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.
Publisher
Cambridge University Press (CUP)
Subject
Logic,Philosophy,Mathematics (miscellaneous)