by Neil Tennant
Any omega-consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Goedel-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 Godel-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 Godel-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 an objection recently raised by Shapiro and by Ketland against the deflationist's account of truth. They both adduce the Godel-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.