Platonic Division and the Origins of Aristotelian Logic

Dissertation, University of California, Berkeley (2017)

Abstract

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic.

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Justin Vlasits
University of Illinois, Chicago

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A Bitstring Semantics for Calculus CL.Fabien Schang & Jens Lemanski - 2022 - In Ioannis M. Vandoulakis & Jean-Yves Beziau (eds.), The Exoteric Square of Opposition. Cham: Springer. pp. 171–193.

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