Aristotle’s Syllogistic as a Deductive System

Abstract

Aristotle’s syllogistic is the first ever deductive system. After centuries, Aristotle’s ideas are still interesting for logicians who develop Aristotle’s work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz’s reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson.

A Formal Analysis of Generalized Peterson’s Syllogisms Related to Graded Peterson’s Cube

“…The theory of syllogistic reasoning was investigated by several authors as a generalization of classical Aristotelian syllogisms ( [1][2][3]). Categorical syllogisms ( [4,5]) consist of three main parts: the major premise, the minor premise, and the conclusion.…”