Supervenience

First published Mon Jul 25, 2005; substantive revision Mon Dec 4, 2023

A set of propertiesA supervenes upon another setBjust in case no two things can differ with respect toA-properties without also differing with respect to theirB-properties. In slogan form, “there cannot be anA-difference without aB-difference”.

As we shall see, this slogan can be cashed out in many different ways.But to illustrate the basic idea, imagine that there is a perfectforger. Her copies of paintings not only fool the art dealers, but arein fact exact duplicates of the originals down to the preciseplacement of every molecule of pigment—indeed, down to everymicrophysical detail. Suppose that she produces such a copy of ElGreco’sA View of Toledo. It is of course differentfrom the original in various respects—it is a forgery, it wasnot painted by El Greco, it is worth quite a bit less atSotheby’s, and so forth. But the forgery is alsoexactlylike the original in other respects. It is the same shape, size,and weight. The surface of the canvas contains the same arrangementsof colors and shapes—a blue rectangle here, a green swirl there.Indeed, itlooks just the same, at least to a single viewerunder identical lighting conditions and so forth. Perhaps it is evenjust as beautiful as the original, though that is morecontroversial.

The properties that the forgery is guaranteed to share with theoriginal are those that supervene upon its microphysical properties.Two paintings that are microphysically just alike are guaranteed to bejust alike in the arrangement of colors and shapes on their canvases.That is, you cannot change the arrangement of colors and shapes on apainting’s canvas without changing its microphysical properties.This is just to say that the arrangement of colors and shapessupervenes on its microphysical properties.

Supervenience is a central notion in analytic philosophy. It has beeninvoked in almost every corner of the field. For example, it has beenclaimed that aesthetic, moral, and mental properties supervene uponphysical properties. It has also been claimed that modal truthssupervene on non-modal ones, and that general truths supervene onparticular truths. Further, supervenience has been used to distinguishvarious kinds of internalism and externalism, and to test claims ofreducibility and conceptual analysis.

Supervenience is related to but distinct from notions like groundingand ontological dependence. We directly address the relation betweenthese notions in §3.5 (much of that section has been part of thisentry since its initial publication in 2005).

1. Introduction

The core idea of supervenience is captured by the slogan, “therecannot be anA-difference without aB-difference.” It is important to notice the word‘cannot’. Supervenience claims do not merely say that itjust so happens that there is noA-differencewithout aB-difference; they say that therecannotbe one.A-properties supervene onB-properties ifand only if a difference inA-propertiesrequires adifference inB-properties—or, equivalently, if andonly if exact similarity with respect toB-propertiesguarantees exact similarity with respect toA-properties. Supervenience claims thus have modal force. Thekind of modal force can vary; different supervenience claims mightattribute different kinds of necessity to the connection betweenB-properties andA-properties (seeSection 3.1.) Even when the modality is fixed, however, there are a number ofdistinct claims that might be expressed by the slogan. A good deal ofphilosophical work has gone into distinguishing these forms ofsupervenience, and into examining their pairwise logicalrelations.

We will begin with a few brief historical remarks (Section 2), and then turn to some general questions about supervenience, such aswhether it is explanatory and whether it is guarantees entailment (Section 3). We will then explore the various versions of supervenience in somedetail (Section 4). The technical work is interesting in its own right, but it isobviously made more interesting by the fact that the differentvarieties of supervenience may be useful for different philosophicalpurposes. Thus, although most of this entry will be concerned withsupervenience itself rather than its applications, we will end with adiscussion of some of the substantive philosophical issues to whichsupervenience is relevant (Section 5).

Readers primarily interested only in an overview of the relationsbetween the main varieties of supervenience should skip toSection 4. The technical definitions are also collated in anAppendix.

2. History

2.1 ‘Supervenience’ as a Philosophical Term of Art

‘Supervenience’ and its cognates are technical terms. Thisis not news; ‘supervene’ is rarely used outside thephilosophy room these days. But it occasionally is, and when it is, ittypically has a different meaning. It is typically used to mean“coming or occurring as something additional, extraneous, orunexpected” (Webster’s New InternationalDictionary, 3^rd edition). This is the sense at issuein the following passages from the Oxford English Dictionary:“upon a sudden supervened the death of the king(1674–48)” and “The king was bruised by the pommelof his saddle; fever supervened, and the injury proved fatal(1867)” (cited in Kim 1990, 2–3). It is also the sense atissue in W.V.O. Quine’s autobiographical remark about hisadolescence: “necking, as it was called, supervened in thefullness of time as necking will” (1985, 43). However, this useof ‘supervenience’ is irrelevant to the philosophical useof the term. The philosophical use of ‘supervenience’ isstrictly proprietary, and so in no way beholden to its vernacularuse(s). In this way, ‘supervene’ is different from termslike ‘cause,’ ‘freedom,’ or‘justice’. ‘Supervene’ receives its sense bystipulation, and the notion so defined is to be judged by itsphilosophical fruits (McLaughlin 1995).

2.2 Origin of the Term

What, then, is the origin of thephilosophical use of theterm? It is not clear. Some have speculated that it originates withthe British Emergentists of the early part of the twentieth century.This is because the British Emergentist Lloyd Morgan (1923) used theterm ‘supervene’ to characterize a relation that emergentproperties bear to their base properties, and his use became fairlywidespread in the literature on emergence. However, Morgan used‘supervene’ in essentially its vernacular sense, ratherthan in its current philosophical sense. He held that emergentproperties are distinct from, and additional to, their baseproperties, and arise unpredictably from them. It was this use, notthe current philosophical use, that became fairly widespread in theliterature on emergence (see Van Cleve 1990; and McLaughlin 1992 and1997b).

It is also frequently claimed that the term ‘supervene’was first used in its contemporary philosophical sense by R.M. Hare,who used it to characterize a relationship between moral propertiesand natural properties (1952, 145). Unlike Morgan, Hare used the termin essentially the current philosophical sense, but he claims that hewas not the first to do so. He claims that the term was so used inOxford in the 1940s, though he does not recall by whom, or in whatcontext (Hare 1984).

It is important to be clear, however, that whether or not Hare was thefirst to use the term ‘supervene’ in the philosophicalsense, he was by no means the first to assert a supervenience thesis.For example, while G. E. Moore did not use the term‘supervene’, he asserted: “one of the most importantfacts about qualitative difference…[is that] two things cannotdiffer in quality without differing in intrinsic nature” (1922,263). And there are many other historical examples of such explicitstatements of supervenience theses. Moreover, though we are not goingto argue the point here, it seems no exaggeration to say thatvirtually every major figure in the history of western philosophy hasbeen at least implicitly committed to some supervenience thesis orother (or to the denial of one).

But regardless of how long the notion of supervenience has beenaround, or who first used the term ‘supervenience’ in itsphilosophical sense, it is indisputable that Donald Davidson played akey role in bringing the idea to center stage. He introduced the term‘supervenience’ into contemporary philosophy of mind inthe following passage:

[M]ental characteristics are in some sense dependent, or supervenient,on physical characteristics. Such supervenience might be taken to meanthat there cannot be two events alike in all physical respects butdiffering in some mental respect, or that an object cannot alter insome mental respect without altering in some physical respect (1970,214).

After Davidson’s appeal to supervenience, Terence Horgan (1982,1984), Jaegwon Kim (1984, 1987, 1988, 1990, 1993), David Lewis (1983),and others began to examine the notion of supervenience itself, and toexplore its usefulness for a wide variety of philosophical purposes.The literature then mushroomed.

3. Supervenience and Other Relations

Philosophers have distinguished many different varieties ofsupervenience. InSection 4, we will lay out those varieties, and note their pairwise logicalrelations. For now, though, we will stick to the core idea ofsupervenience—namely, that there cannot be anA-difference without aB-difference. A number ofgeneral points of philosophical interest can be made just by workingwith that simple and easy idea.

3.1 The Modal Force of the Supervenience Relation

In order to sort out how supervenience connects up to otherrelations—like entailment, reduction, grounding, ontologicaldependence, and explanation—we need to discuss the fact thatsupervenience can hold with varying degrees of modal force. That is,the ‘cannot’ in “there cannot be anA-difference without aB-difference” comes indifferent strengths. For example, it can mean “cannot as amatter of logic,” or it can mean “cannot consistently withthe laws of nature”.

This raises some controversial issues. For the purposes of this essay,we make the following three assumptions. First, we assume thatmetaphysical necessity is just as strong as logical necessity. Thereare, to be sure, metaphysically necessary truths that are not logicaltruths, such as the truth that water = H₂0.But metaphysical necessity is just as strong as logical necessity inthat the space of metaphysical possibility is exactly the same as thespace of logically possibility: the logically possible worlds = themetaphysically possible worlds (see, e.g., McLaughlin 1995; Chalmers1996; and Jackson 1998). This is not entirely uncontroversial, butlittle we have to say turns on it. Second, and more importantly inwhat follows, we assume that at least certain properties that figurein laws of nature do not play their nomic roles essentially, so thatit is logically or metaphysically possible for those properties not tofigure in the laws in question. This is also controversial, but wewill not defend it here. (See Shoemaker 1980, Swoyer 1982, and Ellis2001 for the opposing view.) Finally, we will assume that whatever ismetaphysically necessary is nomologically necessary, but notconversely. (One can hold that there are nomologically necessarytruths that are not metaphysically necessary, even if one holds thatall nomic properties play their nomic roles essentially; see Fine2002.)

Some supervenience relations are metaphysically (or logically)necessary. The propertybeing a haircut or a halibutsupervenes with metaphysical necessity on the two base propertiesbeing a haircut andbeing a halibut: two thingscannot differ with respect tobeing a haircut or a halibutwithout differing either with respect tobeing a haircut orelse with respect tobeing a halibut. Also, the surface areasof perfect spheres supervene with metaphysical necessity on theirvolumes (andvice versa) (Lombard 1986). Some superveniencerelations are metaphysically contingent. Consider the Wiedemann-FranzLaw, which entails that the electrical conductivity of a metalco-varies with its thermal conductivity. This law thus entails thatelectrical conductivity and thermal conductivity mutually supervene oneach other. But on the assumption that the law is metaphysicallycontingent, the supervenience relation is too. It is onlynomologically necessary that there cannot be a difference in one sortof conductivity without a difference in the other sort.

