Global Supervenience

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International Phenomenological Society

Global Supervenience and Identity across Times and WorldsAuthor(s): Theodore SiderReviewed work(s):Source: Philosophy and Phenomenological Research, Vol. 59, No. 4 (Dec., 1999), pp. 913-937Published by: International Phenomenological SocietyStable URL: http://www.jstor.org/stable/2653562 .

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Philosophy and Phenomenological ResearchVol. LIX, No. 4, December 1999

GlobalSupervenienceandIdentityacross Times and WorldsTHEODORESIDERUniversity of Rochester

The existence and importanceof supervenience principles for identity across times andworlds have been noted, but insufficient attention has been paid to their precise nature.Such attention s repaidwith philosophicaldividends. The issues in the formulationof thesupervenience principles are two. The first involves the relevant variety of superve-nience: that variety is global, but there are in fact two versions of global superveniencethat must be distinguished. The second involves the subject matter: he names "identityover time" and "identity across worlds" are misnomers,for in neithercase is identity atissue. The philosophicaldividends then follow. Nathan Salmon's argument hat identityover time needs no "grounds"n matters of qualitativefact can be answered,as can anargument offered by many, that coincident objects (such as statues and lumps of clay)would require objectionably ungrounded differences in identities across times andworlds.

Supervenienceprinciplesasserta kindof functionaldependenceof one sortoffact on another.They take this form:indiscernibilityn such-and-such espectentails indiscernibility in thus-and-so respect. The claim that the mentalsuperveneson the physical is the claim that the mental is a function of thephysical-physical indiscernibility mplies mentalindiscernibility.

Such principles take on interest for various related reasons. One is thatasserting supervenienceis a maximally cautious way to assert dependence:psychophysical supervenience is something all materialists can agree on,even if they disagreeover whethermentalitycan be reducedin any finite orintelligible way. Anotheris that supervenienceis presupposed by analysis.Various analyses of mentality in physical terms differ in details, but allpresuppose supervenience, for a physical analysans will not distinguishbetween physical indiscernibles,andhence the mentalanalysandumwill noteither.

Though the philosophy of mind may be the most familiar area in whichsupervenience has been applied, the same reasons for being interested insupervenience apply elsewhere. The notions of "identity over time" and"transworlddentity"raise some of the same issues as does mentality.Thesesclaiming that facts about identity across worlds and times involve nothing

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over andabove qualitative acts are of interest,bothbecausethey arepresup-posed by attemptedanalysesof identityover time andidentity across worlds,and because they have independentnterest to philosophers nclinedtowardsreduction.

Though attention has indeed been paid to the question of the truth ofsupervenienceprinciples or identityacross times andworlds,most notablyinthe literatureon HumeanSupervenience,1he questionof theirprecisenaturehas not beenadequatelyaddressed.Thepresentpaperapproacheshisquestionfrom various angles. There arerelatively "pure" ssues involving the natureofsuperveniencethat bear on this question,which I address in section I. Mostnotably,where philosophersusually discerna single notion of global super-venience, I argue that there are in fact two importantlydistinct notions.SectionII adds contentto the bare form of supervenienceprinciples ntroducedin section I: I will articulatewhat I take to be defensiblesupervenienceprin-ciples for identity over time and identity across worlds. Along the way, achallenge from NathanSalmon to the very idea of groundingidentity overtime in other facts will be answered. In the final section, the ideas of thepaperwill be given an application:to the familiarcases of spatially coinci-dent objects (for example, statues andlumpsof clay). It turnsout that the dis-tinction between varieties of global supervenienceis crucially importanttothe debateover coincidence.

Supervenience principlesmay be divided into global and local versions. Letus focus on psychophysicalsupervenience; he local versions (e.g., "strong"and "weak"supervenience2)say that physically indiscernible objects mustalso be mentally indiscernible.Thus, my physical propertiesdeterminemymental properties.Global versions are weaker, because they allow that thephysical propertiesof objects throughout he world are relevant to determin-ing mental facts.In this paperI focus on global supervenience.The most familiar sort ofglobal supervenience,which for reasons that will be apparent hortlyI'll call"weakglobal supervenience",may be stated as follows (where A and B aresets of propertiesandrelations):3

See the introduction o Lewis 1986b, Armstrong 1980, Haslanger 1994, Robinson 1989,and Lewis 1994, for example.See Kim 1984a.I take the terminology of weak and strongglobal superveniencefrom chapter5 of Paull1994 (Paull, however, uses the alternate ormulationof strong global superveniencethat Imention in note 10). That chapter contains an illuminating discussion of formulations ofglobal supervenience,from a technical andhistorical point of view. It also contains a dis-cussion of the relationship between strong and weak global supervenience. Paull and Icame upon the distinction between these types of global supervenience ndependently.

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A weaklyglobally supervenes on B =df any two possible worldsthatareworld-B-indiscerniblere alsoworld-A-indiscernible

It remains to explain the notion of worldindiscernibilitypresupposedby thisdefinition.4 One might thinkto try one of the following definitions:worldsare world-A-indiscerniblewhen i) they have the sameA-properties, i) whenthe worlds contain the same objects,and thoseobjectshave the same A-prop-erties and standin the same A-relations,or iii) when the same A-propertiesandrelationsare instantiatedat the same points in space-time.But i) A maycontainproperties ike mental properties,which are instantiatedby objects inworlds andnot entire worlds themselves; ii) we may want to say thatworldswith distinct objects neverthelessare A-indiscernibleif they have the samepatternof instantiationof A-propertiesandrelations;andiii) we may wanttoraise the question of whether spatiotemporalfacts globally supervene onsome chosen set, and so should not build spatiotemporal facts into thedefinition of world A indiscernibility.5A betterstrategy would be to say thatworlds areindiscerniblewhen their domainsareisomorphic.6WhereA is a setof propertiesandrelations, say thata function, , is anA-isornorphismfff isone-to-one, and for every n-place relation, R, in A (count propertiesas 1-place relations)andany n objectsinf s domain,those n objectsstandin R ifftheir images under standin R.7 We can now define the notion of two pos-sible worldsbeing alike withrespectto a set of propertiesand relations:

Supervenience claims can be weakened by restricting the quantifiers over worlds.One might weaken a claim of global supervenience, for example, to the claim that anytwo nomologically possible B-indiscernible worlds are A-indiscernible. I ignore suchrestrictedversions in this paper.

4 See McLaughlin 1997 on the definitionof worldindiscernibility.5 For these criticisms see, respectively, i) Paulland Sider 1992, p. 834; ii) Kim 1988, p. 118;iii) McLaughlin 1997, and Stalnaker1996, fn. 8.

6 McLaughlin 1997 and Stalnaker1996 pursuethis strategyas well.7 Throughout his paper it will be convenientto make certain assumptions. First, I assume

that each object exists in exactly one possible world (so I can speak of absolute ratherthan world-relative instantiationof propertiesand relations; let fusions of objects fromdifferent worlds be excluded from the domain of quantification n this paper); second, inmost cases I will not qualify property nstantiation o times, which amounts to making theassumptionthat the objects of attributionof temporarypropertiesare temporary stages;and third, I will assume that necessarily coextensive properties and relations are identi-cal, and that necessarily equivalent propositionsare identical. I regardthese assumptionsas innocuous because dispensable. If, for example, you believe in genuine transworldidentity, you could replace my "objectx, whose world is w, has propertyP", with "objectx has propertyP at world w". I also make a more substantivepresupposition,that of an"abundant" onception of properties, relations, and propositions (see Oliver 1996 andLewis 1986a, p. 59 ff.) obeying the following principles:

(i) For any class of possible worlds, thereis a propositiontrue at all and only theworlds in the class.

