T-schema deflationism versus Godel's first incompleteness theorem

Abstract

where an instance is the result of writing some sentence of our language in place of 'p' in both places. Call this T-schema deflationism. An immediate objection to T-schema deflationism, as here defined, is that many of the sentences we put in place of 'p' in (T) may be neither true nor false apart from some context of utterance, so that (T) just cannot be the correct scheme for the articulation of the truth conditions of sentences. Still, I think it is worthwhile to consider whether there is any other objection to T-schema deflationism. Let us imagine that our language is one in which every sentence is either true or false or neither absolutely. If Tschema deflationism is objectionable even for such a language, then we may find that any more realistic form of deflationism is objectionable in the same way. T-scheme deflationism, as here defined, is an explicitly vague idea, since it says only that certain instances of (T) comprise a theory of truth for our language and does not say exactly which instances comprise the theory. It is clear that a theory of truth for our language cannot contain all instances of (T), because many instances are liable to be plainly untrue. For instance, suppose our language contains the following sentence: