Statues and Lumps: A Strange Coincidence?

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 shape, 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. This paper evaluates several arguments philosophers have given for thinking that material objects do not coincide. I will argue that they all fail. To clarify the issue between pluralists and monists, and to set the stage for further arguments, I begin with some simple 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 a statue, that the statue and the lump of clay 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 bin while the statue still sits on the mantle, then the statue and the lump of clay will be two different objects. And they also say the lump of clay was not a statue yesterday. Crucially, though, they show no inclination to revise their judgment of present sameness in light of their judgment of future or past 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 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'. More exactly, I am proposing that x is ‘the same’ as y at t iff x and y are identical in all of their non-modal properties intrinsic to t. 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 their number as determined by our need to know how many things 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 t₁ is the same as c at t₂. 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 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 only 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; moreover, next week it will no longer be ‘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.^[2]

I have been exploring the everyday use of the expression ‘the same.’ One might conclude with Myro and Gallois that identity is temporally relative.^[3] But all that has been suggested so far is that the common notion of x and y being ‘the same thing’ is a temporally relative notion. Whether we want to say that identity itself is temporally relative depends upon what we mean by ‘identity,’ calling for further semantic investigation. In everyday speech, ‘identity’ typically means that the qualitative properties of the relata are the same. To the extent that ‘identical’ is used to express something stronger in everyday language, it seems to parallel the use of ‘the same’ that we have been investigating.

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.^[4] According to this notion of ‘identity’, what I will call ‘absolute identity’, the lump of clay and the statue are clearly not identical.

The distinction I am highlighting is not new. If Rea is correct, Aristotle used a similar distinction.^[5] Wiggins, Johnston, and Thomson have distinguished the ‘is’ of identity from the ‘is’ of composition, a temporally relative relation.^[6] 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. Robinson and Lewis distinguish two ways in which we count things.^[7] 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 count by identity-at-t, i.e. in a temporally relative way. Where I perhaps differ is in 1) seeing the family of related expressions tied together, resting on a single temporally relative equivalence relation; 2) holding that in everyday contexts these expressions are generally temporally relative; and 3) believing that many metaphysical puzzles stem from the conflation of absolute identity and sameness.

With the distinction between sameness and absolute identity in hand, I can clarify the issue of the paper. The question is whether multiple objects, such as the statue and the lump of clay, can coincide. By coincidence I actually mean two different things: for most of the paper I will be concerned only with spatial coincidence, or the occupying of exactly the same place at the same time; at the end of the paper, however, I will turn to spatio-temporal coincidence, or the occupying of exactly the same place at all times. By ‘multiple’ I mean more than one as individuated by absolute identity. Monists claim that the statue and the lump of clay are absolutely identical, while pluralists claim that they are not. This said, I now turn to the various reasons for thinking that the statue and the lump of clay are absolutely identical. I present textual evidence that these reasons are not mere straw man arguments, that they have in fact persuaded monists and even dissuaded pluralists, though for the sake of readability I restrict most of this to footnotes.

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. And quite a few philosophers have been motivated towards monism on this basis.^[8] As Lewis says, “It seems for all the world that there is only one.”^[9] But as our little semantic study suggests, 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 between pluralism and intuition was nothing more than a confusion of the two notions of being ‘the 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.”^[10] This, then, is a second reason cited in favor of monism. For it has seemed to many that we will have to flout the common sense principle if we are to say that the statue and the clay are not identical.^[11]

Heller explains some putative counter-examples to the common sense dictum by noting that these are cases of partial identity.^[12] Though the oak tree and one of its branches occupy the same place at the same time, this is because they are partially identical, i.e. because the part of the tree that coincides with the branch just is that branch. Thus, we can reconcile some putative counter-examples with the principle that two things can’t occupy the same place by taking the principle to mean two wholly distinct things. However, this doesn’t seem to save the pluralist, who is trying to argue that the statue and the lump of clay are (at least partially) distinct, for the statue and the lump of clay are made of the very same atoms. Prima facie, every part that belongs to the statue also belongs to the lump of clay.^[13]

We can make progress, though, by recalling that in everyday contexts what we mean by ‘the same’ and ‘one’ are relations based upon sameness rather than absolute identity. For 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 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. But because the statue and the lump of clay are identical in all of their properties intrinsic to the t, the time under concern, they are ‘the same’ thing at t, and they therefore do not constitute a counter-example to the dictum we’ve been considering.

Pluralists, seeking to explain away the conflict with the common sense dictum, have tried to re-interpret the dictum. For example, Wiggins concludes that we must limit the principle to apply only to “two things of the same kind”. Heller, following a common temporal parts strategy, claims that “A physical object is the material content of a region of spacetime.”^[14] Thus, he claims that the statue and the lump of clay are partially identical, coinciding in their temporal parts. But surely these approaches misinterpret what people have in mind. They are denying, e.g., that the baseball can pass through the bat. That is, it seems the common sense dictum is a simple denial that material objects can interpenetrate, whether or not they are of the same sort and whether or not they interpenetrate for only part of their lives.^[15] The statue and the lump of clay are — i.e., are currently — the same thing, so they do not constitute a counter-example 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: Rampant Creation and Destruction

Van Inwagen raises a third reason for thinking that the statue and the lump of clay are identical. Something is said to be a statue, he argues, in virtue of its shape. Yet it seems there is nothing metaphysically special about the shapes in virtue of which something is a statue, so we can with equal right consider another sort of object — call it a ‘gollyswoggle’ — which is a gollyswoggle in virtue of it having some different shape, e.g. the shape I accidentally created just now from the clay. “But if you can make a gollyswoggle by accident by kneading clay, then you must, as you idly work the clay in your fingers, be causing the generation and corruption of the members of a compact series of objects of infinitesimal duration. That is what seems to me to be incredible.”^[16]

