David Lewis, answered from the texts and cited to the page.
Laws of nature are not relations of necessitation between universals, nor irreducible modal facts, nor commands of a divine legislator. They are the theorems of the deductive system that best balances simplicity and informational strength among true systems formulated in the vocabulary of the perfectly natural properties.12 The choice of language matters — a deductive system stated in terms of arbitrary gerrymandered predicates could be made artificially simple or artificially strong — and the restriction to perfectly natural predicates is what removes the language-relativity worry: the perfectly natural properties are the joints in nature that physics will eventually discover, and the laws-of-nature are simply the most informative compact summary that the patterns of those joints permit.3
The view descends from Mill and Ramsey, and Frank Ramsey's formulation in particular is the immediate source. The "unpleasant surprise" is genuine and worth naming: on this view, what is a law here partly depends on patterns elsewhere in the cosmos, since the best deductive system is a global trade-off. That is the price of the regularity- theoretic family of views, and it is, on the trade-offs I take to be defensible, worth paying.
The alternative — that laws are additional facts about the world, primitive necessitations or governings that make the regularities — postulates a mystery connection where there should be explanation, and the postulate buys nothing that the regularities did not already buy.45
Some are simpler, better systematized than others. Some are stronger, more in¬ formative, than others. These virtues compete: an uninformative sys¬ tem can be very simple, an unsystematized compendium of miscellaneous information can be very informative. The best system is the one that strikes as good a balance as truth will allow between simplicity and strength.Papers in Metaphysics and Epistemology, p. 242
Thus it makes sense to speak of the best true systems, and of the theorems common to all the best true systems. I adopt Ramsey's 1928 theory of lawhood, glossed as above, because of its success in explaining some facts about laws of nature. (1) It explains why lawhood is not just a matter of the generality, syntactically or semantically defined, of a single sentence.Counterfactuals, p. 86
Bogdan (Dordrecht: Reidel, 1984). Mill version is not quite the same mine. He says that the question what are the laws of nature could be restated thus: "What are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred?"; so it seems that the ideal system is supposed to be complete regards uniformities, that it may contain only general propositions…Part 5: Probability, pp. 122–123
The analysis I shall put forward can't handle lawless chances, and I take that to be no problem.) There are general laws of radioactive decay that apply to all atoms. These laws yield the chance of decay in a given time, and hence the half-life, as a function of the nuclear structure of the atom in question.Papers in Metaphysics and Epistemology, pp. 241–242
For we can take our actual stan dards as fixed, and apply them in asking what the laws would be in various counterfactual situations, including counterfactual situations in which people have different standards—or in which there are no people at all. Likewise, it fortunately does not follow that the laws are different at other times and places where there live people with other standards.Part 5: Probability, pp. 123–124
The standard descendant of the Mill-Ramsey regularity-of- laws tradition and the principal Humean alternative to the necessitation theory of laws defended by Armstrong (What Is a Law of Nature? 1983), Dretske ('Laws of Nature' 1977), and Tooley (Causation 1987). The dispositionalist alternative (Bird's Nature's Metaphysics 2007, Mumford, Ellis) holds that laws are grounded in irreducible dispositional essences of natural properties. John Carroll (Laws of Nature 1994) and Tim Maudlin (The Metaphysics Within Physics 2007) offer non-Humean systematic alternatives that take laws as primitive. Within the sympathetic literature, Barry Loewer and Helen Beebee have defended and extended the Best System Analysis; Marc Lange (Laws and Lawmakers 2009) locates laws in subjunctive- stability facts as a non-Humean cousin. The view is the load-bearing element in the Humean program for laws, causation, chance, and counterfactuals.