The Paradox Boundary Principle: Conceptual Instability in Scientific Frameworks.

This article proposes a structural interpretation of paradox formation across different domains of knowledge. Paradoxes appear in logic, mathematics, physics, semantics, and complex systems. They are often treated as isolated conceptual puzzles specific to each discipline. This work suggests a different perspective: paradoxes may arise from a common structural condition affecting conceptual frameworks themselves. The central idea introduced in this paper is the Paradox Boundary Principle. According to this principle, paradoxes emerge when the inferential reach of a conceptual framework exceeds its descriptive capacity. In such situations, the framework becomes capable of generating inferences about structures that it cannot coherently represent within its own descriptive resources. The article develops this idea by: formalizing conceptual frameworks in terms of descriptive capacity and inferential power, identifying paradoxes as boundary phenomena of conceptual systems, connecting paradox formation to fixed-point constructions in logic, proposing an information-theoretic interpretation of conceptual instability, examining examples across logic, physics, and complex systems. Under this perspective, paradoxes should not be interpreted primarily as contradictions in reality. Rather, they function as structural indicators of conceptual limits and as signals of transitions between scientific frameworks. The Paradox Boundary Principle therefore offers a unified way to interpret paradoxes as boundary phenomena in the evolution of knowledge.