Paradoxes and the Structural Limits of Conceptual Frameworks in Science : Toward a Structural Theory of Paradox Formation .

Paradoxes have played a central role in the development of logic, mathematics, physics, and philosophy. They are often interpreted as contradictions either within reasoning or within the structure of reality itself. This article proposes a unified structural interpretation of paradox formation. It argues that many paradoxes arise when the conceptual frameworks used to describe phenomena reach the limits of their descriptive capacity. From this perspective, paradoxes are not anomalies of nature but boundary phenomena of conceptual systems. They emerge when the inferential power of a framework exceeds its capacity to represent the structure of the phenomena it attempts to describe. The article develops a structural taxonomy of paradoxes and introduces a conceptual principle according to which paradox formation occurs when logical propagation within a framework exceeds its descriptive capacity. It further proposes geometrical and informational interpretations of paradox emergence and discusses connections with self-reference, fixed-point constructions in logic, and informational limits in scientific description. Across disciplines, paradoxes may therefore function as epistemic indicators of conceptual transitions. Rather than obstacles to scientific progress, they mark the points where existing frameworks reach their limits and where conceptual reorganization becomes necessary. In addition to the main article, this record includes a French text presenting a philosophical synthesis of the work. The English article provides the full theoretical development, whereas the French version offers a shorter conceptual exposition intended for dissemination among French-speaking audiences.