Chapter 18: Laws of Nature

The central problem in the philosophy of laws is distinguishing genuine laws from merely accidental regularities. Consider the following true generalizations:

Both classes of statements are true universal generalizations. But they differ in several philosophically important ways:

The philosophical question is: what grounds these differences? What is it about laws that gives them their distinctive modal force, their ability to support counterfactuals and ground explanations?

The simplest account of laws is the regularity theory, inspired by Hume’s denial of necessary connections in nature. On this view, laws are nothing more than universal regularities — exceptionless patterns in the occurrence of events. “All copper conducts electricity” is a law simply because, as a matter of fact, every piece of copper that has existed, exists, or will exist conducts electricity. There is no deeper “necessity” or “force” behind the regularity.

The naive regularity theory faces an obvious problem: it cannot distinguish laws from accidental generalizations. Both are true universal generalizations. What makes “all copper conducts electricity” a law but “all the coins in my pocket are silver” merely accidental? The regularity theorist needs some additional criterion.

A.J. Ayer suggested that laws are distinguished by their generality and their role in our inferential practices. But this makes the law/accident distinction pragmatic and interest-relative rather than objective — a consequence many philosophers find unacceptable. The most sophisticated development of the Humean approach is the Best System Account.

The Best System Account (BSA), developed by Frank Ramsey and systematized by David Lewis, is the most influential Humean theory of laws. The idea, anticipated by John Stuart Mill, is that the laws of nature are the axioms or theorems of the best deductive system for describing all the facts about the world.

Consider all the particular facts about the universe — the entire mosaic of events across all of spacetime. Lewis calls this the Humean mosaic. Now consider all the deductive systems that could systematize these facts — all possible sets of axioms from which the facts can be derived. These systems compete on two criteria:

There is a tradeoff: the strongest system (a conjunction of all particular facts) is maximally informative but maximally complex. The simplest system (a single tautology) is maximally simple but uninformative. The best system achieves the optimal balance of strength and simplicity. The laws of nature are the regularities that appear as axioms or theorems of this best system.

“A contingent generalization is a law of nature if and only if it appears as a theorem (or axiom) in each of the true deductive systems that achieves a best combination of simplicity and strength.”

The BSA elegantly explains why “all copper conducts electricity” is a law but “all gold spheres are less than one mile in diameter” is not. The former earns its place in the best system because it is a simple, powerful generalization that helps systematize vast amounts of data about electrical conductivity. The latter, while true, adds no systematic value: it is a trivial consequence of contingent facts about how much gold has been collected in one place.

Critics raise several objections. The BSA seems to make laws depend on our standards of simplicity and strength — but shouldn’t laws be mind-independent? Lewis responds that the criteria are objective once a language is fixed, but this raises questions about language-dependence. Others worry that the BSA cannot account for the modal force of laws: if laws are merely the best summary of what happens, why do they support counterfactuals about what would happen?

In the late 1970s and early 1980s, David Armstrong, Fred Dretske, and Michael Tooley independently proposed a radically different account: laws are relations of necessitation between universals. On this view, the law that all F’s are G’s is not merely the universal generalization ∀x(Fx → Gx) but a second-order fact about the universals F-ness and G-ness themselves: N(F, G), where N is a relation of natural necessitation.

Armstrong develops this view most fully in What Is a Law of Nature? (1983). The key idea is that the law “all copper conducts electricity” expresses a necessary relation between the universal being copper and the universal conducting electricity. This relation holds between the universals themselves, not merely between their instances. It is a contingent but necessary connection — contingent in the sense that the universals might not have stood in this relation (in a different possible world), but necessary in the sense that, given the relation, every instance of copper must conduct electricity.

“It is a law that F’s are G’s if and only if the state of affairs N(F, G) obtains, where N is a relation of nomic necessitation holding between the universals F and G.”

The necessitarian account has several advantages over the regularity theory:

The central objection is the “inference problem” raised by Bas van Fraassen: how does the relation N(F, G) between universals entail the regularity ∀x(Fx → Gx)? Armstrong claims N(F, G) entails the regularity by the nature of N. But critics find this mysterious: what is the nature of N such that it has this entailment power? If N just is whatever it takes to ensure the regularity, the account seems circular. If N is something more, what is it?

A more recent approach grounds laws in the essential natures of natural kinds and properties. Dispositional essentialism, developed by Alexander Bird, Brian Ellis, and others, holds that natural properties have their causal/nomic roles essentially — it is part of the nature of negative charge to attract positive charges and repel other negative charges. Laws are then consequences of the essential natures of the properties involved.

On this view, the law that like charges repel is not a contingent regularity (Hume), not an axiom of the best system (Lewis), and not an external relation of necessitation between universals (Armstrong). It is a metaphysically necessary truth, flowing from the very nature of electric charge. A property that did not repel like charges would simply not be negative electric charge.

Bird develops this view in Nature’s Metaphysics (2007):

“The laws of nature are metaphysically necessary. They could not have been otherwise. A world with different laws would be a world with different properties — and hence a world that does not contain the entities we are talking about.”

Dispositional essentialism has several attractive features: it explains the necessity of laws (they are metaphysically necessary), it explains why laws support counterfactuals (they hold in all possible worlds containing the same properties), and it unifies the metaphysics of properties with the metaphysics of laws.

Critics ask whether all fundamental properties are dispositional, whether the view can accommodate the apparent contingency of some laws, and whether the account is compatible with the possibility (entertained in physics) that the fundamental constants of nature might have been different. If the charge of the electron is essential to being an electron, then in a world with a different charge value, there simply are no electrons — but this seems to trivialize the question of whether laws could have been different.

