Scale-Invariant Structural Realism: Geometric Ontology, Renormalization Universality, and Epistemic Closure

Each major theoretical succession in the history of fundamental physics has replaced a less geometric ontology with a more geometric one: forces give way to curvature, substances to symmetries, spatial containers to abstract geometric structures. We argue that this pattern, combined with the geometric character of current physical theory and the empirical evidence for substrate-independent organization at critical points, supports a specific philosophical position we call geometric realism. The position comprises three claims: that geometric organization is ontologically primary and not merely descriptive; that renormalization group universality provides the mechanism through which geometric organization persists across scales and substrates; and that the correspondence between geometric cognizers and geometric reality is structurally necessary. This epistemic closure argument dissolves the general form of Wigner’s puzzle of the unreasonable effectiveness of mathematics — the correspondence between mathematical models and physical reality — without recourse to the multiverse apparatus required by the Mathematical Universe Hypothesis, while narrowing but not eliminating the residual puzzle of why specific mathematical structures developed as pure formalisms anticipate the particular structures physics later requires. We develop geometric realism as an empirically grounded development of ontic structural realism (Ladyman and Ross 2007), arguing that specifying the relevant structure as geometric and identifying renormalization group universality as the mechanism of its persistence enables philosophical work — including the Wigner dissolution — that generic structural realism cannot perform. We engage the framework’s reflexive limits honestly: its truth status is, on its own terms, epistemically undecidable from within the system it describes, and we derive this undecidability as a consequence of the framework’s commitments rather than stipulating it as a premise.