SUPERVENIENCE

There is supervenience when and only when there cannot be a difference of some sort A (for example, mental) without a difference of some sort B (for example, physical). When there cannot be an A-difference without a B-difference, then but only then A-respects supervene on B-respects. Supervenience claims are thus modal claims. They are claims to the effect that necessarily, there is exact similarity in A-respects whenever there is exact similarity in B-respects. So if, for example, mental properties supervene on physical properties, then, necessarily, individuals that are physically indiscernible (exactly alike with respect to every physical property) are mentally indiscernible (exactly alike with respect to every mental property). Thus, A-properties supervene on B-properties just in case how something is with respect to A-properties is a function of how it is with respect to B-properties.

Supervenience has been invoked in nearly every area of analytical philosophy. In addition to its having been claimed that mental properties supervene on physical properties, it has also been claimed that normative properties—moral, aesthetic, epistemic, and so on—supervene on natural properties, that general truths supervene on particular truths, and that modal truths supervene on nonmodal truths. Supervenience, moreover, has been used to distinguish various kinds of internalism and externalism: epistemic, semantic, and mental. And it has been invoked to test claims of reducibility and claims of conceptual analysis, both of which entail supervenience claims. Much of the philosophical work on supervenience itself, as opposed to its philosophical applications, has focused on distinguishing various varieties of supervenience, and examining their pairwise logical relations. But, before turning to the main varieties of supervenience, we can make some central points working just with the idea that there cannot be an A-difference without a B-difference.

1. Model Force

The term cannot in a supervenience claim can express logical impossibility, nomological impossibility (impossibility by virtue of laws of nature), or some other kind of impossibility. If it is logically impossible for there to be an A-difference without a B-difference, then A-properties logically supervene on B-properties; if that is only nomologically impossible, then there is merely nomological supervenience. The property being a bachelor logically supervenes on the set of properties {being unmarried, being a man } because it is logically impossible for individuals to differ with respect to being a bachelor without differing with respect to some property in that set. According to the Wiedemann-Franz law, the electrical conductivity of metals covaries with their thermal conductivity; thus, in metals, electrical-conductivity properties nomologically supervene on thermal conductivity properties (and vice versa).

2. The Relata of the Supervenience Relation

A difference can be a difference in any respect in which there can be a difference: a difference with respect to what properties something has, in what truths hold, in what conditions obtain, in what events occur, in what laws of nature there are, and so on. The relata of the supervenience relation thus seem many and varied. Indeed in "There cannot be an A-difference without a B-difference," A and B may range over nearly all manner of entities. It is often claimed, however, that nonempty sets of properties are the primary relata of the supervenience relation: either A-respects and B-respects will be properties in some nonempty sets of properties A and B, or else A-respects will supervene on B-respects in virtue of A-properties supervening on B-properties (Kim 1984). This view requires an "abundant" (as opposed to a "sparse") conception of properties, according to which properties "may be as extrinsic, as gruesomely gerrymandered, as miscellaneously disjunctive, as you please. … [They] far outrun the predicates of any language we could possibly possess. … In fact, the properties are as abundant as the sets themselves, because for any set whatever, there is the property of belong to that set" (Lewis 1986, 59–60).

Indeed, on this conception, there are even necessarily uninstantiated properties such as being an electron and not being an electron, and so properties are not always ways things might be. In the literature on supervenience, an abundance of properties is often assumed, and such will be assumed in this essay. But whether there is supervenience does not turn on whether there are abundant properties, or, if nominalists are right, even on whether there are properties at all. A nominalist could maintain that what A-predicates are true of something supervenes on what B-predicates are true of it. Nor does it turn on whether there is some uniform category of being the members of which are the primary relata of the supervenience relation. It does not even turn on whether there is a relation of supervenience in anything other than a merely pleonastic sense: talk of A bearing the supervenience relation to B might be taken to be just a way of saying that there cannot be an A-difference without a B-difference. What matters is that there be true statements of the form, "There cannot be an A-difference without a B-difference." And such there are in abundance, including many of philosophical interest.