(ii) For any class of possible individuals,there is a propertyhad by all and only theindividuals n thatclass.

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w1 andw2 areworld-A-indiscernible=df w1andw2 are possible worlds,and there is some A-isomorphism from the domain of (i.e., set ofobjects existing at) w1 onto the domainof w2

The core idea of global supervenienceis that functional determinationoccurs not necessarily at the local level, but ratherat the global level. Weakglobal superveniencemakes this vague idea precise in one way, but thereisanother.8Roughly, the idea is that whetheror not a given n-tuple of objectsstandsin a certainrelation n A is determined,not only by whatproperties nB those objectshave and whatrelations n B they bearto each other,but alsoby what relationsin B they standin to otherobjects, and also by whatprop-erties and relations in B are instantiatedby their worldmates. This seemscorrectlydescribableas a kind of global superveniencebecausethe instantia-tion of the superveningpropertiesand relations can dependon the instantia-tion of the base propertiesand relations across all of the objects throughoutthe possible worldin question.

More carefully, let us define an n-place object sequence as an n-tuple ofobjects, each of which is fromthe samepossible world.Then we can charac-terize the following relation of global indiscernibility between objectsequences:9

n-place object sequences and are globally A-indiscernible=df there is some A-isomorphismfrom the domain of's world onto the domain of 's world that mapsxl toy1, ..., andXntoYn

To make the intuitiveidea clear, let us consider the special case of one-placeobject sequences, which may be taken to be their sole members. Whenobjects (one-place object sequences) are globally A-indiscernible, they arealike with respect to A in a very strongsense: they not only have the samepropertiesin A, but also have the same "worldperspective"with respect toA. If one bears relation R to some objectwith propertyP (whereR and P aremembers of A), then so must the other. If one's world containsexactly 15

(iii) For any positive integer n, and any class of n-tuples of possible objects inwhich each tuple contains objects from some one world, there is an n-placerelation had by all andonly the 'tuplesin the class. (I ignore transworld,multi-grade, and infinite-placerelationsin this paper.)

Since writing this paper, I've learned of two other papers that mention the differencebetween these two sorts of global supervenience: Stalnaker 1996, p. 227, andMcLaughlin 1997. Neither author explores the difference between the formulations indetail, and Stalnakerseems to view the weak version as a misformulationof the intuitiveidea of global supervenience. Also note that each author uses the equivalent formulationof strong global supervenience hatI discuss in note 10.Let us stipulate that where nom, n-place object sequences are never globally indis-cernible from m-place object sequences.

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objects with propertyP, then so must the world of the other. We can nowformulateour second version of global supervenience:10'1

A strongly globally supervenes on B =df any object sequences (perhapsfrom differentpossible worlds)that areglobally B-indiscerniblearealso globally A-indiscernible

Return o psychophysical supervenience:he idea is that what mentalproper-ties I have is determined,not only by what physical propertiesI have, butalso by what physical propertiesother things have, by what physical rela-tions I bear to those objects, and by what physical relations those objectsbear to each other. Objects with the same physical world perspective musthave thesamemental worldperspective.

Here is an example to highlight the difference between strongand weakglobal supervenience.'2Considertwo properties,P and Q, and two possibleworlds as follows:

1 An equivalent way to define strong global supervenience s this:A strongly globally supervenes on B =df for any worlds w, and w2, every B-isomorphism romwl's domainonto iv2's domain s anA-isomorphism

This formulation is due to Phillip Bricker, who thinks it the correct way to formulateglobal supervenience. Proof of equivalence: i) suppose first that A supervenes stronglyglobally on B, according to the original definition; let f be any B-isomorphism from thedomain of w, onto the domain of w2; we show thatf is an A-isomorphism.Let x... .x, beobjects from the domain of wl; let R be any n-place relationin A. In virtue of the exis-tence of f, and are globally B-indiscernible, and hence areglobally A-indiscernible by supervenience; hence there is an A-isomorphism from thedomain of w, onto the domain of w2 under which the members of these 'tuples corre-spond; it follows thatx1...xn stand in R iff f(xl).. .f(xn) stand in R. Strong global super-venience in the new sense thus holds. ii) For the other direction, suppose that Asupervenes globally on B in the new sense, and let and < ... .n> be anyglobally B-indiscerniblen-place object sequences. By definition of global B-indiscernibil-ity, there is a B-isomorphism between the domains of the worlds of these sequences thatmaps xi to yi for all i; by supervenience this function is an A-isomorphism; thereforethese sequences are globally A-indiscernible. Strong global supervenience n the originalsense thusholds.

Hellman and Thompson 1975, p. 559, contains a footnote mentioning a definitionlike the present one.Note that there are purely formal differences between the two varieties; the followingthreeprincipleshold for strong but not weak global supervenience:

(P1) If A superveneson C and B superveneson C, then AuB superveneson C(P2) If A superveneson B then AuB superveneson B(P3) If A supervenes on BuX and B supervenes on CuX, then A supervenes on

CUX12 This example is Phillip Bricker's. The example merely establishes the formal non-equiva-

lence of the two versions of supervenience; it does not on its own establish the(metaphysical)possibility of a set which weakly, but not strongly, globally supervenes onanother set. See Paull and Sider 1992, section 2, on formal vs. "metaphysical"equiva-lence.

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WI W2Px & Qx Pz & -Qz-Py & -Qy -Pu & Qu

These worlds are consistent with weak global supervenienceof {Q on {P},becausetheyareboth world-{P}-indiscernible ndworld-{Q}-indiscernible.Afunction,f, mappingx to z andy to u is a {P}-isomorphism; a function, g,mapping x to u andy to z is a {Q}-isomorphism.) But these worlds falsifythe strong global supervenienceof {Q} on {P}, because objects x andz areglobally {P}-indiscernible without being globally {Q}-indiscernible. (Invirtue of functionf, x and z are globally {P}-indiscernible, but no {Q}-isomorphismcan mapx to z since x has Q whereasz does not.)

