Varieties of Supervenience Robert Stalnaker Noûs, Vol. 30, Supplement: Philosophical Perspectives, 10, Metaphysics, 1996. (1996), pp. 221-241. Stable URL: http://links.jstor.org/sici?sici=0029-4624%281996%2930%3C221%3AVOS%3E2.0.CO%3B2-9 Noûs is currently published by Blackwell Publishing.
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Philosophical Perspectives, 10, Metaphysics, 1996
VARIETIES OF SUPERVENIENCE
Robert Stalnaker
Massachusetts Institute of Technology
1. Introduction
"Supervenience" has been defined in a variety of ways, and different and conflicting things have been said about the relations between different supervenience concepts. The concepts have been deployed in the discussion of a range of different philosophical problems, sometimes to formulate a thesis to be defended (a version of materialism about the mind, or internalism about intentional or experiential states, a Humean thesis about necessary connection, a "reductionist" thesis about personal identity), sometimes to clarify or sharpen a problem by spelling out the common ground between conflicting theses. (Contrasting theses in metaethics, or the philosophy of mind, may agree that evaluations, or attributions of mental states, are supervenient on natural, or physical, facts. Contrasting theses about criteria for personal identity may agree that facts about identity across time are supervenient on momentary mental and physical states, and causal relations between them), sometimes to raise a problem rather than to solve one (how can moral properties be supervenient on natural properties, and yet not be analytically entailed by them?). My aim in this paper will be a modest one; to get clearer about some of the dimensions on which different supervenience concepts differ, and about the role that they play in the formulation of philosophical problems and theses. It is not my intention to defend or attack any particular supervenience thesis, but only to explore the abstract concepts of supervenience, and the intuitive ideas that motivate them. On the abstract definitions, I will make some claims, but my main concern is with the intuitive ideas and philosophical applications. As the leading maven of supervenience, Jaegwon Kim, has emphasized, supervenience is a philosopher's technical term-we can define it as we like to suit whatever philosophical purpose we have for it. There does, however, seem to be an intuitive idea that the technical concepts are trying to articulate and make precise, and that plays a role in evaluating the
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different definitions. In fact, I think there are two different intuitive ideas that motivate the attempts to articulate concepts of supervenience, ideas that there is some tension between. I will begin by trying to say, in a rough and uncritical way, what those ideas are, as I understand them, and what some of the different philosophical projects are to which these idea have been thought to be relevant. Then I will sketch some of the different definitions of supervenience, and discuss the relations between them. Next, I will look at the concepts of necessity relative to which all of the supervenience concepts are defined. I will conclude by raising some questions about the role of concepts of supervenience in the dialectic of metaphysical argument and analysis. 2. Two intuitive ideas of supervenience
A supervenience thesis, on one way of understanding the notion, is a reductionist thesis. To say that the A-properties or facts are supervenient on the B-properties or facts is to say that the A-facts are, in a sense, redundant, since they are already implicitly specified when one has specified all the B-facts. A-facts are not facts "over and above" the B-facts, not something "separate." To state an A-fact, or ascribe an A-property, is to describe the same reality in a different way, at a different level of abstraction, by carving the same world at different joints. To borrow a metaphor from Saul Kripke, if all the facts are supervenient on the B-facts, then God, when he creates the world, is finished when he has determined all the Bproperties of things. It is not that others-God's apprentices perhaps-fill in the picture by adding the A-properties. There is nothing more to be done. Here are some relatively uncontroversial examples of supervenience theses for which this way of understanding the notion seems appropriate: (1)Many of the terms and concepts of meteorology and geology are not to be found in the linguistic and conceptual repertoire of the physicist, but it seems clear that the meteorologist and the geologist are studying purely physical processes and events. The vocabularies of their sciences are different ways of talking about aspects and parts of the same reality that the physicist is concerned with. Whatever might be said about the possibility of reducing those special sciences to physics, it seems reasonable to suppose that the meteorological and geological facts are supervenient on the microphysical facts. After having arranged all the particles and their physical properties and relations throughout history, God does not have to add cold fronts and hurricanes, mountains, oceans, and tectonic plates. (2) It is controversial just what colors are-how they are related to the physical properties of light and the reflectance properties of surfaces, to the physiological properties and perceptual capacities of perceivers, and to the phenomenological character of their experience. But it does not seem contro-
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versial that color properties (to the extent that there are such things as color properties) are supervenient on some or all of the properties and relations of the different kinds mentioned. There are no "further facts" about the colors of things, over and above facts about their optical properties, and how they affect perceivers. (3) Historians may describe events and states in terms of the behavior of complex collective entities: The German army invaded Belgium, the House of Representatives voted to impeach the President, the crowd became angry as rumors of a massacre by government troops spread through it. It seems reasonable to suppose that such claims, if true, are made true by facts about the behavior and patterns of behavior, along with intentions, beliefs and feelings, of particular individuals. And it is not that new properties of the complex collective entities "emerge" from the interaction of individuals, like spontaneous combustion. The properties of and relations between social wholes are constituted by the properties and relations of the relevant individuals. There are philosophical theses that are more controversial than these, but that seem to be claims of the same kind. I will give two examples: (1) David,Lewis describes the doctrine that he calls "Humean supervenience" as follows: All there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. . . . We have geometry: a system of external relations of spatio-temporal distance between points. . . . And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else is supervenient on that.l
(2) Derek Parfit does not, so far as I know, use the term "supervenience," but a thesis he calls "reductionist" seems to be a thesis of this kind: "A person's existence just consists in the existence of a brain and a body, and the occurrence of a series of interrelated physical and mental events." Persons are not "separately existing entities," and there is no "further fact" about personal identity over and above such facts.= But while some, such as Lewis and Parfit, would happily describe their supervenience theses as versions of reductionism, others take pains to distinguish supervenience from reduction. The idea of supervenience is, for example, supposed to help us articulate a nonreductionist version of materialism. Jaegwon Kim takes it as at least a putative component of the concept of supervenience that it "be consistent with the irreducibility of supervenient properties to their base properties,"3 although he also argues against the coherence of nonreductive materialism. In what way is a supervenience thesis supposed to be less demanding than a corresponding reductionist thesis? In at least two ways: First, a reductionist thesis was
