# Statues and Lumps: A Strange Coincidence?

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1 Statues and Lumps: A Strange Coincidence? Mark Moyer Draft Date: 9/1/00 Abstract This paper attacks various arguments for the impossibility of coinciding objects. Distinguishing a temporally relative from an absolute sense of the same, we see that the intuition, this is only one thing, and the dictum, two things cannot occupy the same place at the same time, are individuating things at a time rather than absolutely and are therefore compatible with coincidence. Burke and Heller claim that if objects coincide, there would be no explanation of how objects that are qualitatively the same can belong to different sorts. But we can explain an object s sort by appealing to its properties at other times and other worlds. Burke s temporal supervenience argument rides on a confused notion of identity across time and the statue at t. Heller s modal supervenience argument infers that an object s non-modal properties must determine its modal properties since the modal is grounded in the modal. Popular accounts of modality show that this inference is unwarranted.

2 Last week Matthew combined rare soils to create a large lump of clay. He named the lump of clay Clayton. Arthur found the clay on the workbench last night and shaped it into a beautiful statue of a winged woman. He named the statue Angel and set it on the mantle, where it now sits. Because clay statues sell so poorly, three days from now Arthur will take a bit of clay from the statue, replace it by a bit of lead of the same size, and continue the process for a few hours until the clay making up Angel is entirely replaced by lead, finally throwing the clay into the garbage bin. In the study of material constitution, there is a great divide between those who think that multiple objects can occupy the same place at the same time, call them pluralists, and those who think such spatial coincidence is impossible, call them monists. 1 The argument for pluralism is simple. The lump of clay sat on the workbench last night but the statue did not. The statue could not survive flattening, but the lump could. Because the statue and the lump of clay have different temporal and modal properties, by Leibniz s Law we conclude that the statue and the lump of clay are not identical. My aim is to show that the most influential arguments for monism fail, but I begin with some semantics. The Semantics of The Same My non-philosopher informants tell me that there is one thing on the mantle, that the lump of clay is the statue, that they are the same thing. Of course, they admit that after the clay is replaced by lead, and the lump of clay sits in the garbage dumpster while the statue still sits on the mantle, then the statue and the lump of clay will be two different objects. Crucially, though, they do not revise their judgment of present sameness in light of their judgment of future difference. Thus, when they say they are the same they are not neglecting the fact that the two differ temporally. Similar speaker intuitions occur with cases of fission. Imagine that Al splits like an amoeba to become Cal and Hal. The untutored claim is that there was only one person before the 1 The terminology is Kit Fine s (in conversation).

3 fission, that there were two after the fission, and yet that Al did not die but somehow lived on through Cal and Hal. If we accept these intuitions at face value, the moral is clear. The everyday claim that The statue and the lump of clay are the same thing" is temporally relative. This is a tensed sentence saying that the statue and the lump of clay are now the same thing. The expression 'the same' is not invoking absolute identity but a relation I will call 'sameness'. That is, whether things are 'the same' depends merely upon their temporally intrinsic properties. The same point carries over to sentences using expressions interdefinable with 'the same'. For x and y to be the same thing, for x to be y, for there to be only one thing, for there to be a thing rather than some things such expressions all operate in concert. The whole family of related expressions is temporally relative. To philosophers this interpretation of the same may seem strange. But let us keep in mind that almost all predicates of English are temporally relative. Moreover, the simplest predicates are not only temporally relative but hold in virtue of the way the subject is at the time in question rather than in virtue of any temporally extrinsic properties. Being big, bent, wrinkled, green, smelly, hot, etc. are all properties intrinsic to a time. And, intuitively it is hard to deny that counting the number of objects on the mantle requires simply looking, not learning the history of these objects or considering their possible properties. Thus, having a sameness relation that holds merely in virtue of the properties things have intrinsic to the relevant time is very natural. In fact, if pluralists are correct, then absolute identity would be quite impractical for everyday use. Our concerns are not with the number of temporally and modally distinguished objects there are on the mantle, a quite confusing multitude, but with the number of objects that require dusting, packing, carrying, etc. i.e. with the number as distinguished by their current physical properties. So far I have suggested that the relation picked out by everyday uses of the same holds relative to a single time. But this precludes saying that b at t 1 is the same as c at t 2. That is, there doesn t seem to be any means of having a cross-temporal relation whereby b and c are the same. Yet, some may insist, everyday English clearly allows such talk: I am the same person who 2

