The Asymptote of the Natural: Inductive Density and the A Posteriori Justification of Methodological Naturalism

The debate regarding Methodological Naturalism (MN) is stalled between "Essentialists" (who define science as naturalistic) and "Permissivists" (who view MN as bias). This paper resolves the deadlock by defining MN not as an a priori rule, but as the a posteriori output of Inductive Density ( D I ) -the ratio of explanatory successes to attempted hypotheses over time. Formalizing this history via Bayesian inference, we demonstrate that the "demarcation" of science is a confidence interval driven by the "Great Displacement" of supernatural explanations. We distinguish this view from Lakatosian historiography by providing a probabilistic mechanism for the "washing out" of supernatural priors, ultimately arguing that science excludes the supernatural not because it is impossible, but because it is statistically indistinguishable from algorithmic randomness. A visual introduction: 1 Contents.