Supervenience

Two paintings are exactly alike in every respect that can be seen, measured or chemically analysed: the same pigments, in the same places, on the same canvas, to the same thickness. Could one be beautiful and the other not? Nearly everyone says no. Beauty seems to be a matter of how the thing is, so that if two things are alike in how they are, they cannot differ in how good they are.

That thought is not obviously a theory of anything. It does not say what beauty is, or what makes the painting beautiful, or whether beauty can be reduced to pigment. It says only that one kind of difference needs another kind of difference to accompany it. Philosophers have found this thin thought remarkably useful, and they have found it a good deal thinner than they first supposed.

The core idea

The word came into philosophical use through R. M. Hare, who used it in The Language of Morals (1952) to describe the way moral judgements relate to the natural features of what they judge. If a painting, or a person, is good, then anything exactly like it in all other respects must be good too. Donald Davidson then applied the notion to the mind in "Mental Events" (1970), saying that there cannot be two events alike in all physical respects but differing in some mental respect. Jaegwon Kim's papers of the 1980s, especially "Concepts of Supervenience" (1984), gave the notion its technical shape.

The claim is about two families of properties, and about a pattern of covariation between them. Which things are compared, and across which possibilities, is where the technical work lies, and where the distinct versions of the idea come from. The shape of the claim is a modal one: it concerns what cannot happen, not what does not happen. That a rule against the beautiful twin is true across all actual paintings would be a coincidence. Supervenience says that no possible painting could break it, which is why the notion needs necessity, as the ladder's earlier articles introduced it.

Weak supervenience

Take two items in the same possible world. The weakest thing one might say is that, within that world, items alike in the base are alike in the supervening family.

Consider a world in which everything that has a certain neural state is in pain and everything that lacks it is not. Weak supervenience of pain on neural state holds there. Now consider a second world in which pain goes with a different neural state, and again everything with that state is in pain and nothing without it. Weak supervenience holds there too. In each world, no two things alike in neural state differ in pain.

Yet something is plainly missing. If pain can attach to one physical state in one world and to another in the next, then pain is not tied to the physical in the way that the thought about the paintings was supposed to express. The same worry arises for the paintings. A world could pair beauty with one arrangement of pigment, and another world pair it with a different arrangement, and weak supervenience would be content. Within each world the beauty would still track the pigment, but nothing would fix what the tracking is like from one possibility to the next.

Strong supervenience

The remedy is to compare items across worlds as well as within them.

On this version, the neural state that goes with pain in one world must go with pain in every world. A thing in the first world and a thing in the second that are alike in their neural properties must be alike with respect to pain. The cross-world comparison is exactly what rules out the shifting pairings.

Kim's way of putting the difference is that weak supervenience gives a covariation that holds only within worlds, whereas strong supervenience gives one that holds of necessity: having a given base property necessitates having the corresponding supervening property. Strong supervenience therefore delivers the necessary connection that weak supervenience lacks.

A worked case shows the pairing. Let the supervening property be being a square and let the base be a figure's side-lengths and angles. A figure with four equal sides and four right angles is a square in any world, so strong supervenience holds: the connection between base and supervening property does not vary with the circumstances. Contrast the shifting pairing of pain and neural state above. Each world satisfies weak supervenience, but a thing in the first world and a thing in the second that match in neural state can differ in pain, so strong supervenience fails.

Global supervenience

Both of the first two versions compare individuals. Often what we want is to compare entire worlds.

The point of going global is to allow the base to be the whole distribution of base properties, including relations among things, and not only the properties each thing has on its own. Take being a parent. Two people may be exact intrinsic duplicates, one with a child and one without. The property of being a parent therefore does not strongly supervene on the intrinsic physical properties of the person who has it. But it does supervene globally on the physical history of the world, because two worlds that match physically in every detail match in who has children.

Strong supervenience entails weak supervenience, and the converse fails, as the shifting pairing shows. The relations between global supervenience and the others are more delicate. Global supervenience does not in general entail strong, since it permits the base to be fixed by whole-world patterns, and whether strong entails global depends on how the indiscernibility of worlds is spelled out. Kim's "'Strong' and 'Global' Supervenience Revisited" (1987) and the reply by Paull and Sider, "In Defense of Global Supervenience" (1992), work through the cases. The moral for a reader is that the labels are not interchangeable, and a philosopher who says that one thing supervenes on another has not yet said which claim she is making.

What supervenience does not say

The weakness of the notion is as important as its generality. Supervenience is a claim of covariation, and several things that look like dependence do not follow from it.

It is not asymmetric. If $A$ supervenes on $B$ and $B$ on $A$, nothing is wrong. Any two necessarily coextensive properties supervene on each other, and being triangular and being trilateral are examples. If supervenience were a relation of dependence, each would depend on the other, which is absurd for a pair of properties that are really one.

It is reflexive. Every family supervenes on itself, for there cannot be a difference in a family without a difference in that family. It follows that supervenience cannot by itself mark out a relation of priority.

It is cheap where necessity is cheap. A necessary truth cannot differ between worlds, so any family of properties that is the same in all worlds supervenes trivially on any base at all. A property that every object has in every world, or that none has in any, supervenes on any base whatever.

Most telling is the cross-world pattern for things that are plainly not related by dependence in the intended direction. Socrates and his singleton set are modally tied: the set could not exist without Socrates, and Socrates would not be the sole member of anything without it. Whatever differences there might be in whether the set exists are matched by differences in Socrates. Supervenience therefore holds. But the natural thought is that the set exists because Socrates does, and not the other way round, and supervenience cannot register which way the explanation runs. The same goes for the claim that the mental supervenes on the physical. It is compatible with an emergentist who thinks the mental is a distinct and additional layer of reality that nevertheless varies necessarily with the physical.

What it is used for

The notion earns its place in three areas. In ethics it states what Hare and, before him, G. E. Moore's remark in "The Conception of Intrinsic Value" (1922) that intrinsic value depends solely on intrinsic nature pointed at: moral properties cannot vary independently of natural ones. This is a constraint any metaethical theory has to accommodate, and it has been turned into an argument against some views. If moral properties supervene on natural ones with the strength of a necessity, a theory that treats them as independent items needs to say why the connection is not a miracle.

In the philosophy of mind it supplies a statement of physicalism that is weaker than identity. Mental properties may be realised in many physical ways, so no mental kind is identical with a single physical kind, but they still cannot vary while the physical is fixed. This is the position Davidson found available, and it is what made the notion central to the debate.

In metaphysics it gives a way of stating the claim that one domain adds nothing to another. The idea of a minimal physicalism, on which a world fixed in its physical respects is thereby fixed in every respect, is a global supervenience thesis, and it is a thesis that can be argued for or against without first deciding which properties reduce to which.

Kim's own verdict, in "Supervenience as a Philosophical Concept" (1990), was that supervenience is better seen as a pattern that needs explaining than as an explanation. If the mental strongly supervenes on the physical, there should be a reason, and the candidate reasons are reduction, emergence or something else. He argued further that strong supervenience yields, for each supervening property, a base property or possibly an infinitely long disjunction of base properties that is necessarily coextensive with it, so that the hope of non-reductive physicalism to secure autonomy for the mental was less secure than it looked. Defenders reply that an unwieldy disjunction is not a genuine property, and so the argument does not yield reduction.

What is wanted, then, is a relation that says not just that the base fixes the rest but that the rest holds in virtue of the base, and the advanced tier takes up exactly that relation, for which supervenience was always a stand-in. Before then the intermediate tier turns to a different question about what things are made of across time, namely how one thing can last through change at all.