ARISTOTE ET LA QUESTION DE LA COMPLETUDE Le modèle formel de Kurt Ebbinghaus

Abstract : With the article " Aristotle's natural deduction system " , published in 1974, J. Corcoran has contributed to spread a new insight into Aristotelian logical writings and of the theory of assertoric syllogism in particular. The main claim of this article is that, in the first chapters of the Analytic prior, Aristotle doesn't expose an axiomatic system that would suppose an underlying logic, as thought Łukasiewicz, but a natural deduction system, with metalogical dimensions. Our paper is based on the work of Kurt Ebbinghaus, called " Ein formales Model der Syllogistik des Aristoteles " (1964), which set a landmark for the new insight mentioned above and that was developed within the conceptual framework of Paul Lorenzen's " operative logic ". Ebbinghaus develops a formal reconstruction that shows that Aristotle's perspective is a proof-theoretical one, not only in relation to the underlying inference system but in relation to the study of its metalogical features. The latter indicates a main distinction to Corcoran's own reconstruction. Indeed, while Corcoran's assumes that Aristotle's inferential systems is rooted on an underlying model-theoretical semantics (worked by Corcoran himself), Ebbinghaus understands the theory of syllogisms has been developed under the background of a " rule-based " approach to meaning similar to " game rules. In fact, Ebbinghaus' reconstruction proposes a pragmatist reading of Aristotle's syllogistic, that, so we claim, not only seems to be definitely closer to Aristotle's views, than the model-theoretical semantics developed by Corcoran, but it also yields the theory of syllogism as a unified system.
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Clément Lion, Shahid Rahman. ARISTOTE ET LA QUESTION DE LA COMPLETUDE Le modèle formel de Kurt Ebbinghaus. 2016. ⟨halshs-01399594⟩

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