A "real life" case (relatively speaking) which brings out the differenceinvolves the doctrineof "anti-haecceitism",ccordingto which haecceities-properties ike being Ted-supervene globally on the set, QUAL, of qualita-tive propertiesand relations.('Qualitative'here meanssomething ike 'purelydescriptive'. Purely qualitative facts cannot involve particularobjects; apurely qualitative sentence may not mention any objects by name.) Thestrong version of this supervenienceprincipleis immediatelyrefutedby theexistence of worlds with certain sorts of symmetry,for example, worlds oftwo-way eternalrecurrence. n virtue of functions thatmap each object to itscounterpart in the next epoch, each object will be globally QUAL-indiscernible from its counterpart n the next epoch, but such objects willhave differenthaecceities sincetheyarenumericallydistinctfrom eachother.13The weak version, however, is consistent with the existence of such worlds.Weak global superveniencesays thatany worlds thatareworld-indiscerniblein one set are world-indiscernible n another.Thus, a claim of weak globalsuperveniencecan only be refutedby a pairof two possible worlds,since anyworld is world-indiscernible rom itself with respect to any set (the identitymap is an A-isomorphism,for any set A). The recurrenceworld on its own,therefore,does not refute the weak version of anti-haecceitism.For the weakglobal supervenienceof haecceities on QUAL to hold, all that is required sthatany two recurrenceworlds that are qualitativeduplicateshave the samesequence of individuals. (In section III, I'll give furtherexamples of thephilosophicalsignificanceof the distinctionbetween strongand weak globalsupervenience.)

These versions of global supervenience,andthe distinctionbetweenthem,can be mademore intuitiveby means of certain"equivalenceresults" hat areanalogous to Jaegwon Kim's familiar equivalence result for strong (local)13 I'm assuming that the numerical distinctness of space-time points occupied would notcount as a qualitative difference. Also, I have in mind an anti-haecceitist who is not a

counterpartheorist; things are a little different for a counterpartheorist.

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supervenience.Kim showed that wheneverA stronglysuperveneson B, everyproperty in A is necessarily coextensive with some (possibly infinitary)boolean combination of propertiesfrom B.14It is possible to come up withanalogous results for both versions of global supervenience. Strong globalsupervenienceof A on B also entails propertycorrelationsbetween A andB,althoughthe properties"built out"of B may now be "relational" in a senseto be explained)rather hanboolean combinationsof properties rom B. Weakglobal supervenience,on the other hand,merely entails equivalences betweenpropositions "constructedrom"(again, in a sense to be explained)A and B.

First I'll presentthe propertycorrelationsentailed by strong global super-venience (the result generalizes to relations as well; see note 17). I need toformulatea rigorous notion of what I'll call a generalized A-property.A gen-eralized A-property s to be a property hatis built out of the properties andrelations in a set, A, in a quitebroad sense which allows relationalpropertiesas well as boolean combinations. For example, if propertyP and relation Rare in A, then such propertiesas being related by R to some object with Pwill be generalized A-properties.This may be accomplished n the followingway. The relation of global A-indiscernibilityover 1-place object sequences(i.e., objects) is clearly an equivalencerelation;with each of its equivalenceclasses there is an associatedproperty: he propertyhadby all andonly thosemembers of the equivalence class. I call these properties maximal A-properties. MaximalA-propertiesare, intuitively,the most specific relationalpropertiesone can "construct"rom set A, for two objects share one iff theyareglobally A-indiscernible,and so iff theyhave the sameA-properties, tandin the same A-relations, and similarly for their worldmates.Suppose set Acontains just two properties, P and Q. and a single binaryrelation R. Anexample of an open formulaexpressinga maximalA-propertywould thenbethe following:

x has propertyP but not property Q; there is only one object, y, in theworld other thanx; y has Q but not P; neither x nory bears R toitself; x bearsR to y buty does not bear R to x.

The recipe for coming up with a maximal A-propertyis this: select somepossible object and describe all its features with respect to A, both intrinsicand relational.All relational featuresmust be mentioned, and so along theway it will be necessary to completely describe the distribution of A-properties and relations throughoutthe entirety of that object's possibleworld. My example of a maximal A-property was expressible by a finiteformula,but there is no guarantee hat this will always be possible. For onething, A might containinfinitelymany propertiesandrelations;for another,14 See Kim 1984b,pp. 169-70.

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an object in a world with infinitely many objects might require an infinitedescription. If we allowed ourselves an infinitary language, this barrier toexpressing maximalA-propertieswould disappear; ndeed, we could give amore linguistic account of maximal A-properties:as those picked out bycertainformulas n a suitablychosen infinitaryanguage.1

Given this notion of a maximalA-property,we may now define a general-ized A-property as the disjunctionof some set of maximal A-properties."6This definitionseems to capture he intuitive dea of a property"constructablefrom" set A, in the broad sense which allows arbitrarily omplex relationaldependence. ntuitively,generalizedA-properties reproperties uch that whenan individualhas one, this only involves the propertiesandrelations from setA instantiated by it and its worldmates. Any property defined by an openformula with one free variablein a standard irst orderlanguage with onlylogical apparatus includingquantifiers) lus predicates orpropertiesand rela-tions in A (butno names!) would be an generalizedA-property,but the con-verse fails since generalizedA-propertiesneed not be finitely expressible. (Asbefore,we couldgive a morelinguisticaccount of generalizedA-properties ntermsof those expressible by certainformulas n aninfinitary anguage.)

Given this apparatus,we may statethe firstresult to which I've alluded asfollows:1715 I have in mind a constructionparallelto thatproposedin the appendixof Stalnaker 1996.

Roughly, we obtain one maximal A-property or each possible individualby constructinga complete descriptionof that individual and its worldmates n an infinitary anguage. Butthere is one minorqualificationI would make. Stalnakerdescribes the procedureof con-structinga maximal descriptionof a world (this is parallelto a maximaldescriptionof anobject) as follows: "if there are n members of the domain of w, the descriptionwill beginwith n existential quantifiers."It is important o be explicit that n here may be infinite,since worlds can have infinite domains. Thus,the languagein questionis infinitaryboth inthe sense that it allows infiniteconjunction,and that it allows infiniteblocks of quantifiers.If there is an upper bound on the size of possible worlds' domains,thenthe languagecanhave this size; otherwise the language must allow sentences of arbitrarily arge cardinal-ity. Relatedly, a bug emerges in this strategy if there are worlds with domains so largethey do not form sets, since standard infinitary languages identify sentences with settheoretic constructionsout of primitive vocabulary.

16 For any set, S, of properties,whetherfiniteor infinite,the disjunctionof S is defined as thepropertyhad by an object iff that object has some property n S; its existence is guaran-teed by principle (ii) from note 7. Let us count the null set as a degeneratecase of a setof maximal A-properties; hus, the disjunctionof the null set-the impossible property-will count as a generalizedA-property, or every set, A, of propertiesand relations.

17 I'll prove generalprinciplesof which (SI) and (S2) are special cases:(S1 ') If A strongly globally superveneson B, then any relation in A is necessarilycoextensive with some generalizedB-relation(S2') If A strongly globally superveneson B, then for any n-place relationR in A,and any n-place object-sequence, , that instantiatesR, R is entailed

by 's maximal B-relationHere, the notion of a generalizedA-relation is the naturalgeneralizationof the notion ofa generalized A-property.An n-place maximal A-relation is a relationholding among alland only the n-place object sequences in some equivalence class of the relation of A-

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(S1) If A strongly globally superveneson B, then any property in A isnecessarilycoextensive with some generalizedB-property

A related result is this:(S2) If A strongly globally superveneson B, then for any property,P, in

A, and any possible object, x, which has P, P is entailed by x'smaximalB-property

(One propertyentails another iff any possible object with the first has thesecond as well; similarlyforrelations).

