# A Mathematical Model of Aristotle’s Syllogistic

*Archiv für Geschichte der Philosophie*55 (2):191-219 (1973)

**Abstract**

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct
a mathematical model which reflects certain structural aspects of
Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics.
Our interpretation restores Aristotle's reputation as a logician of
consummate imagination and skill. Several attributions of shortcomings
and logical errors to Aristotle are shown to be without merit. Aristotle's
logic is found to be self-sufficient in several senses: his
theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible.

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Archival date: 2014-11-07

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Citations of this work BETA

The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 -

*History and Philosophy of Logic*32 (4):359 - 374.A Brief History of Natural Deduction.Pelletier, Francis Jeffry

Indirect Proof and Inversions of Syllogisms.Dyckhoff, Roy

Was Ist Ein Vollkommener Syllogismus des Aristoteles?Ebert, Theodor

Aristotle on Universal Quantification: A Study From the Point of View of Game Semantics.Marion, M. & Rückert, H.

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