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traditionally construed as a semantic thesis: reduction is a relation between theories or languages. One theory is reducible to another if (a) all the terms of one are definable in terms of the other, and (b) given the definitions, the reduced theory is derivable from the theory to which it is reduced. In contrast, a supervenience relation is supposed to be metaphysical, and not semantic: it is a relation between sets of properties or facts, and not between theories or language^.^ Second, reduction is point to point, while supervenience is holistic. A reduction requires that each term of the reduced theory be given a definition in terms of the theory to which it is reduced, while a supervenience claim says only that all of the properties from one set somehow determine the properties of the other. Traditional reductionist programs were motivated at least in part by the metaphysical intuition that one kind of fact is, in some sense, the only kind of fact that there really is. But a reductionist thesis might fail for reasons that are irrelevant to this motivation, even in cases where the underlying metaphysical intuition is uncontroversial. For example, a special science, such as meteorology, might be irreducible to physics in part because physical theory does not purport to be, or to entail, a complete description of physical reality. It is not the job of physical theory to describe the particular arrangements of physical forces and particles, but the subject matter of a special science will depend on such particular facts-on the way matter happens to be distributed and organized in a particular corner of the solar system. And if boundary conditions, ceteris paribus qualifications, and assumptions about the domain of application of a special science are tacit presuppositions of the practice of applying its theory rather than explicit consequences of it, it may be that the theory fails to be reducible even to physical theory supplemented with a specification of particular conditions. So traditional reductionism makes a metaphysical claim, but also carries with it some metaphysically irrelevant semantic baggage. The concept of supervenience is supposed to be a concept that helps to isolate the metaphysical part of a reductionist claim-to separate it from claims about the conceptual resources and explicit expressive power of theories we use to describe the world. The separation of metaphysics from semantics is not easy to accomplish, and some of the tensions and obscurities in the concept of supervenience may derive from the failure to have achieved a clean separation. But whether it succeeds or not, I think this is one of the things that the concept of supervenience is designed to do. There is, however, another side to the story. Consider, not materialism or Humean supervenience, but the thesis that moral and evaluative properties are supervenient on natural properties. The problem of the relation between evaluative and natural properties was, after all, the problem that motivated the introduction of the concept of supervenience into contemporary philosophical discussion. The intuitive explanations of supervenience sketched above seem inappropriate-or at least tendentious-when ap-
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plied to the use of the concept in this case. G. E. Moore, certainly, was at pains to deny that ascriptions of intrinsic evaluative properties were just a different way of talking about the same facts that we talk about when we ascribe natural properties. According to Moore, natural properties entail evaluative properties, but the necessary connection between natural and evaluative is synthetic and substantive. If Moore's thesis is properly described as a supervenience thesis, then it cannot be right to identify supervenience with reduction, even a liberal version of reduction that succeeds in isolating the purely metaphysical component of that idea. If the concept is to apply to such theses, a supervenience relation must be, in some cases at least, a metaphysical relation between distinct sets of properties or facts. The distinction between two ways of understanding supervenience that I am trying to make is elusive. When one retreats from the traditional, more restrictive versions of reductionism, then it becomes more difficult to distinguish a reductionist conception of supervenience from the view that supervenience is a sui generis metaphysical relation between distinct families of properties. If G. E. Moore accepts the supervenience of intrinsic evaluations on natural properties, how is he different from the ethical naturalist, who argues that evaluative properties just are natural properties, while at the same time rejecting the possibility of analytic definitions of evaluative expressions in terms of an unproblematically descriptive vocabulary? Or consider the emergentist philosophers of mind from the first half of this century that Jaegwon Kim and others have recently brought back onto the philosophical stage. As Kim describes it, "the doctrine of emergence, in brief, is the claim that when basic physicochemical properties achieve a certain level of complexity of an appropriate kind, genuine novel characteristics, such as mentality, appear as 'emergent' qualities."s These philosophers (who as Kim notes, sometimes used the term "supervenience" to characterize their thesis) seem to be dualists, since the emergent mental properties are "genuine" and "novel." But how are they different from materialists, such as Donald Davidson, who reject the possibility of reductive definitions of the predicates we use to ascribe mental properties? To clarify the distinction, we will have to say more about exactly how supervenience is defined, and also more about the nature of properties, and the nature of the necessity relation that connects supervening properties with the properties on which they supervene.6 2. Strong and Global supervenience
I want now to set aside, for the moment, the difficult metaphysical questions on which I think the intuitive motivation and interpretation of supervenience depend in order to get some more precise concepts to evaluate. If we take for granted the relevant sets of properties-the ones that
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putatively supervene, and the ones on which they are supposed to supervene-and if we take for granted a notion of necessity, then we will have the materials to make the concept precise, relative to those notions, in a way that is neutral on the elusive interpretive contrast that I have tried to point to. Or rather, we will have the materials to make several different supervenience concepts precise. Kim and other have distinguished a weak from a strong concept of supervenience, and both of these have been distinguished from a third notion, global supervenience. There has been controversy about the relations between these different concepts, particularly about the relation between strong and global supervenience. Kim originally argued that they were equivalent, but then was convinced by counterarguments that global supervenience was a weaker relation. In the end, he concluded that the relation between the two concepts was not something that could be settled on formal grounds (he suggested that the question might depend, for example, on the correctness of certain closure conditions on the set of metaphysically possible worlds). I will argue that while the two notions are not in general equivalent (that is, it is not true that for any sets of properties A and B, A globally supervenes on B if and only if A strongly supervenes on B) it is nevertheless true that every global supervenience thesis is formally equivalent to a strong supervenience thesis, and that this equivalence is independent of any metaphysical assumptions. But to get this result, one needs the right definition of global supervenience, and this will require closing a small loophole in the usual definition. All of our supervenience concepts will be defined for two given sets of properties, A and B properties. They are all modal concepts, defined in terms of a given notion of necessity, or a given set of all possible worlds. The rough idea of all of them is that A supervenes on B if the A properties necessarily depend on the B properties. With weak supervenience, individuals within any one possible world can differ with respect to an A property only if they differ with respect to some B property. With strong supervenience, individuals in the same or different possible worlds can differ with respect to an A property only if they differ with respect to some B property. And with global supervenience, two whole possible worlds will differ with respect to the distribution of the A properties of individuals only if they differ with respect to the distribution of B properties. More precisely, here are versions of the usual definition~: (1)"A strongly supervenes on B iff for any worlds w and z, and for any objects x and y, if x has in w the same B-properties that y has in z , then x has in w the same A-properties that y has in 2."' (2) A weakly supervenes on B iff for any world w and any individuals x and y in the domain of w, if x in w has the same B-properties that y has in w, then x has the same A-properties in w that y has in w.