3. Logical Properties of the Supervenience Relation

Supervenience is reflexive, transitive, and nonsymmetric. Trivially, it holds when A = B and so is reflexive. It is also transitive, because if there cannot be an A-difference without a B-difference, and cannot be a B-difference without a C-difference, then there cannot be an A-difference without a C-difference. However, it is neither symmetric nor asymmetric, and so is nonsymmetric. Every reflexive case of supervenience is trivially symmetric. But, for instance, being a bachelor asymmetrically supervenes on {being unmarried, being a man }. James is a man and Vanessa is not, and so they differ with respect to B-properties. But since James is married, they are exactly alike with respect to being a bachelor : neither of them has that property.

4. Supervenience and Entailment

A notion of property entailment can be defined as follows: property P entails property Q if and only if it is logically necessary that whatever has P has Q. Supervenience shares with entailment the properties of being reflexive, transitive, and nonsymmetric. Property supervenience, however, is neither necessary nor sufficient for property entailment. The property being a brother entails the property being a sibling. But being a sibling does not supervene on being a brother. Thus, suppose that Sarah has a sister and that Jack is an only child. Then Sarah is a sibling and Jack is not, though neither is a brother. Property entailment thus does not suffice for supervenience.

It is often claimed in the literature that logical supervenience suffices for entailment (see, for example, Chalmers 1996). But that is not in general true. If A = {P&Q} and B = {P, Q}, then the A-property logically supervenes on B-properties, but no B-property entails the A-property. Indeed, every property F will supervene with logical necessity on its complement, not-F: Two things cannot differ with respect to F without differing with respect to not-F (and vice versa). But of course being F does not entail being not-F (McLaughlin 1995).

There seem, moreover, to be philosophically interesting cases of logical supervenience without entailment. Particular truths do not entail general truths. But general truths (arguably) supervene on particular truths (Skyrms 1981, Lewis 1986a). Bertrand Russell correctly noted: "you cannot ever arrive at a general fact by [deductive] inference from particular facts, however, numerous" (1918/1992, p. 235, quoted in Bricker 2005). He concluded from this that "you must admit general facts as distinct from and over and above particular facts" (1981/1992, p. 236). If, however, general facts logically supervene on particular facts, then there is a sense in which that is not so, for once all the particular facts of a world are fixed, the general facts are fixed as well. A compelling case has been made that general facts logically supervene on particular facts, despite not being entailed by them (Bricker 2005).

5. Supervenience and Ontological Priority

Many of the most interesting cases of supervenience are ones in which the subvenient factors are ontologically prior to the supervenient factors. Supervenience itself, however, is not an ontological priority relation. Ontological priority is irreflexive and asymmetric: Nothing can be ontologically prior to itself or be ontologically prior to something that is ontologically prior to it. But supervenience is reflexive and not asymmetric. Supervenience claims do not, in general, entail "in virtue of" claims. Every property supervenes on its complement, but of course nothing has a property F in virtue of having its complement not-F because nothing has both F and not-F (at least at the same time). Further, properties that everything necessarily has, and ones that nothing could possibly have, supervene on any property whatsoever. The necessary property being an electron or not an electron trivially supervenes on the property being an antique ; and the necessarily uninstantiated property being an electron and not being an electron does well. The reason is that no two things can differ with respect to either such noncontingent property; and so, trivially, for any property, no two things can differ with respect to them without differing with respect to it. But there is no ontological priority in such cases. (McLaughlin 1995)

6. Superduper Venience

Supervenience is just the relation of functional dependence: A-properties supervene on B-properties just in case how something is with respect to A-properties is a function of how it is with respect to B-properties. Given that, when A-properties supervene on B-properties, we expect there to be some explanation of why that is so. In the case of logical supervenience, the explanation might be that A-properties are necessary properties or that they are properties nothing could have. Or the explanation might be that A-properties are identical with B properties. Or the explanation might be that A-properties are determinables of B-properties and B-properties are all the determinates of A-properties, as being colored is a determinable of all the shades of color (being red, and so on), and they are determinates of being colored. And in the case of merely nomological supervenience, the explanation will appeal to a law of nature. (This list of possible explanations is not intended to be exhaustive.) When a supervenience relation is explainable, there is "superdupervenience" (Horgan 1993). Appeals to in principle unexplainable supervenience—supervenience without the possibility of superdupervience—would arguably be mystery-mongering.

