Grounding

Some things hold in virtue of others. The ball is red in virtue of being scarlet. The disjunction is true in virtue of the first disjunct. The set $\{Socrates\}$ exists in virtue of Socrates. The statue exists in virtue of the clay being arranged as it is. The party is going well in virtue of facts about the guests.

None of these is causal — nothing brings anything about, and there is no temporal gap — yet each is clearly explanatory, and each runs in one direction only. Grounding is the name for this relation, and its rehabilitation is the largest development in metaphysics of the past two decades.

What grounding is for

The claim motivating the notion is that a great deal of metaphysics was already using it under other names, badly. Physicalism is the thesis that the mental holds in virtue of the physical; the truthmaker principle says truths hold in virtue of what exists; nominalism says facts about similarity hold in virtue of facts about particulars. Each was standardly formulated using supervenience, and the formulations were inadequate for reasons worth spelling out, because they show what grounding is supposed to add.

Supervenience is modal covariation: $A$-facts supervene on $B$-facts if there can be no $A$-difference without a $B$-difference. Its defects as an account of dependence:

• It is not asymmetric. If $A$ supervenes on $B$, $B$ may equally supervene on $A$. Covariation says nothing about direction, and dependence is directional.
• Necessary truths supervene on everything. There can be no difference in whether $2+2=4$ at all, so it covaries trivially with any base — which makes every necessary truth dependent on everything, absurdly.
• It is not explanatory. That two families of fact covary is something to be explained, not an explanation.

Grounding is offered as the notion supervenience was a bad proxy for: asymmetric, explanatory, and hyperintensional — sensitive to more than the modal profile of what it relates.

The formal profile

The orthodox view takes grounding to be irreflexive, asymmetric, transitive, and well-founded. Each has been challenged, and the challenges are more interesting than the orthodoxy.

Irreflexivity. Nothing grounds itself. But consider the fact that something exists: it is plausibly grounded in the existence of each particular thing, including — on some accounts — itself as one of the facts there are. Fine has constructed cases of apparent self-grounding, and while none is decisive they show the principle is not analytic.

Transitivity. The most seriously challenged. Schaffer's counterexample: a large ball with a single small dent. The fact that the ball has a dent is grounded in the shape of that small region; the fact that the ball is roughly spherical is grounded partly in its having a dent — a small imperfection is consistent with, and part of, being roughly spherical. But the shape of the small region does not ground the ball's being roughly spherical; that depends on the whole. If the cases stand, grounding chains cannot simply be concatenated, and much reasoning about layers is invalid.

Well-foundedness. Every chain terminates in something ungrounded — the fundamental. This is a substantive metaphysical thesis rather than a formal requirement, and denying it gives metaphysical infinite descent, discussed on the fundamentality page.

Two further distinctions are standard and useful. Full versus partial grounding: the disjunction is fully grounded in the true disjunct, but each conjunct only partially grounds a conjunction. Mediate versus immediate: whether the grounding runs through intermediate steps.

Relation or operator?

A dispute about logical form, with consequences.

Relational treatments (Schaffer) take grounding to be a two-place predicate relating entities — facts, or objects, or whatever the relata are. This is convenient, allows quantification over grounding facts, and requires the relata to be entities in the inventory.

Operator treatments (Fine, Correia) take it to be a sentential connective: "$\phi$ because $\psi$", where the flanking positions take sentences rather than terms. This avoids commitment to facts as entities — a real advantage, since one might want grounding without accepting the ontology of facts — and it makes the hyperintensionality easier to handle.

The choice matters for the section's own method. On the relational view, accepting grounding talk incurs commitment by the Quinean criterion; on the operator view it does not, which is exactly the manoeuvre that plural quantification and primitive modality make elsewhere. The same structural choice — new entity or new primitive operator — has now appeared four times in this section.

Grounding and causation

The comparison is instructive because grounding is often introduced as "metaphysical causation." Both are explanatory, asymmetric, and (typically) transitive relations that back "because" claims. They differ in that causation is diachronic and contingent, holding between distinct existences and governed by laws, whereas grounding is synchronic and necessary, holding between things that are not wholly distinct.

Whether the analogy is illuminating or misleading is disputed. Those who press it argue that grounding should be theorised with the tools developed for causation — contrastivity, structural equations, difference-making. Those who resist it note that the necessary connection between ground and grounded is precisely what Hume denied of causes, so the two relations have opposite modal profiles.

The sceptics

Grounding is not universally accepted, and the objections are principled rather than merely conservative.

Hofweber classes grounding talk as esoteric metaphysics: it uses a technical notion that cannot be explained in ordinary terms, is introduced by examples, and is understood only by initiates. If the notion cannot be explained except by pointing at cases, we have no assurance that different theorists mean the same thing by it, and no way to adjudicate disputes about its logic.

Wilson presses the sharper objection. There is no unified "big-G" Grounding relation; there are only the small-g relations metaphysicians already had — set membership, mereological composition, the determinable/determinate relation, functional realisation, constitution, supervenience. These are well understood, have different formal properties, and do different work. Lumping them together under one label loses information rather than gaining unification, and the general notion is idle: every application actually appeals to one of the specific relations.

The defender's reply is that the specific relations have something in common — they are all ways of being less fundamental — and that the general notion is what licenses inference across cases. The exchange has the same shape as the ostrich nominalist's refusal: one side demands an explanation, the other denies that the demand is legitimate, and the dispute is about what metaphysics is entitled to ask.

Where grounding sits

Grounding does not belong to the inventory or the category question but to a third thing the section has been circling: the structure of what there is. It presupposes an inventory and asks how its members stand to one another in respect of priority.

Its importance is that it makes several older theses statable. "The mental is nothing over and above the physical," "there are no numbers over and above the objects counted," and "the whole is nothing but its parts" were all attempts to say that something exists but is not a further addition to being — a claim supervenience could not capture and grounding can.

The next page takes the special case where the dependence is of one entity on another rather than of one fact on others: ontological dependence.