Nancy Cartwright’s How the Laws of Physics Lie (1983) offers a provocative challenge to the standard picture of laws. Cartwright argues that the fundamental laws of physics, taken literally, are false. They describe idealized, unrealizable situations that never actually obtain.

“The fundamental laws of physics do not describe true facts about reality. Rendered as descriptions of facts, they are false; amended to be true, they lose their explanatory force.”

Consider Newton’s law of gravitation: F = Gm₁m₂/r². This law tells us the gravitational force between two bodies. But no real body is subject only to gravitational forces. Every real body is also subject to electromagnetic forces, nuclear forces, friction, air resistance, and so on. The gravitational force law describes what the force would be if gravity were the only force acting — a situation that never actually obtains.

Cartwright distinguishes between fundamental laws (which describe component forces in idealized conditions) and phenomenological laws (which describe what actually happens in specific circumstances). Fundamental laws are explanatory but false; phenomenological laws are true but lack the generality and explanatory power we associate with laws. This creates a dilemma: the laws that explain are false, and the laws that are true do not explain.

Cartwright’s critique has prompted extensive discussion about ceteris paribus laws — laws that hold “all else being equal.” Many philosophers have argued that most real scientific laws are ceteris paribus laws, holding only under appropriate conditions. This is especially evident in the special sciences: the law of supply and demand holds ceteris paribus (assuming rational agents, no government intervention, perfect information, etc.), and biological and psychological generalizations almost always carry implicit ceteris paribus qualifications.

Are there genuine laws in biology, psychology, economics, or sociology? Or are laws restricted to fundamental physics? This question has significant implications for the unity of science and the autonomy of the special sciences.

Jerry Fodor argued in “Special Sciences” (1974) that the special sciences have their own laws, which are not reducible to the laws of physics. Biological laws (Mendel’s laws, the Hardy-Weinberg principle), economic laws (Gresham’s law, the law of diminishing returns), and psychological generalizations (Weber’s law) have genuine explanatory and predictive power, even though they hold only ceteris paribus and their predicates are not identical to physical predicates.

The case of biology is particularly interesting. Are there biological laws? Consider:

Some philosophers (John Beatty, Marc Lange) have argued that there are no distinctively biological laws — biological regularities are contingent on evolutionary history and could have been otherwise. Others (Elliott Sober, Robert Brandon) argue that biology has its own laws, though they may differ in character from the laws of physics — being statistical, ceteris paribus, or domain-restricted.

The debate connects to deep questions about reduction and the unity of science. If the special sciences have their own laws, this supports the autonomy of the special sciences from physics. If all genuine laws are physical laws, this supports a reductionist picture in which the special sciences are ultimately grounded in physics.

Modern physics has revealed a profound connection between laws of nature and symmetry principles. Noether’s theorem (1918) establishes that every continuous symmetry of a physical system corresponds to a conserved quantity: translational symmetry corresponds to conservation of momentum, rotational symmetry to conservation of angular momentum, and time-translation symmetry to conservation of energy.

Symmetry principles function as meta-laws or super-laws — they constrain what the first-order laws can be. The requirement that the laws of physics be Lorentz-invariant (the symmetry of special relativity) dramatically constrains the form that fundamental laws can take. The gauge symmetries of particle physics (U(1), SU(2), SU(3)) determine the structure of the electromagnetic, weak, and strong forces.

This raises a fascinating philosophical question: are symmetry principles more fundamental than the laws they constrain? Eugene Wigner argued that the hierarchy of physical knowledge has three levels: events (particular occurrences), laws (regularities among events), and symmetry principles (regularities among laws). If this is right, then the deepest truths about nature are not laws but symmetries.

Marc Lange has argued that symmetry principles possess a distinctive kind of necessity: they are “meta-laws” that are necessary relative to the first-order laws, just as the first-order laws are necessary relative to accidental generalizations. This creates a hierarchy of natural necessities, with symmetry principles at the top — the most necessary, the most deeply entrenched in the structure of reality.

The debate about laws connects intimately to the broader philosophy of modality — the study of necessity, possibility, and contingency. The central question is whether laws of nature are contingent (they could have been different) or necessary (they could not have been different).

Contingentists (Humeans and most necessitarians like Armstrong) hold that the laws are contingent: there are possible worlds with different laws. The laws of our world are just one set of regularities among many possible ones. This fits naturally with the Humean picture: if laws are just regularities, and regularities could have been different, then laws could have been different.

Necessitarians in the strong sense (dispositional essentialists like Bird and Ellis) hold that the laws are metaphysically necessary: there is no possible world where the laws are different (given the same properties). If negative charge essentially involves repulsion of like charges, then any world containing negative charge must exhibit this repulsion. A “world” where negative charges attract would simply not contain negative charge at all.

Marc Lange has developed an intermediate position, arguing that laws are characterized by a distinctive grade of necessity — natural or nomic necessity — that is stronger than mere contingency but weaker than metaphysical or logical necessity. Laws are necessary given the way the world actually is, but they could have been different in a broader modal sense. This captures the intuition that laws have genuine modal force (they support counterfactuals, they don’t just happen to be true) without committing to the strong claim that they are metaphysically necessary.

The philosophy of laws of nature remains a vibrant area of inquiry. Several open questions drive current research:

The philosophy of laws also connects to foundational questions in physics about the status of symmetry principles, the role of initial conditions, and the arrow of time. Whether the laws of nature are fundamentally time-symmetric (as the fundamental equations suggest) or time-asymmetric (as our experience suggests) remains one of the deepest unsolved problems at the intersection of physics and philosophy.