7. Supervience, Conceptual Analysis, and Reduction

Although logical supervenience does not suffice for conceptual analysis, the latter requires the former: if A-factors can be conceptually analyzed in terms of B-factors, then A-factors logically supervene on B-factors. Supervenience is thus useful in testing claims that a certain a kind of conceptual analysis is possible. According to a simple causal theory of perceptual knowledge, a subject's perceptual knowledge that P can be analyzed as P's bearing an appropriate causal connection to the subject's perceptual belief that P. To test the claim, one need not await a specific proposal as to what kind of causal connection is appropriate. For such a conceptual analysis is possible only if two believers that P cannot differ with respect to perceptually knowing that P without differing with respect to how the fact that P is causally connected to their belief that P. This supervenience thesis is open to refutation by a single counterexample. The well-known "fake barn country" case (Goldman 1976) yields a putative counterexample to this thesis. Thus, the claim that a certain kind of conceptual analysis is possible can be refuted by appeal to a false implied supervenience thesis (or, FIST). Claims that certain kinds of reductions are possible can be similarly tested by their implied supervenience theses. (McLaughlin 1995)

8. Individual/global Supervenience

There is a distinction between individual supervenience and global supervenience. The former concerns differences in individuals; the latter concern differences in possible worlds. The claim that individuals cannot differ with respect to their moral properties without differing with respect to their natural properties (Hare 1952) is an individual supervenience thesis. The claim that possible worlds cannot differ with respect to what general truth hold in them without differing with respect to what particular truths hold in them is a global supervenience thesis.

9. Strong/weak Individual Supervenience

Two nonequivalent kinds of individual supervenience have been formulated as follows (see Kim 1987):

possible-worlds weak individual supervenience

A-properties weakly supervene on B-properties if and only if in any possible world w, B-indiscernible individuals in w are A-indiscernible in w.

possible-world strong individual supervenience

A-properties strongly supervene on B-properties if and only if for any possible worlds w and w*, and any individuals x and y, if x in w is B-indiscernible from y in w*, then x in w is A-indiscernible from y in w*.

The possible worlds quantified over might be all logically possible worlds or only all nomologically possible worlds (and so on); thus, weak and strong supervenience relations can have different modal strengths. As the names suggest, strong supervenience is stronger than weak supervenience (modulo sameness of modality). When the range of worlds is the same, strong supervenience of A-properties on B-properties entails weak supervenience of A-properties on B-properties, but the latter does not in general entail the former. Notions of weak and strong individual supervenience have also been formulated as follows, using the modal operator necessarily rather than quantification over possible worlds (Kim 1984).

operator-weak individual supervenience

A-properties weakly supervene on B-properties if and only if necessarily, for any A-property F, if something has F, then there is a B-property G such that it has G, and whatever has G has F.

operator-strong individual supervenience

A-properties strongly supervene on B-properties if and only if necessarily, for any A- property F, if something has F, then there is a B-property G such that it has G, and necessarily whatever has G has F.

The strong version is formulated exactly like the weak version except that it contains one more necessity operator. The two modal operators in the strong case can be the same or different. When all of the modal operators are the same, strong supervenience entails weak supervenience, but the latter does not in general entail the former.

If necessity is understood as universal quantification over possible worlds, then operator-weak supervenience entails world-weak supervenience, and operator-strong supervenience entails world-strong supervenience. However, the converse entailments do not hold in general. The operator definitions go beyond the idea that B-indiscernible individuals must be A-indiscernible. Operator-strong supervenience with logical necessity guarantees that every A-property is entailed by a B-property. And both operator-weak supervenience and operator-strong supervenience entail that if something has an A-property, then it has some B-property. Neither world-weak supervenience nor world-strong supervenience has that entailment, and so world-strong supervenience fails even to entail operator-weak supervenience (McLaughlin 1995). The property being a bachelor fails to even operator-weakly supervene on {being unmarried, being a man }, even though the former world-strongly supervenes on the later. The weak and strong operator definitions are, however, equivalent to the corresponding world-definitions in the special case of nonempty sets of properties closed under the Boolean operations of complementation and conjunction and/or disjunction, and ones involving quantification (Kim 1987). (The qualifiers world and operator will now be dropped.)

