The structural laws expressed by T, S, and Φ are constitutive features of what Nature consists in, not regularities imposed on an otherwise unstructured field. This does not make every specific physical law necessary: particular law-patterns may remain contingent specifications within the structural minimum. Four major accounts of natural laws compete over what laws are, and each must operate within that minimum.

The Humean best-systems account (Lewis, David, 1973); (Lewis, David, 1994) treats laws as the simplest, strongest systematization of the totality of particular facts: regularities, not necessities. The governing-law account (Armstrong, D. M., 1983); (Dretske, F. I., 1977); (Tooley, M., 1977) treats laws as second-order relations between universals that necessitate the regularities the Humean merely catalogues. The powers-based account (Bird, Alexander, 2007); (Mumford, Stephen, 2004) grounds laws in the dispositional essences of natural kinds: what a thing is determines what it does, and laws are the structural expressions of those essences. The dappled-world account (Cartwright, Nancy, 1983); (Cartwright, Nancy, 1999) refuses the demand for universal nomic structure altogether: laws are local truths about what specific capacities do when exercised in the nomological machines that host them, and the unity of science is a regulative fiction rather than a feature of the world.

The constitutive claim survives all four. If the Humean is right, the best systematization of any possible world's regularities will include T/S/Φ: not merely because no regularity is statable without them (a constraint on the laws' formulation) but because the Humean mosaic of particular facts is already T/S/Φ-structured. Each particular fact in the Humean mosaic is a fact about a being (Φ) at a position (S) at a time (T); the mosaic is not a substrate-neutral collection that happens to admit T/S/Φ-descriptions but a collection of T/S/Φ-structured facts. The constraint applies at the level of what the mosaic *is*, not merely at the level of how the laws describe it. If the governing-law theorist is right, the second-order necessitation relation between universals already presupposes a relational structure (S), a causal order (T), and beings instantiating the universals (Φ); where the account allows laws involving uninstantiated universals (Tooley, M., 1977), the law remains a law for possible instantiations, and any possible instantiation is T/S/Φ-structured ([§2.5](<2.5 Triconditional Necessity.md>)). If the powers-based theorist is right, the convergence is immediate: dispositions are what substances do across time through space. If Cartwright is right, capacities are exercised through nomological machines, and a machine is parts that persist (Φ), standing in relational arrangement (S), and interacting in time (T); the dappled surface still rests on the structural minimum.

Cartwright's rejection of universal nomic structure is a rejection of universal *laws* (the claim that one set of equations governs all of physics) not a rejection of a universal *structural minimum*. The dappled-world position is fully compatible with the structural account: local capacities individually require T/S/Φ to be the capacities they are, and the local-versus-global laws question is settled downstream of the structural requirement, not upstream of it. T/S/Φ are not what Cartwright rejects when she rejects universal nomic structure; they are the precondition for any local capacity to count as a capacity at all.

The objector from the powers or capacities tradition has not stepped outside the structural requirement. They have imported it as their central concept: a disposition without a being that persists (Φ), without relational extension through which it manifests (S), and without a temporal interval between latency and activation (T) is not a disposition at all. The four accounts disagree about why laws hold. They agree (once the structural requirements are made explicit) about what any law requires.

*What is identified.* The constitutive laws at issue here are the structural requirements T, S, and Φ, not every determinate law of physics. Specific dynamical laws, constants, and nomological patterns may vary within that structure, as [§2.8.4](<2.8.4 Necessity Precedes Contingency.md>) explains. Nature is not a contingent physical universe that happens to exist; it is the necessary structural ground within which any determinate law-pattern can obtain. Any classification of laws already presupposes that minimum.[^2-8-1-constitutive-laws-ch4]

[^2-8-1-constitutive-laws-ch4]: The constitutive-laws claim, against the law accounts this section surveys, is engaged in Chapter 4. Both the Humean best-systems account (Lewis, the canonical opponent of the constitutive reading) and the governing-law account (Armstrong, Dretske, Tooley) are taken up at [§4.1.4](<4.1.4 Humean Contingency.md>), and conventionalism about laws (the closest neighbor to the contingent-regularities reading the constitutive claim denies) at [§4.1.7](<4.1.7 Modal Conventionalism.md>).


---

← [2.8 The Whole Line](<2.8 The Whole Line.md>) | [2.8.2 Nature Cannot Be Denied](<2.8.2 Nature Cannot Be Denied.md>) →