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(3) A globally supervenes on B iff any two possible worlds that are Bindiscernible are also A-indiscernible.
'
The relevant notions of indiscernibility is defined as follows: For any set of properties and relations B, two worlds w and z are B-indiscernible iff there is a 1-1 correspondence between the domains of w and z, and any individual in the domain of w has the same B-properties in w as the corresponding individual from the domain of z has in 2.8 One of our definitions needs a patch before we continue, since as it stands, global supervenience is not even sufficient for weak supervenience, and the loophole that permits this is not, I think, intended. Let me use an example with some fictional physics to bring out the problem. Suppose the world consists of elementary particles that come in a range of colors, shapes and flavors. In addition, each particle is either positively or negatively charged. It is a law of nature in this world that particles always come in pairs: for every positive particle, there is a negatively charged one that is indiscernible from it with respect to color, shape and flavor. I assume that this law is a necessary truth, perhaps because the law is constitutive of the charge properties in the sense that nothing in any possible world can have these charge properties unless the law holds,g or perhaps because we are defining supervenience relative to all nomologically possible worlds, rather than all metaphysically possible worlds. Now let the B-properties be the shape, color and flavor properties, and let the A-properties be the charge properties. Aproperties are not even weakly supervenient on B-properties, since even in the same world there are particles alike with respect to B-properties that differ with respect to A properties. But A properties do globally supervene on B properties, since for any two B-indiscernible worlds, there will be one way of mapping the individuals of one onto the individuals of the other that preserves the A-properties. To close the loophole, I suggest we give the following stronger definition of global supervenience: first, relativize the notion of B-indiscernibility to a mapping: two worlds w and z are Bindiscernible, relative to a function of the domain of w onto the domain of z iff the function is 1-1, and each individual in the domain of w has the same Bproperties in w that the corresponding individual has in z ; then revise the definition of global supervenience as follows: (3') A globally supervenes on B iff for any two worlds that are Bindiscernible relative to a mapping from the domain of one onto the domain of the other are also A-indiscernible relative to the same mapping.
Our revised definition of global supervenience does not avoid the counterexamples that have been given to the equivalence of strong and global supervenience,lO nor should it, since strong supervenience is some-
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times intended to make a stronger claim. A philosopher might, for example, be a materialist who is also an internalist about intentional or experiential properties, and such a philosopher might formulate his thesis as a supervenience claim: that intentional or experiential properties of individuals are supervenient on their intrinsic physical properties. It would not be enough to say that the intentional or experiential properties of individuals globally supervene on the intrinsic properties of individuals, since that would be compatible with the mental properties of one individual varying with the intrinsic physical properties of others. But while the thesis that A strongly supervenes on B is not in general equivalent to the thesis that A globally supervenes on B, every global supervenience thesis (with our revised definition) is equivalent to the strong supervenience of A on a set B', which is a certain closure of the set of B-properties-the set of properties that are definable from B properties, using quantifiers, identity, and finite and infinite Boolean combination.11 So a global supervenience thesis is in fact quite strong: Kim has shown that if A strongly supervenes on B, then every A-property is necessarily equivalent to a property definable in terms of B-properties. So our result implies that it is also true that if A globally supervenes on B, then every A-property is necessarily equivalent to a property definable in terms of B-properties. If necessary equivalence is enough for property identity, then we can say that if A globally supervenes on B, the A properties all are properties definable in terms of B-properties. Of course the assumption that necessary equivalence is sufficient for identity is tenable only with a very strong concept of necessity, and will be controversial even with such a concept. This is one of the things that will be at issue when we return to the elusive metaphysical questions. Whatever one says about property identity, in general, this equivalence result does seem to me to show that global supervenience is the appropriate supervenience concept for the statement of many supervenience theses. In particular, I think a materialist is committed, in virtue of his materialism, to no supervenience thesis stronger than the thesis that the mental properties globally supervene on physical properties. Consider a philosopher who accepts this global supervenience thesis but rejects the corresponding strong supervenience thesis. If this philosopher is consistent, it must be that he holds that the set of physical properties is not closed under definability. There are two reasons he might think this: (1) perhaps he thinks that certain properties definable in terms of physical properties are not themselves physical properties; or (2) perhaps it is because he has a robust conception of property according to which certain well-defined attributes (if I may use the word "attribute" neutrally for any way of picking out a set of individuals) do not correspond to properties of any kind, physical or not. The philosopher with the first reason might still say that all properties are definable in terms of physical properties, since he rejects not only the strong supervenience of A (the mental properties) on B (the physical
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properties), but also the strong supervenience of B' (properties definable in terms of the physical) on the physical properties. For this philosopher, the rejection of strong supervenience seems more terminological than substantive, since it is not based on any thesis about what properties exist, or are instantiated, but only on whether or not to categorize certain properties, whose definitions are uncontested, as physical. The case of the philosopher who accepts the global but not the strong supervenience thesis for the second reason is more difficult. To understand her, we need to know more about the robust theory of properties. This philosopher, presumably, believes that mental properties are genuine properties, and since she accepts the global supervenience of the mental on the physical, she will recognize that for any mental property, there is a physical attribute that is necessary and sufficient for it. Her view, presumably, is that these new nonphysical properties emerge from physical non-propertiesfrom complex combinations of physical properties and relations. This philosopher is perhaps a dualist, but her dualism seems to be independent of her rejection of strong supervenience: even if she allowed that the complex physical attributes were physical properties, (and so that a strong supervenience thesis was true), she might still say that mental properties were distinct from the physical properties that are necessarily coinstantiated with them. The claim would be that they were new properties that emerge from the fact that the complex physical properties are realized. This philosopher is a dualist, not because she rejects strong supervenience, but because she rejects the reductionist interpretation of supervenience, whether global or strong. Jaegwon Kim has a different kind of reason for thinking that the global supervenience of the mental on the physical may not be sufficiently strong for materialism. The problem is that global supervenience of the mental on the physical is compatible with large and important mental differences being dependent on trivial and seemingly irrelevant physical differences. Kim asks us to image a possible world exactly like ours physically, except that "one lone hydrogen atom somewhere in deep space is slightly displaced relative to its position in this world." Such a world "could be as different as you please from the actual world in any mental respect" without violating the global supervenience thesis. This consideration leads Kim to conclude that global supervenience is too weak "to give us the kind of dependency relation we should demand if the mental is truly dependent on the physical."l2 Now I agree that no sensible materialist would accept the possibility of a world that differed physically from ours only in this way, while being radically different from it in the distribution of mental properties. But sensible materialists are not only materialists, they are also sensible; one should not define materialism so that there cannot be silly versions of it. It seems to me that a philosopher who held that the mental properties of human beings on earth were constituted, in part, by the precise distribu-