So, supervenience relations can hold with either metaphysical ornomological necessity, and perhaps even with some other kind ofnecessity. The fact that supervenience comes in different modalstrengths is important. Sometimes there is widespread agreement that acertain supervenience relation holds, but dispute over what its modalforce is. One important example is the supervenience of the mental onthe physical. Just about everyone, even a Cartesian dualist, believessome version of this supervenience claim. But there is vigorousdisagreement about whether the supervenience relation holds withmetaphysical or merely nomological necessity. Ask yourself—couldthere be an individual that has no conscious experience at all,despite being physically indiscernible from an individual that isconscious (Kirk 1994; Chalmers 1996)? That is, could there be whatphilosophers call a ‘zombie’? Because it is widely agreedthat the mental nomologically supervenes on the physical, it is widelyagreed that zombies are nomologically impossible—that theirexistence would violate psychophysical laws. But some philosophers(e.g., Chalmers 1996) think that zombies are metaphysically possible.This remains a matter of lively dispute, and resolving it requiresaddressing some hard questions about the relationship betweenconceivability and metaphysical possibility. Suffice it to note thatthe dispute is precisely over the modal force of the‘cannot’ in “there cannot be a mental differencewithout a physical difference.” (For discussions of therelationship between conceivability and metaphysical possibility see,e.g., the essays in Gendler and Hawthorne 2002. For a discussion ofphysicalism, seeSection 5.4 of this entry and the separate entry onphysicalism.)

3.2 Supervenience and Entailment

Is supervenience a form of entailment? The two relations are logicallysimilar in certain ways. The entailment relation is reflexive,transitive, and non-symmetric, and so is supervenience. Supervenienceis reflexive: for any set of propertiesA, there cannot be anA-difference without anA-difference (see, e.g., Kim1984). It is also transitive: ifA-properties supervene onB-properties, andB-properties supervene onC-properties, thenA-properties supervene onC-properties. However, supervenience is neither symmetric norasymmetric; it isnon-symmetric. Sometimes it holdssymmetrically. Every reflexive case of supervenience is trivially asymmetric case; consider also the case of the volume and surface areaof perfect spheres mentioned inSection 3.1. And sometimes it holds asymmetrically. For example, while the mentalmay supervene on the physical, the physical does not supervene on themental. There can be physical differences without mental differences.One uncontroversial way to see this is to note that radicallyphysically different things—a washing machine and a paper bag,say—can be mentally just alike in virtue of lacking mentalproperties altogether. Thus supervenience, like entailment, isreflexive, transitive, and non-symmetric.

Nonetheless, thatB-properties entailA-propertiesis neither necessary nor sufficient forA-properties tosupervene onB-properties. (The notion of property entailmentin play is this: propertyP entails propertyQ justin case it is metaphysically necessary that anything that possessesP also possessesQ.) To see that such entailments donot suffice for supervenience, consider the propertiesbeing abrother andbeing a sibling. Possessing the formerentails possessing the latter; every brother is a sibling. Butbeing a sibling does not supervene onbeing abrother. Two people can differ with respect to being a siblingdespite being exactly alike with respect to being a brother. To seethis, suppose that Sarah has a sister and Jack is an only child. ThusSarah is a sibling and Jack is not, though neither is a brother. SotheB-properties can entail theA-properties, eventhoughA does not supervene onB.

To see that supervenience does not suffice for entailment, recall thatsupervenience can hold with only nomological necessity. In such cases,there is no entailment; thermal conductivity properties do notentail electrical conductivity properties, for example.

But what about supervenience withmetaphysical orlogical necessity? Even that does not in general guaranteethat there areB-properties that entail theA-properties. At best, the logical supervenience ofA onB means that how something isB-wiseentails how it isA-wise. But it does not follow that everyA-property is entailed by aB-property, or even thatsomeA-property is entailed by aB-property.Consider two examples. First, on the assumption that there arenegative properties, every propertyF will supervene withlogical necessity on its complement not-F. After all, twothings cannot differ with respect to whether they areFwithout differing with respect to whether they are not-F, andconversely. But obviously beingF does not entail beingnot-F (McLaughlin 1995, 1997a). Second, consider a case inwhich the property setB contains only the propertyP and the propertyQ, and property setA isthe unit set of the conjunctive propertyP&Q.That is,A = {P&Q}, andB ={P,Q}.A supervenes with metaphysicalnecessity onB. But there is no property inB thatentails theA-property.

Now, there might bespecial sets of properties for which thesupervenience ofA onB guarantees that there areB-properties that entail theA-properties—namely, property sets that are closedunder the Boolean operations of complementation, infinitaryconjunction, infinitary disjunction (see Kim 1984), and operationsinvolving quantification. Closing {F} and {~F} underthese operations will result in the same set, namely {F,~F,F & ~F,F v~F…}. In both cases just above, then, theclosure ofB under these operations in fact containsa property that entails theA-property.

Discussions of supervenience often appeal to property sets that areclosed under such operations. But this is not a trivial assumption,for two reasons. First, it is controversial whether complementation,conjunction, and disjunction are legitimate property-formingoperations. Whether they are largely depends upon what properties aretaken to be. If properties are just the semantic values of predicates,then there are negative, conjunctive, and disjunctive properties,because negative, conjunctive, and disjunctive predicates can havesemantic values. But if properties are universals there may not be anysuch properties (Armstrong 1978, 1989). And if properties are ways athing might be, then property sets cannot be closed under Booleanoperations. That would entail that for any propertyF,beingF and ~F is also a property. However,that is not a way anything might be. (However, see Priest 2010 for anopposing view.) Second, even if it is assumed that theproperty-forming operations are legitimate, the fact is that we arequite often interested in property sets that are not closed underthem. Consider negation. Even assuming that there are negativeproperties, the fact is that we do not standardly count cats as havinggeological properties because they are neither ignaceous, sedimentary,nor metamorphic. And it seems strange to say that Descartes wascommitted to mental substances having physical properties simplybecause he thought they are not spatially extended. Since not everyproperty set is closed under every property-forming operation,supervenience is not in general sufficient for entailment. (Forfurther discussion of supervenience and various property-formingoperations, see Van Cleve 1990; Oddie and Tichy 1990; Bacon 1990,1995; Glanzberg 2001; Bader 2012.)

One particularly interesting case of entailment failure arises whenthe property sets are not closed under quantification. This opens roomfor cases in which the supervening setA contains propertiesformed by quantification, likebeing such that every F is aG, and the subvening setB does not. IfB doesnot include such properties, there are no properties inBthat entail them. As Bertrand Russell noted many years ago, “youcannot ever arrive at a general fact by [deductive] inference fromparticular facts, however numerous” (Russell 1918, 235; quotedin Bricker 2005). But general properties, nevertheless, logicallysupervene on particular ones: no two possible worlds can differ inwhat general facts hold without differing in what particular factshold (see Skyrms 1981, Lewis 1992, and Bricker 2005). Thus, generalfacts logically supervene on particular facts, even though the latterdo not entail the former.

The upshot is that the logical supervenience of property setA on property setB will only guarantee that eachA-property is entailed by someB-property ifA andB are closed under both infinitary Booleanoperations and property-forming operations involvingquantification.

3.3 Supervenience and Reduction

Everyone agrees that reduction requires supervenience. This isparticularly obvious for those who think that reduction requiresproperty identity, because supervenience is reflexive. But on anyreasonable view of reduction, if some set ofA-propertiesreduces to a set ofB-properties, there cannot be anA-difference without aB-difference. This is trueboth of ontological reductions and what might be called“conceptual reductions”—i.e., conceptualanalyses.

The more interesting issue is whether supervenience suffices forreduction (see Kim 1984, 1990). This depends upon what reduction istaken to require. If it is taken to require property identity orentailment, then, as we have just seen (Section 3.2), even supervenience with logical necessity is not sufficient forreduction. Further, if reduction requires that certain epistemicconditions be met, then, once again, supervenience with logicalnecessity is not sufficient for reduction. ThatA supervenesonB as a matter of logical necessity need not be knowablea priori.

3.4. Supervenience and Ontological Innocence

The issues about entailment and reduction are related to a questionabout whether supervenience with metaphysical necessity isontologically innocent—whether theA-properties are anything “over and above” theB-properties.

Some think that supervenience—at least when accompanied bygrounding; seesect. 3.5 below—is indeed ontologically innocent in this sense. Afterall, if the A-properties supervene with metaphysical necessity on theB-properties, then they come along automatically given theB-properties. To borrow Kripke’s metaphor (1972, 153–154),once God fixes the B-properties, she is all done; she does not need todo anything further to get the A-properties going. Indeed, she cannotblock them. Given the distribution of B-properties, there is nofurther question about which A-properties are instantiated. So, it isclaimed, the latter are nothing over and above the former. However,other people vigorously resist this idea. How can the A-properties notcount as a further ontological commitment, if they are numericallydistinct from the B-properties? (Both Jonathan Schaffer (2015) andKaren Bennett (2017, chapter 8.2) have recently argued that the bestway to make sense of this is as follows. Grounded entities arenonfundamental, and nonfundamental entities do not count against thesimplicity of a theory, although they do count towards the totalnumber of things there are.)

This dispute is central to various issues in metaphysics and thephilosophy of mind. For example, nonreductive physicalists often saythat mental properties are distinct from but nonetheless“nothing over and above” physical ones. Their reductivistopponents, however, clearly think that this is illegitimate. This canbe seen in the charge that nonreductive physicalists face theexclusion problem—that they are unable to account for the causalefficacy of the mental without claiming that all of its effects are“double-caused.” (See the entry onmental causation.)

Another example concerns composition. Some people—those whobelieve in “unrestricted mereologicalcomposition”—think that any two or more things whatsoevercompose a larger thing. They typically claim that while the (single)fusion is notidentical to its (many) parts (the exception isBaxter 1988), it does supervene on them, and is thus “nothingover and above” those parts. So, for example, there is amereological fusion of your left elbow, Tony Blair, and theMississippi River, and it is distinct from, but nothing over andabove, those three parts. Lewis, speaking of a fusion of a trout and aturkey, says that “it is neither fish nor fowl, but it isnothing else: it is part fish and part fowl” (1991, 80) and that“mereology is innocent” (87). However, opponents ofunrestricted mereological composition are unsurprisingly unconvinced:“what does ‘nothing over and above’ mean? Thisslippery phrase has had a lot of employment in philosophy, but what itmeans is never explained by its employers” (van Inwagen 1994,210). Indeed, the thought that composition is not in the leastontologically innocent has led some to claim that there aren’tany composite objects (or that living organisms are the only compositeobjects; see van Inwagen 1990, Merricks 2001, Dorr and Rosen 2002, andthe entry onmereology).

So, on the one hand, there is what might be called the“supervenience intuition”. Many nonreductive physicaliststhink that the metaphysically necessary supervenience of the mental onthe physical means that mental properties are nothing over and abovephysical ones, and most (all?) believers in unrestricted mereologicalcomposition think that the metaphysically necessary supervenience offusions on their parts means that fusions are nothing over and abovethose parts. On the other hand, there is what might be called the“distinctness intuition”—if mental properties andmereological fusions aredistinct from physical propertiesand mereological atoms, respectively, then surely they count assomething over and above them.

