The Expressive Power of Contextualist Truth

Abstract

The truth predicate is often argued to be naïve, in the sense that a sentence φ and its truth ascription ‘φ is true’ are in some sense equivalent (in all non-opaque contexts). A relatively weak form of naïveté requires the truth predicate to obey introduction and elimination rules to the effect that φ and ‘φ is true’ are interderivable (from possibly open assumptions). It has been forcefully argued that naïveté is required in order to account for crucial and non-eliminable uses of the truth predicate, notably blind ascriptions (such as ‘Everything Lois says is true’), infinitary generalizations (such as ‘All theorems of Peano Arithmetic are true’), and their combinations (Field, 2008; Beall, 2009; Horsten, 2012). Call this argument the Argument for Naïveté. Since naïveté is incompatible with classical logic (given a modicum of syntax theory), the argument can be taken to establish that, in order to fulfill its expressive role, the truth predicate requires a suitable non-classical logic. This chapter analyses the Argument for Naïveté, and argues that it is fundamentally misguided. It is then shown that some contextualist theories of truth, despite being fully classical, feature expressively adequate, contextshifting versions of the naïve truth introduction and elimination rules that are strong enough to validate arguments involving blind ascriptions and infinitary generalizations and yet weak enough to avoid paradox-driven triviality.