The results for weak global supervenience are nearly exactly analogous.We'll want"generalizedA-propositions"o be propositions hat are"builtoutof' propertiesand relationsin A in a broadsense-as propositionsthe hold-ing of which depends only on the distributionof the propertiesand relationsin A across the entireworld. Define a maximalA-propositionas one true atall andonly the worlds in some equivalenceclass of worldsunder herelationof worldA-indiscernibility; eneralizedA-propositionsmaythen be definedasdisjunctionsof sets of maximalA-propositions."8ntuitively, generalizedA-propositionsare thepropositionsyou couldunderstand f you only understoodA-properties and relations. The true maximal A-proposition would beexpressed by a sentence like the following; "There are objects x, y, z,which havesuchand suchproperties n A and stand n suchand such relationsin A". This sentence would describehow things fare with the propertiesandrelations in A in complete detail. Less than maximal A-propositions willalso concernonly the distributionof propertiesand relations n A, but needn'tbe so specific in theirdescriptionof thatdistribution. Again, using infinitarylanguages, a more linguistic-looking accountof generalized A-propositionswould be possible.) We have, then,an analogof (SI):19

indiscernibility; generalized A-relations are then disjunctions of sets of maximal A-relations (again counting the null set-see note 16). Note that in virtue of (ii) and (iii)from note 7, and the assumption that necessarily coextensive relations are identical,every object sequence stands in exactly one maximal A-relation.

Let's begin by proving (S2'). I'll use boldface variables like x as variables for n-tuples. Where Re A, let x have R; let Q be x's maximal B-relation; I'll show that anypossible object sequence, y, that has Q must have R as well. Since x andy each have Qthey are globally B-indiscernible, and therefore globally A-indiscernible by super-venience; hence, since x has R, y has R as well.

Next (Si ): let R be any memberof A; I'll show that R is necessarily coextensivewith Q. the disjunctionof all the maximalB-relationsthat entail R. By definitionof Q. anypossible object sequence that has Q has R as well. Suppose on the other hand that somepossible object sequence, x, has R. Where Q' is x's maximal B-relation,(S2') implies thatQ' entails R; Q' is thereforea disjunctof Q and hence x has Q.

18 I count the disjunctionof the null set-the impossible proposition-as a generalized A-proposition.See note 16.

19 The proofs of (WI) and (W2) are analogousto those of (SI) and (S2). See also Paull andSider 1992, section 5 andAppendix3.

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(WI) If A weakly globally superveneson B, then any generalized A-proposition is necessarily equivalent to some generalized B-proposition

We also have a companionto (S2):(W2) If A weakly globally supervenes on B, then for any possible

world, w, and any generalized A-proposition,p, that is true atw,p is entailed by themaximalB-proposition hatis trueat wOne way to see the difference between strong and weak global superve-

nience, then, is through these equivalence results. Returning to psycho-physical global supervenience,the weak version implies that every mentalproposition s equivalentto some (extremely complex!) physical proposition,and so fixing the physical facts true at a world fixes the mental facts truethere. But it does not follow from this that mentalpropertiesare necessarilycoextensive with physical properties,even if we allow relational physicalproperties.Even after fixing the physical propertiesof an object,relationalaswell as intrinsic, its mental properties may not be fixed. Only the strongversion of the supervenience principle implies these furtherclaims. Here isanotherway to see the difference betweenfixing mentalpropertiesandfixingmental propositions. Suppose you were omniscient with respectto the distri-bution of the members of MENTAL, the set of mental properties andrelations, but, as in the standardexamples involving "de se" or "indexical"belief, ignorant of who you were.20You would then know exactly whichgeneralized MENTAL-propositionsheld at your-world for you would knowwhich maximal MENTAL-proposition was true at your world), but youwould not know which maximalMENTAL-property ou had.

IIOur discussion of supervenience has so far been highly abstract;in thissection I'll focus on the formulation of global supervenienceprinciples forone specific domain: identity over time and identity across worlds. Thesesupervenience principlesare of considerablephilosophical interest (witnessthe literatureon DavidLewis's HumeanSupervenience, or example), and yetthey turn out to be quite tricky to state. One might have thought that theprincipleswould have the form "theidentityrelationglobally supervenes onset B", whereB wouldbe some set plausibly thoughtto determine acts aboutidentity over time. But this will not do. Any 1-1 function is an {=}-isomor-20 See, for example, Lewis's case of the two gods, in Lewis 1983, p. 139.21 A side point of interest about these equivalence results is that they form the basis of a

response to Jaegwon Kim's (1987, 1988, 1989, 1990) "waywardatom" argument thatglobal supervenience is insufficient for any intuitive sort of dependence. See Paull andSider 1992.

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phism, andhence, trivially,the identityrelationsupervenesglobally (whetherstrongly or weakly) on any set whatsoever. It would be a confusion torespond that the principle should ratherassert the supervenience of theidentity-over-timerelation,for "identityover time"is not anotherspecies ofidentity, but rather dentity itself.22

One could attemptto reformulatethe definitions without one-one func-tions, but the definitions in their present form seem highly intuitive. Theattemptwould be unmotivatedanyway,becausethere s independent eason tothink thatcontroversyover "identityover time" isn't really controversyoveridentity at all. David Lewis has argued nicely that the natureof the identityrelation is rarelyat issue in philosophy:23Identity is utterly simple and unproblematic.Every thing is identical to itself; nothing is everidentical to anything else except itself.... We do state plenty of genuine problems in terms ofidentity. But we needn't state them so. Therefore they are not problems about identity. Is itever so thatan F is identicalto a G? Thatis, is it ever so thatthe same thing is an F, and also aG? More simply, is it ever so that an F is a G? The identity dropsout.I think Lewis's claim applies to the case at hand. The traditionalproblemsof"identityover time" are misnamed.When we wonder aboutthose problemswe are wondering primarilyabout what have been called issues of persis-tence,24 not aboutthe natureof the identity relation. Supervenienceprinciplesin these areas shouldthereforeconcernpersistence,not identity.

By questionsof persistence,I have in mindquestionssuch as the follow-ing: can a personsurvivetotal amnesia?Cana statue survivethe replacementof more than 50% of its originalmatter?Can a physical objecthave a tempo-rally discontinuous existence? These questions all concern the concept ofobjects existing at times. The question of whether a person could survivetotal amnesia is the questionof whethera personcould exist both before andafter an attackof amnesia.These questionscan be phrasedas questionsaboutidentity:Is there ever a statuethatexists at some time, and is identical to astatuethat,at some latertime, has replacedmore than50%of its matter?Butthey needn't be so phrased;we could say simply: Is there ever a statue thatexists at some time and also at some later time at which it has replaced morethan50% of its matter?The fact that the question can be phrased n the firstway doesn't imply that the question concerns the nature of the identityrelation, any more than the fact that the question "is it possible to love twopersons at once?"can be rephrasedas "Is it possible for there to be a person22 Even a radical who suggests that everyday objects (such as persons, tables and chairs)are really instantaneousstages does not deny this. If 'I was identical to that young boy'means that I bear the I-relationto a stage that is identical to thatyoung boy, 'is identicalto' still expresses ordinaryidentity; what is nonstandard s the treatmentof tense. SeeSider 1996.23 See Lewis 1986a, pp. 192-93.24 This use of the term has been popularizedby David Lewis. See Lewis 1986a, p. 202.




