Paradox as Structural Feature: A Coupling-Dynamics Account of Self-Referential Systems

This paper argues that paradoxes of self-reference — paradigmatically the liar and Russell's paradox — are the limit case of a coupling-dynamics mechanism that operates throughout the coupling spectrum between assessment channels and the systems they assess. Under this account, paradox is not a failure of reasoning but the specific dynamical signature of total self-referential coupling: a fold catastrophe in which the hysteresis distance between attractors has collapsed, producing oscillation rather than stable contradiction. The paper applies the coupling-dynamics framework developed in a companion paper to derive the central result: three of the framework's five structural axioms specify local features of a paradoxical configuration, and successful coupling-reduction interventions therefore fall into exactly three structurally distinct classes corresponding to these three axiomatic loci. Class I (architectural restriction): Russell's type theory, Tarski's hierarchy, ZF's restricted comprehension. Class II (grounding dissolution): Kripke's fixed-point construction. Class III (inferential loosening): the substructural approaches of Ripley, Zardini, Mares and Paoli, and French. Dialetheism — which accepts the coupling configuration and modifies only the consequence relation — is not a coupling-reduction intervention of any kind, and therefore occupies a structurally distinct position outside the taxonomy. Gödel's incompleteness theorem is read, on a Shapiro-template treatment, as the formal signature of the cusp regime for Gödel-sufficient systems. This paper is part of the Coupling Geometry research programme. The framework's axiomatic foundation is presented in a companion paper: https://doi.org/10.5281/zenodo.20137424. Manuscript under review at Philosophical Logic.