In Chapter 2 we saw that, under pressure from several constraints, a compositional theory of truth emerges as the leading candidate for supplying the outline for a theory of meaning. We continue our discussion of truth and meaning in this chapter, focusing on Alfred Tarski's groundbreaking work on semantics as the model for compositional truth theories and on Davidson's discussion of the applicability of Tarski's work to natural languages.

Tarski's theory of truth

As a mathematician and logician, Tarski's focus is somewhat specialized, at least considered from our current vantage point in the philosophy of language. He is especially interested in the semantic paradoxes (e.g. the liar paradox: “This sentence is false”) and also in the relation between the set of sentences of a specified formal language that are true and the set of sentences belonging to the language that can be proved. (Intuitively, these two classes should bear some close relation to one another.) Tarski's results are of considerable importance to mathematical logicians; one of those results is that while we can define the metalogical concept of being provable in L (i.e. being provableL) in the language L itself, we cannot, on pain of contradiction, define in L the concept of being trueL. Hence the concepts of being provableL and being trueL, although closely allied in some way, are not equivalent.

In the course of his work, Tarski applies mathematical logical methods to the concept of truth, and he shows how to construct a compositional truth theory for a formal language.