Supervenience

The notion of supervenience describes a relation between sets of properties. The central idea is that properties belonging to a set A supervene on properties belonging to a set B, the so-called supervenience base, iff any two individuals or possible worlds that are exactly alike with respect to B-properties are exactly alike with respect to A-properties. In other words, any two things that differ with respect to A-properties must differ with respect to B-properties. Mental properties supervene on physical properties, for instance, iff any two individuals that instantiate exactly the same physical properties must instantiate the same mental properties.

The supervenience relation in its contemporary use first rose into prominence in metaethics. According to Richard M. Hare, any two persons or actions satisfying exactly the same non-moral description have to be ascribed the same moral attributes; otherwise, the logical rules for the use of terms like ‘good’ would be violated. Thus supervenience is employed to formulate adequacy conditions on the use of moral terms. Later, Donald

Davidson introduced the notion into the philosophy of mind to describe the controversial relationship between the mental and the physical. Nowadays, philosophy of mind still is one of the most important fields of application of the supervenience relation. However, the notion also plays a central role in various other fields of analytic philosophy. In contemporary metaphysics, there are debates on whether modal properties supervene on non-modal properties and whether dispositions supervene on categorical properties. In ethics and aesthetics, supervenience is used to describe the relationship between normative and descriptive properties as well as between aesthetic and natural properties.

1 2. Definitions of supervenience

2.1. Weak and strong supervenience

The intuitive definition of supervenience given above leaves open whether the supervenience relation relies on comparisons between single individuals or between whole possible worlds.

Depending on how this issue is decided, one can spell out the definition of supervenience in different ways. If supervenience is taken to rely on comparisons between single individuals, the two standard notions are weak and strong supervenience, usually defined in the following way:

Weak supervenience (WS): A-properties weakly supervene on B-properties iff for any possible world w and any individuals x and y, if x and y have the same B-properties in w, then x and y have the same A-properties in w.

Strong supervenience (SS): A-properties strongly supervene on B-properties iff for all possible worlds w1 and w2 and any individuals x and y, if x in w1 has the same B-properties as y in w2, then x in w1 also has the same A-properties as y in w2.

To illustrate the intuition behind (WS) and (SS), suppose that mental properties weakly supervene on physical properties and that x instantiates the mental property of being happy in some possible world w. Then, it follows from (WS) that all individuals who inhabit w and have the same physical properties as x are happy, too. The crucial difference between (WS) and (SS) is that the former only requires that individuals inhabiting the same possible world and having the same B-properties are alike with respect to A-properties, whereas strong supervenience involves cross-world comparisons between individuals. Accordingly, mental properties strongly supervene on physical properties iff any two individuals, whether they are

2 world-mates or inhabit different possible worlds, have the same mental properties if they are alike in any physical respect. (SS) hence implies (WS), i.e. whenever A strongly supervenes on

B, then A weakly supervenes on B, but the converse does not hold.

2.2. Global supervenience

In contrast to weak and strong supervenience, which rely on comparisons between single individuals, the notion of global supervenience takes the distribution of properties over whole possible worlds into account. The underlying idea is that A globally supervenes on B iff any possible worlds w1 and w2 that are exactly alike with respect to B are also exactly alike with respect to A. Suppose that Φ is a set containing properties and relations of a certain type, e.g. physical properties and relations. Then, the claim that w1 and w2 are exactly alike with respect to Φ is typically interpreted as the claim that there is a Φ-preserving isomorphism between w1 and w2, i.e. a one-one mapping Γ of the inhabitants of w1 onto the inhabitants of w2, such that for any Φ-property F, an individual x has F in w1 iff Γ(x) has F in w2, and for any Φ-relation R, the tuple instantiates R in w1 iff <Γ(x1), ..., Γ(xn)> instantiates R in w2.

Accordingly, w1 and w2 are alike with respect to B iff there is a B-preserving isomorphism between them. The three standard definitions of global supervenience all rely on this notion:

Weak global supervenience (WGS): A-properties weakly globally supervene on B-properties iff for any possible worlds w1 and w2, if there is a B-preserving isomorphism between w1 and w2, then there is an A-preserving isomorphism between w1 and w2.

Intermediate global supervenience (IGS): A-properties intermediately globally supervene on

B-properties iff for any possible worlds w1 and w2, if there is a B-preserving isomorphism

3 between w1 and w2, then there is a B-preserving isomorphism between w1 and w2 which is also an A-preserving isomorphism.

Strong global supervenience (SGS): A-properties strongly globally supervene on B-properties iff for any possible worlds w1 and w2, any B-preserving isomorphism between w1 and w2 is an

A-preserving isomorphism.