This can be made to look as though it is just a terminological issueabout how to best use phrases like “nothing over andabove” and “ontological innocence”. But there arevery real issues here. The central difference between the two sides isthat one emphasizes the fact that the two kinds of properties orentities are numerically distinct, and the other emphasizes the factthat there is nonetheless a closenonidentity relationbetween them. And what matters in any given case is i) just whichparticular nonidentity relation holds, and ii) whether the fact thatthat relation holds is enough to defuse whatever problem is on thetable.

In the mereological fusion case, the issue is really just whetherfusions exist at all. Those who believe in unrestricted mereologicalcomposition think that the existence of the atoms entails theexistence of the fusions, and their opponents do not. The debate hereis only about whether the fusions are (or would be if they existed)anything “over and above” their parts insofar as thatwould perhaps make them a significant ontological commitment, leadingsome (not Schaffer or Bennett; see above) to be suspicious of theprinciple of unrestricted mereological composition.

In the nonreductive physicalism case, the issue is about whether allnonidentity relations are on a par as far as the exclusion argument isconcerned. Nonreductive physicalists think that mental propertiessupervene with metaphysical necessity upon physical properties(whether they are also entailed by physical properties depends uponwhat property-forming operations the set of physical properties istaken to be closed under; seeSection 3.2). The interesting question is not whether this enables them to trulysay that mental properties are “nothing over and above”physical ones, but rather whether it enables them to solve theexclusion problem. (For views that more or less say that it does, seeYablo 1987, Shoemaker 2001, Bennett 2003, Melnyk 2003). Note that thisissue also arises in the case of mereological fusions; Merricks (2001)uses a version of the exclusion problem to argue against the existenceof nonliving composites.

One more example, which is similar to the fusion case. We have justseen that general truths supervene with metaphysical necessity onparticular truths, but are not entailed by them (Section 3.2). This led Russell to say that “you must admit general facts asdistinct from and over and above particular facts” (1918, 236).It would be a mistake to focus too much on Russell’s claim thatgeneral facts are “over and above” particular facts; heclearly just means that they are numerically distinct from particularfacts. The interesting issue is rather whether Russell is right thatwe must admit general facts into our ontology at all. (See Bricker2005 for an argument to the contrary.)

All told, there may not be a straightforward answer to the question ofwhether supervenience with metaphysical necessity is ontologicallyinnocent. Whether it is depends upon whether it is a tight enoughrelation to do the work required to solve whatever concern is in play,and that will obviously depend upon what that concernis. Sowhether metaphysically necessary supervenience is “ontologicallyinnocent” may well depend upon the case. In one case,metaphysically necessary supervenience might do the job, in anothercase entailment might be required, and in another perhaps nothingshort of numerical identity will do.

3.5 Supervenience, Grounding, and Ontological Dependence

There is now a large literature on grounding and ontologicaldependence, including an entry for each in this encyclopedia. Roughly,one fact grounds another when the latter obtains in virtue of theformer: the former in some sense makes the latter obtain. It is aproductive, generative relation. (Bennett 2017 claims that there areseveral such relations, which she calls building relations. Talk ofproduction and generation naturally invites a question about therelation between grounding or building and causation; see Schaffer2016, Bennett 2017 chapter 4, Bernstein 2017, and A. Wilson 2018 fordiscussion of the relation between grounding and causation.) Roughly,an entity ontologically depends on another when the former would notexist without the latter. Much, much more can be and has been saidabout these relations, but this is enough for our purposes.

Grounding and ontological dependence are distinct from each other. Thesimplest way to see this is by means of the kinds of case thatrevealed to David Lewis that causation is distinct from causaldependence (1973): preemption and overdetermination. Just as cases ofcausal overdetermination and preemption involve causation withoutcausal dependence, so too do cases of ‘groundingoverdetermination’ and ‘grounding preemption’involve grounding without ontological dependence. For example, thefact that I exist grounds the fact that something exists, but theobtaining of the latter fact does not depend upon the obtaining of theformer; the fact that something exists is massively overgrounded.

Because grounding and ontological dependence are distinct, the claimthat supervenience is not the same as grounding is distinct from theclaim that supervenience is not the same as ontological dependence.Nonetheless, many of the same considerations are relevant.

One such consideration is that these relations may not have the samerelata. Supervenience is typically said to be a relation betweenproperties or families of properties, but at least some ofgrounding’s advocates say that it is a relation between factsonly (e.g. Rosen 2010, Audi 2012), and ontological dependence seems toobtain between members of a variety of ontological categories.However, it is not clear how seriously to take this kind of concern,since notions of fact supervenience and property grounding can easilybe defined.

A second way to see that supervenience is not identical to eithergrounding or ontological dependence is to note that the latter tworelations are widely (though not universally) thought to beirreflexive and asymmetrical. Nothing can ground or ontologicallydepend upon itself, and nothing can ground or ontologically depend onsomething that also grounds or depends on it. But as we have seen,supervenience is reflexive and not asymmetrical (seeSection 3.2). (For challenges to the claim that dependence and/or grounding areirreflexive and asymmetric, see Jenkins 2011, Bliss 2014, Wilson 2014,and Barnes 2018; for a reply to these challenges, see Bennett 2017,sect. 3.2).

A third way to see that supervenience is not the same as eithergrounding or ontological dependence is that the following conditionalsare false:

ifA supervenes onB,B groundsA
ifA supervenes onB,A ontologicallydepends onB

As McLaughlin put it in 1995, a mere supervenience claim does notentail any “in virtue of” claim. Here are a couple of waysto see this. As noted above, for any propertyF, beingF supervenes on being ~F: two things cannot differwith respect to beingF without differing with respect tobeing ~F. But, of course, being ~F does not groundbeingF, and beingF does not ontologically dependon being ~F!

Another way to see that the conditionals are false is to notice thatproperties everything has necessarily and ones that nothing canpossibly have supervene, with the same sort of necessity, onany property whatsoever. (The fact that the necessary and theimpossible supervene on anything and everything poses not one buttwo problem for attempts to use supervenience to definephysicalism. SeeSection 5.4.) The propertybeing self-identical supervenes on the propertybeing an antique; the propertybeing both a kangaroo andnot a kangaroo supervenes upon the propertybeing dusty.The reason is simple enough. No two things can differ with respect toeither necessary or impossible properties, period; thus no two thingscan differ with respect to such properties without also differing withrespect toB-properties, for any property setB.Nothing can be both a kangaroo and not a kangaroo, so no two thingscan differ with respect to that property, and thus no two things candiffer with respect to that property without also differing withrespect to being dusty, or being purple, or being a steam engine, etc.But it is not the case that being both a kangaroo and not a kangaroois ontologically dependent upon being dusty, or that being dustygrounds being both a kangaroo and not a kangaroo. Being dusty hasnothing to do with it at all.

For yet another reason for denying that the supervenience ofA-properties onB-properties entails anything aboutgrounding or ontological dependence, see the discussion of certainforms of global supervenience in Section 4.3.5.

Author’snote: the main ideas in this section have been in place since theoriginal 2005 edition, though the section was substantively revised in2018 to be more careful about the differences between grounding,ontological dependence, and ontological priority. (The 2023 revisionmerely involved trivial edits.)

3.6 Supervenience, Realization, and Emergence

Like ‘supervenience’, both ‘realization’ and‘emergence’ are philosophical terms of art. Theirdefinitions are stipulative and thus can only be judged by theirtheoretical usefulness, not by accord with common usage.

Realization is primarily taken to be a relationship betweenproperties, though derivative notions of property instance realizationand state of affairs realization have been defined. We will focus onproperty realization. There is more than one use of the term‘property realization’ in literature. Perhaps the leadinguse is the one found in the literature on the functionalist theory ofmind. (See, e.g., Block 1980; Melnyk 2003, 2006). On the functionalview of realization, one propertyG realizes anotherF just in caseG occupies (or fills or plays) thecausal role associated withF, ‘theF-role’—that is, just in case instances ofG have the kinds of causes and kinds of effects that comprisetheF-role. Thus, for instance, a neural property willrealize pain just in case it has the kinds of causes and effects thatcomprise the pain-role. (According to analytical functionalism, thepain-role is the causal role that folk psychology associates withpain; according to psychofunctionalism, it is the causal role thatscientific psychology associates with pain.) If more than one propertyplays theF-role, thenF is multiply realizable.(See the entry on multiple realizability.)

Sydney Shoemaker (2007, chapter 2) defines a related notion ofproperty realization, which he calls the ‘subset view ofrealization’. He says that “as a first approximation,propertyP has propertyQ as a realizer just in case(1) the forward-looking causal features of propertyP are asubset of the forward-looking causal features of propertyQ,and (2) the backward-looking causal features ofP have as asubset the backward-looking features ofQ” (2007, 12).Once again, ifP has more than one realizer, thenPis multiply realizable. (McLaughlin (2007) argues that this subsetnotion of realization, will not serve Shoemaker’s purposes.)

There are other, less well-entrenched notions of realization in theliterature (e.g., Gillett 2003; Shoemaker 2007, chapter 3), but itwould take us too far afield to spell these out in detail.

What is the relation between supervenience and realization, in eitherof the above senses? It looks like realization is sufficient forsupervenience, at least for non-local versions of supervenience. Butsupervenience is not sufficient for realization, for reasons that arefamiliar from section 3.5: necessary properties supervene on anything,and properties supervene on their own negations. Further, becauserealization is a distinctively causal notion, there are additionalconsiderations here. The interesting case has to do with epiphenomenalproperties—those that have no causal powers and play no causalrole. Perhaps mathematical properties are epiphenomenal in this way.LetF be such a property, and let it supervene uponG.F is not functionally-realized byG,sinceG does not playF’s distinctive causal role(F does not have one). So this is another reason to deny thatsupervenience is sufficient for functional realization. ButFis Shoemaker-realized byG. That’s becauseF’s causal powers are the null set, and the null set is asubset of every set. Epiphenomenal properties are thusShoemaker-realized by anything at all, includingG.(Shoemaker’s view of realization, like his view about the causalindividuation of properties (1980), is simply not well-suited to theepiphenomenal case.)

