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What are the laws of nature — are they mere descriptions of cosmic regularities, or do they express genuine necessities that govern what happens? The Humean regularity view, refined by Lewis's Best Systems Account, holds that laws are the axioms of the simplest and strongest systematization of all the particular facts — they describe but do not govern. The necessitarian view (Armstrong, Dretske, Tooley) holds that laws are relations of nomic necessitation between universals: it is not just that all copper conducts electricity, but that the universal copper-hood necessitates the universal conductivity. The debate connects to causation (do laws ground causal connections?), counterfactuals (do laws support them because they are necessary or merely because they are robust regularities?), and the metaphysics of science more broadly.
Read Armstrong's What Is a Law of Nature? chapters 1-5 for the necessitarian account, then Lewis's 'New Work for a Theory of Universals' section on Best Systems for the Humean alternative. Evaluate each against the identification problem: how do we distinguish genuine laws from accidental regularities?
You already know the regularity theory of causation from Hume: causation is not a necessary connection we observe directly, but a pattern of constant conjunction — we call A the cause of B because A-events are regularly followed by B-events. Laws of nature are intimately related: the law that copper conducts electricity just *is* the regularity that every instance of copper is followed by electrical conductivity. But this Humean picture faces an immediate challenge — what distinguishes a genuine law from a mere accidental regularity?
Consider two true generalizations: "All copper conducts electricity" and "All the coins in Griffin's pocket today are dimes." Both describe universal regularities — everything that satisfies the antecedent satisfies the consequent. But only the first looks like a law. Crucially, the law *supports counterfactuals*: if this piece of iron were copper, it would conduct electricity. The accidental regularity does not: if this quarter were in Griffin's pocket today, it would not thereby become a dime. The challenge for any theory of laws is to explain this difference — why some regularities have the modal force of necessity while others are cosmic coincidences.
David Lewis's Best Systems Account (BSA) is the most sophisticated Humean answer. On this view, the laws are the theorems of the axiomatic system that best balances *simplicity* (few axioms) and *strength* (entailing many true facts about the world). A law is not just any regularity — it is one that earns its place in the optimal systematization of all particular facts. "All coins in Griffin's pocket are dimes" adds no strength that a more general truth couldn't subsume, so it does not appear in the best system. The counterfactual support laws provide falls out of their systematic role rather than requiring any metaphysical addition beyond the regularities themselves.
The necessitarian alternative, developed by Armstrong, Dretske, and Tooley, holds that laws are real relations of nomic necessitation between universals. It is not just that copper-instances are followed by conductive-instances; rather, the universal *copper-hood* necessitates the universal *conductivity*. This second-order relation N(F, G) is what makes the regularity necessary rather than accidental, and what explains why laws support counterfactuals — they could not have been otherwise. The cost is ontological: you must accept universals as real and posit a distinctive necessitation relation over and above their instantiation.
Both accounts struggle with the identification problem: how do we tell which regularities in nature are laws and which are accidents? For the Humean, the answer is holistic — only by examining the entire system of facts can you determine which generalizations are law-like. For the necessitarian, the answer requires investigating which universals stand in the necessitation relation — a metaphysically loaded inquiry with no obvious empirical method. The debate is not merely academic; it shapes how we understand the explanatory power of science, whether physical laws could have been different, and what it means for a process to be *governed* by a principle rather than merely conforming to it.
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