The notions of global supervenience are all logically weaker than the notion of strong supervenience (SS). This becomes evident, for instance, if it is assumed that externalism about mental content is true. According to externalism, mental properties, such as beliefs, do not solely depend on an individual’s intrinsic physical properties, but also on the environment in which it is placed. In other words, if externalism is true, mental properties fail to strongly supervene on intrinsic physical properties. To see this, suppose that John living on Earth and

Twin-John living on Twin-Earth instantiate exactly the same intrinsic physical properties. If then John and Twin-John both believe that the transparent liquid called ‘water’ in their community quenches thirst, John has a belief about H2O, whereas Twin-John has a belief about XYZ. According to externalism, this means that John and Twin-John are in different belief states and consequently have different mental properties. Thus, (leaving aside the fact that John’s body partially consists of H2O, whereas Twin-John’s body partially consists of

XYZ), John and Twin-John have exactly the same intrinsic physical properties, but different mental properties and strong supervenience fails. The criterion of global supervenience is not violated, however. Earth and Twin-Earth, which can be considered as two different possible worlds, are radically different in some physical respect, viz. the chemical structure of the transparent liquid called ‘water’. Therefore, there is no isomorphism preserving physical

4 properties between them and none of the three criteria of global supervenience will be violated if John and Twin-John have different mental properties.

In general, as long as there is no formal restriction on the structure of the properties contained in A and B, the three notions of global supervenience are logically distinct from

(WS) and (SS). Karen Bennett shows, however, that each of the definitions of global supervenience is equivalent to strong supervenience if A and B contain intrinsic properties only. Moreover, Robert Stalnaker proposes a proof to the effect that if the supervenience base contains properties involving complete B-descriptions of possible worlds, (SS) is equivalent to

(SGS). Yet, both Bennett’s and Stalnaker’s arguments are restricted to the case where A and B contain properties only. Oron Shagrir argues that if A and B contain relations, (SGS) is crucially distinct from (SS), since (SS) is defined for properties only and (SGS) can make claims about dependence relationships between sets of relations which cannot be made using

(SS).

3. Supervenience and Other Relations

Supervenience is a term of art which does not correspond to any common-sense notion. In particular, it cannot be equated with a causal or explanatory relationship. That supervenience cannot be equated with a causal relationship follows directly from the observation that supervenience is a synchronous relation, whereas causality is a diachronic relationship. That supervenience claims alone are not sufficient for grounding an explanatory relation becomes clear in view of the fact that supervenience is a reflexive relation – each set of properties trivially supervenes on itself according to all notions of supervenience specified above.

However, identity does not count as an explanatory relationship. If Peter has the mental property of being happy, for instance, this cannot suitably be explained by the fact that Peter is happy.

5 Given that supervenience is not a causal or explanatory relationship, many authors claim that supervenience expresses a dependence relation: if A supervenes on B, then the properties contained in A are dependent on the properties contained in B. It is questionable, however, whether supervenience is strong enough to ground a dependence relation. If dependence is understood as an ontological priority relation, i.e. in such a way that A’s supervenience on B implies that the B-properties are ontologically prior to or more fundamental than the A-properties, supervenience cannot be equated with dependence.

Suppose, for instance, that A = {being a father} and B = {being male, having at least one child}. Then, A supervenes on B and vice versa. But the mutual supervenience relation holding between A and B does not imply that the properties contained in B are more fundamental than the property of being a father or that the latter property is more fundamental than the properties contained in B

It is possible, however, to interpret supervenience as a certain kind of functional dependence. Consider a complete physical description of an individual (or a possible world).

Supervenience of the mental on the physical then implies that there is exactly one mental description, such that any individual (or possible world) satisfying the physical description under consideration also satisfies this particular mental description. Accordingly, the supervenience relation between the mental and the physical can be interpreted as a function from combinations of physical properties to combinations of mental properties: any possible combination of physical properties instantiated by an individual or possible world will be mapped onto exactly one combination of mental properties.

6 4. Applications

4.1. Physicalism

One major field of application of supervenience is the definition of physicalism in the philosophy of mind. Physicalism is usually understood as the thesis that fixing all the physical facts is sufficient for fixing all the facts. Thus, physicalists claim that the non-physical, particularly the mental, is necessitated by and systematically covaries with the physical. This implies, for instance, that zombies, creatures that are physically like us but have no mental properties whatsoever, are metaphysically impossible. On the basis of this intuition, several authors, notably Frank Jackson and David Lewis propose a definition of physicalism, according to which physicalism is true in a world w iff any physical duplicate of the actual world is a duplicate simpliciter of w. This condition can be interpreted as a global supervenience claim: physicalism is true in w iff each possible world which is like w in all physical respects is also like the actual world in all nonphysical respects. Thus, for example, if physicalism is true in the actual world, then there are no metaphysically possible worlds that are like the actual world but in which the physical duplicates of some humans are zombies.

According to this definition of physicalism, the humans and their physical duplicates are also alike in all nonphysical respects.

