declarative sentence has a signification of its own over and above the signification of its parts.

The MESA Research Group ("Metaphysics and Science in Aristotle"), settled in Campinas, moved to online format during the pandemic. The Seminars have been, and are being, held on the "preread format" with a diversified group of invited speakers (ranging from PhD students and other permanent members of the MESA group to established scholars),

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments.

Accanto all'analisi sistematica delle teorie del ragionamento la logica antica ha sviluppato una "via antinomica" al pensiero, producendo una mole notevole di argomenti, formule, soluzioni per paradossi ed aporie. A guidarci nella ricostruzione di questa storia, dall'antichità ai suoi sviluppi medievali (nella forma degli insolubilia) e alle formalizzazioni logiche moderne (come nel caso del paradosso di Russell), è stato il paradosso del mentitore. Riferito ad un taumaturgo cretese del VII secolo a.C., Epimenide, lo ritroviamo in tutti i passaggi cruciali della storia della logica antica: in Aristotele, che ne offre una soluzione all'interno delle Confutazioni sofistiche, in Crisippo e nei filosofi della scuola megarica, in particolar modo nelle riflessioni di Diodoro Crono sulla natura dei condizionali. Il paradosso, in filosofia, non è stato solo una curiosità o un gioco intellettuale, ma l'occasione per verificare la solidità strutturale e la coerenza interna delle teorie logiche. La storia di questo percorso mostra come l'interesse nei confronti dei grandi paradossi, elaborati per la prima volta dalla filosofia greca, sia rimasto costante ed intenso, ed abbia sempre agito da stimolo per il dibattito logico-epistemologico, fino alle soluzioni complesse delle teorizzazioni moderne di Lewis, Tarski, Russell. Diodoro era alla corte di Tolomeo Soter quando Stilpone gli indirizzò alcuni argomenti dialettici; non sapendoli risolvere sull'istante, si ebbe il rimprovero del re [...]. Uscito dal banchetto, dopo avere scritto intorno ad un problema logico, morì per disperazione. (Diogene Laerzio, Vite dei filosofi, II, 111).

This article is focused on answering the question to what extent one can be a sceptic. Sextus Empiricus’s Outlines of Scepticism serves as a guide. In section 1, it is investigated whether three logical laws have a certain foundation or are subject to doubt. In section 2, Sextus’s way to deal with these laws is examined; the question arises how dogmatic his approach is. After that, a possible ‘reply’ by Sextus to the criticism receives attention. Section 3 is concentrated on a possible alternative to Sextus’s approach. Besides logical laws, some important methods are concerned.

"A 'self-refutation argument' is any argument which aims at showing that (and how) a certain thesis is self-refuting. This is the first book-length treatment of ancient self-refutation and provides a unified account of what is distinctive in the ancient approach to the self-refutation argument, on the basis of close philological, logical and historical analysis of a variety of sources. It examines the logic, force, and prospects of this original style of argumentation within the context of ancient philosophical debates, dispelling various misconceptions concerning its nature and purpose and elucidating some important differences which exist both within the ancient approach to self-refutation and between that approach, as a whole, and some modern counterparts of it. In providing a comprehensive account of ancient self-refutation, the book advances our understanding of influential and debated texts and arguments from philosophers like Democritus, Plato, Aristotle, Epicurus, the Stoics, the Academic sceptics, the Pyrrhonists and Augustine.

***REVIEWS
'Castagnoli's book analyzes with brilliance, incision, sensitivity, and exhaustive depth more than a dozen classes of Ancient Greek and Roman self-refutation arguments ... "Ancient Self-Refutation" is an extremely edifying, useful, and serious book of philosophy. Each of Castagnoli's chapters is full of philosophical freshness, perspicuity and information, and each must from now on serve as essential reference.' (Christopher Moore, Bryn Mawr Classical Review)

'In this thoroughly stimulating and in every way impressive book, Castagnoli offers a comprehensive examination and analysis of a large number and variety of self-refutation arguments in ancient philosophy ... C.'s command of such exceedingly wide and complex material is nothing short of masterful, as is his acutely rigorous, sharply focussed and immensely detailed use of tools - philological, historical, logical - for the handling of it.' (Vasilis Politis, Classical Review 62 (2012))

'... a good book, difficult in places, but rewarding, and one that offers a different angle on many vexed texts. It is also scrupulous about looking at texts in their context, at precursors and presuppositions, and at argumentative thrust... a good model to follow when doing ancient philosophy.' (Benjamin Morison, Phronesis 57 (2012))

