The paradoxicality of Curry
Fatima Scha

Abstract:
Curry’s paradox is a peculiar paradox for at least two reasons: it is largely left out by common definitions of paradoxicality and it challenges paraconsistent solutions to the paradoxes because it can persist in a paraconsistent system. In this thesis, we study the dynamics of this paradox by adapting Kripke’s definition of paradoxicality (Kripke, 1975) and a definition of paradoxicality introduced by Hsiung (2024) such that they include more of Curry’s paradox. We moreover explore the possibility of a notion of paradoxicality that can distinguish Curry’s paradox from other paradoxes like the Liar, by embedding the definition in a paraconsistent logic. The result is an overview of different formal characterisations of paradoxicality, that capture Curry’s paradox and its relatives to various degrees.