The intuitive definition of physicalism leaves open how the underlying global supervenience should be interpreted. It is widely agreed however, that (WGS) and (IGS) are too weak to ground physicalism since they are compatible with what Karen Bennett calls intra-world variation, i.e. two individuals inhabiting the same possible world and having exactly the same physical properties, but different mental properties. Yet, if there can be two individuals inhabiting the same possible world who are in exactly the same bodily state, but have radically different mental properties, such that one of them feels happy, say, whereas the other feels sad, the requirement that mental properties systematically covary with physical

7 properties is violated. The notion of (SGS) excludes intra-world variation. Accordingly, if physicalism is to be understood as a global supervenience claim, then global supervenience should be interpreted as (SGS).

It is controversial, however, whether physicalism can adequately be defined in terms of supervenience. We will mention here two challenges. One is that a global supervenience requirement might be too strong. It captures the intuition that zombies are not metaphysically possible. However, it rules out that there are worlds which are very similar to the actual world, but contain extra entities, such as angels or ghosts. Yet physicalists do not have to rule out non-physical entities, e.g. angels or ghosts, as logically or metaphysically possible. The central tenet of physicalism only is that in worlds like our world, all non-physical entities are necessitated by and systematically covary with the physical and that therefore our world is not inhabited by any angels or ghosts. Jackson therefore proposes to restrict the supervenience thesis to worlds which are minimal physical duplicates of w, i.e. worlds which are like w in all physical respects and which do not contain any extra entities (a similar approach was proposed by Lewis, Horgan, and Chalmers). If only such worlds are taken into account, the definition of physicalism is compatible with the assumption that angels or ghosts are metaphysically possible.

Another challenge is that a supervenience-based criterion of physicalism might be too weak. One problem is that global supervenience theses cannot rule out the existence of necessary non-physical beings, e.g. the assumption that God exists in every metaphysically possible world, which is incompatible with physicalism. Moreover, it can be argued that physicalism not only requires the existence of an ontological covariance relation between non- physical and physical properties, but also that this covariance can be explained in a physicalistically acceptable way. Terence Horgan therefore proposes to replace the ordinary notion of supervenience, which cannot ground an explanatory relationship, by the stronger

8 notion of superdupervenience – a supervenience relation which does not just hold for metaphysical reasons, but is in addition explainable in a physicalistically acceptable way.

However, even though it is controversial whether supervenience alone is sufficient for defining physicalism, it is widely agreed that some supervenience requirement is a necessary condition of physicalism. Even proponents of opposing views take for granted that if there is a systematic relationship between mental and physical properties at all, then it must obey some supervenience principle. This is the reason why supervenience has a crucial role to play in the debate on physicalism and the mind-body problem.

4.2. Coincidentalism

Another important application of supervenience pertains to the debate over coincident entities.

Coincidentalism is the view that there are pairs of numerically distinct entities that are made of the same parts. Coincidentalists argue, for example, that a statue and the lump of matter from which it is made are coincident yet numerically distinct entities, since they differ in their modal properties: the lump but not the statue can survive being flattened. A pattern of supervenience argument against Coincidentalism is that their modal properties cannot differ.

The modal difference between the statue and the lump must be grounded in qualitative non- modal properties and relations (BASE), such as their subatomic structure. Modal properties, in other words, supervene on non-modal, BASE, properties and relations. But given that the statue and the lump – as coincident entities – share exactly the same BASE at the time they coincide, we must conclude that the statue and the lump cannot differ modally.

Coincidentalists can reply that there are understandings of supervenience under which the alleged conclusion does not follow: the statue and the lump can still differ in their modal properties. Assume, for example, that modal properties weakly globally supervene on BASE.

Weak global supervenience requires that BASE-indiscernible worlds be modal-indiscernible.

9 It requires that in a BASE-indiscernible world, one object has the modal properties of the statue, and another the modal properties of the lump. But this requirement is certainly in accord with the entities' coincidence, as the statue and the lump can have different modal properties.

In responding, some have pointed out that not every notion of supervenience counts as an adequate notion of dependence. We must be sure, for example, that weak global supervenience relations reflect adequate grounding relations. However, Bennett's intra-world variation example (section 4.1), among other examples, gives reasons to think that weak global supervenience is not a notion of dependence, and thus cannot establish the grounding of the modal in the non-modal. More recently, Theodore Sider suggests that there is a fundamental modal relation between a statue and the lump of matter. This relation, of opposite-possibly surviving being squashed, means that exactly one might have survived being squashed. It strongly globally supervenes on BASE. The strong global supervenience of the modal (monadic) properties (surviving being squashed) on BASE fails. But these monadic properties are artifacts of the language we ordinarily speak, and so the supervenience-failure does not indicate a real metaphysical non-dependence. Here, too, supervenience does not settle the metaphysical debate, but it advances our understanding of unsettled issues.

Oron Shagrir The Hebrew University of Jerusalem

Vera Hoffmann-Kolss Universität Osnabrück

See also Causation, Philosophical Views of; Determinism (in Philosophy and the Social

Sciences); Distributed Cognition and Extended Mind Theory; Emergence; Explanation,

Theories of; Mind-Body Relation