What about emergence? The term is used in a variety of ways, in thesciences as well as philosophy. These uses are so wildly divergentthat it is not clear that there is a common core notion. (See theessays in Bedau and Humphreys 2008, in Gibbs, Hendry, and Lancaster2019, Wilson 2021, and the entry onemergent properties.) But one canonical source of emergence talk is the British Emergentisttradition, particularly the work of C.D. Broad. Broad thought ofemergent properties as fundamental properties possessed by complexobjects (Broad 1925; McLaughlin 1992, 1997, 2019). A number ofphilosophers have suggested that Broad’s notion can be characterizedby means of supervenience with mere nomological necessity (e.g. vanCleve 1990, Chalmers 2006). One question that arises, then, is whetherthe appeal to nomological as opposed to metaphysical necessity candistinguish emergence from tighter relations like realization; JessicaWilson (2005; 2021, 143–149) and others have argued that itcannot.

3.7 Supervenience and Explanation

Supervenience claims, by themselves, do nothing more than state thatcertain patterns of property (or fact) variation hold. They are silentabout why those patterns hold, and about the precise nature of thedependency involved (see Kim 1993, 167; 1998, 9–15; Blackburn1984, 186; Schiffer 1987, 153–154; and McGinn 1993, 57). But fewsupervenience theses are plausibly brute, that is, unexplainable. Itis natural to look further, and to try to explain whyA-properties supervene onB-properties. When suchsupervenience is explainable, there is‘superdupervenience’ (a term coined by William Lycan; seealso Schiffer 1987; Horgan 1993; and Wilson 1999).

Sometimes it is easy to see what explains a supervenience thesis.Consider the examples of trivial supervenience relations fromSection 3.5. It is obvious why there cannot be anA-difference without aB-difference ifA is a set of necessary orimpossible properties—namely, because there cannot be anA-difference at all. The supervenience relation is explainedby the necessity or impossibility of the supervening properties. It isalso obvious whyA-properties supervene onA-properties. Of course, property identity claims aresometimes nota priori knowable; consider, for example, thefact that the propertybeing water is identical with thepropertybeing H₂0. Still the factthatbeing water is identical withbeingH₂0 explains why there cannot be adifference with respect to being water without a difference withrespect to being H₂0. And supervenience withonly nomological necessity can be explained by appeal to laws ofnature. It is in virtue of the Wiedemann-Franz Law that electricalconductivity supervenes with nomological necessity on thermalconductivity.

Because we expect supervenience theses to be explainable, it is hardfor us to rest content with a supervenience thesis if we do not seewhat would explain why it is true. If it is claimed, for instance,that moral properties supervene on non-moral properties, we expectthere to be an explanation of why this is so. Appeals to unexplainablesupervenience theses can thus seem to be mystery mongering.

3.8 Tallying Up

Supervenience gives us less than some philosophers have thought. Evenlogically or metaphysically necessary supervenience is compatible withthere being noB-properties that entail anyA-properties. Supervenience is not itself explanatory, anddoes not guarantee that theA-properties either reduce to,ontologically depend upon, or are grounded by theB-properties. It might provide a way to capture the thoughtthatA-properties or facts are not a further ontologicalcommitment over and above theB-properties or facts, but thisis controversial. At heart, all a supervenience claim says is thatA-propertiescovary withB-properties.Nevertheless, as we shall see inSection 5, supervenience has a variety of philosophical uses.

4. Varieties of Supervenience

The slogan “There cannot be anA-difference without aB-difference” is applied both toparticularindividuals and to entirepossible worlds. In the formercase, the slogan expresses the idea that two individuals cannot differinA-respects without also differing inB-respects.This sort of claim is an individual supervenience claim. In the lattercase, the slogan expresses the idea that two possible worlds cannotdiffer with respect to their world-wide pattern of distribution ofA-properties without also differing with respect to theirworld-wide pattern of distribution ofB-properties. That sortof claim is a global supervenience claim. Both individual and globalsupervenience claims come in a variety of modal strengths. In thissection, we will distinguish various forms of both individual andglobal supervenience, and examine some logical relationships amongthem.

4.1 Weak and Strong Individual Supervenience

Kim (1984, 1987) distinguished two different kinds of individualsupervenience, weak and strong. They are defined by means ofquantification over possible worlds, as follows:

A-propertiesweakly supervene onB-properties if and only if for any possible worldwand any individualsx andy inw, ifx andy areB-indiscernible inw,then they areA-indiscernible inw.
A-propertiesstrongly supervene onB-properties if and only if for any possible worldsw₁ andw₂ and any individualsxinw₁ andy inw₂, ifx inw₁ isB-indiscernible fromy inw₂, thenxinw₁ isA-indiscerniblefromy inw₂. (Kim1987.)

x andy areA-indiscernible if and only ifthey are exactly alike with respect to everyA-property;similarly forB-indiscernibility. (Here times are omitted,but of course objects may beA-indiscernible at one time, butnot at another.) The possible worlds quantified over might include allmetaphysically possible worlds, or only nomologically possible worlds(etc.), depending upon what degree of modal force is intended.

As the names indicate, strong individual supervenience is strongerthan weak individual supervenience. (We shall hereafter followestablished usage and drop the word ‘individual’ unlessclarity requires it.) Weak supervenience says that there is nopossible world that contains individuals that areB-indiscernible butA-discernible. Strongsupervenience entails that there are no possible individuals that areB-indiscernible butA-discernible,whether theyare in the same world or different worlds. When the range ofworlds is the same, strong supervenience theses entail weaksupervenience theses, but the latter do not in general entail theformer. It is important to note, however, that whenA isrestricted to intrinsic properties, strong and weak supervenience arearguably equivalent; see Section 4.3.4.

Occasionally philosophers appeal to weak supervenience rather thanstrong supervenience. Hare, for example, said that his claim thatvalue properties supervene on other properties was intended to be anappeal only to weak supervenience (1984, 4). And Davidson similarlyclaimed that his appeal to supervenience was intended to be an appealonly to weak supervenience (1985, 1993, esp. 4n4). (He said this inresponse to Kim (1984), who argued that Davidson cannot appeal tostrong supervenience on pain of commitment to strict psychophysicallaws, which are incompatible with Davidson’s well-known thesisof the anomalism of the mental, according to which there are no strictpsychophysical laws. See the entry on anomalous monism.)

But appealing to weak supervenience while denying strong generates acertain explanatory burden. You will recall that we always want anexplanation of why a supervenience relation holds (seeSection 3.7). Thus someone who asserts a weak supervenience thesis but denies thecorresponding strong supervenience thesis must provide an explanationof why the weak supervenience thesis is true that does not entail thatthe relevant strong supervenience thesis is true as well. And that canlook mysterious: if there can be things indifferent worldsthat areA-discernible but notB-discernible, whycan’t there be two such things within a single world? Ifeverything within each world that isB-indiscernible isA-indiscernible, how can different worlds enforcedifferentB→A property pairings? (SeeBlackburn on the need to explain the “ban on mixedworlds,” 1973, 1985, and especially 1984, 184.)

Sometimes there is an explanation of why weak supervenience holdsdespite the fact that strong supervenience does not. If, within aworld, two individuals assert exactly the same propositions, then theyare exactly alike vis-à-vis having asserted a true proposition:the one asserted at least one true proposition if and only if theother did. The reason is that a proposition will have a uniquetruth-value relative to a world. The following weak superveniencethesis thus holds: for any worldw, and any individualsx andy inw, ifx andyare indiscernible with respect to what propositions they haveasserted, then they are indiscernible with respect to having asserteda true proposition. Contingent propositions, however, are true in someworlds and false in others. It is thus possible for two individuals indifferent worlds to assert exactly the same propositions, and yetdiffer with respect to having asserted a true proposition. The onemight assert many true propositions, while the other fails to assertany true proposition. It follows that the following strongsupervenience thesis is false: for any worldsw₁ andw₂, any individualsx inw₁ andy inw₂, ifx inw₁ is indiscernible fromyinw₂, with respect to whatpropositions they have asserted, thenx inw₁ is indiscernible fromyinw₂ with respect to havingasserted a true proposition.

In contrast, it is by no means clear why mental properties wouldweakly supervene on physical properties without strongly superveningon them; and the analogous question arises for moral properties andnonmoral properties. Davidson and Hare owe us an explanation of whymental and moral properties weakly supervene, respectively, onphysical and nonmoral ones—and it must be an explanation thatdoes not entail that strong supervenience holds as well. SimonBlackburn’s well-known argument against moral realism basicallyconstitutes an attempt to answer this question for Hare. ThoughBlackburn speaks of ‘supervenience’ and‘necessitation’ rather than weak and strong supervenience,his argument against moral realism rests onexactly thedemand for explanation that we have been exploring. He claims, 1) thatmoral properties weakly supervene on nonmoral properties, but do notstrongly supervene on them, 2) that this requires explanation, and 3)that projectivists can do this better than moral realists (1973,1985.) We are content to note that some such answer is required fromanyone who holds a weak supervenience thesis without the correspondingstrong supervenience thesis.

One final matter concerning the notions of weak and strongsupervenience remains to be discussed. This is that they are sometimesformulated differently, by means of modal operators rather thanquantification over possible worlds:

Aweakly supervenes_m onB if and only if necessarily, if anythingx has somepropertyF inA, then there is at least one propertyG inB such thatx hasG, andeverything that hasG hasF, i.e., iff
□∀x∀F∈A[Fx→ ∃G∈B(Gx &∀y(Gy →Fy))]
Astrongly supervenes_m onB if and only if necessarily, if anythingx has somepropertyF inA, then there is at least one propertyG inB suchx hasG, andnecessarily everything that hasG hasF, i.e., iff
□∀x∀F∈A[Fx→ ∃G∈B(Gx &□∀y(Gy →Fy))]
(Kim 1984)

Notice that strong supervenience_m isformulated just like weak supervenience_m,except that it contains one more necessity operator.

Kim initially maintained that the modal operator versions areequivalent to the above possible world definitions of weak and strongsupervenience respectively (see esp. 1987, 79–82). But they arenot; they are stronger. On certain assumptions (e.g. that modaloperators are to be understood as quantifiers over worlds), the modaloperator versions of strong and weak supervenience respectively entailthe possible world versions; but notvice versa (McLaughlin1995).

The reasoning here is basically the same as that given inSection 3.2 above for why supervenience does not guarantee entailment. Bothweak_m and strong_m superveniencesay i) that it is necessary that everything that has anA-property has someB-property or other, and ii)that thatB-property entails theA-property. Butneither i) nor ii) follows from the possible world versions of eitherweak or strong supervenience—unlessB is assumed to beclosed under the Boolean operations of complementation, infinitaryconjunction, infinitary disjunction, and property-forming operationsinvolving quantification (McLaughlin 1995). Without that assumption,the possible worlds versions allow things withA-propertiesto lackB-properties altogether, anda fortiori tolack anyB-property that entails theirA-properties.Of course, possible worlds supervenience requires that each pair ofB-less intraworld (weak) or interworld (strong) individualsmust have thesameA-properties, but the possibleworld versions allowB-less individuals to haveA-properties. The modal operator versions do not.

