Abstract

The aim of this article is to explain the proofs Aristotle calls proofs "by exposition" and to find out the rules and principles these proofs rest on. The first part shows why previous attempts to explain Aristotle's method of "exposition" have failed. The second part develops a new explanation and reconstructs all of Aristotle's expository proofs on the basis of a few simple rules. The last part shows that the new interpretation of Aristotle's method has very important consequences regarding, firstly, the extent to which Aristotle's logic is valid, secondly, the relationship between syllogistic and geometric exposition and, last but not least, the correct understanding of the principles underlying Aristotle's logical system and the correct understanding of what a "complete" syllogism is. Thus, the article solves a number of fundamental problems concerning the interpretation of Aristotle's syllogistic