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  1. 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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  • 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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  • Paradoxical Versus Modulated Conditional Inferences: An Explanation From the Stoicism.Miguel López-Astorga - 2016 - Manuscrito 39 (1):61-72.
    According to standard propositional logic, the inferences in which the conditional introduction rule is used are absolutely correct. However, people do not always accept inferences of that kind. Orenes and Johnson-Laird carried out interesting experiments in this way and, based on the general framework of the mental models theory, explained clearly in which cases and under which circumstances such inferences are accepted and rejected. The goals of this paper are both to better understand some aspects of Stoic logic and to (...)
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  • Themes in Plato, Aristotle, and Hellenistic Philosophy, Keeling Lectures 2011-2018, OPEN ACCESS.Fiona Leigh (ed.) - 2021 - University of Chicago Press.
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  • From Figure to Argument: Contrarium in Roman Rhetoric. [REVIEW]Manfred Kraus - 2007 - Argumentation 21 (1):3-19.
    In Roman rhetoric, contrarium was variably considered either a figure of speech or an argument. The paper examines the logical pattern of this type of argument, which according to Cicero is based on a third Stoic indemonstrable syllogism: $$ \neg ({\hbox{p}} \wedge {\hbox{q}});<$> <$>{\hbox{p}} \to \neg {\hbox{q}}{\hbox{.}} $$ The persuasiveness of this type of argument, however, vitally depends on the validity of the alleged ‹incompatibility’ forming its major premiss. Yet this appears to be the argument’s weak point, as the ‹incompatibilities’ (...)
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  • From Aristotle's Syllogistic to Stoic Conditionals: Holzwege or Detectable Paths?Mauro Nasti De Vincentis - 2004 - Topoi 23 (1):113-137.
    This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle's syllogistic and the Stoic doctrine of conditionals, notably between Aristotle's metasyllogistic equimodality condition and truth-conditions for third type conditionals. In fact, as is shown in §1, Aristotle's condition amounts to introducing in his metasyllogistic a non-truthfunctional implicational arrow '', the truth-conditions of which turn out to be logically equivalent to truth-conditions of third type conditionals, according to which only the impossible follows from the (...)
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  • 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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  • 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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  • Chrysippus’ Indemonstrables and the Semantic Mental Models.Miguel López-Astorga - 2017 - Eidos: Revista de Filosofía de la Universidad Del Norte 26:302-325.
    Resumen Atendiendo a la lógica estándar, solo uno de los cinco indemostrables propuestos por Crisipo de Solos es realmente indemostrable. Sus otros cuatro esquemas son demostrables en tal lógica. La pregunta, por tanto, es: si cuatro de ellos no son verdaderamente indemostrables, por qué Crisipo consideró que sí lo eran. López-Astorga mostró que si ignoramos el cálculo proposicional estándar y asumimos que una teoría cognitiva contemporánea, la teoría de la lógica mental, describe correctamente el razonamiento humano, se puede entender por (...)
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  • The Peculiarities of Stoic Propositional Logic.David Hitchcock - 2005 - In John Woods, Kent A. Peacock & A. D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods. University of Toronto Press. pp. 224--242.
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  • Ancient Logic.Susanne Bobzien - 2006 - In Stanford Encyclopedia of Philosophy.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...)
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  • 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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  • Indirect Proof and Inversions of Syllogisms.Roy Dyckhoff - 2019 - Bulletin of Symbolic Logic 25 (2):196-207.
    By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.
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  • ΑΝΑΛΥΣΙΣ ΠΕΡΙ ΤΑ ΣΧΗΜΑΤΑ Restoring Aristotle’s Lost Diagrams of the Syllogistic Figures.Marian Wesoły - 2012 - Peitho 3 (1):83-114.
    The article examines the relevance of Aristotle’s analysis that concerns the syllogistic figures. On the assumption that Aristotle’s analytics was inspired by the method of geometric analysis, we show how Aristotle used the three terms, when he formulated the three syllogistic figures. So far it has not been appropriately recognized that the three terms — the major, the middle and the minor one — were viewed by Aristotle syntactically and predicatively in the form of diagrams. Many scholars have misunderstood Aristotle (...)
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  • Some Sketchy Notes on the Reaper Argument.Vladimir Marko - 2012 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 19 (3):361-387.
    The paper deals with the possible readings of The Reaper Argument premisses. Some conjectures related to the Stoics’ alleged proof of the argument are discussed.
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  • Arguing by Question: A Toulminian Reading of Cicero’s Account of the Enthymeme.Manfred Kraus - unknown
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  • The First Rule of Stoic Logic and its Relationship with the Indemonstrables.Miguel López Astorga - 2016 - Tópicos: Revista de Filosofía 50:9-23.
    Además de los indemostrables, la lógica estoica incluye varias reglas de reducción. En este trabajo, analizo la primera de ellas con el fin de comprobar si fue derivada formalmente a partir de los indemostrables o los estoicos pudieron plantearla a partir del uso de sus capacidades naturales de razonamiento. De esta manera, trato de mostrar que tenemos razones para apoyar ambas posibilidades y, basándome en un enfoque semántico como el de la teoría de los modelos mentales, de ofrecer argumentos al (...)
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  • Apie Sąsajas Tarp Indijos Ir Stoikų Logikos.Miguel López-Astorgas - 2016 - Problemos 90:137-143.
    Šiuo straipsniu mėginama parodyti, jog Indijos ir stoikų logika yra panašesnės viena į kitą nei į standartinę logiką. Šiuo tikslu analizuojama ištrauka iš Kathāvatthu, kurioje pateikiamas sąlyginio teiginio apibrėžimas dažnai interpretuojamas kaip atitinkantis modernioje teiginių logikoje vartojamą materialiosios implikacijos sampratą. Teigiama, jog tokia interpretacija nėra visiškai pagrįsta. Todėl daroma išvada, jog tai, kas iš tiesų sakoma aptariamoje ištraukoje, nuosekliai susiję su Chrisipo Soliečio pasiūlytu sąlyginio teiginio teisingumo kriterijumi.
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  • Alexander of Aphrodisias and the Problem of Instrumentality 'of Logic. Notes on in A. Pr. 2, 22-33'.Ricardo Salles - 2009 - Estudios de Filosofía (Universidad de Antioquia) 40:223-243.
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