It should therefore come as no surprise that the cases that served ascounterexamples to the claim that supervenience is a form ofentailment also serve as counterexamples to the equivalence of thepossible worlds and modal operator formulations of supervenience.BeingF strongly supervenes on being not-F, butfails to even weakly supervene_m on it.{P &Q} strongly supervenes on {P,Q}, but fails to even weaklysupervene_m on it. The possible worldversions of weak and strong supervenience are weaker than thecorresponding modal operator versions. The latter go beyond the basicidea that there cannot be anA-difference without aB-difference. Again, though, the modal operator versionsare equivalent to the possible worlds versions if the basesetB is closed under Boolean operations, and operationsinvolving quantification.

4.2 Regional Supervenience

Terence Horgan (1982) has proposed a version of supervenience in termsof individual regions of space-times, rather than in terms of objects.A weak and a strong version of Horgan’s “regionalsupervenience” can be formulated as follows:

A-propertiesweakly regionally supervene onB-properties if and only if for any possible worldwand any space-time regionsr₁ andr₂ inw, ifr₁ andr₂ areB-duplicates inw, then they areA-duplicates inw.
A-propertiesstrongly regionally supervene onB-properties if and only if for any possible worldsw₁ andw₂ and any space-time regionsr₁ inw₁ and space-time regionr₂ inw₂, ifr₁ inw₁ is aB-duplicate ofr₂ inw₂, thenr₁ inw₁ is anA-duplicate ofr₂ inw₂.

Regional supervenience is a form of individual supervenience thattakes the individuals to be regions of space-time. Nonetheless, it isworth separate mention because Horgan (1982) has argued that it hassome of the attractive features of global supervenience.

4.3 Global Supervenience

Often, claims of the form ‘there cannot be anA-difference without aB-difference’ are notmade about individuals, nor about nonmaximal space-time regions, butrather about entire possible worlds. This is global supervenience,typically formulated as follows:

A-propertiesglobally supervene onB-properties if and only if for any worldsw₁ andw₂, ifw₁ andw₂ have exactly the same world-widepattern of distribution ofB-properties, then they haveexactly the same world-wide pattern of distribution ofA-properties.

The notion of a global supervenience thesis has been employed for anumber of philosophical purposes. Notably, it has been used tocharacterize physicalism (seeSection 5.4), and to capture David Lewis’ Humean supervenience thesis:“all there is to the world is a vast mosaic of local matters ofparticular factÉ all else supervenes on that” (1986a,ix-x).

Global supervenience is often claimed to serve purposes that neitherstrong nor weak individual supervenience will serve. First, it issometimes claimed that global supervenience naturally handlesrelational properties likebeing an original Van Gogh orbeing a dollar bill. As we shall see, however, strong or weaksupervenience can handle relational properties too. Second, globalsupervenience naturally handles the supervenience of factors otherthan properties or relations. On a Humean view of laws of nature, forinstance, laws of nature are general facts that supervene onparticular facts. But that can be captured by individual propertysupervenience, even if only in a baroque way. A third potentialdifference between global and individual supervenience is that theformer, but not the latter, is compatible with the supervening andsubvening properties being possessed by different individuals (seeHaugeland 1982). Thus, for example, global supervenience is useful ifthere can be distinct but spatio-temporally coincidentobjects—it leaves room to say that the properties of a claystatue supervene upon the properties of the distinct lump of clay thatconstitutes it (seeSection 5.5).

What the difference between individual and global supervenience reallycomes to will be discussed throughout the rest of this section.

4.3.1 Strong Individual Supervenience and Global Supervenience

It is clear that strong individual supervenience entails globalsupervenience (see Kim 1984). The question that has attractedattention is the converse—whether global supervenience entailsstrong individual supervenience. In this section, we describe theinitial stages of this debate, which took place when the going notionof global supervenience was that outlined just above. In Section4.3.2, we explain how that notion has been replaced by a family ofmore precise notions, and explore how it affects the question ofwhether global supervenience entails strong individual supervenience.(Most of the reminder of this section paraphrases McLaughlin 1995,55–56.)

The debate began when Kim purported to show that “globalsupervenience is nothing but strong supervenience” (1984, 168).In response, Brad Petrie (1987) argued that global supervenience doesnot entail strong supervenience. His strategy was to try to provide acounterexample to a strong supervenience thesis that is not acounterexample to the corresponding global supervenience thesis. Hereis his case. Let setA = {S} and thatB ={P}. Consider two worldsw₁ andw₂ that are as follows: worldw₁ contains exactly two objects,x andy. And worldw₂ contains exactly two objects,x* andy*. The following purports to be a completedepiction of the contents of those worlds:

W₁		W₂

Px		Px*
Sx		~Sx*
Py		~Py*
~Sy		~Sy*

The existence ofw₁ andw₂ is incompatible with the thesisthatA strongly individually supervenes onB becausex in w₁ isB-indiscerniblebutA-discernible fromx* inw₂. But the existence of theseworlds is not itself a counterexample to theglobalsupervenience ofA onB. Sincew₁ andw₂do not have the same global pattern of distribution ofB-properties, it seems not to matter that the worlds do nothave the same global pattern of distribution ofA-properties.Thus Petrie claimed that “since global supervenience is, andstrong supervenience is not, consistent with this example, the twoconcepts of supervenience are not equivalent” (1987, 121).

In response, Kim conceded that global supervenience fails to entailstrong supervenience (1987, 318), and went on to claim thatPetrie’s example also shows that global supervenience fails toentail weak. Notice thatw₁ aloneviolates the weak supervenience ofA onB, but alsofails to be a counterexample to the global supervenience ofAonB. Kim thus concluded that global supervenience fails toentail weak or strong individual supervenience.

Paull and Sider pointed out that these argument strategies are no good(1992). The problem is that one cannot simply point to two worlds thatdo not themselves falsify a global supervenience thesis, and thenclaim that the case is compatible with that thesis. Those two worldsmight entail the existence of other worlds that arenotcompatible with the global supervenience thesis. A globalsupervenience thesis is a claim aboutall worlds, not justtwo. The upshot is that although a global supervenience thesis failsto entail either a weak or strong supervenience thesis in virtue oflogical form, it might nevertheless be the case that plausiblemetaphysical principles entail that whenever the former holds, so doesthe latter.

Paull and Sider appeal to a plausible principle to show that theexistence of Petrie’sw₁ andw₂ entail the existence of a pairof worlds that constitutes a counterexample to the globalsupervenience ofA-properties onB-properties (1992,838). The basic idea is that for any object in any possible world,there is another world containing an “isolated duplicate”of it. Intuitively, the duplicate exists all alone in its world; moreprecisely, an object y is isolated in a world “if and only ifthat world contains only (i)y, (ii)y’sparts, and (iii) objects whose existence is entail by any of theobjects mentioned in (i) and (ii)” (1992, 838–9).Crucially, isolated duplicates share the intrinsic properties of thethings with which they are duplicates. (Two caveats. First, this isnot intended to be adefinition of ‘intrinsic’.For some attempts to do so, see e.g., Lewis 1983a, Langton and Lewis1998, and a variety of articles inPhilosophy and PhenomenologicalResearch 63). Second, notice that the principle does not say thateach thing can itself exist in isolation; it simply says that eachthing has a duplicate that does. It consequently does not entail thatnothing has any essential extrinsic properties.)

Paull and Sider’s isolation principle does the job. Consideragain the worldsw₁ andw₂ that Petrie described. Petriepurported to describe the worlds in full. Thus,P andS are presumably supposed to be intrinsic properties. Itfollows from the isolation principle that there is a worldw₃ that contains an isolatedduplicate ofx—call it“z”—and a worldw₄ that contains an isolatedduplicate ofx*—call it “z*.” AsPaull and Sider note, these worlds will be as follows:

W₃		W₄

Pz		Pz*
Sz		~Sz*

Unlikew₁ andw₂,w₃ andw₄ constitute a counterexample tothe global supervenience ofA-properties onB-properties. They have the same pattern of distribution ofB-properties, but different patterns of distribution ofA-properties. So, Paull and Sider claim that Petrie failed toshow that global supervenience does not entail strongsupervenience.

But Paull and Sider went on to provide a new argument for that claim.They appealed to a setB containing just two properties,P andQ, and a setA containing only oneproperty,M. An object hasM just in case it hasP, and some other object isQ. That is to say,Mx =_dfPx &∃yQy. This definition guarantees thatAglobally supervenes onB. They then described the followingtwo worlds:

W		W*

Ma		~Mc
Pa		Pc
~Mb
Qb

This pair of worlds shows thatA does not strongly superveneonB. And the principle of isolation cannot be applied togenerate a counterexample to global supervenience. An isolatedduplicate of a would be bothA- andB-indiscerniblefrom c (an isolated duplicate of a wouldnot have M).Consequently, Paull and Sider concluded that global and strongsupervenience are not equivalent. (1992, 841).

Klagge (1995) objected to this line of argument. He pointed out thatPaull and Sider include an extrinsic propertyM in thesupervenient setA, but only intrinsic propertiesPandQ in the subvenient or base setB. And, heclaimed, if we allow that there are the sorts of property-formingoperations required to construct extrinsic propertyM, thenPaull and Sider have not exhaustively characterized worldswandw*. For, given those property-forming operations, it isplausible that there will, for instance, be a propertyP#that can be defined as follows:P#=_dfPx &∃y(y≠x). (Basically, a thing isP# just in case something else isP.)a inw andc inw* differ on this property;a hasP# whilec does not. That is right.But Klagge took that to show thatw andw* do notprovide a counterexample to the strong supervenience ofA onB after all. That, however, does not follow. It would followonly ifa andc thereby counted asB-discernible, and they do not. Paull and Sider stipulatethatB contains onlyP andQ. Thus,a andc areB-indiscernible, despite thefact thata hasP# andc does not.

But Klagge was clearly right that Paull and Sider’s exampleinvolves a supervenient setA that contains an extrinsicproperty and a subvenient setB that contains only intrinsicproperties, and he was right that this is important. It invites thequestion whether global supervenience might entail strongsupervenience whenA andB are sets of intrinsicproperties. And it invites the question whether global superveniencemight entail strong supervenience whenA andB bothinclude extrinsic properties of certain sorts. Indeed, in response toPaull and Sider, Kim suggests that “equivalence seems to fail,through the failure of implication from global to strongsupervenience, only when extrinsic properties are present in thesupervenient set but disallowed from the subvenient base” (1993,170; see also McLaughlin 1997a, 215). We will return to thesequestions in the next several sections. Answering them requiresgetting clearer about global supervenience; to this we now turn.