4 waved to you yesterday. Likewise, Angel, the statue standing here now, and Clayton, the lump of clay created last week, are the very same thing. How can we accommodate such sentences with a relation that only relates things at a single time? The answer is that while the relation invoked by the same does not span times, the things related typically do. The sentence I am the same person who waved to you yesterday claims that sameness obtains now between the referent of I and the referent of the person who waved to you yesterday, though these things now related by sameness have features obtaining at other times, e.g. the latter s waving to you yesterday. Of course, I and the person who waved to you yesterday are absolutely identical, so they are also related by sameness at all times at which they exist, but, say I, the sentence is merely asserting sameness at a time, something weaker than absolute identity. Similarly, Angel and Clayton are now the same, though it is also true that Clayton is that which was created last week. Clayton has persisted through time: last week it was created, but now it is the same as Angel. Thus, a statement claiming that two things are the same can be understood as predicating sameness now even if it identifies the relata in terms of properties they have at past or future times. Philosophers, though, seem to have something different in mind by the same and identical. Philosophers take the same and identical to be synonymous, and typically intend a relation characterized by Leibniz s Law where b and c are identical iff b and c have exactly the same properties, including temporally extrinsic and modal properties. According to this notion of identity, what I will call absolute identity, the lump of clay and the statue are clearly not identical. As I see things, the conflation of sameness and absolute identity is the root of much evil in metaphysics. 2 2 The ambiguity I am highlighting is not new. If Rea is correct, Aristotle relied on some such ambiguity. ( Sameness without Identity. ) Wiggins, Johnston, and Thomson have distinguished the is of identity from the is of composition. It is true, they would urge, that the statue is the clay, but that is because this means simply that the statue is composed of the clay. (Wiggins, Sameness and Substance; Johnston, Constitution is not Identity ; Thomson, The Statue and the Clay. ) Robinson and Lewis distinguish two ways in which we count things. According to one way, the statue and the lump of clay are two things, for they differ modally, if not temporally. According to the other, the statue and the lump of clay are one thing, for to count in this way is to 3

5 Reason 1: The Intuition That There s One Object In our examination of the semantics of the same, we have already considered one reason cited in favor of monism, viz. our pre-theoretic intuition that only one object sits upon the mantle. 3 As Lewis says, It seems for all the world that there is only one. 4 But this is a claim that carries no cross-temporal or cross-modal force. Using a relation of absolute identity we can make finer distinctions, so what according to everyday tensed claims of English may be one object are multiple objects according to the philosopher s tenseless language. This is merely to say that the statue and the lump of clay do not differ in any ways intrinsic to this moment and this world, though we can distinguish them when considering their temporal and modal properties. The putative conflict with intuition was nothing more than a confusion of the two notions of being the count by identity-at-t, i.e. to count in a temporally relative way. (Lewis, On the Plurality of Worlds, p. 218; Lewis, Survival and Identity, p. 63; Robinson, Can Amoebae Divide Without Multiplying? ) 3 Myro motivates his monist position as follows: Suppose that on Monday morning I take a piece of wax and fashion it into a vase, which I then put on my mantelpiece to stand there in lonely splendour.... It would have been natural for me to say on Monday: this piece of wax is a vase... And also: this vase is a piece of wax... For this and other reasons, it seems not unnatural to conclude that the vase is identical with the (cunningly shaped) piece of wax. ( Identity and Time, pp ) Myro tries to escape the consequences of Leibniz s Law, arguing that identity is temporally relative. Rea motivates his monist position in a similar way: A bronze statue is a lump of bronze... Which lump of bronze is the statue? Presumably, it is the lump that makes up the statue. ( Constitution and Kind Membership, p. 169) Rea tries to escape the argument for their distinctness by following Burke in appealing to a theory of dominant kinds, arguing that the lump of clay that constitutes the statue is identical with the statue whereas the lump of clay from which the statue was made is not. ( Constitution and Kind Membership, p. 179) Van Inwagen considers an intelligent snake, tied into the shape of a hammock, which asks itself: Is there an object a hammock that is numerically distinct from me but currently spatially coincident with me? According to van Inwagen, A really intelligent intelligent snake in the curious circumstances we have imagined will conclude after only a very brief moment of reflection, No, no... there s nothing here but me. (Material Beings, p. 127) The conclusion he eventually wants us to draw, is that statues and lumps of clay do not exist, only statue-wise arrangements of particles. At least in some cases, pluralists also feel drawn by the intuition. Lewis follows Robinson, arguing that a metaphysical account of the number of objects in a place will conflict with our natural way of counting. Thus he concludes, It seems for all the world that there is only one. We will have to say something counter-intuitive. (On the Plurality of Worlds, p. 218; see also Robinson s Re-Identifying Matter, p. 320) That is, according to Lewis, one of the costs of a pluralist view is that the metaphysical account denies common sense. Similarly, Lewis says, Surely I am nothing over and above my particles: I am them, they are me. The are of composition is just the plural of the is of identity. ( Rearrangement of Particles, p. 71) This is some of the evidence that at least one motivation for taking a monist position has been the pre-theoretical intuition that the statue and the clay are the same thing. (see also Thomson, The Statue and the Clay, p. 149) 4 On the Plurality of Worlds, p