'L’intérêt de ce livre est multiple. D’une part, il présente une série d’analyses particulièrement fines de séquences argumentatives qui vont effectivement de Démocrite à saint Augustin ... l’attention portée à la situation argumentative et à la lettre du texte permet de produire de nouvelles compréhensions des arguments ... D’autre part, ce texte fait voir, de manière particulièrement concrète, le sens de la pratique de la dialectique ... le livre comporte un certain nombre de positions méthodologiques qui sont en elles-mêmes intéressantes.' (Stéphane Marchand, Aitia 2 (2012))

'Castagnoli provides an impressive and valuable overview of the history of ancient self-refutation arguments. At the same time, he examines each of these arguments in detail, explaining their context and discussing different ways of interpreting them. Since the individual arguments differ significantly in their structure and strategy, C. does not attempt to propose a general definition of what an ancient self-refutation argument is (pp. 2–5, 353). Nevertheless, his synoptic treatment contributes to a better understanding both of the individual arguments and of their general nature.' (Marko Malink, forthcoming in Classical Philology)

'The book is fascinating, well-written, and a joy to read. The development of the denition of self-refutation from the initial pages where the idea is murky and undened to the concluding chapter where a detailed discussion of the unique properties of self-refutations are summarized makes the book read like a mystery, where one is given clues along the way and only at the end is the final story unveiled and made clear. Accessible to both the scholar and the layman, it would serve well as supplementary material on a course on ancient dialectics as well as a resource for the historian and philosopher of the ancient Greek and Latin tradition.' (Sara Uckelman)"

The aim of this paper is to question the absence, in the second part of Plato’s Parmenides, of the word kosmos and kindred words such as diakosmos etc., whereas they are frequent in others of Plato’s dialogues, a question all the more necessary if one admits that this second part should be understood as a “toolbox for cosmology” as Luc Brisson has rightly showed. One may be astonished about such an absence whereas the study of the relevant texts concerning the historical Parmenides reveals that he uses such words as kosmos and diakosmos. Now the study of this second part shows that the use of opposites obeys a logic of enantiomorphic, antilogic, heuristic and circular affections (pathé) and that the eight hypotheses are based on a systematic combinatory use of opposites, the mechanism of which is the radical opposition between separation and radical participation, an opposition which is invalidated by the Sophist. 
The comparison with the Sophist, the Timaeus, and the Philebus, makes it possible to tell why the enantiomorphic logic of the pathemic participation is sterile. It is so because it fails to reconcile the contraries in a selective and musical “sumplokè” capable of building a kosmos involving a mathematical model (logistikè) that could establish a medium between the opposites. Parmenides’ model functions as a repellent for this kosmological model, the inspiration of which is Pythagorean (whether it is Plato’s fiction or not is not a question we shall enter here) because, among all, it lacks of harmony and music by privileging diakrisis and the goddess Necessity, associated to parturitions incapable of generating a kosmos.

ABSTRACT: This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen's negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall's connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness.

"ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment).
‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories."

In this article, I tackle a heretofore unnoticed difficulty with the application of Pyrrhonian scepticism to science. Sceptics can suspend belief regarding a dogmatic proposition only by setting up opposing arguments or considerations for and against that proposition. Since Sextus provides arguments exclusively against particular geometrical definitions in Adversus Mathematicos III, commentators have argued that Sextus’ method is not scepticism, but negative dogmatism. However, commentators have overlooked the fact that arguments or considerations in favour of particular geometrical definitions were absent in ancient geometry, and hence unavailable to Sextus. While this might explain why they are also absent from Sextus’ text, I survey and evaluate various strategies to supply arguments in support of particular geometrical definitions.

https://philpapers.org/rec/WILCTP-9

ABSTRACT: The 3rd BCE Stoic logician “Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,95[4].” After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F.Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ logic differed from Stoic logic, and consequently, whether Hipparchus actually refuted Chrysippus. This paper closes these explanatory gaps. (1) I reconstruct Hipparchus’ notions of conjunction and negation, and show how they differ from Stoic logic. (2) Based on evidence from Stoic logic, I reconstruct Chrysippus’ calculations, thereby (a) showing that Chrysippus’ claim of over a million conjunctions was correct; and (b) shedding new light on Stoic logic and – possibly – on 3rd century BCE combinatorics. (3) Using evidence about the developments in logic from the 3rd to the 2nd centuries, including the amalgamation of Peripatetic and Stoic theories, I explain why Hipparchus, in his calculations, used the logical notions he did, and why he may have thought they were Stoic.

ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy.

Epitteto (50-135 ca.) conta tra i massimi pensatori di scuola stoica. Come Socrate, non ha mai scrit-to niente (il Manuale e le Diatribe sono opera di Arriano, storico e magistrato romano che ne seguì le lezioni a Nicopoli). La versione di Giacomo Leopardi è del 1825.

ABSTRACT: In this paper I argue (i) that the hypothetical arguments about which the Stoic Chrysippus wrote numerous books (DL 7.196) are not to be confused with the so-called "hypothetical syllogisms", but are the same hypothetical arguments as those mentioned five times in Epictetus (e.g. Diss. 1.25.11-12); and (ii) that these hypothetical arguments are formed by replacing in a non-hypothetical argument one (or more) of the premisses by a Stoic "hypothesis" or supposition. Such "hypotheses" or suppositions differ from propositions in that they have a specific logical form and no truth-value. The reason for the introduction of a distinct class of hypothetical arguments can be found in the context of dialectical argumentation. The paper concludes with the discussion of some evidence for the use of Stoic hypothetical arguments in ancient texts.

Inhalt:
I. Einleitung (S. 1)
II. Funktionen der Logik (S. 2)
III. Dialektisches Argumentieren (S. 9)
IV. Rhetorisches Argumentieren (S. 33)
V. Zwischenfazit (S. 37)
VI. Argumentative Wissensvermittlung in der Consolatio Philosophiae (S. 38)
VII. Fazit (S. 46)

Ziel dieser Studie ist es zu zeigen, wie Boethius von Anfang an die Funktion der Logik an die durch sie gewonnenen Fertigkeiten knüpft, über Argumentationen gewonnenes Wissen zu prüfen und mithilfe von Argumentationen ausgehend von anerkannten Einsichten neues Wissen zu vermitteln. Die Methode der argumentativen Wissensvermittlung, wie Boethius sie in seinen Texten zur Topik, die zu den letzten Schriften seines Schaffens zählen, entwickelt, steht im Fokus der vorliegenden Untersuchung. Dabei soll detailliert nachvollzogen werden, wie nach Boethius einer Argumentation (argumentatio) „Kraft“ (vis bzw. virtus) und damit der Wissensvermittlung größtmögliche Glaubwürdigkeit verliehen werden kann (fidem facere). Zusätzlich wird eine Vorstellung verschiedener Argumentationsstrategien der Consolatio Philosophiae einen Einblick gewähren, wie sich Boethius eine Umsetzung seiner Theorie auch in literarischen und außerschulischen Wissensvermittlungspraktiken vorstellte.

refubium.fu-berlin.de/handle/fub188/25731
ISSN 2199 – 2878

ABSTRACT: Galen’s Institutio Logica is the only introduction to logic in Greek that has survived from antiquity. In it we find a theory that bears some resemblance to propositional logic. The theory is commonly understood as being essentially Stoic. However, this understanding of the text leaves us with a large number of inconsistencies and oddities. In this paper I offer an comprehensive alternative interpretation of the theory. I suggest that it is Peripatetic at base, and has drawn on Stoic elements, but adapted them to an overall decidedly non-Stoic conception of logic and language, a conception indebted to Aristotelian logic in many respects. This interpretation makes it possible to reduce the seeming inconsistencies dramatically. The Peripatetic theory on which Galen draws was possibly developed in the first century BCE. Importantly, it differs from Stoic logic in that it shuns the latter’s syntactic approach, and considers certain linguistic assumptions and language conventions as part of the logical theory itself. My reconstruction of the theory results in a logic of propositions which differs wildly both from Stoic logic and from the ‘classical’ propositional logic of the 20th century. Interestingly, though, the theory in Galen shows that the ancients grappled with a number of logico-linguistic problems that over the last two decades have again become a matter of debate among contemporary logicians and linguists.

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century—before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz,

L. Gazziero, « “Utrum figura dictionis sit fallacia in dictione. Et quod non videtur”. A Taxonomic Puzzle or How Medieval Logicians Came to Account for an Odd Question by an Impossible Answer », dans L. Cesalli, A. de Libera et F. Goubier (éd.), Formal Approaches and Natural Language in Medieval Logic, Barcelona - Roma, Fédération Internationale des Instituts d'Etudes Médiévales 2016, p. 241-269 [ISBN: 978-2-503-56735-8 – http://www.brepols.net/Pages/ShowProduct.aspx?prod_id=IS-9782503567358-1].

