STRONG HOMOMORPHISMS, CATEGORY THEORY, AND SEMANTIC PARADOX

Abstract

AbstractIn this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox$\mathcal {L}_{\mathsf {P}}$: strong$\mathcal {L}_{\mathsf {P}}$-homomorphisms. In particular, we show that (i) strong$\mathcal {L}_{\mathsf {P}}$-homomorphisms between$\mathcal {L}_{\mathsf {P}}$constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of$\mathcal {L}_{\mathsf {P}}$constructions can be recast as special cases of our central result regarding strong$\mathcal {L}_{\mathsf {P}}$-homomorphisms, and (iii) that we can use strong$\mathcal {L}_{\mathsf { P}}$-homomorphisms to provide a simple demonstration of the paradoxical nature of a well-known paradox that has not received much attention in this context: the McGee paradox. In addition, along the way we will highlight how strong$\mathcal {L}_{\mathsf {P}}$-homomorphisms highlight novel connections between the graph-theoretic analyses of paradoxes mobilized in the$\mathcal {L}_{\mathsf {P}}$framework and the methods and tools of category theory.