A Kantian inquiry into the cognitive origins of logical and semantic paradoxes

Abstract The article aims to uncover the underlying cognitive foundations of the logical and semantic paradoxes. It is divided into two sections. The first part explores the cognitive and logical dimensions to unravel the reasons behind our vulnerability to paradoxes. By focusing on two established triggers—allowing excessively large sets in a system and resorting to impredicative definitions—it is argued that Kant’s insights into reason’s pursuit of unity and an unconditioned condition shed light on paradoxes arising from treating too large multiplicities as sets. Concerning impredicative definitions, it is argued that Kant’s analysis of the qualitative negation of qualities explains why pseudo-sets resulting from such definitions are not representable thought entities. Drawing on Kantian insights, this section reinterprets Cantor’s distinction between completed sets and inconsistent multiplicities and examines two famous solutions: Zermelo’s axiom schema of separation and von Neumann’s nonset class V. The second part contends that Kantian diagnoses are relevant to both logical and semantic paradoxes, elucidating the structures of sample paradoxes for each type. The Burali-Forti paradox and Russell’s paradox are examined as logical paradoxes, which result in pseudo-sets, illustrating Kant’s concept of nihil negativum—the empty object without a concept. The semantic paradoxes considered are Grelling’s and Berry’s paradoxes, whereby how self-reference and the use of nonapplicable predicates contribute to their paradoxical nature are explained. The study concludes by asserting that while current solutions effectively address paradoxes, additional support is needed in their cognitive dimensions, or areas where Kant’s epistemology provides profound insights.