Truth is Simple

John Burgess published a paper with the title ‘The Truth is Never Simple’ (Burgess 1986). What he meant was that the extension of the truth predicate in a typed, and even more so in a type-free approach, is complicated. This cannot be disputed. But we argue that the intension of the truth predicate is simple, in the sense that the content of the concept of truth is given by a simple and natural collection of truth-biconditionals. In other words, we claim that some form of disquotationalism must be in some sense correct. From a logical point of view, this takes us to the area of proof-theoretic approaches to truth, and away from the area of modeltheoretic approaches to truth, which was the focus of Burgess (1986). Arguments by Shapiro (1998) and Ketland (1999), based on observations by Tarski, have shown that certain standard formulations of disquotationalism are untenable. The fact that truth is compositional cannot be fully accounted for by disquotational axioms alone. Moreover, disquotational principles alone do not seem to do justice to the role that truth plays in metamathematical reasoning. In particular, compositional truth principles can be used to show that