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 <x1, ..., xn> 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.