Statistical Quasi-Equivalence Improved with LLMs: Language as Ontological Leverage in Epistemic Modeling

This paper introduces the concept of Statistical Quasi-Equivalence (SQE) as an epistemic regime that clarifies why statistical models — including large language models (LLMs) — can be highly functional while still falling short of ontological validity. Although such models demonstrate strong predictive performance, they operate through approximation, correlation, and ad hoc structure, lacking traceable causal foundations. We propose that statistics occupies the second ontological place: it is epistemically superior to heuristics or unfounded speculation, but insufficient to establish theories of reality. This distinction is formalized through four metrics — accuracy (G), traceability (R), causality (C), and ontological distance (L = 1 − R × C) — along with a three-tiered classification system (Z1–Z3) and falsifiability tests (FATEs) that assess whether a model can transition from functional to ontological adequacy. Particular attention is given to LLMs, which, although fundamentally statistical, inherit ontological structures from human language — improving their approximation to reality without crossing into causal understanding. SQE provides a principled framework for evaluating this epistemic gray zone, where models function well but do not yet explain.