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  1. The Peripatetic Program in Categorical Logic: Leibniz on Propositional Terms.Marko Malink & Anubav Vasudevan - 2020 - Review of Symbolic Logic 13 (1):141-205.
    Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such as reductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the (...)
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  2. Demonstration and the Indemonstrability of the Stoic Indemonstrables.Susanne Bobzien - forthcoming - Phronesis.
    Since Mates’ seminal Stoic Logic there has been uncertainty and debate about how to treat the term anapodeiktos when used of Stoic syllogisms. This paper argues that the customary translation of anapodeiktos by ‘indemonstrable’ is accurate, and it explains why this is so. At the heart of the explanation is an argument that, contrary to what is commonly assumed, indemonstrability is rooted in the generic account of the Stoic epistemic notion of demonstration (apodeixis). Some minor insights into Stoic logic ensue.
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  3. Sextus Empiricus' Fourth Conditional and Containment Logic.Yale Weiss - 2019 - History and Philosophy of Logic 40 (4):307-322.
    In his Outlines of Pyrrhonism 2.110–113, Sextus Empiricus presents four different accounts of the conditional, presumably all from the Hellenistic period, in increasing logical strength. While the interpretation and provenance of the first three accounts is relatively secure, the fourth account has perplexed and frustrated interpreters for decades or longer. Most interpreters have ultimately taken a dismissive attitude towards the fourth account and discounted it as being of both little historical and logical interest. We argue that this attitude is unwarranted (...)
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  4. Greek and Roman Logic.Robby Finley, Justin Vlasits & Katja Maria Vogt - 2019 - Oxford Bibliographies in Classics.
    In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” (...)
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  5. Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    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 (...)
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  6. F. W. Zimmermann: Al-Farabi's Commentary and Short Treatise on Aristotle's De Interpretatione. Pp. Clii + 287. Oxford: O.U.P. For the British Academy, 1981 . Paper, £22.50. [REVIEW]James E. Montgomery - 1989 - The Classical Review 39 (1):143-144.
  7. Prior Analytics 1 - Striker Aristotle. Prior Analytics Book I. Pp. Xx + 268. Oxford: Clarendon Press, 2009. Cased, £50 . ISBN: 978-0-19-925040-0. [REVIEW]Paolo Biondi - 2010 - The Classical Review 60 (2):370-372.
  8. Alexander of Aphrodisias: On Aristotle's Prior Analytics 1.1-7.Jonathan Barnes, Susanne Bobzien & Katerina Ierodiakonou - 1991 - London: Duckworth.
    ABSTRACT: English translation of the 2nd/3rd century Peripatetic Philosopher's Alexander of Aphrodisias commentary on Aristotle's non-modal syllogistic, i.e. on one of the most influential logical texts of all times. -/- Volume includes introduction on Alexander of Aphrodisias and the early commentators, translation with notes and comments, appendices with a new translation of Aristotle's text, a summary of Aristotle's non-modal syllogistic and textual notes.
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  9. Analyticity, Balance and Non-Admissibility of Cut in Stoic Logic.Susanne Bobzien & Roy Dyckhoff - 2019 - Studia Logica 107 (2):375-397.
    This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a (...)
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  10. Paraenesis and Argument in Arrian’s Dissertations of Epictetus.Jula Wildberger - 2013 - In Michael Erler (ed.), Argument und literarische Form in antiker Philosophie. Berlin; New York: De Gruyter. pp. 411-434.
    Close reading of the argumentative and logical structure of Diatribe 1.4 and the means of protreptic persuasion used in it. The paper argues that Arrian represents Epictetus as using deliberately bad arguments to showcase and exemplify the audience's muddled thinking.
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  11. „Kauza Afthonios“: Ilustrácia k otázke správneho riešenia antických paradoxov.Vladimir Marko - 2014 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 1 (20):88-103.
    The article deals with the question of correct reconstruction of and solutions to the ancient paradoxes. Analyzing one contemporary example of a reconstruction of the so-called Crocodile Paradox, taken from Sorensen’s A Brief History of Paradox, the author shows how the original pattern of paradox could have been incorrectly transformed in its meaning by overlooking its adequate historical background. Sorensen’s quoting of Aphthonius, as the author of a certain solution to the paradox, seems to be a systematic failure since the (...)
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  12. Štyri antické argumenty o budúcich nahodnostiach (Four Ancient Arguments on Future Contingencies).Vladimir Marko - 2017 - Bratislava, Slovakia: Univerzita Komenského.
    Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument.
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  13. Logic Gallery.Marans David - 2016
    A century-by-century panorama of Formal Logic.... 171 individual pages for figures from Aristotle to the present.... Quotations, bio screeds, links to other sources, and seldom seen illustrations.
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  14. Platonic Anticipation of Stoic Logic [Corrected Title: Platonic Anticipations of Stoic Logic].Attila Fáj - 1972 - Apeiron 6 (1):1-24.
  15. "Dialectic and Its Place in the Development of Medieval Logic", by Eleanore Stump. [REVIEW]Sheldon M. Cohen - 1992 - Ancient Philosophy 12 (1):199.