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tion of hydrogen atoms in distant parts of space is no less a materialist because of the bizarre and unmotivated character of his materialism. If a philosopher who accepts a thesis that the mental supervenes on the physical is a dualist, it is not because his supervenience thesis is global rather than strong, but because of his intuitive interpretation of that relation. If he thinks that new and distinctive mental properties emerge, by a kind of metaphysically necessary causality, from complex physical interactions, then he is no materialist, even if his supervenience claim is a very strong, internalist one that says that mental properties supervene on the intrinsic physical properties of the creatures that have them. But if he is using the concept of supervenience to say that everything in the world is physicalthat apparently nonphysical properties are just other ways of talking about the complex physical properties and relations of things, then he is a materialist, even if he says no more about just which aspects of the physical world are the ones that constitute the mental properties.13 Although I think global supervenience is strong enough for materialism, this is not to say that one shouldn't seek out stronger relations that might be useful for saying something more specific about the relations between mental and physical properties. Kim's response to his wayward atom example is to suggest a strengthening of global supervenience that requires not only that B-indiscernible worlds be A-indiscernible, but also that worlds that are very similar with respect to the distribution of Bproperties be similar with respect to the distribution of A-properties. AS Kim recognizes, considerable work would have to be done to make such a notion precise, and it is difficult to say in advance of doing the work how plausible, and how substantive, such a thesis might be. But staying with a rough intuitive notion of similarity, it is not clear to me that a sensible materialist should expect such a thesis to be true. Why should the materialist expect there not to be mental characteristics that are, in Kim's words, "in general critically sensitive to minuscule physical differencesn?14In any case, whether it would be a sensible materialism or not, it does seem clear that materialism is compatible with the acceptance of a divergence of similarity of the mental from similarity of the physical.15 4. What kind of necessity? I have argued that the distinction between global supervenience and some stronger version is not a way to spell out the intuitive contrast that I sketched in section 2-supervenience as a liberal kind of reduction, vs. supervenience as some kind of substantive metaphysical dependence. I want to look now at a different dimension on which supervenience concepts may be stronger or weaker: the notion of necessity relative to which concepts of weak, strong and global supervenience are defined. If supervenience is to have the force of a reductionist thesis, then it might seem that
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it must be defined in terms of a very strong concept of necessity. How could ascriptions of A-properties be just another way of describing the reality that is described by the ascription of B-properties if the dependence of one on the other holds only in some restricted set of possible worlds-for example the set of physically or nomologically possible worlds? Even a substance dualist about mind and body might believe that the coming to be of minds was caused, as a matter of lawful but contingent fact, by physical events and circumstances. And a realist about necessary connections who was also a determinist would regard a version of David Lewis's Humean supervenience thesis, restricted to all worlds with the same causal laws as ours, as trivially true. But on the other hand, if supervenience is defined in terms of an unrestricted concept of metaphysical necessity, then many supervenience theses will be stronger than they are intended to be. While supervenience requires the distribution of B-properties to determine the distribution of A-properties, the intuitive idea, even when understood in a reductionist spirit, was supposed to allow for the possibility that the Aproperties might supervene instead on something else. In our world (according to the materialist), everything is physical, and so the mental supervenes on the physical. But in some other possible world, ectoplasm might infuse the bodies of beings with a mental life, and their mental properties might supervene on states of that nonphysical substance. Such a world might have physical objects and properties like our world, along with the extra nonphysical substances and properties, or it might be wholly nonphysical, with a wholly different set of properties on which the mental supervenes. But if things have mental, but no physical properties in some possible world that is within the scope of the necessity concept in our definition of supervenience, then the mental will not even weakly supervene on the physical, since things with no physical properties at all, or with only negative physical properties, will all be physically indiscernible from each other, even when they may differ with respect to mental properties. Even Lewis's Humean supervenience thesis is, according to him, a contingent thesis. There are, in the actual world, no real relations (other than spatio-temporal relations) that are not supervenient on the local qualities of things, but in other possible worlds there are. (And, Lewis says, he is prepared to learn from physicists that the thesis in not even true of the actual world.)l6 Lewis provides an attractive way of reconciling the intuition that some supervenience theses are contingent with the liberal reductionist account of the intuitive force of a supervenience thesis.17 He begins with the assumption that in any possible world, there is a set of basic properties and relations-the properties that suffice to determine the world. Materialism might be defined as the (contingent) thesis that the physical properties are the basic properties in our world. Other worlds might have different basic properties, including properties that are "alien" to our
