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  1. An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC.Szymon Chlebowski, Andrzej Gajda & Mariusz Urbański - forthcoming - Studia Logica:1-31.
    The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.
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  2. Lógica modal megárico-estoica: posibilidad y necesidad como operadores atléticos.Jose Alejandro Fernández Cuesta - 2021 - Human 10.
    In this article we introduce a possible way to interpret the possibility and necessity notions developed within the Megaric-Stoic logic as alethic modal operators. Megaric-Stoic semantics will be introduced as metaphysical background for necessity and possibility definitions and arguments will be offered in order to give up the prevailing interpretations which include ad hoc variables. After proposing the survey of diodoric definitions from relational modal semantics, a series of topics that deserve being revisited from this perspective will be pointed out.
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  3. Dialectic After Plato and Aristotle.O. Yu Goncharko - forthcoming - History and Philosophy of Logic:1-6.
    The general content of the book is dedicated to the dialectical practices and their logical tools and techniques developed after Plato and Aristotle within the philosophical schools of the Hellenis...
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  4. Saving the Square of Opposition.Pieter A. M. Seuren - 2021 - History and Philosophy of Logic 42 (1):72-96.
    Contrary to received opinion, the Aristotelian Square of Opposition (square) is logically sound, differing from standard modern predicate logic (SMPL) only in that it restricts the universe U of cognitively constructible situations by banning null predicates, making it less unnatural than SMPL. U-restriction strengthens the logic without making it unsound. It also invites a cognitive approach to logic. Humans are endowed with a cognitive predicate logic (CPL), which checks the process of cognitive modelling (world construal) for consistency. The square is (...)
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  5. Euclid’s Kinds and (Their) Attributes.Benjamin Wilck - 2020 - History of Philosophy & Logical Analysis 23 (2):362-397.
    Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at (...)
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  6. Stoic Logic and Multiple Generality.Susanne Bobzien & Simon Shogry - 2020 - Philosophers' Imprint 20 (31):1-36.
    We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We consider (...)
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  7. Robert König/Lois Marie Rendl (Hgg.), Schlusslogische Letztbegründung: Festschrift für Kurt Walter Zeidler zum 65. Geburtstag, Berlin u. a.: Peter Lang 2020. [REVIEW]Harald Holz - 2020 - Philosophisches Jahrbuch 127 (2):360-363.
    Diese Festschrift umfasst 22 nationale und internationale Beiträge zu Ehren des Jubilars, darunter von solch renommierten Autoren wie Werner Flach, Christian Krijnen, Ulrich Blau, Erhard Oeser, Hans-Dieter Klein, um nur diese zu nennen. – Sie enthält ferner eine Stellungnahme von K. W. Zeidler, wo dieser im Dialog mit den Beiträgern jeweilige kritische Punkte seiner Schlusslogischen Letztbegründung klar zu stellen sich bemüht. – Ein Siglen- und Abkürzungsverzeichnis sowie eine Bibliographie des Jubilars runden die Ausgabe ab. Kurt Walter Zeidler darf als einer (...)
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  8. ON CICERO's FABIUS ARGUMENT.Vladimir Marko - 2020 - Filozofia 75 (8):677 – 692.
    This article aims to show that it is impossible to put Cicero’s testimonies regarding The Fabius Argument in a consistent inferential order. Either we must suppose that additional premises are tacitly assumed in the text or we must com-pare it with other sources, which leads to inconsistencies in the proof’s reconstruction. Cicero’s reconstruction of the progression of the argument has formal shortcomings, and the paper draws attention to some of these deficiencies. He interpreted sources in a revised and intentionally simplified (...)
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  9. Can the Pyrrhonian Sceptic Suspend Belief Regarding Scientific Definitions?Benjamin Wilck - 2020 - History of Philosophy & Logical Analysis 23 (1):253-288.
    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 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 in favour of particular geometrical definitions were absent in ancient geometry, and (...)
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  10. Demonstration and the Indemonstrability of the Stoic Indemonstrables.Susanne Bobzien - 2020 - Phronesis 65 (3):355-378.
    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. Some minor insights into Stoic logic ensue.
