Tarski as Intuitionistic Formalist

Abstract

Accepting the basics of Intuitionistic Formalism, Tarski sought to extend it. In particular, inspired perhaps by Leśniewski’s steps toward formalized syntax [Leśniewski, 1929], [Leśniewski, 1992e], Tarski began to look at the issues that arose when one’s discourse about a deductive theory was itself expressed in a deductive theory. This is the sort of project that would have attracted an ambitious young contributor: investigate whether the going view among his teachers about “metamathematics” could handle metamathematical concepts themselves. His first published contributions to this project were several papers on axioms for the consequence relation. We will look at those works in order to see the beginning of Tarski’s project. After that we will look at his most extensive contribution to the general project, “Some Methodological Investigations on the Definability of Concepts”, which collects work from 1926 and 1932.