The Ontological Limits of Probability and the Statistical Imperative of the World

This paper argues that the hypothesis of independent and identically distributed trials—central to mathematical probability—does not correspond to the ontological structure of reality. Empirical phenomena exhibit statistical restoration rather than independence: systems tend toward equilibrium rather than remaining in stochastic dispersion. By examining induction, physical continuity, and complex systems, I propose that statistical regularity is an ontological property of the world itself, while probability is a derivative epistemic language used to describe that property. This reinterpretation undermines the conventional dismissal of the “gambler’s fallacy” as irrational, reframing it as a form of inductive reasoning grounded in the world’s self-restorative dynamics.