Aristotle's underlying logic

Abstract

This chapter presents Aristotle's system of logic while also revealing the mathematical sophistication of his logical investigations. Modern logicians believe that the possibility of mathematical logic, an important part of which involves generating models, consists in making a clear distinction between syntax and semantics. They also believe that the clear distinction between syntax and semantics resulted from borrowing symbolic notations from mathematical practice and then applying them to the studies of deductive logics, but the earlier thinkers, lacking such notations could not have made such distinctions. The chapter provides Aristotle's underlying logic much as he himself did in the works of the Organon. It is natural and not surprising that modern logicians and commentators, when treating Aristotle's logic, focus principally on prior analytics: Prior Analytics is the most “logical” of the treatises. The chapter describes the statement of his understandings of “formal deducibility” and “logical consequence” and summarizes the four proof-theoretic accomplishments of his logical investigations.