6 same thing. The pluralist is not denying that the statue and the lump of clay are related by sameness, only that they are absolutely identical. Reason 2: Two Things Cannot Occupy the Same Place at the Same Time According to Wiggins, It is a truism frequently called in evidence and confidently relied upon in philosophy that two things cannot be in the same place at the same time. 5 This, then, is a second reason cited in favor of monism. For it seems that we will have to flout the common sense principle if we are to say that the statue and the clay are two things. 6 However, if in everyday contexts what we mean by the same, one, and the like are relations based upon sameness rather than absolute identity, then the truism Wiggins cites is merely claiming that two things, i.e. something x and something y differing in their temporally intrinsic properties, cannot occupy the same place at the same time. Thus understood, the truism does not conflict with the possibility of there being absolutely two things, i.e. something x and something y differing merely in their temporally extrinsic or modal properties, occupying the same place at the same time. The lump of clay sits upon the mantle. The statue also sits there. By Leibniz s Law they cannot be absolutely identical. Yet common sense has no trouble saying that they sit in the same place at the same time. Pluralists have tried to re-interpret the common sense dictum. For example, Wiggins concludes that we must limit the principle to apply only to two things of the same kind and 5 On Being in the Same Place at the Same Time, p Zimmerman, taking a monist view, describes himself as seeking a way to preserve the principle of one object to a place surely a worthy goal. ( Coincident Objects: Could a Stuff Ontology Help?, p. 19) Van Inwagen speaks of the desperate expedient of admitting that it is conceptually possible for there to be two conterminous material objects. ( The Doctrine of Arbitrary Undetached Parts, p. 129 ) He avoids this desperate expedient by denying that statues and many other ordinary objects exist. According to Burke, Presumably, those who accept coincidence do so only because they see no congenial way to avoid it. ( Preserving the Principle of One Object to a Place, p. 237 in Rea) He avoids it by denying that the lump of clay that sat on the workbench last night is identical to the lump of clay which now sits before us and which is identical to the statue. Sider says there really is a strong pre-theoretical motivation to reject spatial coincidence between distinct material objects. ( All the World s a Stage, p. 446) This motivation leads Sider to claim that all objects are momentary time slices. Doepke, in contrast, takes a pluralist stance and so instead seeks an explanation that will relieve what he calls our discomfort with theories committed to coincidence. ( Spatially Coinciding Objects, p. 10) 5

