Shifts as Fixed Points of Self-Referential Systems: A Formal-Structural Framework for Analyzing Scientific Revolutions

This paper proposes a formal-structural framework for understanding scientific paradigm shifts that extends Kuhn's classical analysis. We argue that paradigms can be understood as stable fixed points of self-referential processes of distinction-making. Paradigm shifts, correspondingly, are fixed-point displacements occurring when repairs at lower structural levels no longer suffice to maintain stability. Drawing on Spencer-Brown's calculus of distinctions, we derive four hierarchical levels at which paradigmatic stability operates (implicit distinctions, categories, relevance structures, and logic) and define a systematic set of transformation operators that characterize transitions between paradigms. A crucial feature of the model is its requirement of self-application: an adequate model of paradigm shifts must structurally generate and explicitly mark its own blind spots. We demonstrate the framework's diagnostic power through application to two case studies—the Newton-Einstein transition and the classical-to-quantum transition—and perform a rigorous self-application that reveals the framework's necessary limitations while demonstrating its internal coherence as a fixed point of its own descriptive apparatus.