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world.18 Now in terms of this notion, we can define a relative necessity concept, necessity relative to the set of all possible worlds that share the same total set of basic properties. Then the relevant global supervenience thesis will assert supervenience relative to this notion of necessity. The supervenience of the mental on the physical is then contingent because it is a contingent fact that the set of physical properties is the complete set of basic properties that distinguish between things in our world. And although it is contingent, our supervenience thesis is still reductionist in spirit, justifying the claim that the physical is, in a sense, all there is: all that appears to be something over and above the physical is just another way of talking about the physical. Now what is interesting, and disquieting, about this way of solving the problem is that the concept of supervenience is no longer what is doing the work of formulating the reductionist thesis in a way that isolates its metaphysical component. On this account, the materialist's global supervenience thesis is this: Relative to all possible worlds that have the same total set of basic properties and relations as our world, the mental globally, supervenes on the physical. But this thesis is a trivial consequence of the materialist thesis that was stated without the notion of supervenience: that the set of all basic properties and relations of our world is the set of physical properties and relations. What is unsettling about this is that we started with a rough intuitive idea: the idea that one set of properties was in a sense redundant-just a different way of cutting up a world that could be, in some sense to be explained, completely described in terms of the properties and relations in another set. It seemed clear that this rough idea needed to be sharpened, and the concepts of supervenience, with their precise definitions in terms of given sets of properties and a given necessity concept were attempts to pin this idea down. But now we are told that to apply these newly sharpened tools in a way that allows for the contingency of the thesis, we need to define the relevant necessity concept in terms of the idea of a set of basic properties-a set that provides for a complete characterization of the world-a set, we might be inclined to say, on which all else supervenes. But if we need to take this notion for granted in applying our supervenience concept, how have we explained it? I don't mean to be suggesting that Lewis's proposal is not correct, or that it does not help to explain how supervenience theses can be both reductionist and contingent. I am just suggesting that philosophical analysis may have taken us less far from the intuition with which we began than we might have hoped. To try to get a little clearer about the contingency of supervenience I will consider Lewis's simplest and most uncontroversial example, a kind of toy model of the metaphysical relation. "A dot-matrix picture has global properties-it is symmetrical, it is cluttered, and whatnot-and yet all
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there is to the picture is dots and non-dots at each point in the matrix. The global patterns are nothing but patterns in the dots. They supervene: no two pictures could differ in their global properties without differing, somewhere, in whether there is or isn't a dot."lg But of course if we added some properties beyond those that distinguish between the actual pictures, the pictures might have different global properties even while maintaining exactly the same dot-non-dot configuration. Our actual pictures, let us suppose, are monochromatic: the dots are all black, and the empty spaces all white. But suppose we add some color-some dots are red, and some green. With the addition of color, two pictures with the same dot-non-dot pattern might differ with respect to global properties such as symmetry. More generally, the same global properties that, in the case of the dotmatrix pictures, supervene on the pattern of dots will apply to things other than dot-matrix pictures, and because of the wider application of such properties, they are not definable in terms of the patterns of dots. Even if we could give a definition, in terms of dot configurations, that succeeded in distinguishing the symmetrical or cluttered pictures from those that were not, this would not define the holistic properties, which are not only holistic, but also more abstract and general than the properties on which they, in a sense, supervene. When we turn from the toy model to the actual metaphysical theses, the situation is similar: properties that we are inclined to call supervenient are properties that are more abstract, and so might apply to things even if the properties on which they seem to supervene did not. Consider abstract geometric properties such as shape. A surface of a physical object might be hexagonal, but so might be a shadow. And if there were nonphysical properties of surfaces, they might define a hexagonal shape as well. If there could be nonphysical objects that occupied space (perhaps made of some kind of spiritual fluid), then there might be things with shape properties, but no physical properties, in which case the worlds in which such objects existed would be worlds in which shape does not supervene on the physical. One might be inclined to respond that spatial properties just are physical properties, and not properties that supervene on the physical. If so, choose instead some more abstract and topic neutral higher order property or relationship that might be realized in a variety of different ways. It seems reasonable to think that for any two possible worlds, however different the basic properties that distinguish between things in them, there will be some properties that are abstract and general enough to distinguish between things, or patterns of things, in both of them. If this is right, then if there are any possible worlds that are not physical worlds, there will be properties that distinguish between things in our world, but that do not supervene on the physical in all metaphysically possible worlds. The general picture suggested is something like this: We distinguish between possibilities by distinguishing different ways in which individuals
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can be located in some logical space-a property space. But the property spaces in which we locate individuals are themselves contingent: empirical inquiry tells us not only how properties and relations are realized by individuals, but also what the properties and relations are. It is a contingent fact that physical space has a certain structure, and that things we locate in it are distinguished by such properties as mass and charge, or color and flavor. So to allow for all possible worlds, we need to recognize the possibility of property spaces that are different from the one in terms of which we distinguish individuals in our world. And whatever the structure of the different possible property spaces, there will inevitably be relationships between them, and more abstract properties based on abstract structures that are common to different property spaces. (In fact, it seems reasonable to think that the only way we can form a conception of a property space different from one that distinguishes things in our world is though the way it compares and contrasts with ours.) But the more abstract properties are essentially derivative. Once you pin down the basic property space, and the location of all individuals in it, you have pinned down the world-all that is the case. This is a nice clean abstract framework for articulating a metaphysical theory-a theory about the way we locate the world in logical space, and about the structure of the particular region of it that we locate the world in. But a representation of a particular structure of such a kind-of particular property spaces and possible property spaces-is the end point of a philosophical project, and not the place where it begins. We begin with the fact that we describe the world in various overlapping and interrelated ways. We assume that the mental and linguistic acts and attitudes in which we group and distinguish between things are to be understood in terms of properties of and relations between the things: we distinguish between things because there are differences in the things to be distinguished. To bring some order to our understanding of the practices, we need to ask two kinds of questions: first, how are our thoughts and linguistic expressions related to the properties of and relations between the things that those thoughts and expressions are about? Second, what are these properties and relations, and how are they related to each other? To address and distinguish the two kinds of questions, we need a framework for representing the properties and relations-a representation of what distinctions there are to be made by the mental and linguistic acts we use to make them that abstracts away from the way we represent those distinctions. But as we have seen, it is an empirical matter what distinctions there are to be made by the properties and relations that actually distinguish the things in our world, and it is an empirical matter that we mere mortals are not omniscient about. As Quine taught us some time ago (although not with these words), the metaphysician's task of describing the structure of logical space-the space of all possible worlds-is not so easily separated from the scientist's task of locating the actual world in it.