7 other pluralists insist it is claiming that two things cannot occupy exactly the same place at all times. But surely this is not what people have in mind. They are denying, e.g., that the baseball can pass through the bat, even for a moment. That is, it seems the common sense dictum is a simple denial that material objects can interpenetrate. Thus, with our ambiguity in hand we can reconcile the common sense dictum with pluralism, for the dictum denies the interpenetration of different objects, i.e. objects that differ in their temporally intrinsic properties. The statue and the lump of clay are i.e., are currently the same thing, so they do not constitute a counterexample to the common dictum. A ball passing through the bat, on the other hand, would provide a counter-example since the ball and the bat, or even the parts of the ball and bat that overlap, differ in their temporally intrinsic properties: the ball is made of yarn while the bat is made of wood. Reason 3: Supervenience and the Physical Of the many reasons for thinking the statue and the lump of clay are identical, one seems to have emerged as the challenge for pluralists. Though it has three major variations which I will distinguish, the same general sort of argument against coincidence has been supported by many. 7 Burke presents the general argument by asking, In virtue of what does the object identified under statue satisfy statue? In virtue of what does the object identified under piece of copper satisfy piece of copper? Given the qualitative identity of these objects, what explains their alleged difference in sort? 8 Burke rejects the idea that an object s sort is a basic property it has. As Zimmerman notes, this would mean there could be two worlds in all ways physically identical except that one contains a human body and the other does not. 9 7 See Burke s Copper Statues and Pieces of Copper ; Burke s Cohabitation, Stuff and Intermittent Existence ; Rea s Supervenience and Co-Location ; Zimmerman s Theories of Masses ; van Inwagen s Material Beings, p.290n45; Sosa s Subjects Among Other Things, pp ; Heller s The Ontology of Physical Objects, pp ; and Bennett s On Differing Modally. See also Levey, Coincidence and Principles of Composition. 8 Copper Statues and Pieces of Copper, pp Theories of Masses, p

8 Variation 1: Current Properties Determine Sort Central to Burke s challenge is the claim that Angel and Clayton are qualitatively identical. Indeed, they consist of the very same atoms. 10 Burke means this as a tensed claim, saying that Angel and Clayton are currently qualitatively identical. This, then, is the first major variation of the argument I wish to distinguish: An object s physical properties intrinsic to any time t determine its sort. Objects that coincide at t are identical in their physical properties intrinsic to t.? It is impossible for objects to coincide and have different sorts. But why should one think that the current physical properties of something would determine its sort? 11 In a revealing footnote, Burke explains how the monist can meet the explanatory challenge he is laying down: On theories that allow only one object to a place, differences in sort are readily explained. The difference in sort between a tree and a mouse is attributable to the difference in their qualities. In contrast, the tree and the quantity of cellular matter are indistinguishable, so, runs the objection, what current properties could underlie something s being one rather than the other? The pluralist can protest that the two are currently indistinguishable, but not indistinguishable simpliciter. For the monist, this is not enough: the fact that next week the statue will be on the mantle while the lump of clay will be in the dumpster may determine that the statue and the lump of clay will have different sorts next week, but what determines that they have different sorts right now? Notice that this question, and the whole line of reasoning, presupposes that whatever constitutes the difference between the two things in the future is not thereby adequate to constitute their difference now and is therefore not adequate to explain their different sorts. What this means is that the monist is here wielding a notion of being the same that is relative to a time. He is using tensed sentences and is individuating objects by their temporally intrinsic properties. 10 Copper Statues and Pieces of Copper, p By current properties I mean properties intrinsic to the current moment, i.e. properties that hold only in virtue of how things are now. Similarly, by actual properties I will mean to exclude all modal properties. 7

9 Thus, all of the monist s intuitions are beside the pluralist s point. In other words, recognizing the ambiguity of sameness and absolute identity resolves our problem, for the monist intuition is an intuition that multiple objects individuated by temporally intrinsic properties cannot coincide and yet differ in sort, whereas the pluralist s point is only that multiple objects individuated by modal and temporally extrinsic properties can coincide and yet differ in sort. Variation 2: Current Properties Determine Identity Through Time I ve been addressing one variation of the supervenience argument against coincidence. In fact it is not clear that this is a line of reasoning Burke has in mind, though I think it is at least one of the underlying intuitions. Burke explains that in the extraordinary case in which the objects differing in sort are qualitatively identical, as a statue and a qualitatively identical object produced by a volcano, then the object s history does explain the difference. 12 But, adds Burke, though monists can explain an object s sort by its history, pluralists can not. follows:... now what could account for a difference in the cross-time identities of [Angel and Clayton]? The two are composed of just the same atoms. And since they are coextensive, any object spatiotemporally continuous with one is spatiotemporally continuous with the other. If one but not the other is identical with a certain past or future object, the only apparent explanation for this is that one but not the other is like that object in sort. In short, historical differences between [Angel and Clayton] could be explained only by reference to the very difference they are themselves supposed to explain: the alleged differences in sort. 13 Thus, the second major variation of the monist s supervenience argument runs as Differences in cross-temporal identity relations are determined by differences in objects current physical properties. Objects that currently coincide are identical in their current physical properties.? Objects that currently coincide can not differ at other times. And thus it would be impossible for Angel and Clayton to coincide now but not later. 12 Copper Statues and Pieces of Copper, p. 14n4. 13 Copper Statues and Pieces of Copper, p

