Structure and Ontic Structural Realism

The fundamentality page defined the fundamental by grounding and dependence — relations among entities. There is another way to get at the same idea, which starts not from entities but from vocabulary: some ways of describing the world carve it at the joints, and the fundamental description is the one written entirely in joint-carving terms.

Pushed far enough, this suggests a position on which what is fundamental is not any entities at all, but structure.

From naturalness to structure

Lewis's naturalness was introduced to solve a specific problem. If properties are just sets, then any set of objects is a property, and there is no distinction between green and Goodman's grue, or between a genuine similarity and an arbitrary grouping. Lewis's response was to take perfect naturalness as primitive: some properties carve at the joints, and these are the ones that ground objective similarity, figure in laws, fix what counts as a duplicate, and act as reference magnets.

Sider's generalisation drops the restriction to properties. Any piece of ideology — predicate, connective, quantifier, operator — either carves at the joints or does not. Structure is the primitive, and the fundamental description of the world is the one whose every term is joint-carving.

The consequence for this section is that fundamentality becomes a feature of notions as well as of things. There are two questions where there appeared to be one: which entities are fundamental, and which concepts are. They can come apart — one might hold that the fundamental entities are particles while denying that any of our predicates for them carve.

The application to the quantifier is what makes ontological disputes substantive, and it is developed on the ontological realism page. What belongs here is the more general point: naturalness was already doing structural work throughout metaphysics, and Sider's move is to notice that the work is not restricted to properties.

Ontic structural realism

The more radical position holds that structure is not merely what is fundamental about the entities but is all there is. Ontic structural realism (Ladyman and Ross, French, Ladyman) claims that relations are ontologically prior to relata, or that there are relations without relata at all — that objects are at best nodes in a structure with no independent identity.

The position has two independent motivations, and they are usually run together though they should not be, since an objection may answer one and leave the other standing.

The argument from theory change. What survives scientific revolutions is mathematical structure rather than posited objects. Fresnel's equations for optical phenomena were retained in Maxwell's theory while the luminiferous ether was discarded. Generalising: the historical record of abandoned entities — phlogiston, caloric, the ether — gives a pessimistic induction against object-realism, while the retention of structure supports realism about structure. This was Worrall's "best of both worlds" argument, and it is an argument about epistemology that ontic structural realism converts into a claim about ontology.

The argument from current physics. Independently, our best theories seem not to contain well-behaved objects:

• Permutation invariance. Identical particles in quantum mechanics have no properties distinguishing them; on French and Redhead's reading they violate the identity of indiscernibles and are not individuals at all. What is well defined is the structure of the state space, not which particle is which.
• The hole argument. Diffeomorphism invariance in general relativity means that which spacetime point plays which role carries no physical content. What is physical is the invariant structure.
• Quantum field theory. The particle concept does not survive interaction, localisation, or a change of observer, and field operators are distributions with no values at points — so neither particles nor fields supply the bearers.

The second argument is the stronger, and it is worth being clear about the difference: the first is compatible with there being objects we cannot know about, the second says there are none.

Objections

Relations without relata is unintelligible. The standard complaint: a relation is by definition something relating things, and a structure with no items in it is a mathematical form, not a physical reality. The structuralist's replies are that "relata" in the objection means individuals with primitive identity, which is precisely what is denied; and that objects can be admitted as derivative — nodes whose identity is exhausted by their structural position — which yields a moderate version at the cost of the slogan.

Which structure? If reality is structure, some account is needed of what distinguishes physical structure from the indefinitely many mathematical structures that are not instantiated. Without one, the position collapses into a Pythagoreanism on which reality is mathematics. Appealing to modal structure — the structure of what can and cannot happen — is the usual answer, and it makes ontic structural realism dependent on the dispositions and powers debate, since it needs modality to be in the world.

Weak discernibility undercuts the physics argument. If Saunders is right that identical particles are weakly discernible by irreflexive relations, they are two objects after all, and the strongest quantum motivation for eliminating objects is answered. This is why the individuation debate matters here: it is the same question asked at a different level of generality.

Where structure sits

Structure is the section's third answer to what fundamentality consists in, alongside grounding and dependence, and it is the one that does not presuppose an inventory. Where the other two ask how entities stand to one another, this one asks what vocabulary the world's own description is written in — and in the ontic version, denies that entities are required at all.

Its significance for the section as a whole is that it is the point where the category question is answered by rejecting the framing. Every category scheme surveyed earlier assumed a division among entities: substances and modes, particulars and universals, objects and events. Ontic structural realism proposes that the deepest description has no such divisions because it has no items to divide — a proposal that is either the most radical position in the section or, as its critics say, not a position at all.