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5. Supervenience in philosophical explanation and argument Some philosophers find the very idea of supervenience to be obscure and unhelpful. Stephen Schiffer, for example, in an often quoted passage, complains that "invoking a special primitive metaphysical relation of supervenience to explain [for example] how non-natural moral properties were related to physical properties was just to add mystery to mystery, to cover one obscurantist move with an~ther."~O As Schiffer understands supervenience, it seems to be part of the idea that a supervenience claim states a "brute metaphysical fact." It is clear that he has in mind a notion of supervenience that is motivated, not by the reductionist intuition, and the attempt to isolate the metaphysical component of that intuition, but rather by the idea of supervenience as some kind of substantive relation-some kind of metaphysical superglue. I am inclined to agree with Schiffer that the more metaphysically extravagant interpretation of supervenience is obscurantist, perhaps incoherent, but as I have been suggesting, the distinc'tion between this intuitive conception and the more austere one with a reductioriist motivation is elusive. Do our explorations of the abstract concept and the kind of necessity relative to which it might be defined, help us make this distinction clearer? Let us cross-examine an imaginary emergentist and see if we can pin him down. The emergentist view, as I understand it, is something like this: when certain configurations of purely physical events and circumstances arise, they cause certain nonphysical mental phenomena to occur, and these mental phenomena in turn have causal effects on subsequent physical events. Now suppose we ask the following counterfactual question of the philosopher who holds this view: Is there a conceivable situation that is physically like the actual world, but that cuts out the mental middleman, a situation in which the same configurations of purely physical events and circumstances arise, but mentality fails to emerge, and instead, these complex physical configurations directly cause the same subsequent physical phenomena that are in fact caused by mental phenomena? Here are some different answers to this question that the emergentist I envision might give: (1)"The situation you describe is conceivable, in some sense, but it is a metaphysically impossible situation-one in which the metaphysical laws connecting the mental with the physical fail to hold." This is an answer I regard as unintelligible, since the metaphysically possible worlds, as I understand the term, are all the possible worlds. There are descriptions that create the illusion that one has coherently described a possibility when one has not, but metaphysically impossible worlds are like nonexistent objects- there are no such things. (But hasn't Saul Kripke taught us that there are epistemological possibilities that are metaphysically impossible, such as that water is not H,O, or that Margaret Truman is not the daughter of Harry and Bess? Yes, but he has also taught us how to understand such possibilities as
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metaphysical possibilities, differently described. There are metaphysical possibilities in which some epistemic counterpart of Margaret Truman is not the daughter of Harry and Bess, and it is possibilities such as these that are relevant to representing someone's ignorance of Margaret's relationship to her parents.) As we have seen, one can and usually should define a supervenience concept in terms of some restricted necessity, and nothing prevents one from restricting the claim to a subset of possible worlds that satisfy some conditions that one calls "metaphysical laws." But if the laws are really substantive, and so restrictive, then it will be a contingent fact that they hold. One can't strengthen the claim or significance of such generalizations by calling them "metaphysical." (2) Our emergentist might instead give this more interesting answer: "The situation you have described is indeed a metaphysical possibility, but it is not a counterexample to supervenience, since the physical properties of things are different in this counterfactual situation. The physical laws, and so at least some of the physical properties, must be different in a world such as you describe. It is implicit in the physical powers of physical things that when they combine in certain ways, mentality will emerge. And even if you think it does not seem right to categorize those dispositional properties as physical, it is still true that to get the possible situation you describe we must alter the physical powers of things to replace the physical effects of the mental, and that is enough to make our counterfactual situation physically discernible." If this answer makes sense, then it seems that we might have supervenience in all metaphysically possible worlds, or at least all worlds that share the same basic properties with ours, even when the mental properties are themselves basic properties, in Lewis's sense-properties that are not derivative, either by being more abstract like functional properties, or definable as complex physical properties. It is not obvious that there couldn't be possible worlds in which some basic properties are supervenient on others, relative to possible worlds sharing the same basic properties. And there need be no brute metaphysical mystery here: the emergentist might say that it is an empirical causal fact that when a certain level of complexity is reached, life, or mentality, emerges. This may be a coherent position. I am not sure, because I am not sure what it is for a property to be basic. I am inclined to think that a property is just a way of grouping individuals, and that a way of grouping individuals can be a basic property only if it is one that allows for distinctions-at least possible distinctions- between individuals that cannot be explained in some other way. If this is right, then there is something wrong with the idea of a basic, but supervenient property. But if our emergentist's second answer is coherent, it is a position that the philosopher with the reductionist motive wants his supervenience thesis to exclude. It is part of what he wants to say that the supervenient properties are not among the basic properties, but are either definable or derivative by being more abstract.
