Laws of nature, also called natural laws or physical laws, are generalizations that describe regularities or patterns observed (or posited) in the natural world. In the physical sciences, the term most often refers to statements such as the laws of thermodynamics or Newton's laws of motion, which describe how physical systems behave under specified conditions. The deeper metaphysical question of what a law of nature *is* - whether it is a mind-independent feature of reality, a description of regularities, a relation between universal properties, or a product of human conceptual organization - is itself contested among philosophers of science. See laws-of-nature-metaphysical-status-debate.
Working scientists generally use “law” as an informal honorific for well-confirmed, broadly applicable generalizations - usage that does not require settling the underlying metaphysical question of what makes something a law. Within philosophy of science, several competing accounts attempt to specify the truth-conditions or grounding of laws.
The regularity theory (sometimes called the “Humean” view, after David Hume's skepticism about necessary connections in nature) holds that laws are nothing more than true, exceptionless generalizations - patterns in what actually happens, with no further metaphysical glue binding them. The best-system account, associated with John Stuart Mill, Frank Ramsey, and developed extensively by David Lewis, refines this by identifying laws as the axioms and theorems of whichever true deductive system best balances simplicity and informativeness about the totality of particular facts (the “Humean mosaic”).
Opposed to these are necessitarian theories, which hold that laws involve some form of genuine necessity or governing relation, not merely a pattern. The most prominent version, developed independently by David Armstrong, Fred Dretske, and Michael Tooley, holds that laws are relations of natural necessitation between universals. See laws-of-nature-necessitarian-universals-viewpoint-debate for objections to this view, including circularity concerns raised by van Fraassen and others. Other necessitarian approaches ground lawhood in the essential dispositional natures of properties themselves (dispositional essentialism), associated with thinkers such as Brian Ellis and Alexander Bird, who argue that at least some laws are metaphysically necessary in virtue of the causal powers built into natural properties.
A further point of contention concerns whether laws, on any of these accounts, *govern* the behavior of objects (a “governing” conception) or merely *describe* a pattern that obtains without any object being beholden to it (a “descriptive” conception). This distinction cuts across the regularity/necessitarian divide and bears on related questions about causation, counterfactuals, and the direction of explanation. From a constructive empiricist standpoint, Bas van Fraassen has argued against treating laws as a serviceable category in the philosophy of science at all, proposing that talk of “laws” can be replaced by talk of symmetries and invariances without metaphysical loss. See laws-of-nature-history for the development of these debates from antiquity through the scientific revolution and into twentieth-century philosophy of science.