4.3.2 Different Versions of Global Supervenience

Until now, we have been relying mainly on a notion of globalsupervenience that is defined in terms of what amounts to a notion ofA/B-indiscernibility of worlds:

A-propertiesglobally supervene onB-properties if and only if for any worldsw₁ andw₂, ifw₁ andw₂ have exactly the same world-widepattern of distribution ofB-properties, then they haveexactly the same world-wide pattern of distribution ofA-properties.

But what is meant by a ‘world-wide pattern ofdistribution’ ofA- orB-properties? Thenotion is usually cashed out by appeal to the notion of there being acertain kind of isomorphism or mapping between worlds. For anyproperty setf, define the notion of anf-preservingisomorphism as follows:

An isomorphism I between the inhabitants of worldsw₁ andw₂ preservesf-propertiesif and only if for anyx inw₁,x has af-propertyP inw₁ just in case the image ofx under I (the individual to which I mapsx) hasP inw₂.

This purposely avoids appeal to any special relationship that themapped individuals may bear to each other (such, e.g., occupyingcorresponding locations in their respective worlds). This is to remainas neutral as possible on such issues, and because any features usedto pick out the mapped things would automatically then globallysupervene on any properties whatever (see McLaughlin 1995, 1997a). SeeSteinberg 2014 for an alternative way of characterizing world-widepatterns of property distribution.

Given this notion, various different forms of global supervenienceemerge. Stalnaker 1996, McLaughlin 1996, 1997a, and Sider 1999 alldistinguish between a weak and a strong notion of globalsupervenience, as follows:

A-propertiesweakly globally supervene onB-properties iff for any worldsw₁ andw₂, if there is aB-preserving isomorphism betweenw₁ andw₂, then there is anA-preserving isomorphism between them.
A-propertiesstrongly globally supervene onB-properties iff for any worldsw₁ andw₂, everyB-preservingisomorphism betweenw₁ andw₂ is anA-preservingisomorphism between them.

Shagrir (2002) and Bennett (2004a) have both formulated anintermediate version:

A-propertiesintermediately globally supervene onB-properties if and only if for any worldsw₁ andw₂, if there is aB-preserving isomorphism betweenw₁ andw₂, then at least one isomorphismbetween them is bothA-and-B-preserving.

Indeed, any number of versions of global supervenience can beformulated, simply by specifying exactly how manyA-and-B-preserving isomorphisms there must bebetween worlds between which there is aB-preservingisomorphism. Such versions all count as forms of intermediate globalsupervenience, however, and will be ignored in what follows. Noticetoo that it is not always clear which version is intended when someoneappeals to the notion of global supervenience. Shagrir (2002) andBennett (2004a) suggest that there is some reason to think that peopleoften intend intermediate; Leuenberger (2009) argues that none of theprecisified versions really captures the original concept. Shagrirlater argued that strong does the most “justice to the notion ofglobal supervenience” (2013).

It is easy to see that strong global supervenience entailsintermediate global supervenience, which in turn entails weak globalsupervenience. IfeveryB-preserving isomorphismbetween two worlds must itself beA-preserving, then if thereare anyB-preserving isomorphisms between two worlds at all,at leastone of them must beA-preserving. So,strong global supervenience entails intermediate. And if at least oneof any existingB-preserving isomorphisms between two worldsmust itself beA-preserving, then it obviously follows thatif there is aB-preserving isomorphism between two worlds,there must also be anA-preserving one. Thus, intermediateglobal supervenience entails weak global supervenience.

It is also easy to see that strong individual supervenience entailsstrong global supervenience. Suppose thatA-properties failto strongly globally supervene onB-properties. That meansthat there are two worldsw₁ andw₂ between which there is aB-preserving isomorphism that fails to beA-preserving. So, for somex inw₁, the image ofx under Iinw₂—call it y—has alland only the sameB-properties asx inw₁, but differs fromx inw₁ in at least one of itsA-properties. But that is just to say thatx inw₁ isB-indiscernible yetA-discernible fromy inw₂. It follows thatB-properties fail to strongly supervene onA-properties. Thus, strong individual supervenience entailsstrong global supervenience, and thereby also entails intermediate andweak global supervenience as well.

But strong global supervenience fails to entail strong individualsupervenience, at least whenA andB are anynonempty sets of properties. Showing this only requires tinymodifications to Paull and Sider’s argument that the notion ofglobal supervenience spelled out just in terms of world-wide patternsof distribution of properties fails to entail strong individualsupervenience (Section 4.3.1), and so we will not state the argumenthere. (See Shagrir 2002, 188.) Once again, the key to the argument isa case in which the supervening set contains extrinsic properties, andthe subvening set does not.

Let us now see what is the case when the supervening and subveningproperty sets are brought into line with each other. Recall theearlier hypothesis that global and strong individual are equivalentwhen Paull-Sider style cases are blocked (see Section 4.3.1). So,then, does strong global entail strong individual when the superveningset contains only intrinsic properties? When the subvening setcontains both intrinsic properties and all of the extrinsic propertiesthat can be generated from them?

The answer to both questions is “yes.” And it turns outthat related argumentative strategies can also be reapplied back tothe case of weak and strong individual supervenience. We outline thesestrategies in the next two sections. However, some of the proofsthemselves are complicated, and we thus refer to the reader to theoriginal literature.

4.3.3 Equivalences for an Extrinsic Base

Strong global supervenience entails strong individual supervenience aslong as the base setB is taken to be closed undercomplementation, infinitary conjunction, infinitary disjunction, andproperty-forming operations involving quantification and identity. Kimanticipates this equivalence (1993, 170), and Robert Stalnakerprovides the proof (1996, 238). It should also be noted that JohnBacon argues that if sets of propertiesA andB areclosed under the operations mentioned above and also an operation hecalls “resplicing,” then weak and strong individualsupervenience both hold or fail to hold together (1986). ForB to be closed under resplicing is for it to be the case thatfor any propertyP such that its extensionPw in aworldw is the extension of some property inB,P is a member ofB.

We have already noted that it is controversial whether suchproperty-forming operations are legitimate, and, even if they are, weare often interested in property sets that are not closed under them.SeeSection 3.2. Still, so long as the property-forming operations are legitimate,then even ifB itself is not closed under them, there willalways be a larger setB⁺ which is. That is goodenough to entail that for every strong global supervenience thesisthere is a logically equivalent strong individual superveniencethesis. Indeed, if all of these property-forming operations (includingBacon’s resplicing) are legitimate, then there are property setswith respect to which weak individual supervenience, strong individualsupervenience, and strong global supervenience are all equivalent.

But since there has been considerable dispute over the legitimacy ofthe various alleged property-forming operations, the issues remainunresolved.

4.3.4 Equivalencies for Intrinsic Properties

If we bring the property sets into line by restricting both thesupervening and subvening sets to intrinsic properties—howeverexactly the notion of an intrinsic property is to be captured(see e.g. Langton and Lewis 1998)—we get even clearer results.Many varieties of supervenience turn out to be equivalent forintrinsic properties.

Both Shagrir (2002) and Bennett (2004a) argue that strong individualsupervenience is equivalent to strong global supervenience whenA andB are sets of intrinsic properties. Bennettalso argues that in such a case evenweak globalsupervenience entails strong individual supervenience. The argumentrelies upon Paull and Sider’s isolation principle, explained inSection 4.3.1 above; the basic idea is to show that anycounterexamples to strong individual supervenience can be“isolated” to generate counterexamples to weak globalsupervenience—i.e., pairs of worlds between which there is aB-preserving isomorphism but noA-preservingone.

Here, again, we can also obtain related results aboutindividual supervenience. Mark Moyer (2008) argues that weakand strong individual supervenience are equivalent in the special caseof intrinsic properties. He appeals to a recombination principlesimilar to Paull and Sider’s principle of isolation, but with atwist. The intuitive idea is that any two things in any two worlds canbe isolated from their surroundings and then put into a world witheach other. More formally:

Recombination Principle. For any worldsw₁ andw₂, any individualx inw₁ and any individualy inw₂, there is a worldw₃ that contains individualsx′ andy′ such thatx′ inw₃ is an intrinsic-duplicate ofx inw₁ and y′ inw₃ is an intrinsic-duplicate ofy inw₂.

If this principle is right, then any cross-world pair of individualsthat witness the violation of a strong supervenience claim haveintrinsic-duplicates within a single world. If the superveningproperties are intrinsic, those duplicates will violate weaksupervenience as well.

If all of these results are right, then weak individual supervenience,strong individual supervenience, weak global supervenience,intermediate global supervenience, and strong global supervenience areall equivalent in the special case whenA andB are sets of intrinsic properties.

4.3.5 Individual and Global Supervenience Redux

In Section 4.3.3, we saw that weak and strong individual supervenienceare equivalent to strong global supervenience in the special case inwhich the base setB is closed under certain property formingoperations. And in 4.3.4, we saw that weak and strong individualsupervenience, and weak, intermediate, and strong global supervenienceare all equivalent in the special case in whichA andB are sets of intrinsic properties. The upshot is that strongglobal and strong individual supervenience come apart “only whenextrinsic properties are present in the supervenient set butdisallowed from the subvenient base,” as Kim and otherspredicted (Section 4.3.1). See Shagrir 2009 for discussion of the caseof relations.

However, weak and intermediate global supervenience are not equivalentto strong individual supervenience even when extrinsic properties arelet into the base—more precisely, when the base is closed underthe relevant property-forming operations. So, perhaps they havedistinctive philosophical work to do, work that cannot be done bystrong individual supervenience. For example, Sider (1999) appeals toweak global supervenience to handle cases of spatio-temporalcoincidence, though he retracts this in his (2008). SeeSection 5.5.

But it is controversial whether these forms of supervenience arestrong enough to be philosophically useful. As both Shagrir (2002) andBennett (2004a) have pointed out, only strong global supervenienceguarantees that the world-wide distribution ofB-propertiesdetermines the world-wide distribution ofA-properties. Bothweak and intermediate global allow what is called ‘intraworldvariation’—both allowB-indiscernible individualsin a world to have differentA-properties. (Contrast weakindividual supervenience, which allows crossworld variation, but doesban “mixed worlds.”) Indeed, weak global supervenienceallows theA-preserving andB-preservingisomorphisms to be utterly independent of each other. Suppose somepropertybeing griffic merely weakly globally supervenes onthe physical. Then although a world physically just like this one hasto contain the same number of griffic things as this world, it doesnot matter which things they are. In this world it might be the EiffelTower and the Queen Mother; in the physical duplicate it might be atea towel and the Grand Canyon.

In any case, those who assert a weak or intermediate globalsupervenience thesis while denying the corresponding strong globalsupervenience thesis need to provide an explanation of why weak orintermediate global supervenience holds that does not entail thatstrong global supervenience holds. (Recall the discussion of weak andstrong individual supervenience in4.1). That is, they need to explain what enforces the links betweenA- andB-preserving isomorphisms that are requiredby weak and intermediate global, without also enforcing the claim thateveryB-preserving isomorphism itself beA-preserving.

At present, these issues remain open, and the status of weak andintermediate global supervenience is controversial.

4.4 Similarity Based Supervenience

This essay has thus far focused on varieties ofindiscernibility-based supervenience. But in some cases wemight be interested in a notion according to which things that arevery much alike inB-respects must also be very much alike inA-respects. This is similarity-based supervenience (Kim1987). (The remainder of this section closely paraphrases McLaughlin1995).

Weak and strong versions of similarity-based supervenience can bedefined in the expected fashion:

Aweakly supervenes_sim onB if and onlyif for any worldw, and for anyx andy inw, ifx andy are not largely differentwith respect toB-properties, then they are not largelydifferent with respect toA-properties.
Astrongly supervenes_sim onB if and onlyif for any worldsw₁ andw₂,and for anyx inw₁ andy inw₂, ifx inw₁ is notlargely different fromy inw₂ withrespect toB-properties, thenx inw₁ is not largely different fromy inw₂ with respect toA-properties.

These are versions of individual supervenience; global versions canalso be formulated. Strong implies weak, but not conversely, exceptfor the special case of intrinsic properties. (The latter can be shownby slight modification of Moyer’s argument mentioned in Section4.3.4.)

Similarity-based supervenience is logically independent ofindiscernibility-based supervenience: neither implies the other.Similarity-based supervenience fails to imply indiscernibility-basedsupervenience. It may be that there can beA-differenceswithoutB-differences, but that there cannot belargeA-differences withoutlargeB-differences. And indiscernibility-based superveniencelikewise fails to imply similarity-based supervenience. The reason isthat there may be smallB-differences that are criticalpoints for bigA-differences. When that happens,similarity-based supervenience will fail, even thoughindiscernibility-based supervenience may hold. For example, it mightwell be the case that small physical differences can be accompanied bylarge mental and moral differences. Similarly, a small physicaldifference like a misplaced brush stroke might have a large effect onthe aesthetic value of a painting. Suffice it to note that it remainsan open question whether there are any interesting philosophical usesof similarity-based supervenience.

4.5 Multiple Domain Supervenience

Thus far this essay has focused primarily on single domainsupervenience (the exceptions are the discussions of weak andintermediate global supervenience).A form of superveniencecounts as single domain when and only when theA- andB-properties are possessed by the very sameindividuals—when the way something is inA-respects isa function of the wayit is inB-respects. Both weakand strong individual supervenience are clear cases of single domainsupervenience. But in some cases, what we want to say is that therecannot be anA-difference in certain things without aB-difference in certainother things—distinctthings to which the former things are related in a certain way. Whenand if this is the case, there is multiple domain supervenience.

One place such a notion seems useful is in discussions of coincidenceand material constitution. Those who think that a clay statue isdistinct from the lump of clay that make it up will claim that certainproperties of the statue must supervene on properties of the lump ofclay that constitutes it. For example, there could not be two statuesthat are discernible in shape without the statues being constituted bylumps of clay discernible in shape. For further discussion, seeSection 5.5.

Kim (1988) has formulated a weak and strong version of multiple domainsupervenience. LetD₁ andD₂ be non-empty domains ofindividuals,R be a relation betweenD₁ andD₂, andR|x bethe subset ofD₂ to whichx isR-related. We can define the followingnotions:

(A,D₁)weaklymultiple domain supervenes on (B,D₂) relative toR just incase necessarily for anyx andy inD₁, ifR|x andR|y areB-indiscernible, thenxandy areA-indiscernible.

(A,D₁)stronglymultiple domain supervenes on (B,D₂) relative to relationRjust in case for anyx andy inD₁ and any worldsw₁ andw₂, ifR|x inw₁ isB-indiscernible fromR|y inw₂,x inw₁ isA-indiscernible fromy inw₂. (Kim 1998)

WhenR is identity, these are equivalent, respectively, tosingle domain weak and single domain strong individual supervenience.It is becauseR might be a relation other than identity, forexample material constitution, that the definitions have the potentialfor added utility. Here again, slight modification of Moyer’sargument (Section 4.3.4) can be used to show that weak and strongmultiple domain supervenience are equivalent when the supervening setis intrinsic.

Coincidence-friendly supervenience is another kind of multiple-domainsupervenience (proposed by Dean Zimmerman 1995, 88)). It can beformulated as follows (see Bennett 2004, 520):

Coincidence-Friendly Supervenience : For allx andy, and all worldsw₁ andw₂, ifx inw₁ isB-indiscernible fromy inw₂, then for eachthingx* inw₁ to whichx isR-related, there is somethingy* inw₂ that isR-related toy and that isA-indiscernible fromx*.

That is a strong version, but a weak version can be formulated asfollows:

Weak Coincidence-Friendly Supervenience: For any worldw and anyx andy inw, ifx inw isB-indiscernible fromyinw, then for each thingx* to whichx isR-related inw, there is something y* thaty isR-related inw andx* isA-indiscernible fromy*.

Here again, whenR is identity, these forms of supervenienceare equivalent, respectively, to weak and strong individualsupervenience. And here again, the weak and strong versions areequivalent whenA is a set of only intrinsic properties.

Weak and strong coincident-friendly supervenience count as kinds ofmultiple-domain supervenience, but they differ from Kim’s weakand strong multiple domain supervenience in at least one importantrespect. The final quantifier in the definitions ofcoincident-friendly supervenience is existential, rather thanuniversal as it is in Kim’s weak and strong multiple domainsupervenience. As a result, Kim’s multiple domain superveniencesays that ifa andb areB-indiscernible,each thingR-related to a must beA-indiscerniblefromeverythingR-related tob.Coincidence-friendly supervenience says only that each thingR-related to a must beA-indiscernible fromsomethingR-related tob. This matters ifR isB-indiscernibility, as it plausibly is in thecase of spatio-temporal coincidence—the main philosophicalapplication of multiple-domain supervenience.

Finally, Ralf Bader (2013) has developed versions of multiple-domainsupervenience to model relations between complex entities and theirparts, including those permitted by non-classical metrologies.

5. Applications

5.1 An Argumentative Strategy

Recall that everyone agrees that the reduction ofA toB implies the supervenience ofA onB (Section 3.3). This gives rise to one central use of supervenience. Arguing againsta supervenience thesis that must be true if some program of reductionor conceptual analysis is to succeed is a common way of arguing thatthe program cannot succeed. McLaughlin (1984, 1995) calls this styleof argumentation ‘argument by appeal to a false impliedsupervenience thesis’—or, for short, argument by appeal toa FIST.

Here are a few well-known arguments by appeal to a FIST. Supposesomeone claims that there are neurophysiological properties, perhapsyet to be discovered, to which intentional properties like believingthatP reduce. This claim implies that intentional propertiessupervene on neurophysiological properties. The Twin Earth thoughtexperiments given by Tyler Burge (1979) and Hilary Putnam (1975) are(putative) counterexamples to that supervenience claim; they are casesof neurophysiologically indiscernible people whose thoughts havedifferent contents.

Another argument by appeal to a FIST is Chalmers’ appeal to the(putative) metaphysical possibility of zombies (seeSection 3.1 andSection 5.4). This is intended to show that phenomenal properties do notmetaphysically supervene on, and thus do not reduce to, physicalproperties. This line of argument is available even thoughphysicalists have not yet proposed any such reduction. If it succeeds,then the project of reducing phenomenal properties to physicalproperties is doomed to failure.

Consider a third example, from epistemology.A simple causaltheory of perceptual knowledge says that a subject’s perceptualknowledge thatP can be analyzed in terms ofP’s bearing the right kind of causal relation to thesubject’s belief thatP. To test this claim, we neednot await proposals as to what the kind of causal relation in questionis. For this project of conceptual analysis can succeed only if twobelievers thatP cannot differ with respect to perceptuallyknowing thatP without differing with respect to howP is causally connected to their belief thatP.Alvin Goldman’s fake barn country case (1976) yields a(putative) counterexample to this supervenience claim.

Of course, it is controversial whether any of these argumentssucceed, because it is controversial whether the allegedcounterexamples to the supervenience claims are really possible. Butin all three cases, the style of argument is the same—argumentby appeal to a FIST. (See McLaughlin 1984, 1995.)

5.2 Internalism/Externalism

Distinctions between internalism and externalism arise in many areasin philosophy—philosophy of mind, philosophy of language,epistemology, and ethics. All of these distinctions can becharacterized by means of supervenience theses. For example, aninternalist about mental content accepts, and an externalist denies,that what a mental state is about supervenes upon neurophysiologicalproperties, or “what’s in the head.” The dispute isabout whether two thinkers can differ in the contents of their mentalstates without also differing in some neurophysical respect.Similarly, an internalist about epistemic justification accepts, andan externalist denies, that whether a belief is justified supervenesupon the mental properties of the believer. The dispute is aboutwhether two believers can differ in whether their beliefs arejustified without also differing in some mental respect. And aninternalist about moral motivation accepts, and an externalist denies,that moral motivation supervenes upon moral judgment. The dispute isabout whether two (rational) people can differ in how they aremotivated to act without also differing in their judgments about whichof those actions they ought to perform.

Relatedly, supervenience can also be used to capture the traditionaldistinction between internal and external relations. As Lewis hasnoted (1986b, 62), an internal relation (such asbeing tallerthan) supervenes on the intrinsic natures of its relata. Anextrinsic relation (such asbeing 3 kilometers from ) doesnot. The main difference between this case and those above is thathere there is no real dispute about whether the supervenience thesisholds or not; it is widely agreed that there are two kinds ofrelations.

5.3 Haecceitism

Haecceitism is the view that identity properties, likebeing KofiAnnan orbeing that particular table, do not superveneon qualitative properties. On this view, every two numericallydistinct things differ haecceitistically, but no other differencefollows. Questions about whether there could be qualitativelyindiscernible but numerically distinct things becomes important inmodal metaphysics.

