Deflationism and the Godel Phenomena

Abstract

Any (1‐) consistent and sufficiently strong system of first‐order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first‐order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non‐trivial fashion. The extended methods of formal proof must capture the essentials of the so‐called ‘semantical argument’ for the truth of the Gödel sentence. We are concerned to show that the deflationist has at his disposal such extended methods—methods which make no use or mention of a truth‐predicate. This consideration leads us to reassess arguments recently advanced—one by Shapiro and another by Ketland—against the deflationist's account of truth. Their main point of agreement is this: they both adduce the Gödel phenomena as motivating a ‘thick’ notion of truth, rather than the deflationist's ‘thin’ notion. But the so‐called ‘semantical argument’, which appears to involve a ‘thick’ notion of truth, does not really have to be semantical at all. It is, rather, a reflective argument. And the reflections upon a system that are contained therein are deflationarily licit, expressible without explicit use or mention of a truth‐predicate. Thus it would appear that this anti‐deflationist objection fails to establish that there has to be more to truth than mere conformity to the disquotational T‐schema.