Ontological Dependence

A hole cannot exist without something it is a hole in. A smile cannot exist without a face. The set $\{Socrates\}$ could not have existed had Socrates not. In each case one entity's existence requires another's, and the requirement runs one way.

Ontological dependence is this relation. It differs from grounding in relating entities rather than facts, and it is the older notion — Aristotle's distinction between substance and the categories that exist only in a substance is a dependence claim.

Varieties

Two cross-cutting distinctions generate the main kinds.

Rigid versus generic. Rigid dependence is on a particular individual: $\{Socrates\}$ depends on Socrates, that very man, and could not have existed with a different member. Generic dependence is on there being some thing of a kind: a person depends on there being cells, but not on any particular cell, and survives their wholesale replacement. Missing the distinction produces bad arguments in both directions — an organism's generic dependence on matter does not make it dependent on the matter it happens to have.

Existential versus essential. Existential dependence concerns what must exist for the dependent thing to exist. Essential dependence concerns what must be mentioned in saying what the dependent thing is. These come apart, and the divergence is the subject of the next section.

A third distinction is sometimes needed: identity dependence, where what the thing is — its identity conditions — is fixed by another. A set's identity is fixed by its members; a boundary's by what it bounds.

The modal analysis and its failure

The obvious account uses necessity:

$$x\text{ depends on }y{=}_{\mathrm{df}}\square (x\text{ exists}\to y\text{ exists})$$

It fails in exactly the way the modal analysis of essence fails, and the parallel is not a coincidence.

It gets the direction wrong. Necessarily, if Socrates exists then $\{Socrates\}$ exists. So on the analysis Socrates depends on his singleton — which is backwards. The set depends on the man; the man does not depend on the set. Necessitation is symmetric here and dependence is not.

It over-generates. Necessarily, if Socrates exists then $2+2=4$, and the number 2 exists, and the empty set exists. So Socrates depends on every necessary existent, which is not a substantive claim about Socrates at all.

Fine's repair is the same as for essence: replace modality with real definition. $x$ depends on $y$ just in case $y$ is a constituent of $x$'s essence — just in case one cannot say what $x$ is without mentioning $y$. Saying what $\{Socrates\}$ is requires mentioning Socrates; saying what Socrates is does not require mentioning the set. The asymmetry the modal account could not see is visible immediately, because essences are not symmetric even where necessitation is.

This is the second place in the section where the same repair is applied to the same failure, and it is the strongest evidence for Fine's general claim that modality is the wrong tool for these notions.

Applications

The notion earns its keep by classifying cases the section has already met.

Two entries repay attention. The trope case is where bundle theory and substance–attribute theory disagree most sharply: if tropes depend rigidly on their bearers, they cannot be what bearers are made of, so the bundle theorist must deny the dependence. And the created abstracta — characters, works — are the cases that make trouble for the abstract/concrete distinction, since they are unlocated and acausal yet historically dependent.

Dependence and fundamentality

Dependence supplies one natural definition of fundamentality: an entity is fundamental if nothing else depends on it for its existence — or better, if it depends on nothing else. The dependence structure of reality is then a partial order, and the fundamental entities are its minimal elements.

Two questions follow, both taken up on the next page. Does the order terminate — must there be minimal elements at all? And is dependence the right relation for fundamentality, or is grounding, or naturalness, or the relation of parts to wholes? These give different answers in cases that matter: a whole may depend on its parts while being prior to them in Schaffer's sense, so dependence and priority can run in opposite directions.

Where dependence sits

Like grounding, this belongs to the structural rather than the inventory or category question. Its distinctive contribution is that it operates on entities, which makes it the natural tool for the many places in this section where something exists but not independently — modes, tropes, boundaries, holes, sets, works, characters.

It also gives a precise sense to a phrase used loosely throughout: nothing over and above. To say the fusion is nothing over and above its parts, or the statue nothing over and above the clay, is to make a dependence claim, and whether it is true is settled by whether one can say what the fusion is without mentioning anything beyond the parts. That is a determinate question, which is more than the phrase had before.