Negative Self-Reference in Legal Norms, Logic, and Epistemology

Abstract

Introduction. The article examines the problem of negative self-reference in legal norms, logic, and epistemology, which creates fundamental vulnerabilities in social and formal systems (e.g., the paradox of the self-repealing of the basic law, Russell's and Gödel's paradoxes). These vulnerabilities can be exploited against the interests of society, which emphasizes the practical significance of finding ways to eliminate them. Methods. The study was conducted using a complex of theoretical methods, including logico-semantic analysis, the method of formalization, and the axiomatic method. A key element was the method of critical analysis applied to the revision of Cantor's diagonal method. The materials included works by Cantor, Russell, Whitehead, Gödel, Wittgenstein, and contemporary authors on the digitalization of law. Results. The work identifies a vulnerability in Cantor's proof of the existence of uncountably infinite sets. This challenges the established scientific paradigm and removes the fundamental restriction imposed by Gödel's theorems on the completeness of higher-order predicate calculi. Conclusion. The findings reveal a theoretical possibility for the syntactic isolation and elimination of negative self-references in semantic constructions, including legal norms. This allows for the creation of more reliable, complete, and paradox-proof legal and management systems.