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To state his view as a supervenience thesis, he has some work to do specifying the supervenience base, and the notion of physical indiscernibility so as to ensure that the counterfactual possibility described above is one that is both physically indiscernible from the actual world, and within the scope of the relevant necessity concept.21 The philosopher who uses supervenience with a reductionist motive does not seem obscurantist in the way that Schiffer points to, since he rejects the idea of a "brute metaphysical fact," but one may still be inclined to think that a supervenience thesis, by itself does not do very much philosophical work. In fact, I think one should think of a supervenience thesis not as thesis that, if accepted, ends discussion and solves a problem, but a thesis that sharpens a problem and directs the further discussion. Two philosophers who accept that the mental is supervenient on the physical, and who understand this in the reductionist way, may disagree sharply about what kind of supervenient property mental properties are: For example, whether they are complex properties definable (even if only infinitely) in terms of the physical, or more abstract, higher order functional properties, or some mix. But the common ground shared by philosophers who agree about the supervenience thesis is important: consider two philosophers who agree with the Parfittean reductionist thesis about personal identity: the identity of persons is supervenient on the physical and mental properties of and relations between momentary states. But they disagree about the proper analysis of persons: one defends a psychological continuity criterion, while the other defends an account that puts more weight on bodily continuity. What is the nature of their disagreement? If the two philosophers really agree about the supervenience thesis and a reductionist understanding of it, and really agree about the nature of the supervenience base, then they have succeeded in separating semantic from metaphysical questions: their disagreement is purely semantic, since the force of the supervenience claim is that the facts about momentary states are all the facts-the rest is just how we choose to talk about those facts, about how the words we use are in fact related to them, or about what attitude we choose to take toward them. That does not mean that the dispute is unimportant, but it does change its character. The philosopher who is inclined to accept a certain reductive analysis of personal identity because she thinks that it gets the metaphysical facts right, is, I think, one who really accepts the "further fact" view, and so who rejects the common ground. It may be that the real distinction between the supervenience theorist with a reductionist motive and the one who thinks of it as a causal or metaphysical relation is in the character of the philosophical disagreement that follows agreement about a supervenience thesis. If personal identity, or mentality, or intrinsic value, emerges from configurations of more basic properties, then the questions about just which more basic properties correlate with the supervenient properties are substantive metaphysical questions. But if
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there are no further facts beyond the basic facts, then we have finished doing metaphysics, and turned to something else once we have accepted the supervenience thesis, and begun discussing the more specific questions about which distinctions of the kind we agree are there to be made are the ones that the supervenient properties make. Appendix The claim to be proven is that the global supervenience of A on B is equivalent to the strong supervenience of A on B', where B' is the set of properties definable in terms of B properties, in an infinitary language with identity, quantifiers and truth functional operators. It is obvious that strong supervenience implies global supervenience, and that the global supervenience of A on B is the same as the global supervenience of A on B'. What needs to be shown is that if A globally supervenes on B, then A strongly supervenes on B'. First, define a complete B-description of a world w as follows: if there are n members of the domain of w, the description will begin with n existential quantifiers. If variable x corresponds to individual a, then the description will contain a conjunct Fx for each of a's B-properties F, and a conjunct -Fx for each Bproperty that a lacks. The description will also include conjuncts x#y for each pair of distinct variables x and y that are bound by the existential quantifiers, and a universal generalization saying that everything is one of the n things. Obviously, any two worlds that have the same complete B-description will be B-indiscernible with respect to a mapping of the domain of one onto the domain of the other. Now suppose that A globally supervenes on B. Let w and z be any two possible worlds, and a and b any two individuals from the domains of w and z , respectively, such that a has all the same B'-properties in w that b has in z. Let 6 be the complete B-description of w, and let x be the variable in the description that corresponds to a. Drop from 4 the quantifier that binds x, and the result is an open sentence with one free variable that expresses the maximal B' property that a has in w. Since b has the same B'-properties in z as a has in w, it follows that b has this property in z. But then the existential generalization of this open sentence, which is equivalent to 4, is true in z , and so w and z are B-indiscernible, relative to a mapping that maps a to b. So since we are assuming that A globally supervenes on B, it follows that w and z are also A-indiscernible, relative to the same mapping. So a has all the same Aproperties in w that b has in z . Therefore, A strongly supervenes on B'. Notes
1. Lewis (1986a), IX-x. ' 2. Parfit (1984), 211, 210. 3. Kim (1993), 140. 4. Although in some influential early discussions of the general concept of supervenience, and its application to the clarification of a materialist thesis, the notion was defined in terms of predicates, and languages or models of them. See for example, Haugeland (1982) and Hellman and Thompson (1975).
