The article discusses the problem of the naturalistic methodology of social ontology. Following Katherine Hawley's (2018) analysis, the author considers three approaches: conceptual analysis, the ameliorative (or normative) approach, and inference to the best explanation (from best social science to social ontology). Hawley concludes that only the first two can provide a viable naturalistic social metaphysics, and the latter cannot. The author, drawing on the notion of naturalistic limitations of social ontology, shows that only a conclusion to the best explanation (...) can lead to a consistent realistic social ontology; this methodology avoids the problem of being rooted in concepts that do not have an empirical basis, which contradicts realism, and also does not imply normative prescription, which also contradicts the realistic description of the world. The problem critics attribute to inference to the best explanation - the lack of a predictively strong theoretical core of social theory from which to infer social ontology - can be resolved by satisfying three criteria (Turner, 2007): physical realizability, computability, and cognitive realism. The author proposes to implement them through the introduction of naturalistic restrictions into game theory. Formal models of coordination described by a correlated equilibrium - coupled with evolutionary explanations of the cognitive mechanisms responsible for the causal processes that make formally described coordination possible - may provide the desired theoretical core from which ontology can be derived. (shrink)