What is a law of nature?

Abstract

Laws of nature constitute a central ontological category in the philosophy of science, providing the necessary ground for induction and scientific explanation. The dominant Regularity theory, which reduces laws to mere Humean uniformities, fails to distinguish between accidental and nomic regularities and cannot adequately account for unrealized physical possibilities, uninstantiated laws, or the inherent explanatory power of scientific principles. Instead, laws are contingent, second-order relations of necessitation holding between universals. This state of affairs, symbolized as N(F, G), is itself a universal that manifests in the behavior of particulars. Such a framework provides an objective basis for counterfactual assertions and addresses the problem of induction by identifying laws as the best explanation for observed regularities. Functional and probabilistic laws are accommodated within this schema as higher-order relations or probabilities of necessitation, respectively. Although laws remain contingent across possible worlds, they possess a robust internal necessity that mere regularities lack. This ontological shift moves away from the Humean rejection of necessary connections toward a realism that accommodates the structure of modern scientific theory. – AI-generated abstract.