Notes oN the FouNdiNg oF Logics aNd MetaLogic: aristotLe, BooLe, aNd tarski

This paper is more a series of notes than a scholarly treatise. It focuses on certain achieve‐ ments of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed intending to broaden and to justify Aristotle’s, and giving a modern perspective to both logics. Choice of these three logicians has other advantages. In history of logic, Aristotle is the best representative of the earliest period, Boole the best of the transitional period, and Tarski the best of the most recent period. In philosophy of logic, all three were amazingly successful in having their ideas incorporated into mainstream logical theory. This last fact makes them hard to describe to a modern logician who must be continually reminded that many of the concepts, principles, and methods that are taken to be “natural” or “intuitive” today were all at one time discoveries.