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who loves some personat a time, and who is identicalto someone who lovesa second personat thattime?" implies thatthe formerquestion is a questionabout identity.25

Notice that in the familiar debates involving "identity over time", thehaecceities of objects involved are irrelevant. When we discuss a case ofamnesia, we want to know whether the person at the beginning of thethought experiment survives;it is irrelevantwhetherthatpersonis Frank orJoe. The markof a question purelyaboutpersistenceis thatwhile it is aboutwhat goes on at more thanone time, it can be askedusing quantifiersratherthan names;we can ask: is there a person with such and such features whoexists at times t1 and t2? That the questions primarilyconcern persistenceratherthanhaecceity can also be seen by inspectingthe theories in the area.The various theoriesof personal dentity (for examplethe memory theoryandthe bodily continuity theory) give conditions underwhich a person at onetime persists until some othertime; they don't give necessary and sufficientconditions for a given haecceity's being instantiated. t is possible to runthetwo concernstogether, by askingfor example:what are the conditionsunderwhich Frank exists at times t1 andt2?Here we ask not only aboutwhat I amcalling persistence,but also aboutwhatconditionswould have to be satisfiedto have Frank present, and that is a question abouthaecceity. It is the formerquestions, I am suggesting, which are really at issue in the discussions of"identityover time".26

In formulating supervenience principlesrelevant to the traditionalques-tions of identity over time, then, we should formulatesupervenience princi-ples for persistence.27A familiar principle of this sort asserts roughly that

25 It may be objectedthattraditional heorizingabout"identityover time" does indeed con-cern identity, since certain solutions to traditional puzzles postulate non-standardaccounts of identity, for example that identity is intransitiveor sortal-relative see Geach1967 on relative identity.) The best response is to clarify the vague assertion that thepuzzles in questiondon't "concern" he identityrelation.The core insight here is that oneneed not hold non-standardviews of identityto understand he phenomenain this neigh-borhood. Indeed, I would go furtherand say that all of the sensible views in the area ofidentity over time share the same, standard onception of the identity relation.

26 The difference between questions of haecceity and persistence may also be illustratedwith the famous example of the rotating homogeneous continuous disk, due to SaulKripke and David Armstrong. (See Armstrong 1980. Kripke's example was given in anunpublished ecture.)A principle statingthatpersistence superveneson matters of tempo-rally local qualitative fact would require that the disk rotates in both or neither of thepossible worlds in the example, but the principle does not concern haecceities, and soleaves open the question of whetherthe worlds contain the same or different disks.

27 I focus on global supervenience principles here, although local principles have beendefended. For example, in the literature on personal identity concerning BernardWilliam's duplication argument (Williams 1956-57), there is a principle discussedaccording to which identity between x and y cannot depend on the presence of someother object, z. This is in effect a local supervenience principle for the genidentityrelation. For theories that violate this principle see Nozick 1981, chapter 1, and Parfit

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persistencesupervenesglobally on temporally ocal qualitative acts. (A tem-porally local fact concerns only a single instant in time; thus, the fact that acertain event was the first event of a certain kind in history would not betemporally local, because of what it requiresof previoustimes.) The preciseformulationof this principle dependson whetherwe accept a metaphysics oftemporalparts.If we do, we may formulatesupervenienceclaims for identityover time as concerning the "genidentity"or "unity"relation, which holdsbetween the successive stages of a continuing object. One such principlemight look as follows:

(P) The genidentity relationsupervenes weakly globally on the set, B,of temporally local qualitative properties and spatio-temporalrelations

(P) may be refined in various ways. As stated, it concerns the genidentityrelation; but it is natural o distinguishthe relations thatunify the temporalpartsof different kinds of entity.28One might want to claim that all of thesegenidentity relations-genidentity relations for persons, statues, electrons,etc.-supervene on B. Alternatively,one mightwant to claim thatonly somedo. Yet anotherpossibility is to augmentB with certaingenidentityrelationsand then claim that the rest supervene on this set. One might claim, forexample, that the genidentityrelations for macroscopic objectssupervene onthe set containing the members of B plus the genidentity relation for micro-scopic particles. Anotherrefinementmight be to assert (P) as a contingentthesis, by restricting he class of possible worlds that the supervenienceclaimconcerns. 29

Things are a bit more complicatedif we reject temporalparts.The com-plication is due to the fact that for any set, A, world-A-indiscernibleworldsmust have the same number of objects (since their domainsmust map one-one onto each other). Considera pairof possible worlds thatare alike in all

1984, part three; and see Noonan 1989, Chapter 7 for necessary revisions to and adetailed discussionof Williams's principle.

28 It is possible to resist admitting multiple genidentity relations by defining a singlegenidentityrelation as the relation that holds between object stages iff there is a continu-ing object of some kind or otherof which each is a stage. But thereis a limitationin thisapproach.The above definition defines genidentityin terms of the notion of a continuingobject; but temporal partstheorists like to reverse the order of definition and define con-tinuing objects as maximal aggregates of pairwise genidentical stages. But this definitionwould fail, given the suggested definition of 'genidentity', if one spacetime worm canever be a proper part of another. Just this situation, in fact, is commonly suggested tooccur in the case of coinciding statues and lumps: the statue spacetime worm is a properpart of the lump spacetime worm. It is better to multiply genidentity relations; one canthen define statues as maximal aggregates of objects that pairwise stand in the statuegenidentityrelation;and analogouslyfor lumps.

29 This is Lewis's way of defending Humean Supervenience against the challenge of therotatingdisk. See the introduction o Lewis 1986b.




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temporally local mattersof qualitativefact, each of which contains, seem-ingly, a single object:a solitary electron which persists throughoutall time.But supposethatin fact this description s only accurate n one world;in theother world the electron thatis presentat firstgoes out of existence at sometime and is replacedby a duplicate electron. (The replacementmust be per-fectly "seamless" since the worlds are stipulated to match perfectly withrespect to temporallylocal qualitativematters of fact.) If such worlds exist,they ought to count as an exception to the claim thatpersistencesupervenesglobally (whetherstronglyor weakly) on temporally ocal qualitativemattersof fact. However, the second worldhas one more object than the firstworld,and so thereareno isomorphismsof any kindbetween theirdomains;buttheclaim that A globally supervenes(in either sense) on B is only falsified incases involving B-isomorphicworlds.Note that the problemdoes not arise ifthe metaphysics of temporalparts is correct.Assuming time is continuous,there would be the same infinite number of objects in each world, for eachworld would have an instantaneouselectron temporalpartat each moment,and each would containthe same numberof mereological sums of temporalparts. The difference between the worlds would be reflectedin the patternofinstantiationof the genidentityrelation,not in the numberof objects.In the absence of temporalparts thereare various ways to proceed, but Iprefer the following. Define an "ersatztemporalpart"as a pair of an objectand a time at which the object exists. Say that two ersatz temporal parts and aregenidenticaliff x=x'. If we take the domain of a possi-ble world to be the set of its ersatz temporalpartsrather than its genuineobjects, then we can retain (P) as the form of our supervenienceprinciple.(We will need to make certainnaturaladjustments.Take property nstantia-tion, for example: we'll need to say that instantiatespropertyP in anextended sense iff x instantiatespropertyP at time t in the ordinarysense.) Itmight be thoughtthat our supervenienceprinciplenow essentially concernsidentity, since the definition of genidentitynow appealsto identity.But thatdefinition could be rephrasedas follows: ersatzpairsaregenidentical ff thereis some object thatis the firstmember of each. The supervenience principleratherconcerns thetemporalrelationexists-at, for whatdetermines hepatternof instantiationof the genidentityrelation over ersatzpairs is the totality offacts about when various continuantobjectsexist.

