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  1. A Mereological Reading of the Dictum de Omni et Nullo.Phil Corkum - forthcoming - Archiv für Geschichte der Philosophie.
    When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates the (...)
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  • The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics.Marko Malink - 2015 - Phronesis 60 (3):267-309.
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  • The Arithmetical dictum.Paolo Maffezioli & Riccardo Zanichelli - 2023 - History and Philosophy of Logic 44 (4):373-394.
    Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the relation of divisibility on positive integers. The adequacy of this interpretation, labeled here ‘arithmetical dictum’, is assessed both theoretically and textually with respect to the existing interpretations, especially the so-called ‘mereological dictum’.
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  • What Is a Perfect Syllogism in Aristotelian Syllogistic?Theodor Ebert - 2015 - Ancient Philosophy 35 (2):351-374.
    The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status over the (...)
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  • Dialectic, the Dictum de Omni and Ecthesis.Michel Crubellier, Mathieu Marion, Zoe Mcconaughey & Shahid Rahman - 2019 - History and Philosophy of Logic 40 (3):207-233.
    In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...)
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