10. Supervenience and Internalism/externalism Distinctions

Individual supervenience has proved useful for formulating various kinds of internalism/externalism distinctions. For example, according to internalists about mental content, what content a mental state has will strongly supervene on intrinsic properties of the subject of the mental state. Content externalists deny such supervenience, and indeed typically deny there is even weak supervenience: they typically hold that two subjects within a possible world can be intrinsic duplicates while being in mental states with different contents. (Twin-Earth cases [Putnam 1975] are invoked in would-be arguments by appeal to FISTs against internalist theories of content.) Similarly, an internalist about epistemic justification asserts that whether a belief is justified strongly supervenes on what mental states the subject is in. Epistemic externalists deny that, and indeed deny that whether a belief is epistemically justified even weakly supervenes on what mental states the subject is in. Moreover, supervenience has been employed to capture the traditional distinction between internal and external relations (Lewis 1986a): internal relations (such as being taller than ) strongly supervene on the intrinsic natures of its relata, whereas external relations (such as being three kilometers from ) fail to even weakly supervene on the intrinsic natures of its relata.

11. Weak Supervenience without Strong Supervenience

There can be weak supervenience without strong supervenience. But when this is the case, we expect an explanation of why weak supervenience holds that does not entail that strong supervenience holds as well. In any possible world, if two individuals assert exactly the same propositions, then they are exactly alike in having asserted a true proposition: The one will have asserted a true proposition if and only if the other did. The explanation is that any proposition will have a unique truth value relative to a world. But since contingent propositions are true in some worlds but not in others, strong supervenience fails in the case in question. It has been claimed that, although moral properties weakly supervene on natural properties, they do not strongly supervene on them (Hare 1952). And it has been claimed that, although mental properties weakly supervene on physical properties, they do not strong supervene on them (Davidson 1985). Defense of these claims requires an explanation of why weak supervenience holds despite the failure of strong supervenience. Although attempts have been made to provide such an explanation in the moral case (Blackburn 1993), there has been no attempt in the mental case. Many philosophers doubt such an explanation is possible in the mental case.

12. Global Supervenience

Global supervenience has been invoked in the formulation of various philosophical doctrines (see, for example, Horgan 1982, 1984; Haugeland 1982; Post 1987). David Lewis's (1986a, x) doctrine of Humean Supervenience, according to which everything supervenes on the pattern of perfectly natural qualitative properties across space-times points, is a global supervenience thesis. Although Donald Davidson (1970) proposed a weak individual supervenience thesis to characterize the dependency of mental properties on physical properties, several attempts have been made to characterize physicalism as a global supervenience thesis (Lewis 1983, Chalmers 1996, Jackson 1996).

For example, Frank Jackson has proposed the following formulation: Any possible world that is a minimal physical duplicate of our world is a duplicate simpliciter of it (1998, p. 12). A physical duplicate of our world is any world exactly like it in every physical respect—with respect to its worldwide pattern of distribution of physical properties and relations, its physical laws, and so on. A minimal physical duplicate is any physical duplicate that contains nothing other than what is metaphysically necessary to be a physical duplicate. It is controversial whether this thesis suffices for physicalism; unlike physicalism, it seems compatible with the existence of a necessarily existing God. But even if it does not suffice, if physicalism requires it, then it earns its keep. A substantive condition of adequacy on physicalism would be that it explain why the supervenience thesis is true. And physicalism itself would rendered testable, even in the absence of a fully adequate formulation. Given that we are phenomenally conscious, if, as some philosophers (Chalmers 1996) maintain, a "zombie world" is possible—a world that is a minimal physical duplicate of our world but entirely devoid of phenomenal consciousness—then physicalism is false. Of course, the success of this would-be refutation by appeal to a FIST turns on the controversial issue of whether a zombie world is indeed possible.

