A Disquotational Theory of Truth as Strong as Z 2 − $Z_{2}^{-}$

Abstract

T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s (1935) observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee (1992), the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors (e.g. Glanzberg (2005)) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus spelling doom to deflationist and minimalist truth theories in particular. The situation is indeed worrisome as formal theories of minimalist truth are (almost) missing so far. This makes it very hard to properly evaluate the tenets of minimalism. In the present article, we will show how to find safe instances of the T-schema just by relying on syntactic features of the sentences of our language—in particular, we will explore Quine’s (1937) idea of stratification. Based on that, we will introduce some disquotational truth theories that are deductively very strong.