Nota bene: uncorrected final proofs

L’une des particularités de l’exégèse latine des Sophistici elenchi a trait à un rapprochement à la fois récurrent et improbable entre paralogismes de l’accident et paralogismes liés à la forme de l’expression. Dans un premier temps, l’essai s’attache à montrer à quel point les commentateurs latins étaient sensibles aux problèmes d’ordre taxinomique, qu’ils ont systématiquement abordés en mobilisant des puissant outils d’analyse, tels que la distinction entre la forme et la matière d’un argument ou encore la distinction entre ce qu’ils appelaient la causa defectus et la causa apparentiae d’un raisonnement fallacieux. Dans un deuxième temps, l’essai montre comment et pourquoi, en dépit de leur compréhension très fine des principes de la classification aristotélicienne des procédés sophistiques, ces mêmes commentateurs, primo, ont pu se poser la question, à l’apparence extravagante, de savoir si les paralogismes liés à la forme de l’expression sont bel et bien des paralogismes qui dépendent de l’expression (« utrum figura dictionis sit fallacia in dictione ») et, secundo, ce qui est encore plus paradoxal, lui répondre par la négative (« quod non videtur »)

Corcoran, John. 1994. The Founding of Logic: Modern Interpretations of Aristotle's Logic. Ancient Philosophy, 14, 9–24.

Since the time of Aristotle's students, interpreters have considered PRIOR ANALYTICS, hereafter PA, to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments.  More explicitly,  PA was taken to be about “methods of logic” in Quine’s sense: methods for determining of a consequence of given premises that it indeed is a consequence of them and—which are quite different— methods for determining of a proposition not consequence of given premises that it indeed is not a consequence of them. PA took for granted the theses (1) that not ever valid argument is obviously valid and (2) that not ever invalid argument is obviously invalid.

People studied PRIOR ANALYTICS in order to learn more about deductive reasoning and to improve their own reasoning skills.  These interpreters understood Aristotle to be focusing on two epistemic processes:  first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow.  Despite the overwhelming tendency to interpret the syllogistic as FORMAL EPISTEMOLOGY, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic.

When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as FORMAL ONTOLOGY and at the same time by a desire to protect Aristotle from possible charges of psychologism.  They thought they saw Aristotle applying the INFORMAL axiomatic method to formal ontology, not as making the first steps into formal epistemology.  They did not notice Aristotle's description of deductive reasoning.  Ironically, the FORMAL axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation.

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables.

Gregory of Nyssa's understanding of the individual is largely neglected, but offers fascinating insight into the specific conditions determining theological adaptations of philosophical theories in late antiquity. The paper starts from sketching differing philosophical views to argue that Gregory, due to his theological angle, was drawn to one particular theory, found especially in Porphyry, but that this very theory led to further doctrinal difficulties, which he tried to avoid by falling back on an alternative philosophical account.

The aim of the present paper is to analyse the archeology of the concept of contradiction, more precisely in Plato, and to reveal the influence that the latter had on Aristotle's reflection on contradiction and contrariety. This paper will show that it is possible to find examples of a notion of contradiction in Plato's refutative dialogues, in which Socrates is described as refuting his interlocutors by demonstrating the contrary of their initial thesis. However, Plato never used the word antiphasis to name the act of contradicting oneself (this word seems to be the invention of Aristotle), but preferred the expression enantia legein heautôi, which means " to say the contrary to oneself " .

As a chapter in the history of ancient logic, Plato's so-called 'method of collection and division' is a very controversial one. Division, in particular, even if normally dubbed 'logical division' in the learned literature, at close inspection proves to be far from clear as a logical procedure, namely in its logical form and deductive power. In the ancient Academy as well as in Peripatetic and Stoic logic, ötaípeotg as eidetic division has mainly to do with abstract entities like -yévn or ei' 611 (however interpreted) and their real definition or description. It is presumably in this sense that both the Sophist and the Statesman are characterised as 'logical' dialogues in Thrasyllus' edition of Plato's work, on a par with the Parmenides and the Cratylus, a characterisation that is likely to go back to the ancient and middle Academy?