  16. The Logistic Interpretation of Aristotle's Categorical Syllogistic.Charles F. Breslin - 1968 - Proceedings and Addresses of the American Philosophical Association 42:99.
  17. Sophroniscus’ Son is Approaching: Porphyry, Isagoge 7.20–1.Francesco Ademollo - 2004 - Classical Quarterly 54 (1):322-325.
  18. Studien Zur Grundlegung der Logik Und der Logischen Interpretationsmittel, MIT Besonderer Berücksichtigung von Texten Griechischer Denker. [REVIEW]Jonathan Barnes - 1977 - The Classical Review 27 (1):123-124.
  19. Aristotle's Syllogistic From the Standpoint of Modern Formal Logic. [REVIEW]Richard Robinson - 1953 - The Classical Review 3 (2):118-119.
  20. Introduzione Alia Logica Stoica. [REVIEW]Jonathan Barnes - 1986 - The Classical Review 36 (1):143-144.
  21. Il Significato Della Logica Stoica. [REVIEW]W. E. W. St G. Charlton - 1968 - The Classical Review 18 (1):119-120.
  22. La Logica Stoica: Testimonianze E Frammenti – Testi Originali Con Introduzione E Traduzione Commentata. Vols. II, III, IV, VA, VI, VIIA. [REVIEW]Jonathan Barnes - 1987 - The Classical Review 37 (2):311-312.
  23. The Paradox of Future Truth. [REVIEW]R. W. Sharples - 1987 - The Classical Review 37 (2):217-218.
  24. Galeno: Iniciación a la Dialéctica. [REVIEW]Jonathan Barnes - 1983 - The Classical Review 33 (2):336-337.
  25. Aristotle's Syllogistic From the Standpoint of Modern Formal Logic. [REVIEW]Richard Robinson - 1958 - The Classical Review 8 (3-4):282-282.
  26. La Logica Stoica: Testimonianze E Frammenti – Testi Originali Con Introduzione E Traduzione Commentata. [REVIEW]Jonathan Barnes - 1988 - The Classical Review 38 (2):426-427.
  27. Aristotle’s Concept of Dialectic. [REVIEW]G. L. J. - 1978 - Review of Metaphysics 32 (2):353-354.
    The aim of this study is to understand the place of Aristotle’s dialectic in his overall theory of intellectual activity. On the way to this goal, the reader is treated to a novel and exciting interpretation of the nature of dialectic. Evans argues that Aristotelian dialectic is a method for progressing from what is intelligible to some group of discussants to what is intelligible without qualification. Evans goes behind this distinction to discover how dialectic can be, as Aristotle claims, the (...)
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  28. Aristotle on Hypothetical Arguments and the Completeness of the Syllogistic.Tal Glezer - 2007 - Ancient Philosophy 27 (2):323-334.
  29. Restoring Olympiodorus’ Syllogistic.Harold Tarrant - 1997 - Ancient Philosophy 17 (2):411-424.
  30. The Unity of the Protagoras: On the Structure and Position of a Platonic Dialogue.Claus-Artur Scheier - 1994 - Graduate Faculty Philosophy Journal 17 (1/2):59-81.
    The following analysis of the Protagoras intends: contrary to the traditional tendency to consider the dialogue comparatively amorphous and polythematic, to clarify its argumentative architectonic; contrary to the scholarly view accompanying this tendency that of concern is an early dialogue, to make plausible the genesis of this dialogue after the Symposium; and to lay the groundwork for a more detailed discussion of the thesis that Plato, in his “middle” dialogues, makes the transition from Eleatic logic in its Megarian refraction, which (...)
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  31. Three Conceptions of Formal Logic.Thom Paul - 2010 - Vivarium 48 (1-2):228-242.
    Aristotle's logical and metaphysical works contain elements of three distinct types of formal theory: an ontology, a theory of consequences, and a theory of reasoning. His formal ontology (unlike that of certain later thinkers) does not require all propositions of a given logical form to be true. His formal syllogistic (unlike medieval theories of consequences) was guided primarily by a conception of logic as a theory of reasoning; and his fragmentary theory of consequences exists merely as an adjunct to the (...)
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  32. On Wiebe’s “Existential Assumptions for Aristotelian Logic”.D. F. Siemens - 1993 - Journal of Philosophical Research 18:271-275.
    This comment calls attention to the nature of the Aristotelian and classical logics, and the difficulty of representing their judgments and inferences by means of Venn diagrams. The meaning of ‘all’ in the different calculi produces problems. A second problem is that the specification of existence in Venn diagrams for statements and arguments cannot be restricted to a single class, overlooked by Wiebe. This problem is further complicated by his adoption of classical syllogistic, which is inconsistent. Aristotle’s term logic is (...)
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  33. La Structure Logique du Langage Ordinaire chez les Stoiciens.Ada Bronowski - 2014 - In Jean-Michel Counet (ed.), Philosophie et Langage Ordinaire de l'Antiquité à la Renaissance. Edition Peeters. pp. 83-96.