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Kim (1993), 134. The distinction I am pointing to between two intuitive ideas of supervenience is close to a distinction made by Terence Horgan between supervenience and what he calls "superdupervenience"-"ontological supervenience that is explainable in a materialistically acceptable way." I find much to agree with in Horgan's insightful discussion, but I would rather not tie the distinction to materialism, which is just one application of the concept of supervenience. If one requires, for superdupervenience, only that the supervenience relation be explainable in some way compatible with one's basic metaphysical commitments, then there will presumably be no room for a positive use of a concept of supervenience weaker than the superduper kind. This particular formulation comes from an excellent recent discussion of the abstract concepts of supervenience, Paull and Sider (1992), 834. It is equivalent to definitions given by Kim. Paull and Sider bring time into their definition of indiscernibility (an individual's B-properties at time t in w must be the same as the corresponding individuals B-properties at t in 2.) But in giving the abstract definition, I prefer to assume that, where appropriate, the temporal relations will be in the relevant set of properties and relations, and should not have separate mention. One reason is that one application of the concept of supervenience might be to a thesis about the supervenience of spatio-temporal relations on something else. It seems reasonable to think that Leibniz held such a supervenience thesis. Another reason is that the identification of times across possible worlds might be problematic. See Sider and Paull (1992), 852. See Shoemaker (1980) for a defense of a theory of properties according to which properties are explained in terms of causal powers. According to this kind of theory, the causal laws relating the properties are essential to them. See Petrie (1987) and Paull and Sider (1992) for discussions of counterexamples to the equivalence of strong and global supervenience. See the appendix for the argument for this equivalence. Kim (1993), 277, 278. In Paull and Sider (1992), 841-847, there is a critique of Kim's wayward atom argument. Kim (1993), 91. Presumably, "being mentally similar to" would itself be a mental relation, and so the materialist will be obliged to accept that this relation is determined by the physical properties and relations of the things that stand in it. But even if this relation were definable in physical terms, two things might be mentally dissimilar while being physically similar. I am skeptical about whether one who accepts Lewis's general metaphysical picture ought to accept the contingency of Humean supervenience. For on his account, Humean supervenience (in contrast with a more radical thesis that might be called Leibnizian supervenience) is compatible with some irreducible relations - the spatio-temporal relations-and these relations play a crucial role in the metaphysical theory, since it is spatio-temporal relations that individuate the possible worlds. Different possible worlds can have very different systems of spatio-temporal relations-Lewis even allows that there might
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be worlds that are not spatio-temporal at all in any ordinary sense, but have a system of relations that is "analogous" to spatio-temporal relations. Might it be that any relations will be analogous to spatio-temporal relations (or part of the system of such relations) if they are real relations, not supervenient on the arrangement of qualities? Without some criterion to distinguish real relations that are compatible with Humean supervenience (because they are spatiotemporal, or at least analogous to spatio-temporal) from those that are not, the thesis threatens to become not only necessary, but trivial, since no one will contest that all properties and relations are supervenient on arrangements of qualities, together with facts about the instantiation of those relations that are not supervenient on the arrangement of qualities. So I think the nontriviality, as well as the contingency, of Humean supervenience depends on some account of criteria for being a spatio-temporal relation. (Suppose, as Lewis speculates might happen, the problems of interpretation of quantum mechanics are solved in a way that justifies the claim that there are irreducible nonlocal relations. He suggests that this would give us empirical reason to reject Humean supervenience. But what if we decide instead that these relations are part of the structure of space-time? The problem here is analogous to a more familiar problem about the characterization of physicalism. Is a world with.different basic properties from our world a world in which physicalism is false, or is it a world with a different physics in which the thesis of physicalism is true? See Lewis (1986b), section 1.6, for a discussion of the issue. 17. See Lewis (1983). 18. In the current climate of opinion, it is perhaps prudent to emphasize that David Lewis's term, "alien property" does not refer to a property of a space alien, but to a property that does not exist, where a property's existing is to be distinguished from its being instantiated. There may be existent propertiescomplex properties such as being a golden mountain-that are uninstantiated. And it is perhaps also possible that there be alien properties-properties that do not actually exist-that are nevertheless instantiated, paradoxical as that may sound. Of course (at least on an actualist interpretation of possible worlds) there are no alien properties, since there are no things of any kind that do not exist, but just as there might have been people who don't in fact exist, so there might have been properties that don't in fact exist. What does exist is the possibility of such properties. Presumably, the complements of alien properties would be alien as well, and if so, then it is possible that there be alien properties that are actually instantiated. For example, if there might have been things that don't in fact exist, then there might have been relational properties, such as the property of being related in some way to some one particular one of such things. Since the things don't exist, these relational properties presumably don't either. But some such possible properties, such as the property of being distinct from some particular merely possible person, are actually instantiated by actual people. Of course I haven't given you an particular example of such an alien relational property-there are no examples, since it is only possible that there be such properties, and the possibility is an irreducibly existential one. 19. Lewis (1986b), 14.
Varieties of Supervenience 1 241 20. Schiffer (l987), 153-54. 21. The materialist may find this easier to do if he accepts Lewis's Humean supervenience as well as materialism. For according to this thesis, the laws and causal powers of things are themselves supervenient on regularities. The two situations we have presented the emergentist (one with intermediate mentality, one with the middleman eliminated) seem to satisfy the same physical regularities, but to differ only in the causal explanations of them, and so would seem to violate Humean supervenience. But this conclusion assumes that the basic physical properties are the same in the two worlds, and not just similar. Without some criteria for identifying properties across possible worlds, Humean supervenience may not have the teeth it seems to have. On the view of properties defended in Shoemaker (1980) according to which laws and causal powers are constitutive of properties, Humean supervenience seems to hold, but not in the way that is intended. References
Haugeland, John (1982). "Weak supervenience," American Philosophical Quarterly 19:93-103. Hellman, Geoffrey and Frank Thompson (1975). "Physicalism, ontology, determination and reduction," Journal of Philosophy 7231-564. Horgan, Terence (1993). "From Supervenience to superdupervenience: meeting the demands of a material world," Mind, 102:555-586. Kim, Jaegwon (1993). Supervenience and Mind. Cambridge: Cambridge University Press. Lewis, David (1983). "New work for a theory of universals," Australasian Journal of Philosophy 61:343-377. Lewis, David (1986a). Philosophical Papers, 11. Oxford: Oxford University Press. Lewis, David (1986b). O n the Plurality of Worlds. Oxford: Basil Blackwell Ltd. Parfit, Derek (1984). Reasons and Persons. Oxford: Oxford University Press. Paull, R. C. and T. R. Sider (1992). "In defense of global supervenience," Philosophy and Phenomenological Research 52:833-854. Petrie, Bradford (1987). "Global supervenience and reduction," Philosophy and Phenomenological Research 48:119-130. Schiffer, Stephen (1987). Remnants of Meaning. Cambridge: MIT Press. Shoemaker, Sydney (1980). "Causality and Properties," in Peter van Inwagen (ed.), Time and Cause. Dordrecht-Holland: D. Reidel Publishing Co.