10 The argument tries to show that the pluralist cannot account for the history, or crosstemporal identity, of the statue and the lump of clay. Note, though, that the monist will likewise have trouble. According to Burke s account the situation we have been considering consists of a statue/lump that is cross-temporally identical to the statue/lump that will sit on the mantle in one week. 14 But we can consider a situation that is the same in all respects from now through next week though yesterday instead of the clay being intentionally shaped into a winged woman it accidentally acquired the shape of a winged woman when it rolled off the workbench. According to Burke this second situation consists of a current lump of clay that is cross-temporally identical with the lump that will sit in the garbage in one week and is not cross-temporally identical with the lump that will sit on the mantle in one week. How can Burke account for the difference in identity across time of these two objects if not by appealing to their sorts? It seems his account fails his own challenge. The first problem with Burke s argument is that there is no such thing as an account of a thing s identity over time. 15 Identity is a two-place relation. Thus, you cannot account for the identity holding between a statue at t and a statue at t since the relata of the identity relation are not things at times but simply things. And we cannot explain the identity of the statue with itself other than to repeat that it is the same, i.e. identical, statue being considered as both relata. Burke draws on the intuition that an object s sort determines its identity conditions and its identity conditions determine with which objects it is cross-temporally identical. For example, a statue s identity across time is determined by, inter alia, spatio-temporal continuity. But, as I ve said, we re not really talking about identity here. So let me try to say what we are talking about. For those that are willing to talk of temporal parts, we can talk about the conditions under which a temporal slice at t of a statue x and a temporal slice at t of a statue y are temporal slices of the same statue. And here the answer is roughly that already suggested, that temporal slices of 14 See his Preserving the Principle of One Object to a Place. 15 Sider makes this point in Global Supervenience and Identity across Times and Worlds. Cf. Lowe, What is a Criterion of Identity?, esp. pp ; and Jubien, Identity Conditions. 9

11 statues belong to the same statue if they are spatio-temporally continuous. So temporal part talk gives us a way to discuss Burke s worry. For those that are not willing to talk of the temporal slice of an object at t we can instead speak of the properties intrinsic to t that are instantiated by the object. We can then ask under what conditions the set of properties intrinsic to t instantiated by statue x and the set of properties intrinsic to t instantiated by statue y are property instantiations of the same object. Talk of temporal parts is dispensable, but I will use it as a shorthand. The second problem with the argument concerns what Burke means when he talks about the statue at t. One thing he might mean is not really the statue but the statue considered only insofar as it exists at t; that is, he might mean the temporal slice at t of the statue. If he means the temporal slice of the statue, then it is reasonable to worry about the so-called conditions for identity through time. For, as we ve seen, these can be expressed as relations that hold between temporal slices. But now we don t get the asymmetry that Burke was suggesting. The current temporal slice of the statue sitting on the mantle is part of the same object as the future temporal slice of the statue that will sit on the mantle in one week. But the current temporal slice of the lump of clay sitting on the mantle is also part of the same object as the future temporal slice of the statue that will sit on the mantle one week from now, for the current temporal slice of the statue is the current temporal slice of the lump of clay. There is only one current temporal slice to be considered, so we can t ask, as Burke seems to try to ask, why one bears some relation with something in the future that the other doesn t bear. On the other hand, perhaps when Burke talks about the statue at t he simply means the statue. Pluralists say there are two things at t, but these things are not individuated by properties intrinsic to t. Thus, in this case we do find Burke s asymmetry: the statue sitting on the mantle now is identical to the statue sitting on the mantle in one week, and the lump of clay sitting on the mantle now is not. But in this case we are no longer explaining the history of the statue; we are simply saying that a statue x and a statue y are identical but a lump of clay z and a statue y are not. 10

