New Insights on Syllogistic and Cut

Abstract

There is a quite intentional resemblance between the Cut Rule and Aristotle’s Syllogism. In this paper some deep connections between Sequent Calculus and Syllogistics will be investigated. Taking into consideration Alvarez & Correia’s ´axiomatization of Syllogistics, currently the most complete available in the literature, I will show how this ancient logical system can be put into correspondence with the structural features of a special Sequent Calculus system, SS. On the grounds of this discovery I will present some improvements of the expressive power of Alvarez & Correia’s system. As for the philosophical consequences of ´the correspondence, I will give answers to several concerns Manuel Correia had on his system. A somewhat new philosophical relevance of the Cut-Elimination Theorem will be highlighted in the end.