Finite Continuity: A Recursive Three-Layer Model of Systemic Persistence Under Erosional Pressure

Abstract This paper proposes a systematic three-layer model for understanding how cognitive, interpretive, and ontological systems persist under conditions of structural decay. Challenging classical frameworks that dichotomize stability and chaos, we introduce the concept of finite continuity—the regulated continuation of a system through, rather than in the absence of, failure. The model operates across three interdependent layers: (1) Ontology, where the world is conceptualized as a field of continuous erosion, bounded by thresholds of sufficiency; (2) Epistemology, where knowledge is redefined not as correspondence with reality, but as the management of cognitive failures (R_1, R_2, R_3) within a finite framework of hermeneutic friction (FFH); and (3) Hermeneutics, where meaning emerges from resistance, not from its removal. Drawing on Heidegger's Being and Time (1927/1962), Foucault's archaeology of knowledge (1969/1972), Quine's underdetermination thesis (1951, 1960), and recent work in systems theory (Luhmann, 1995), we argue that finite continuity constitutes the general form of systemic survival. The model's originality lies in its recursive structure: hermeneutic outcomes feed back into ontological conditions, reshaping the very thresholds that define systemic endurance. This is formalized as T_s(t+1) = \mathcal{F}(T_s(t), M(t), E(t+1)), capturing the dynamic co-evolution of interpretive history and ontological conditions. The framework offers substantive implications for philosophy of science (paradigm resilience), political theory (institutional survival), and normative ethics (ethics beyond principles), by reframing crisis as the normative condition of intelligibility rather than its exception. Finite continuity, we conclude, is neither tragic resignation nor triumphalist mastery; it is the dignified form of persistence in a world that never ceases to undo itself. Keywords: Finite Continuity; Erosional Ontology; Hermeneutic Friction; Epistemological Failure; Systemic Persistence; Recursive Model; Threshold Dynamics; Pragmatic Fallibilism; Interpretive Resistance; Scientific Paradigm Resilience