Laws of Nature

Nothing travels faster than light; every action has an equal and opposite reaction; like charges repel. These are laws, and they are distinguished from accidental regularities — every sphere of gold is less than a mile across, and always will be, but that is not a law.

The ontological question is what a law is. Is it an entity in its own right, a relation among universals, a consequence of what properties are, or merely a summary of what happens? The epistemology of laws — how they are confirmed, what makes a generalisation lawlike — is a separate subject, and this page stays on the ontological side.

Humean regularity and the best system

The Humean tradition denies necessary connections in nature. All that exists is the mosaic: the total distribution of local qualities across spacetime, one thing after another. Laws are not additional items; they are patterns in the mosaic.

Naïve regularity theory — a law is a true universal generalisation — fails at once, since it cannot distinguish laws from accidents and counts "all gold spheres are under a mile wide" as a law.

The best system account (Mill, Ramsey, Lewis) is the sophisticated version. Consider all true deductive systematisations of the mosaic. Each can be evaluated for strength (how much it entails) and simplicity (how briefly it can be axiomatised), and these trade off: the list of every particular fact is maximally strong and hopelessly unsimple; "everything is self-identical" is simple and weak. The laws are the theorems of the system that best balances them.

This elegantly separates laws from accidents. Including the gold-sphere generalisation adds an axiom for negligible gain in strength, so it does not make the best system; the conservation laws pay for themselves many times over.

Two objections:

• Mind-dependence. Simplicity and strength are relative to a language. In a perverse language with a predicate $F$ true of all and only the actual particular facts, "everything is $F$" is a very simple and very strong axiom, and the "best system" is a triviality. Lewis's reply is to require that the systems be formulated in terms of perfectly natural properties, which blocks the trick — but it means the account depends on primitive naturalness, and so on a substantial piece of metaphysics of the sort Humeans usually avoid.
• No explanation. On this account laws do not make anything happen; they are summaries. But we take laws to explain the regularities, and a summary of the regularities cannot explain them. Humeans reply that explanation is unification, and that a systematising summary is exactly what unifies.

Nomic necessitation

The leading realist alternative is the DTA account (Dretske, Tooley, Armstrong): a law is a second-order relation of nomic necessitation holding between universals. That all $F$s are $G$s is a law when the universal $F$ stands in the necessitation relation $N$ to the universal $G$:

$$N(F,G)\Rightarrow \forall x(Fx\to Gx)$$

Laws are thus genuine entities — states of affairs relating universals — and they explain the regularities because the regularity follows from the law rather than constituting it. This requires realism about universals, which is why Armstrong's theory of laws and his theory of universals are one package.

Van Fraassen's objections are the standard difficulties, and Lewis's statement of the second is the most quoted line in the literature:

• The identification problem. Which relation is $N$? What distinguishes it from any other second-order relation that happens to hold between $F$ and $G$?
• The inference problem. How does $N(F,G)$, a fact about two universals, entail the regularity that every particular $F$ is $G$? Calling the relation "necessitation" does not give it the power to necessitate. In Lewis's words: "I say that $N$ deserves the name of necessitation only if... it can enter into these remarkable relations. But I do not see how it can."

The realist's reply is that the entailment is primitive — $N$ is a sui generis relation whose nature is to necessitate — and the Humean's rejoinder is that this is a name for the mystery rather than a solution to it. The exchange is a good instance of the general pattern the problem of universals page identified: the dispute is over which primitive is acceptable.

Laws from powers

The third option removes laws from the inventory entirely. If properties are essentially powers, then what a charged particle does is fixed by what charge is, and there is no need for a further entity to govern it. Laws are then true descriptions of how things must behave given their natures — necessary, but not because a law-entity enforces them.

The advantages are that the inference problem cannot arise (the connection between property and behaviour is one of essence, not of an external relation), the laws come out metaphysically necessary rather than contingent, and no additional category is required.

That laws come out necessary is also the main objection. It seems possible that the laws could have been different — that gravity might have obeyed an inverse-cube law — and dispositional essentialism must deny it, or else say that in such a world the properties would be different ones, so that it is not gravity obeying a different law. That is a coherent position and a revisionary one.

Antirealism

Two positions deny there are laws in anything like the intended sense.

Cartwright: the fundamental laws of physics are literally false. They describe idealised situations — frictionless planes, isolated systems — and hold only ceteris paribus. What is true and useful is a patchwork of local, domain-specific models; the world is "dappled," not governed by a unified system. This bears directly on fundamentality, since it denies the layered picture on which everything answers ultimately to fundamental physics.

Van Fraassen: there are no laws, and science does not need them. What science provides is empirically adequate models; "law" is a piece of metaphysics projected onto the practice.

Humean supervenience and its threat

Lewis's broader thesis, Humean supervenience, holds that everything supervenes on the mosaic of local matters of particular fact: all there is, is a spatiotemporal arrangement of intrinsic properties at points, and everything else — laws, chances, causation, counterfactuals — supervenes on it.

Quantum entanglement is the standing threat. Entangled systems are non-separable: the state of the whole is not determined by the intrinsic states of the parts together with their spatiotemporal relations. If that is right, the mosaic of local qualities does not fix the physical facts, and Humean supervenience is false — not for philosophical reasons but empirically. The formal situation is set out in Bell nonlocality and the interpretive options in the remark on the philosophy of Bell's theorem.

Lewis himself acknowledged the difficulty and described Humean supervenience as a thesis about how things might have been — a philosophy worth developing even if quantum mechanics falsifies it.

Where laws sit

Laws sit at the junction of the inventory and category questions: whether the inventory contains law-entities, and if so what category they fall under — relations among universals, patterns in the mosaic, or nothing at all because the work is done by properties.

The page also shows how tightly the section's disputes interlock. One's account of laws is nearly determined by one's answers elsewhere: a nominalist cannot take the DTA route, a dispositionalist has no need of laws as entities, and a Humean about laws needs primitive naturalness to make the best-system account work — which is a commitment first incurred back in the problem of universals.