Title:
Towards non-classical deflationism
Abstract:
Although non-classical theories of truth have drawn considerable attention from logicians and philosophers, discussions of deflationism in the context of axiomatic theories of truth have mostly been confined to classical compositional truth. In this talk, I challenge this assumption and argue that classical compositional truth cannot be used as a formal rendering of deflationist claims. Specifically, it cannot distinguish between essential properties of truth, such as compositionality, and contingent properties of the truth predicate inherited from its ambient theoretical framework. I argue that this collapse of the essential/inessential distinction is fatal for the deflationist.
I draw on recent developments in axiomatic theories of truth, showing the equivalence between generalized compositional principles and induction principles (Enayat & Pakhomov 2019). I generalize these results to the case of untyped classical truth. By contrast, we show that the equivalence does not hold in a theory of non-classical truth axiomatizing Kripke’s fixed-point construction.
I conclude the talk with a discussion of the prospects of non-classical deflationism and the challenges this position would need to overcome.