Superveniencetheses for identityover time, then,whether ocal or global,concern the genidentityrelationfor stages, whetherersatz or genuine,andnotthe identityrelation. This fact allows us to answeran importantchallenge tothe searchfor "grounds"or identityover time. NathanSalmon has arguedforthe following theses:

T6: For every x and every y, if x = y, then the fact that x = y does notrequireany "criteria f identity"of thingsof x' s sort or kind.

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T7: For every x and every y, if x = y, then the fact that x = y is notgrounded in, or reducible to, qualitative nonidentityfacts about xand y other than x's existence, such as facts concerningmaterialorigins, bodily continuity,or memory.

T8: For every x and every y, if x = y, then the fact that x =y obtainsby virtue of x's existence, and not at all by virtue of anyother qual-itative nonidentity facts about x and y, such as facts concerningmaterialorigins, bodily continuity,or memory.

If true, these theses would be extremely significant. As Salmon puts it,"Much of the literature on cross-time identity (and especially on personalidentity), for example, presupposes he opposite of one of more of theses T6,T7, and T8."3"1 oreover, the search for supervenienceprinciples for identityover time is motivated n large partby the belief that facts aboutidentityovertime must be groundedin more basic facts. Since supervenience is surelynecessaryfor grounding,whateverexactly groundingamounts to, there mustbe true supervenience principles if identity over time is to be grounded.Salmon's argumentis parallel to GarethEvans's famous argument againstvague identity, and runs as follows:3"Consider thesis T7: Whateverx may be, the trivial fact thatx = x is not atall groundedn, orreducible to, any facts about x like those concerningx's materialorigins, x's bodily continuitythrough time, or x's memoryof past experiences. If the fact thatx = x is grounded n any otherfact aboutx, it is only grounded n the mere fact that x exists. Thusx has the complex propertyof being such that the fact that x is identical with it is not grounded in any qualitative non-identity facts about x other than x's existence. Hence, by Leibniz's Law, for every y, if x andy areone and the very same, then y also has this complex property.Thus, if x = y, then the factthat x = y is not grounded in any qualitative nonidentity facts about x (which are also factsabouty) otherthan x's existence.

It may be that a vague variant of this argument has also had someinfluence. The identity relation is a logical relation, and is therefore in afundamentallydifferentontological categoryfrom qualitativepropertiesandrelations; for this reason identity might be thought to need no basis inmatters of qualitativefact. But in fact, neither this nor Salmon's argumentundermines herequirementhatidentityover time be grounded n qualitativefacts, once thatrequirement s properlyunderstood.Neither does Salmon'sargumentunderminethe search for criteriaof identity over time. Salmon'sprinciples T6-T8 are perhaps true,but they are irrelevant,for they concernidentity.As I have argued, "identityover time" has nothingto do with iden-tity; the issue is ratherpersistence.One can hold thatpersistencefor personsis groundedin facts aboutmemory and other psychological traits;but this30 Salmon 1986, p. 112.31 Salmon 1986, pp. 112-13.




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does not require assuming that the identityrelationis grounded n memory.What is grounded n memory s rather herelationof genidentitybetween per-son stages-the "unityrelationfor persons"-whether those stages are takenas genuineor ersatz.

Though Salmon does not pursue this, an argumentsimilar to his mightbe advanced against those who claim that "transworld dentity" must begrounded.Thereply to this argumentwould be analogous.Whatis actually atissue in discussion of transworldidentity is not the natureof the identityrelation, butrather he natureof de re modalproperties.Considerone of thestandardparadoxesof identityacrossworlds,"Chisholm'sParadox".32 iventhatAdam has a certain set of qualitative properties,Q1,and thatNoah hasanother set of qualitative properties,Q2, there is an argument rom initiallyplausible premises about essential andaccidentalpropertiesto a conclusionthat is difficult to swallow: that there is a world qualitativelyjust like theactual world, butin which Adam andNoah have swappedqualitativeroles-the object with the properties n Qi is Noah and the object with the proper-ties in Q2 is Adam. The puzzle may be resolved by appealing to varioustheories of de re modality,for example counterpart heory,or an intransitiveaccessibility relation,or anextremelyrestrictiveaccount of essence; but noneof these solutions involves any claims about the identityrelation.33 o whenwe claim that transworld dentitymustbe grounded,whatwe shouldreally beclaiming is that facts aboutde re modalpropertiesmust be grounded n cer-tain other facts, and this claim is untouchedby argumentsconcerning theidentity relation. Despite Salmon's argument,then, the thoughtthatpersis-tence and de re modalitymustbe grounded n some way in mattersof qualita-tive fact is a perfectly reasonable one. In the final section I'll discuss theapplicationof this thoughtto the much discussed case of two materialobjectssharing spatial location.

IIIDavid Wiggins and many others have claimed that a statueand the lump ofmatterfrom which it is made are coincident numericallydistinct entities, dis-tinguished by their persistence conditions: the lump but not the statue cansurvive being flattened.34n many cases the statueand the lump are distin-guished by theirhistoricalproperties,but in certaincases, the statueand thelump have the same history and are distinguished merely by their modalproperties.35

32 See Chisholm 1967.33 Salmon 1986 contains an extensive discussion of this and otherparadoxes;see his foot-

note I for further references.34 See Wiggins 1980, pp. 30-31.35 See Gibbard 1975.

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An interesting pattern of argument against coincidence claims that itwould requireobjectionably"ungrounded" ifferencesbetweenthe coincidententities. This argument,different versions of which are offered by MichaelBurke, Mark Heller, David Oderberg,Peter Simons, Ernest Sosa and DeanZimmerman,runs as follows.36Coincident entities would shareall momen-tary propertiesat any time they coincided,would have exactly the same sub-atomic structure,and would have the same subatomic particles as parts.Given this similarity, what could groundthe differences in persistence andmodal propertiesbetween them?Surely facts aboutpersistence andmodalityare not utterly "brute",butratherhave some basis in otherfacts; and surelythese other factswill be sharedby coincident entities.

This argumenthas, I believe, a lot of intuitive appeal. I suspect that thisargumentmakes precise a common worry thatcoincident entities would bedistinct only in a mysterious or ungroundedway. But what I want to showhereis that even if themajorpremise-the rejectionof brutefacts concerningpersistence and modality-is granted,it is still not clear that the argumentsucceeds. The problem with the argument results from the distinctionbetween the two types of global supervenience introducedn section I.

