Logical paradoxes in law application: formal rationality vs principles of justice

The article examines the problem of logical paradoxes arising in legal application processes due to conflicts between the formal rationality of legal norms and principles of justice. The relevance of this research is determined by the increasing complexity of legal systems, the development of analytical jurisprudence, and the necessity to reconsider the boundaries of applying formal-logical approaches in contemporary legal science and practice. A systematic analysis of logical paradoxes embedded in the structure of legal norms and judicial procedures has been conducted to clarify the fundamental limits of formal logic in jurisprudence and theoretically substantiate the need to turn to broader principles of justice when resolving legal conflicts. The research employs methods of formal-logical analysis, structural-functional approach, comparative-legal method, and hermeneutical approach to the interpretation of legal norms and precedents. Classical paradoxes of legal application are analyzed: the paradox of norm self-application (using the example of appellate appeal), the paradox of presumption of innocence in the context of preventive measures, the paradox of limitation periods under conditions of technological progress, and the paradox of fair punishment as a conflict between individualization and equality. Specific manifestations of logical contradictions in international public law are examined, particularly the chronological paradox of customary international law formation and the doctrinal paradox of collegial adjudication in international judicial institutions. The connection between Gödel's incompleteness theorem and legal systems has been confirmed, representing an original authorial contribution to legal epistemology. The application of mathematical logic to the analysis of legal phenomena opens new perspectives for understanding structural limitations of normative systems. The work synthesizes classical works of the positivist school with critical approaches of contemporary research, providing a balanced theoretical foundation. It is proven that logical paradoxes are not technical defects of legal technique, but fundamental characteristics of any complex normative systems, reflecting the principled impossibility of complete formalization of law according to Gödel's incompleteness theorem. It is established that principles of justice function as meta-norms that ensure structural integrity of the legal system under conditions of logical contradictions and allow law to remain a rational instrument of social regulation without being limited exclusively to formal logic.