The issue here is an instance of something more general. Supervenienceplays a useful role in answering questions about the identity andindividuation conditions for things belonging to some kind. AsDavidson pointed out, there is aprima facie puzzle (1980,ch. 5) about how to address such questions. The answer to the question“When are two events identical?” istrivial—“Never.” And the answer to the question“When is an event identical with itself?” is likewisetrivial—“Always.” But surely there is a substantivequestion lurking here. Davidson himself opted to get around this worryby means of semantic ascent. But an alternative is to move to whatDavid Lewis calls ‘a nonduplication principle’ (see J.Bennett 1988). Instead of asking when two events are identical, we canask a fill in the blank question: ‘no two events can be justalike with respect to ______’? Davidson would fill in the blankwith ‘their causes and effects’. Kim would fill in theblank with ‘their subject, time, and constitutiveproperty’ (1976); others fill in the blank in other ways.

What matters here is just that nonduplication principles aresupervenience theses. They are supervenience theses that take thesupervening setA to be the identity facts for particularentities of whatever kind is in question. There cannot be a differencein whether an event has a property likebeing event e withouta difference in its causes and effects (Davidson) or in its subject,constitutive property, and time (Kim). Note that any view that acceptsa nonduplication principle for some sort of entity isipsofacto anti-haecceitist. Both Davidson and Kim areanti-haecceitists about events.

5.4 Characterizing Physicalism

Roughly speaking, physicalism is the view that somehow or other,everything is settled by the physical. This is of course vague along anumber of dimensions. One question, beyond the scope of this essay, iswhat exactly ‘physical’ means (see Stoljar’s entryon physicalism). Another question is about the scope of thequantifier: should it really range over everything, or should thethesis be restricted to the mental (thus leaving room for non-physicalentities like platonic numbers, abstract universals, or God)? Whilethe sociological question of which of these theses is usually intendedis also beyond the scope of this essay, the distinction will appearagain. And a third question is what exactly ‘settled by’means.

This last question is the relevant one here, because for a roughly 30year period beginning with Davidson’s “Mental Events”(1970, 214), philosophers used supervenience as a placeholder for theneeded relation. That is, physicalism was regularly characterized asthe view that everything—or perhaps just themental—supervenes on the physical. More specifically, it wasfrequently characterized as a i) metaphysically necessary ii) strongglobal supervenience thesis that is iii) restricted to only a certainrange of worlds. We shall say a bit about each in turn, beforementioning the more recent turn to instead characterizing physicalismin terms of grounding.

5.4.1 Why say that the thesis is metaphysically necessary?

Physicalists take the supervenience thesis to hold with metaphysicalnecessity, because a merely nomologically necessary superveniencethesis is compatible with dualism. Dualists can maintain that thereare fundamental psychophysical laws that maintain the supervenienceconnection (McLaughlin 1992, Chalmers 1996). Since no physicalist willagree, capturing physicalism requires a supervenience thesis thatholds with full-blown metaphysical necessity.

5.4.2 Why use strong global supervenience?

Physicalism is characterized in terms of global supervenience asopposed to individual supervenience because an individual’s mentalstates do not locally supervene on her intrinsic brain states forreasons that do not impugn physicalism as intuitively understood.Notably, the contents of her propositional attitudes depend upon thesurrounding environment if any kind of externalism is true (See Putnam1975 and the entry on externalism).

But why strong global supervenience instead of one of the weaker twovarieties, intermediate or weak (see4.3.2)? The answer is that neither of those is strong enough. An intermediateglobal supervenience thesis would allow a world physicallyindiscernible from this one, in which precisely the same mentalproperties are instantiated as are instantiated here, but in whichphysically indiscernible individuals swap mental lives. A weak globalsupervenience characterization of physicalism would go further. Itwould allow a world physically indiscernible from this one, in whichprecisely the same mental properties are instantiated as areinstantiated here, but in which they are differently distributed amongentities without any restriction. For example, a weak globalsupervenience characterization of physicalism is compatible with theexistence of a world physically indiscernible from this one in whichTaylor Swift and Peter Singer exchange mental lives (see4.3.5). Physicalism should not allow either sort of mental propertyswapping.

5.4.3 Why restrict the thesis to a certain range of worlds?

Still, physicalism cannot just be the thesis that the mental facts (orall the facts) strongly globally supervenience withlogical/metaphysical necessity on the physical facts and laws, becausemany physicalists want to allow for the metaphysical possibility ofthings like ghosts or Cartesian souls. They think that there actuallyaren’t any such things, not that there could not be any, noreven that there could not be any compatibly with the physical facts ofour world. They thus do in fact allow that two worlds could bephysical duplicates but differ mentally, in virtue of only one of themcontaining disembodied spirits, say. (Note that because the worlds arephysical duplicates, those spirits either exert no causal influence onthe physical at all, or else only exert redundant,‘overdeterministic’ causal influence on the physical.)

Various philosophers have offered various ways of defining physicalismto allow for this possibility, while continuing to rely upon globalsupervenience. The key in all cases is to limit the range of worlds inwhich the global supervenience thesis holds. For example, David Lewistook physicalism to be the claim that

Among worlds where no natural properties alien to our world areinstantiated, no two differ without differing physically; any two suchworlds that are exactly alike physically are duplicates (Lewis 1983b,364).

Jackson offers the following:

Any world which is a minimal physical duplicate of our world is aduplicatesimpliciter(Jackson, 1998, 12).

where a minimal physical duplicate is what results from duplicatingall the physical facts and “stopping right there.” And DavidChalmers says that physicalism is true in a world w just in case everypositive fact that obtains in w also obtains in any world physicallyindiscernible from w (1996, 39–40). Each of these threedefinitions allows for worlds in which physicalism fails: worlds thatare physical duplicates of the actual world, and in which there areghosts or souls.

5.4.4 Beyond supervenience physicalism

Unfortunately, even these sophisticated supervenience formulationsfail to provide an adequate characterization of physicalism. There areat least three reasons for this failure, and necessarily existingentities or necessarily obtaining facts generate not one but two ofthem.

Recall that necessary beings (whether entities, facts, or whatever)supervene on anything whatsoever, for the simple reason that suchthings exist in every world. Because no two worlds can differ inwhether they exist, full stop, no two worlds can differ in whetherthey exist without differing inx, for whateverxyou like (seesection 3.5).

The first problem that necessary beings pose is only a problem forwide scope physicalism, the version of the view that says that trulyeverything, not just the mental facts, supervenes on the physicalfacts. The difficulty is that some putative necessarily existingthings, like Platonic numbers or God, do not seem physicalisticallykosher. Yet their actual existence is compatible with a globalsupervenience formulation of physicalism.

The second problem is a problem for both wide scope physicalism and anarrower version only about the mental. As discussed insection 3.5), the fact that necessarily existing things supervene on anythingwhatsoever shows that supervenience is not ontological dependence ordetermination. After all, the putative fact that God exists globallysupervenes on the fact that my cat is named Snoop without the formerin any way depending on the latter. This is supervenience on thecheap, not anything strong enough for physicalism. (For other putativecounterexamples to the sufficiency of the supervenience thesis, seeWitmer 1999 and Hawthorne 2002.)

The third issue is closely related to the second, though it doesn’tturn on necessary existence in particular. It is that many think thecorrect statement of physicalism should be in some way explanatory ina way that the bare supervenience claim is not. One version of this isto say that physicalism should say that the physical facts explain themental ones. The supervenience claim alone says no such thing, asshown by the case of necessary existents as well as the case ofproperties supervening on their negations. A different version of thisis to say that physicalism requires‘superdupervenience’—that physicalism should explainwhy the relevant global supervenience theses holds (see Blackburn1984, Horgan 1993, Melnyk 2003, and Wilson 2005). Concerns like theseshould be familiar from sections3.5 and3.7).

Some think that these concerns can be avoided by moving fromcharacterizing physicalism in terms of supervenience to characterizingphysicalism in terms of grounding (e.g. Rosen 2010, 111; Dasgupta2014, 557; Schaffer 2017, section 4). Because grounding is supposed tobe hyperintensional, it is not the case that necessary beings or factsare grounded by just anything. And grounding is supposed to backexplanations as well.

However, whether the appeal to grounding really advances anything is amatter of dispute (Wilson 2016). See Stoljar’s entry on physicalismfor further discussion. Further, note that we have only raisedchallenges for the claim that a strong global supervenience thesis issufficientfor physicalism. It remains open that some suchthesis isnecessary for physicalism. If it is, then groundingphysicalism needs to entail supervenience physicalism. (Forconsiderations against, see Skiles 2014; for considerations in favor,see Bennett 2017, 3.3.) And if it is, physicalism would remaintestable by exposing it to would-be arguments by appeal to FISTS, suchas the zombie argument.

5.5 Coincident Entities and the “Grounding Problem”

It is fairly widely held that more than one object can occupy the samespatio-temporal location. Such objects are said to bespatio-temporally coincident. The classic example is a statue,Goliath, and the lump of clay that constitutes it, Lumpl (see Gibbard1975). On one version of the story, Lumpl sits around on a shelf for afew days before the sculptor shapes it into Goliath on a Thursdaymorning. It looks like Lumpl existed on the previous Wednesday andthat Goliath did not, and consequently looks like Leibniz’s Lawentails that they are distinct objects. On another version of thestory, Lumpl and Goliath are created and destroyed at precisely thesame moment. Here the two do not have different temporal properties,but they do have differentmodal ones—Lumpl would stillexist if we squashed it into a ball, but Goliath would not. Again,Leibniz’s Law apparently entails that they are distinct. (SeeRea 1997a for many interesting papers on this issue.)

The main objection to the view that Goliath and Lumpl are distinct iswhat can be called ‘the grounding problem’. How can Lumpland Goliath differ in their modal properties, given that they arealike in everyother way? What grounds their difference inpersistence conditions? In virtue of what do they have the persistenceconditions they do?

The grounding problem is sometimes characterized in terms ofsupervenience failure. Lumpl and Goliath differ in their persistenceconditions without differing in their physical or categoricalproperties (see Yablo 1987 for a discussion of categoricity). And itis true that many forms of supervenience fail: weak and strongindividual supervenience and strong global supervenience all fail. Butthere are forms of supervenience thatcan hold. Both weak andintermediate global supervenience hold, as does (as the name suggests)coincidence-friendly supervenience, and possibly other versions ofmultiple-domain supervenience (c.f. Zimmerman 1995, Rea 1997b, Sider1999, Baker 2000). All of these forms hold on the plausible assumptionthat any two regions physically/categorically just like this one willcontain an object with Goliath’s persistence conditions, and anobject with Lumpl’s persistence conditions.

But the crucial question is not whether any form of supervenienceholds, but rather whether those that hold constitute a satisfactoryanswer to the grounding problem. For a defense of the positive answer,see Sider 1999; for a defense of the negative answer, see Bennett2004b. For a new take, see Sider 2008.

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