Global property supervenience has often been formulated as follows:

global supervenience

A globally supervenes on B if and only if, for any possible worlds w₁ and w₂, if w₁ and w₂, have exactly the same worldwide pattern of distribution of B-properties, then w₁ and w₂ have exactly the same worldwide pattern of distribution of A-properties.

It is now usually acknowledged that the notion of a worldwide pattern of distribution of properties should be understood in terms of a kind of property-preserving isomorphism between worlds as follows (McLaughlin 1996, 1997; Stalnaker 1996):

An isomorphism I between the inhabitants of any worlds w₁ and w₂ preserves F-properties if and only if, for any x in w₁, x has an F-property in w₁ just in case the image of x under I (the individual to which I maps x) has P in w₂.

13. Weak, Intermediate, and Strong Global Supervenience

A variety of different kinds of global supervenience has been formulated:

A-properties weakly globally supervene on B-properties if and only if, for any worlds w₁ and w₂, if there is a B-preserving isomorphism between w₁ and w₂, then there is an A-preserving isomorphism between them (McLaughlin 1996, 1997; Stalnaker 1996; Sider 1999).

A-properties intermediately globally supervene on B-properties if and only if, for any worlds w₁ and w₂, if there is a B-preserving isomorphism between w₁ and w₂, then there is at least one isomorphism between them that is both A-and-B-preserving (Shagrir 2002, Bennett 2004).

A-properties strongly globally supervene on B-properties if and only if, for any worlds w₁ and w₂, every B-preserving isomorphism between w₁ and w₂ is an A-preserving isomorphism between them. (McLaughlin 1996, 1997; Stalnaker 1996; Sider 1999). Strong global supervenience entails intermediate global supervenience, which entails weak global supervenience. But the converse entailments all fail to hold in general.

There seem to be no cases of philosophical interest in which weak global supervenience holds, but both strong and intermediate global supervenience fail to hold. In some cases of interest, however, intermediate global supervenience holds, even though strong global supervenience may fail to hold. Many philosophers maintain that two numerically distinct objects can have the same spatiotemporal location and so be spatiotemporally coincident. A frequently cited would-be example is a clay statue and the lump of clay that makes it up. Even if they are spatiotemporally coincident throughout their existence—created at the same time and destroyed at the same time—they nevertheless have different modal properties: for example, the lump could survive being squashed, while the statue could not. But they have exactly the same categorical properties (mass, size, shape, and so on). If the statue is indeed not the lump, then the statue's modal properties will neither individually strongly nor individually weakly supervene on its categorical properties. (Multiple-domain individual supervenience will hold, however [see Kim 1988 and Zimmerman 1995].) And modal properties will fail to strongly globally supervene on categorical properties. But weak global supervenience (Sider 1999) and intermediate global supervenience (Bennett 2004) will both hold. An appeal to intermediate global supervenience would not by itself, however, solve "the grounding problem," the problem of how individuals with exactly the same categorical properties can differ in their modal properties (Bennett 2004). A solution to the grounding problem would have to explain why intermediate global supervenience holds and do so in a way that does not entail that coincident objects are identical.

14. Some Equivalancies

The plethora of technical definitions of kinds of supervenience gives the appearance of more variety than there is. Strong individual supervenience entails strong global supervenience (Kim 1984), but strong global supervenience does not in general entail strong individual supervenience (Paull and Sider 1992). Nevertheless, strong individual supervenience and strong global supervenience are equivalent in cases in which the base set of properties B is closed under Boolean operations and ones involving quantification and identity (Stalnaker 1996). Strong individual supervenience is also equivalent to strong global supervenience in cases in which A and B are sets of intrinsic properties (Shagrir 2002, Bennett 2004). It has, moreover, been compellingly argued that in cases in which A and B are sets of intrinsic properties, weak and strong individual supervenience are equivalent as well. Weak individual supervenience, strong individual supervenience, and strong global supervenience are equivalent for sets of intrinsic properties.

See also Davidson, Donald; Knowledge and Modality; Lewis, David; Modality, Philosophy and Metaphysics of; Physicalism; Reduction; Russell, Bertrand Arthur William.

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