12 Thus, when Burke asks how the statue at t can be identical across time with something to which the lump of clay at t is not identical across time, his question rides on two ambiguities, on whether the statue at t means the statue or the temporal slice of the statue at t, and on whether identity across time means identity or a co-part relation. There are multiple co-part relations. Even Burke must allow this since he thinks there are different sorts with different so-called identity conditions. The conditions for two parts being parts of the same statue are different than the conditions for two parts being parts of the same lump of clay. But this suggests that the current slice can be co-statue-part related to some slices and yet co-lump-part related to different slices. The problem is when we confuse these co-part relations with identity, for there is only one identity relation, which tempts us to conclude that there is only one identity across time relation and, equivocating, therefore only one set of slices to which the current slice of the statue can be related by identity across time. Let me try to answer Burke s question about what explains what. The spatio-temporal distribution of physical properties determines, in virtue of what it is to be a statue, whether, and if so exactly where and when, there is a statue. It is somewhat misleading to use the expression the statue s history for the distribution of physical properties, since the distribution of relevant properties extends outside the spatio-temporal region of the statue e.g. certain conditions must precede the creation of a statue. But, this caveat noted, we can agree with Burke that a statue s history explains its sort. But what, Burke asks, explains its history? Here we have another ambiguity. If we mean by its history just what explained the statue s sort, then Burke is asking what explains the fact that there is this particular spatio-temporal distribution of physical properties. The answer to that is easy, at least for our purposes: the initial conditions of the universe together with the laws of nature explain why there is this distribution of physical properties. But Burke shifts the sense of its history and instead appears to be asking for an explanation of the path the statue traces through time. This, though, is a question we just answered. Given this particular distribution of physical properties through space and time, and 11

13 given what it is to be a statue, i.e. the identity conditions for statues, this temporal slice will be costatue-part related with these other temporal slices, which together trace this particular path through time. I appeal to the general conditions for what it is to be a statue in this explanation, but I don t appeal to whether anything is a statue or is a slice of a statue. Thus, there is no circularity, as Burke suggests. We explain this statue s sort by its history but not its history by its sort. Variation 3: Actual Properties Determine Sort We can see now that both the monist and the pluralist are able to explain an object s sort by its history, so pluralists seeking to defend spatial coincidence have thereby met the challenge. However, most philosophers who believe objects can spatially coincide also believe they can spatio-temporally coincide, i.e. coincide throughout their lifetimes. Consider Gibbard s case of a statue formed by joining two half-statues and later destroyed by being smashed into pieces, where pluralists say that a statue, call it Goliath, and a lump of clay, call it Lumpl, coincide spatiotemporally. 16 No temporal properties of the one is lacked by the other, yet modal properties do distinguish them, for Lumpl would have survived flattening while Goliath would not have. Thus, the third variation of the supervenience argument arises, for how can the pluralist who believes in spatio-temporal coincidence account for Lumpl and Goliath having different sorts? They have the same actual properties, so it seems they should be of the same sort. Once we retreat from the claim that an object s sort is determined by its current properties to the claim that an object s sort is determined by the properties it has throughout its life, the question arises why we should not make a similar retreat with modality. That is, if we re going to explain an object s sort using not only its current properties but also its properties at other times, why should we explain its sort using only its actual properties but not also its properties at other worlds? If objects are temporally and modally individuated, it seems to makes sense that an 16 Contingent Identity, p. 96 in Rea. 12

