Strong Homomorphisms, Category Theory, And Semantic Paradox

In 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: Strong-homomorphisms. In particular, we show that (i) strong-homomorphisms between constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of constructions can be recast as special cases of our central result regarding strong-homomorphisms, and (iii) that we can use strong-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-homomorphisms highlight novel connections between the graph-theoretic analyses of paradoxes mobilized in the framework and the methods and tools of category theory.