Supervenience s indeed at issue, despite the fact thatthe argument endsto be formulated n the literaturen termsof the "grounds"or "basis"for thedifferences between coincident entities. As near as I can tell, facts about A-properties are said to be grounded in facts about B-properties when i) Asuperveneson B (according o one or anotherdefinitionof supervenience),andii) facts about B-properties are in some sense (whether ontologically orexplanatorily) "priorto" facts about A-properties.37The notion of priorityinvolved in grounding s somewhatelusive, but we needn'tworryabout thatsince the groundingargumentagainstcoincidence appeals only to the super-venience component of grounding. Supervenienceprinciples say that same-ness in one respectentails sameness in some other respect; thus it is super-venience principles that seem to be violated by the statue and the lump,which differ in theirhistoricalproperties,ortheir modalproperties depending

36 See Burke 1992, Heller 1990 pp. 30-32, Oderberg1996, p. 158, Simons 1987 pp. 225-26,Sosa 1987 section G, and Zimmerman1995 pp. 87-88. Simons andOderbergonly defendthe argument against coincidence in the case of objects of the same "substantialkind";they accept coincidence for objects of different substantialkinds. This is a strange atti-tude, since the grounding argumentwould work equally well in both cases. Perhapstheyare thinking that the different substantialkinds of the coinciding objects could groundtheir differences, but what grounds the differencein their substantialkinds? After writingthis paper I discovered that Zimmermanbriefly discusses a reply to the coincidenceargument hat is similar to the reply I develop in the text.37 Clause ii) is not redundant: s has often been noted, the notion of supervenience does notby itself entail any relation of priority.For example, according to standarddefinitions,supervenience is reflexive and not asymmetric, whereas relations of priority areirreflexive and asymmetric.See Kim 1990.




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claim. For the weak principle to hold, it will need to be true that any possi-ble world that is world-BASE-indiscernible rom w must contain two objects,one with the modalpropertiesof the statue, the other with the modal proper-ties of the lump (becausea world must containsuch objects for there to be amodal isomorphismbetween it and w). But this seems like a perfectly accept-able thingfor thedefenderof coincidenceto say.

Once we are sensitive to the distinction between strong and weak globalsupervenience,the argumentretainsappeal only to the extent thatwe oughtto hold the strong global supervenienceclaim in addition to the weak. Ofcourse, if there is strong intuitive or theoreticalreason to hold both versions,then the argumentremainspowerful.But if intuition andtheory require onlythat some supervenience principle or other holds, then the argument isundermined,ince the defenderof coincidencecanconsistentlyacceptthe weakversion of the supervenienceprinciple.Althoughit isn't vital to my purposeshere to decide this issue, I do think that the argument s indeed weakenedbythese considerations.The argumentagainstcoincidenceinitially seemed pow-erful because of the appearance that coincidence would require utterlyungroundedor brute modal properties, "utterlybrute" in the sense of "notsupervenient in any way". That would be really bad. But now it has beenshown that the defender of coincidence is not stuck with this consequence.(The defender of coincidence could, of course, simply reject the need for anysupervenience principles whatsoever. I find this implausible, but have noquarrelwith it here; my point is that this heavy-handedapproach sn't neces-saryto answer the argument.)

Materialistic or physicalistic philosophersare committedto thinkingthatmentalpropertiesmust supervene n some way on physical properties.Thereis then an apparentchallenge to this view, based on the examples of TylerBurge and others in which molecule-for-moleculeduplicatesdiffer in theirbeliefs, about arthritis or instance.4')Materialists eel-correctly, it seems tome-that they can adequatelyrespondto this challenge by pointing out thatthe examples threaten only local supervenience;the examples leave globalsupervenience(in either of its varieties)untouched.Whatmaterialistic heoryand intuition requireis that some variety or other of supervenience holds;thus the challenge may be answeredby pointingout the existence of a sortofsupervenience unrefuted by the example. Perhaps the case of coincidentobjects is parallel.

My reply to the coincidence argument s successful only if weak globalsupervenience counts in some intuitive sense as a kind of dependencyrelation. But one might worry that it does not.4' Consider the propertyof40 See Burge 1979 and Putnam 1979.41 I thank Eva Bodanszky and an anonymous referee for this objection; the example is

Bodanszky's.

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being a locomotive,on one hand,and the propertyof being a caboose on theother hand, understood in such a way that locomotives and cabooses arepresent only in trains,and that every train has exactly one locomotive andexactly one caboose. Any two possible worlds that are world {being acabooseI-indiscerniblewill be world indiscerniblewithrespectto thepropertybeing a locomotiveas well, since caboose-indiscernibleworlds must have thesame numberof trains,and hence the same numberof locomotives.42Hence,being a locomotive weakly globally supervenes on being a caboose (thereverse holds as well). But, it may be argued, being a locomotive doesn'tdependin anyintuitiveway on beinga caboose.

In evaluating any argumentabout the intuitive notion of dependence,it isimportant to remember that 'dependence' is just as ambiguous as is'supervenience'.Justas there aremanyvarietiesof supervenience(e.g., localandglobal), there area varietyof types of dependence.So one must take carenot to conclude that no form of dependencyholds in a particularcase justfrom the fact that one form of dependence conspicuously fails to hold. Inthecase of the trains, whether a given thing is a caboose obviously doesn'tdetermine whether it is a locomotive. Consequently, the property being alocomotivequite clearlydoes notdependin a local way on the propertybeinga caboose. (Likewise, being a locomotive fails to supervenestrongly globallyon being a caboose, and so a certaintype of global dependencefails.43)But itisn't clear that there's no sense in which being a locomotive depends onbeing a caboose. Remember the very fact of weak global supervenience,which in this case amountsto the fact thatany two worlds that are alike withrespect to the numberof cabooses are also alike withrespectto the numberoflocomotives. This itself seems like a sort of dependency! This may bebolstered by recalling(WI) fromsection I, which entails in this case thatanypropositionthat "involves"only the propertyof being a locomotive will benecessarily equivalentto some propositionthat involves only the propertyofbeing a caboose. Propositionsaboutlocomotives, therefore,have their truthvalues settled by propositionsabout cabooses. I conclude that weak globalsuperveniencedoes providea legitimatesort of dependencyafterall.

42 Notice thatthe supervenienceprinciplein questionis not the principlethat the set {beinga caboose, being a locomotive) supervenes weakly globally on the set {being acaboose). This principlefails, assumingthat there can be single car trains,whose singlecars are both locomotives and cabooses. A world with two single-car trains would becaboose-indiscernible rom a world with two two-cartrains,but these worlds wouldn't be{being a caboose, being a locomotive -indiscernible.See note 11.43 Let L be any locomotive that's not a caboose; let f be the function that is just like theidentity function from the domain of the actualworld onto itself, except that it maps L tothe Eiffel tower, andvice versa. This function is a caboose-isomorphism rom the domainof the actual world onto itself (since neitherL northe Eiffel tower is a caboose), and so Land the Eiffel tower are globally caboose-indiscernible; but they are not globallylocomotive-indiscernible ince only L is a locomotive.