14 object s sort could be determined by its modal properties as well. So why not appeal to an object s modal properties? This is the question Heller takes up, trying to argue that there are coincident objects but not objects, like Lumpl and Goliath, coincident throughout their lives. The problem, says Heller, is that There must be some non-modal basis for the modal differences between the lump of clay and the statue. 17 Thus the third variation of the supervenience argument: An object s actual physical properties determine its sort. Objects that spatio-temporally coincide are identical in their actual properties.? Objects that spatio-temporally coincide have the same sort. And this conclusion directly rules out cases like Lumpl and Goliath, as well as indirectly undermining the thought that there are any cases of spatio-temporal coincidence. The third variation of the supervenience argument relies upon the claim that the modal is grounded in the non-modal. Does that mean that each object s modal properties are determined by its non-modal properties? As Sider and Zimmerman have suggested, perhaps modal grounding only requires that the worldwide distribution of modal properties be determined by the worldwide distribution of non-modal properties. 18 The former sort of grounding relation is what Heller s argument requires, but the latter, weaker sort of grounding leaves open the possibility of spatiotemporal coincidence. To date, neither pluralists nor monists have offered an elucidation of the modal grounding intuition that would make clear what it in fact requires. All agree that modal grounding is required, but monists have given no reason to think that the stronger sort of grounding is necessary, and pluralists have given little reason to think that the weaker sort of grounding is sufficient The Ontology of Physical Objects, p Sider, Global Supervenience and Identity across Times and Worlds, 1 & 3; Zimmerman, Theories of Masses and Problems of Constitution, p I say little because I think Sider s sketching a clear picture of how facts about GOUND and BASE could functionally determine facts of persistence and de re modality via weak global supervenience principles gives us some reason to think that a weaker supervenience relation is sufficient. (see Global Supervenience and Identity across Times and Worlds, 1 & 3) 13

15 To fully settle the issue, we would have to determine exactly how the modal is grounded in the non-modal. A straightforward consequence would be whether spatio-temporal coincidence is compatible with modal grounding. I do not intend to defend an account of the relation of the modal to the non-modal. However, what I will do is very briefly recall the general lines of two general accounts and show that these only require the weaker sort of grounding. Thus popular, admittedly sketchy ideas of how the modal is grounded in the non-modal show us that coincidence is not ruled out by the requirement for modal grounding. 1. According to one brand of conceptualism, our concept of a statue somehow generates statues together with all of their modal properties. But we have different concepts for statues and lumps; that is, statues and lumps each have their own identity conditions. Apparently, then, the thought is that our concept of a statue generates statues in those spatio-temporal regions having the appropriate non-modal properties. Similarly, lumps are generated in virtue of our concept of a lump. However, since the same spatio-temporal region can satisfy both concepts, it appears that the non-modal determines the modal by way of our concepts in a way that allows spatiotemporal coincidence. 2. Lewis spells out linguistic ersatzism as requiring axioms that specify macrophysical conditions, such as when a statue exists, in terms of microphysical conditions, such as spatiotemporal distributions of microphysical properties. 20 A possible world, i.e. one combination of microphysical properties, contains a statue iff the conditions specified by the statue axiom obtain. These axioms are, more or less, the identity conditions for the objects. But notice that these allow spatio-temporally coinciding statues and lumps of clay having different modal properties. If these atoms are arranged in this way then, says one axiom, you thereby have a lump of clay. But another axiom says that you thereby have a statue. Again it seems that modal grounding requires only a weak grounding relation rather than a strong one, that spatio-temporal coincidence is fully compatible with the modal being grounded in the non-modal. 20 See Lewis, On the Plurality of Worlds, pp

16 This brief look at two accounts of the relationship of the modal to the non-modal supports the view that modal grounding only requires a weak grounding relation, that spatio-temporal coincidence is not in any way ruled out but in fact is to be expected. This leaves it open to the monist to sketch his own account of modality according to which a strong grounding relationship is required, but it is hard to see how such an account might go. As long as he admits into his ontology different sorts with different conditions for what it is to be that sort, which will be hard to avoid if the account is to accord at all with everyday speech, then it will be difficult to find any motivation for saying that a certain collection of atoms can satisfy at most one of those sorts. Conclusion The error of monism begins with the natural belief that only one object sits on the mantle, that the lump of clay is a statue. Once we distinguish the temporally and modally relative relation of sameness from the relation of absolute identity, we see that these beliefs offer no evidence for the absolute identity of the statue and the lump of clay. Burke offers a temporal supervenience argument, but it conflates different notions of identity across time and the statue at t. Heller offers a modal supervenience argument, but it presupposes that modal grounding requires a stronger relation than current accounts of modality suggest. Thus, perhaps coincidence is not so strange after all. 15

