The geometry of diagrams and the logic of syllogisms

Abstract

Aristotle accounts for three figures on which syllogisms are formed. On the first figure it is possible to prove the completeness of all of the possible syllogisms. But on the second and on the third figures completion is not possible, therefore, premises based on the second or on the third figure are converted in such a way as to count as premises on the first figure. Aristotle's procedure leads to difficulties discussed and corrected in the course of this paper.