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My treatmentof the temporalversion of the anti-coincidenceargument ssimilar to my treatmentof the modal version. Considera statue,S, made upof a lump, L. According to defenders of coincidence, if S is flattened t goesout of existence, butL survives. Thus, before flattening,S and L are coinci-dent entities, distinguishedby their total histories. Burke arguesagainst thisaccountas follows:44In the presentcontext, to say that objectsx and y differ in theirhistories is to say that for somepast or future time, x andy differ with respect to the properties (of certain types) that theyexemplify at that time. This, in turn,is to say that for some past or futuretime and for someproperty of one of those types), it is true of x or y, but not of both, thatit is numerically denti-cal across time with an object exemplifying that propertyat that time. But now what couldaccount for a difference in the cross-time identities of [S] and [L]? The two are composed ofjust the same atoms. And since they are coextensive, any object spatiotemporallycontinuouswith one is spatiotemporally ontinuouswith the other ...

Burke anticipates a challenge to his argument based on theKripke/Armstrongotatingdisk (see note 26). Consider two possible worlds,alike in thateach contains a uniformhomogeneous disk, but unalike in thatthe disk is rotating n only one of the worlds.Since the disks are uniformandhomogeneous, the worlds share all temporallylocal qualitativefacts. But ifthe facts aboutthe persistenceof thepartsof the disks were likewise the samebetweenthe two worlds,then the disks couldnot differin whethertheyrotate.The example thereforeappears o establishthatpersistencefails to superveneon the totality of temporally local qualitative facts, and thus might bethought to establish that cross-time identities (i.e., facts about persistence)need no grounds. But as Burkepoints out, the exampledoesn't establish thatall cross-time identitiesareungrounded, ince it is consistentwith the exam-ple that the identity over time of the disk and certain of its parts may begrounded n the identitiesover time of its smallerparts.Perhapsthe smallestpartsof the disk have utterlyungroundeddentityover time. Let us introducea set, GROUND,which includesi) temporally ocal qualitativepropertiesandrelations, ii) spatiotemporalrelations,and iii) genidentityrelations betweentemporalpartsof very smallobjects.Burkecan consistently acceptthe exam-ple of the rotating disk, and base his argumentagainst coincidence on theclaim that genidentity relations between temporal parts of macroscopicobjects (like statuesandlumps) superveneglobally on GROUND.

Burkeexplicitly addresseshis argument o defenders of coincidence whorejecttemporalparts;to avoid begging any questions,therefore, et us followthe strategyof section II andunderstandhe supervenienceprinciple ust for-mulatedas concerningersatztemporalparts-pairs of continuingobjectsandtimes. Thus, the argument s this: the coinciding statue andlump violate theglobal supervenienceof the genidentityrelationbetweenersatztemporalparts4 Burke 1992, p. 15.

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of macroscopic objects on GROUND, a set which includes temporally localqualitativepropertiesand relations of ersatz temporal parts, spatiotemporalrelations betweenersatztemporalparts,and the genidentityrelation betweenersatz temporalpartsof very smallobjects.

The reply is the same as before: only the strong version of the super-venience principle s inconsistentwith the example. Considera one-one map,f, from the domain of the world in question onto itself, which maps everyersatz temporal part to itself except that it maps to and viceversa, where t is some time before the flattening.In virtue of the intrinsic,compositional and relational symmetry between S and L at t, this map is aGROUND-isomorphism.Hence, where t' is some time after the flattening,the following pairs of ersatz temporal parts are globally GROUND-indis-cernible: and . But since the members of thefirst pair are genidentical whereas the membersof the second pair are not,these pairs are not globally genidentity-indiscernible. The strong super-venience of genidentity on GROUND therefore fails in virtue of this singleworld,but no single world can on its own falsify weak global supervenience.To upholdthe weak global supervenienceof genidentityon GROUND, thedefender of coincidence must simply hold that any possible world that isGROUND-isomorphicto the world in question must contain two objects, astatue anda lump,which coincide initially, butonly one of which, the lump,survivesbeingflattened.

I would like to conclude by providinga clear pictureof how facts aboutGROUNDandBASE could "functionallydetermine" acts of persistenceandde re modalityvia weakglobalsupervenienceprinciples,despitethe existenceof coincident entities. Let us first consider the statue andlump thatcoincideat all times; the puzzle is how facts about the properties and relations inBASE could "maketrue"differentfacts involving the statue and the lump,given their similarity.The answer lies in a fact mentionedin section I, thatweak global supervenienceclaims entail propositionalratherthanpropertycorrelations. Let us assume the weak global supervenience of de re modalpropertieson BASE. In virtueof (W2), every propositionthat is truein theworld in question, and which "involves" only de re modal properties, isentailed by thatworld's maximalBASE-proposition,"the basic proposition"let us call it. Thus, the basic proposition-the most specific true (at thatworld) proposition that involves only propertiesand relations in BASE-entails4

45 Actually sentence (1) is about both modality and basic facts. But we could just take thesupervenience principle as being: BASEu (the set of modal properties) supervenes onBASE. On the strongconstrualof global supervenience his formulation s equivalent,butnot on the weak construal-see principle (P2) from note 11. Similar remarksapply to (2)below.

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(1) There are two objects that sharelocation at all times, one of whichhas the modal properties of a statue, the other of which has themodal propertiesof a lump

When God createdthe world, all he needed to do was decree that the basicproposition was true.46 t then followed from thatdecree that there are twocoinciding objects, one of which has one set of modalproperties, he other ofwhich has another.And notice that the symmetrybetween the two objects isirrelevant:God's decree resultedin the truthof an existential proposition-thatexpressed by (1). The symmetrybetween the statue andthe lump doesindeed rule outone sort of determination f modal properties: ince the statueand the lump have the same maximal BASE-property but different modalproperties, hemodal propertiesof a given object aren'talwaysentailed by itsmost specific BASE property. That is, the instance of (S2) in this case isfalse. But (S2) is only entailedby strong global supervenience,and, as I'veargued,so long as we can acceptat least one form of supervenience, t's legit-imate to reject other, stronger upervenienceclaims.

The story is similar in the temporalcase. An extremely specific proposi-tion specifying the totality of facts involving properties and relations inGROUND entails the truthof an existential sentence:

(2) Thereis an object, x, thatis statue-shapedbefore the flatteningandexists afterthe flattening;andthere is anotherobject, y, that has thesame temporally local qualitative properties as x before theflattening,but,unlikex, does not exist after the flattening

Alas, thereis no compelling argumentbasedon supervenienceprinciplesto rule out coincidence between numericallydistinct statues and lumps ofclay. Is there some clear notion of "grounding"ndependentof the conceptofsupervenience, on which coincident entities would have objectionablyungroundeddifferences?I doubt t: supervenience eems theonly clearpartofotherwisedark alkof grounding. do, however,thinkthat coincidence shouldbe rejected. The rejection of coincidence lies elsewhere: in the existence ofbetteralternatives.47

46 Stalnaker1996, p. 222, cites Saul Kripkeas the source of the helpful metaphorof think-ing of supervenience n terms of God's creation of the world.47 The better alternatives I have in mind involve replying to the temporal version of theargument by identifying materialobjects with short-lived temporal parts (see my Sider1996), and rejecting the modal version by accepting counterparttheory (see Lewis1971). Thanks to John G. Bennett, Eva Bodanszky,David Braun,Phillip Bricker,MichaelBurke, Earl Conee, Mark Heller, R. Cranston Paull, Brock Sides, and an anonymousreferee for helpful comments.




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Global Supervenience