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Communication dans un congrès Année : 2022

The dialogical syllogistic: formalizing Aristotle’s logic in the dialogical framework

Résumé

Using the dialogical framework of Lorenzen and Lorenz, I will present a pragmatic, interaction-based reconstruction of Aristotle’s assertoric syllogistic that can express, syllogisms, ecthesis, direct and indirect deductions, reductions and the inconclusive moods. The dialogical framework enables to explicit the underlying dialogical context of the practice of dialectical debates, and, coupled to the notation of Per Martin-Löf’s Constructive type theory to yield the dialogical variant Immanent Reasoning (Rahman et al.), the reconstruction reveals how the meaning of Aristotle’s quantification is based on a dialogical, no-counterobjection interpretation of the dictum de omni et de nullo (Marion and Rückert, Crubellier et al). The result is a powerful formal tool capable of expressing all of Aristotle’s assertoric syllogistic in a dialogical framework. References: • Michel Crubellier, Mathieu Marion, Zoe McConaughey & Shahid Rahman (2019) Dialectic, the Dictum de Omni and Ecthesis, History and Philosophy of Logic, 40:3, 207-233, DOI: 10.1080/01445340.2019.1586623 • Lorenzen, Paul and Kuno Lorenz, 1978, Dialogische Logik, Darmstadt: Wissenschaftliche Buchgesellschaft. • Marion, Mathieu and Helge Rückert, 2016, “Aristotle on Universal Quantification: A Study from the Point of View of Game Semantics”, History and Philosophy of Logic, 37(3): 201–229. doi:10.1080/01445340.2015.1089043 • Martin-Löf, Per, 1984, Intuitionistic Type Theory. Notes by Giovanni Sambin of a Series of Lectures given in Padua, June 1980, Naples: Bibliopolis. • Rahman, Shahid, Zoe McConaughey, Ansten Klev, and Nicolas Clerbout, 2018, Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level, (Logic, Argumentation & Reasoning 18), Cham: Springer International Publishing. doi:10.1007/978-3-319-91149-6
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halshs-04390769, version 1 (12-01-2024)

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  • HAL Id : halshs-04390769 , version 1

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Zoe Mcconaughey. The dialogical syllogistic: formalizing Aristotle’s logic in the dialogical framework. UNILOG, Jean-Yves Beziau, Apr 2022, Chania Crète, Greece. ⟨halshs-04390769⟩
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Dernière date de mise à jour le 28/04/2024
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