Classical Solutions to the Semantic Paradoxes

In the face of semantic paradoxes — the Liar and its ilk — there are two main roads one can take: one can give up naive principles (such as the equivalence between a sentence φ and its truth predication “φ’ is true’), or give up classical logic. Classical approaches choose the former option: they retain classical logic and reject naive semantic principles. In this chapter, I will review the main classical approaches to semantic paradoxes, and the related theories of truth (and other semantic notions). I will present theories of various kinds — typed and type-free, restrictionist and compositional, non-hierarchical and hierarchical — and analyze how they avoid paradox-driven triviality, where they identify the fault with paradoxical reasonings, and to what extent they can recover and account for the inferential and semantic roles that semantic notions play.