Tarski's Definition of Truth

Abstract This chapter provides a detailed explanation of Tarski's definition of truth for formalized languages. It begins by indicating how he conceived the problem, how his criterion of adequacy guarantees that any definition satisfying it introduces a predicate that applies to all and only object‐language truths, and how he approached the technical problem of formulating a definition that would allow him to derive what he regarded as a “partial definition” of truth for each sentence of the object language. Next, the formal techniques employed in his inductive definitions are explained, along with the method of turning those definitions into explicit definitions (where possible), and the way in which his definitions can be shown to be materially adequate. The explication concludes with a discussion of the relationship between truth and proof in the language of arithmetic, and the outlines of Tarski's theorem of the arithmetic indefinability of arithmetical truth.