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  11. Two Interpretations of Two Stoic Conditionals.Alan Hájek - 2009 - History of Philosophy & Logical Analysis 12 (1):206-221.
    Controversy has surrounded the interpretation of the so-called 'Diodorean' and 'Chrysippean' conditionals of the Stoics. I critically evaluate and reject two interpretations of each of them: as expressing natural laws, and as strict conditionals. In doing so I engage with the work of authors such as Frede, Gould, Hurst, the Kneales, Mates, and Prior. I conclude by offering my own proposal for where these Stoic conditionals should be located on a 'ladder' of logical strength.
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  12. 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 asreductio 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 17th (...)
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  13. 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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  14. 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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  15. 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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  16. Lynn E. Rose. Aristotle's Syllogistic. Charles C. Thomas, Publisher, Springfield, Illinois, 1968, Vii + 149 Pp. [REVIEW]Ivan Boh - 1971 - Journal of Symbolic Logic 36 (4):670-671.
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  17. 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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  18. 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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  19. 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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  20. „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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  21. 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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  22. 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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  23. "Dialectic and Its Place in the Development of Medieval Logic", by Eleanore Stump. [REVIEW]Sheldon M. Cohen - 1992 - Ancient Philosophy 12 (1):199.
  24. Logic, Science and Dialectic: Collected Papers in Greek Philosophy.G. E. L. Owen & Martha Nussbaum - 1987 - Phronesis 32 (2):242-252.
  25. Language, Thought and Falsehood in Ancient Greek Philosophy.Nicholas DENYER - 1991 - Phronesis 36 (3):319-327.
  26. The Logistic Interpretation of Aristotle's Categorical Syllogistic.Charles F. Breslin - 1968 - Proceedings and Addresses of the American Philosophical Association 42:99.
  27. Sophroniscus’ Son is Approaching: Porphyry, Isagoge 7.20–1.Francesco Ademollo - 2004 - Classical Quarterly 54 (1):322-325.
  28. 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.
  29. Aristotle's Syllogistic From the Standpoint of Modern Formal Logic. [REVIEW]Richard Robinson - 1953 - The Classical Review 3 (2):118-119.
  30. Introduzione Alia Logica Stoica. [REVIEW]Jonathan Barnes - 1986 - The Classical Review 36 (1):143-144.
  31. Il Significato Della Logica Stoica. [REVIEW]W. E. W. St G. Charlton - 1968 - The Classical Review 18 (1):119-120.
  32. 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.
  33. The Paradox of Future Truth. [REVIEW]R. W. Sharples - 1987 - The Classical Review 37 (2):217-218.
  34. Galeno: Iniciación a la Dialéctica. [REVIEW]Jonathan Barnes - 1983 - The Classical Review 33 (2):336-337.
  35. Aristotle's Syllogistic From the Standpoint of Modern Formal Logic. [REVIEW]Richard Robinson - 1958 - The Classical Review 8 (3-4):282-282.
  36. La Logica Stoica: Testimonianze E Frammenti – Testi Originali Con Introduzione E Traduzione Commentata. [REVIEW]Jonathan Barnes - 1988 - The Classical Review 38 (2):426-427.
  37. 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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  38. Aristotle on Hypothetical Arguments and the Completeness of the Syllogistic.Tal Glezer - 2007 - Ancient Philosophy 27 (2):323-334.
  39. Restoring Olympiodorus’ Syllogistic.Harold Tarrant - 1997 - Ancient Philosophy 17 (2):411-424.
  40. 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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  41. 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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  42. 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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  43. The Stoics on Ambiguity. [REVIEW]David Blank & Catherine Atherton - 1995 - Philosophical Review 104 (2):267.
  44. 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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  45. The Stoic Doctrine of Generic and Specific Pathē.Robert J. Rabel - 1977 - Apeiron 11 (1):40 - 42.
  46. Apuleius and the Square of Opposition.Carmen Johanson & David Londey - 1984 - Phronesis 29 (2):165-173.
  47. 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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  48. 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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  49. A Companion to Philosophical Logic.Dale Jacquette (ed.) - 2002 - Malden, MA, USA: 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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  50. 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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