    Rather than considering ordinary language as deficient and incapable of grasping the structure of reality, the Stoics set out a theory, based on their notion of a lekton, by which ordinary language is a reflection of the structure of lekta which themselves are constitutive of reality.
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  34. The Stoic Doctrine of Generic and Specific Pathē.Robert J. Rabel - 1977 - Apeiron 11 (1):40 - 42.
  35. Apuleius and the Square of Opposition.Carmen Johanson & David Londey - 1984 - Phronesis 29 (2):165-173.
  36. Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument From Democritus to Augustine.Luca Castagnoli - 2010 - Cambridge University Press.
    A 'self-refutation argument' is any argument which aims at showing that a certain thesis is self-refuting. This study was 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 (...)
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  37. Categorical Μὴ Κατὰ Χρόνον Propositions in Alexander of Aphrodisias’ Modal Syllogistic.Luca0 Gili - 2015 - Apeiron 48 (4):1-17.
    Journal Name: Apeiron Issue: Ahead of print.
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  38. A Companion to Philosophical Logic.Dale Jacquette (ed.) - 2002 - Wiley-Blackwell.
    This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.
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  39. ARISTOTELIAN LOGIC AND EUCLIDEAN GEOMETRY.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (1):131-2.
    John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the premises: (...)
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  40. Ancient Logic and its Modern Interpretations Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972. [REVIEW]John Corcoran (ed.) - 1974 - Reidel.
    Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic.
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  41. A Missed Encounter.A. E. Benjamin - 1987 - Grazer Philosophische Studien 29 (1):145-170.
    In this paper I hope to show that Geach misunderstands the nature of Plato's argument in the Euthyphro and more importantly the reasoning behind the dialectical strategy adopted by Socrates. Furthermore I shall argue that Geach's reading of the Euthyphro engenders serious difficulties, that stand in the way of understanding the manner in which Plato construes the problem of determining the nature of, and relationship between universal and particulars, which is of great significance because it is precisely this problem, in (...)
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  42. Aristotle's Many-Sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...)
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  43. Mind and Sign: Method and the Interpretation of Mathematics in Descartes's Early Work.Amy M. Schmitter - 2000 - Canadian Journal of Philosophy 30 (3):371-411.
    Method may be second only to substance-dualism as the best-known among Descartes's enthusiasms. But knowing that Descartes wants to promote good method is one thing; knowing what exactly he wants to promote is another. Two views seem fairly widespread. The first rests on the claim that Descartes endorses a purely procedural picture of reason, so that right reasoning is a matter of proprieties of operation, rather than respect for its objects. On this view, a method for regulating our reason would (...)
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  44. Vollkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant. Eine Stellungnahme zu Theodor Eberts Gegeneinwänden. Teil 2.Michael Wolff - 2010 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 41 (2):359 - 371.
    In an earlier article (see J Gen Philos Sei (2010) 41: 341-355) I have compared Aristotle's syllogistic with Kant's theory of "pure ratiocination". "Ratiocinia pura" („reine Vernunftschlüsse") is Kant's designation for assertoric syllogisms Aristotle has called 'perfect'. In Kant's view they differ from non-pure ratiocinia precisely in that their validity rests only on the validity of the Dictum de omni et nullo (which, however, in Kant's view can be further reduced to more fundamental principles) whereas the validity of non-pure ratiocinia (...)
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  45. Logical Matters.Jonathan Barnes - 2012 - Clarendon Press.
    This volume presents 27 essays on logic in ancient philosophy by Jonathan Barnes, one of the most admired philosophers of his generation.
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  46. Luca Castagnoli. Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument From Democritus to Augustine.Mary Katrina Krizan - 2011 - Augustinian Studies 42 (2):316-319.
  47. Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument From Democritus to Augustine. By Luca Castagnoli. [REVIEW]Allan Silverman - 2012 - Ancient Philosophy 32 (2):458-461.
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  48. Robert Muller (éd.), Les Mégariques. Fragments et témoignages. [REVIEW]Susanne Bobzien - 1987 - Gnomon 59:648-51.
    ABSTRACT: Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985, with focus on his commentary on ancient paradoxes.
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  49. Alexander of Aphrodisias on Aristotle's Theory of the Stoic Indemonstrables.Susanne Bobzien - 2014 - In M. Lee (ed.), Strategies of Argument: Essays in Ancient Ethics, Epistemology, and Logic. Oxford University Press. pp. 199-227.
    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 (...)
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  50. A Brief Prehistory of Philosophical Paraconsistency.William H. F. Altman - 2010 - Principia: An International Journal of Epistemology 14 (1):1-14.
    Celebrando o papel de Newton da Costa na história da paraconsistência, este trabalho examina o uso e abuso da deliberada auto-contradição. Iniciado por Parmênides, desenvolvido por Platão, e continuado por Cícero, uma antiga tradição filosófica usava deliberadamente discursos paraconsistentes para revelar a verdade. Nos tempos modernos, o decisionismo tem usado uma deliberada auto-contradição contra a revelação Judaico-Cristã. DOI:10.5007/1808-1711.2010v14n1p1.
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