17 Cited Works Bennett, Karen. On Differing Modally, unpublished. Burke, Michael B. Cohabitation, Stuff and Intermittent Existence, Mind 89 (1980), pp Burke, Michael B. Copper Statues and Pieces of Copper: A Challenge to the Standard Account, Analysis 52 (1992), pp Burke, Michael B. Preserving the Principle of One Object to a Place: A Novel Account of the Relations Among Objects, Sorts, Sortals, and Persistence Conditions, Philosophy and Phenomenological Research 54 (1994), pp Reprinted in Rea, Material Constitution. Doepke, Frederick. Spatially Coinciding Objects, Ratio 24 (1982), pp Reprinted in Rea, Material Constitution. Gibbard, Allan. Contingent Identity, Journal of Philosophical Logic 4 (1975), pp Heller, Mark. The Ontology of Physical Objects: Four-Dimensional Hunks of Matter, Cambridge: Cambridge University Press, van Inwagen, Peter. The Doctrine of Arbitrary Undetached Parts, Pacific Philosophical Quarterly 62 (1981), pp van Inwagen, Peter. Material Beings. Ithaca: Cornell University Press, Johnston, Mark. Constitution is not Identity, Mind 101 (1992), pp Reprinted in Rea, Material Constitution. Jubien, Michael. The Myth of Identity Conditions, in Philosophical Perspectives 10, Metaphysics (1996), pp Levey, Samuel. Coincidence and Principles of Composition, Analysis 57 (1997), pp Lewis, David. On the Plurality of Worlds. Oxford: Basil Blackwell, Lewis, David. Rearrangement of Particles: Reply to Lowe, Analysis 48.2 (1988), pp Lewis, David. Survival and Identity, in The Identities of Persons, ed. Amelie O. Rorty (University of California Press, 1976). Reprinted in Lewis s Philosophical Papers. Lowe, E. J. What is a Criterion of Identity?, Philosophical Quarterly 39 (1989), pp

18 Myro, George. Identity and Time, in The Philosophical Grounds of Rationality, eds. Richard E. Grandy and Richard Warner. New York: Clarendon Press, Reprinted in Rea s Material Constitution. Rea, Michael C. Constitution and Kind Membership, Philosophical Studies 97 (2000), pp Rea, Michael C., ed. Material Constitution: A Reader. New York: Rowman & Littlefield, Rea, Michael C. Sameness without Identity: An Aristotelian Solution to the Problem of Material Constitution, Ratio XI (1998), pp Rea, Michael C. Supervenience and Co-Location, American Philosophical Quarterly 34 (1997), pp Robinson, Denis. Can Amoebae Divide Without Multiplying?, Australasian Journal of Philosophy 63 (1985), pp Robinson, Denis. Re-Identifying Matter, The Philosophical Review 91 (1982), pp Sider, Theodore. All the World s a Stage, Australasian Journal of Philosophy 74 (1996), pp Sider, Theodore. Global Supervenience and Identity across Times and Worlds, forthcoming in Philosophy and Phenomenological Research. Sider, Theodore. Recent Work on Identity Over Time, Philosophical Books 41 (2000), pp Sosa, Ernest. Subjects, Among Other Things, Philosophical Perspectives, 1, Metaphysics, ed. James E. Tomberlin. Atascadero, CA: Ridgeview, Reprinted in Rea s Material Constitution. Thomson, Judith Jarvis. The Statue and the Clay, Noûs 32 (1998), pp Wiggins, David. On Being in the Same Place at the Same Time, Philosophical Review 77 (1968), pp Wiggins, David. Sameness and Substance. Cambridge, Massachusetts: Harvard University Press, Zimmerman, Dean W. Coincident Objects: Could a Stuff Ontology Help?, Analysis 57.1 (1997), pp Zimmerman, Dean W. Theories of Masses and Problems of Constitution, Philosophical Review 104 (1995), pp

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