There are two problems with van Inwagen’s argument. First, everyday intuitions in fact come down against the position he is ultimately trying to motivate, viz. that statues and lumps of clay do not exist. For we certainly do have the intuition that when Michelangelo sits down with the lump of clay and shapes it ever so perfectly, at the end of this process, he has created something. If van Inwagen’s appeal to intuition is to guide us, it seems we should at least say that in this case there is a new thing over and above what was there before Michelangelo’s work. Van Inwagen is correct that we think a single new thing has been created rather than a great multitude, and he is also correct that there is nothing special, metaphysically, about statue-shaped pieces of clay rather than gollyswoggle-shaped pieces. But this suggests that our intuition that only a single thing was created is a pragmatic affair dealing with what things are relevant to us. If we discovered that the shape of a gollyswoggle is the exact shape necessary to cause the angels to sing, and therefore many people wanted to make gollyswoggles, then we would begin to think of this shape as especially relevant and we would think that in shaping the clay in just that way we have created a new thing. In other words, the intuitions to which van Inwagen appeals indicate that judgments about what things exist or what new things have been created are guided by perceptions of relevance. That is, in such questions it seems we can let any possible shape count as a new object, though which things we are willing to countenance in a particular context is a matter of pragmatics restricting our quantifiers.

A second problem with van Inwagen’s argument is that it too rests upon an ambiguity of tense. When we consider the new gollyswoggle that has been created, we might be drawn by the intuition that, as van Inwagen suggests, we have not created some new object but have merely given the same old lump of clay a new shape. What exists after the reshaping is still just the lump of clay and not a new thing. And, of course, in some sense, this is entirely correct. But we have already seen the sense in which it is and the sense in which it is not correct. For if we consider what is there in the temporally relative sense, then the gollyswoggle and the lump of clay are the very same thing — the gollyswoggle is nothing more or less than the lump of clay, so nothing new has been created. But if we consider what is there in the absolute sense, individuating things by their temporal and modal properties, then surely we have something that differs from the lump of clay. In short, van Inwagen’s argument rides on the same ambiguity we have already explored.

Reasons 4, 5, & 6: Relations between properties

The fourth reason for thinking the statue and the lump of clay are identical is that this is the best explanation of why they have such similar properties. As Thomson argues, they “plainly stand in some intimate relation to each other—they currently occupy the same place, they currently have the same shape, size, color, texture, smell, and so on and on. In what relation do they stand to each other if not identity?”^[17]

Zimmerman considers his body and its constituting mass, each of which weighs 140 pounds. If these are different objects, he wonders, “how can it be so easy to lift both these 140-pound physical objects at once?”^[18] Lewis says “It reeks of double counting to say that here we have a dishpan, and we also have a dishpan-shaped bit of plastic that is just where the dishpan is, weighs just what the dishpan weighs (why don’t the two together weigh twice as much?), and so on. This multiplication of entities is absurd on its face; and it only obfuscates the matter if we say that the plastic and the dishpan are ‘relatively identical’ while implying that they are absolutely not identical.”^[19] That two coincident things don’t weigh twice as much (or occupy twice as much space, or cost twice as much, or . . .) is thus the fifth reason for thinking them identical. Lewis is actually offering this argument for the case in which the dishpan and the piece of plastic are spatio-temporally coincident. But notice how the same argument, drawing on the same intuitions, works equally well in the case of spatial coincidence as well. In both cases our intuitions seem to require a denial of Leibniz’s Law, so why in the temporal case does Lewis deny these intuitions and say “We will have to say something counter-intuitive,” and in the modal case say that whoever denies these intuitions is ‘obfuscating the matter’?^[20] Since these are parallel arguments, a parallel explanation is surely desirable.

Rea holds that the statue and the lump of clay “cannot be distinct because they share all of the same parts and (we assume) for any x and y, if x and y share all of the same parts, x = y.”^[21] This is the sixth reason for thinking the statue and the lump of clay are identical.

All of these reasons argue that there are strange connections between the properties of the statue and the properties of the lump of clay — whether it be having identical weights, having weights that don’t combine additively, or having all the same parts — which are best explained by the objects being identical. Of course, when we talk about the properties they ‘have’, this is meant as a tensed predication. The statue and the lump of clay weigh the same at t, the time under consideration. Similarly, their weights combine non-additively at t, and they share all the same ultimate parts at t. But after the clay is replaced by lead, then they will not weigh the same, their weights will combine additively, and they will not share any parts. In short, the argument gives us reason not to think that the statue and the lump of clay are absolutely identical but only that they are identical in all ways intrinsic to a particular moment. And this, of course, is exactly what we have recognized with our ambiguity. In other words, Thomson, Zimmerman, and Rea have merely given us reasons for thinking the statue and the lump of clay are ‘the same’, where this is understood as a temporally relative relation of sameness, but not for thinking that they are absolutely identical. Only if we confuse the two would we infer that pluralism conflicts with common sense.

Reason 7: 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 variations which I will distinguish, the same general sort of argument against coincidence has been supported by Heller, Zimmerman, Burke, van Inwagen, Sosa, and Bennett, to name a few.^[22] The general argument, here in Burke’s words, begins with an explanatory challenge:

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?^[23]

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.^[24] Thus, Burke considers two possible answers to the challenge, two possible ways to explain how an object satisfies one sort rather than another: 1) in virtue of the object’s history, and 2) in virtue of the object’s persistence conditions. I disagree with Burke’s claim that the second of these ways will not succeed, though I will postpone discussion of this possibility until we examine Heller’s argument. I therefore want to turn to Burke’s first suggestion instead. Before doing that, though, I’d like to try to understand the intuition motivating the challenge.

Variation 1: Current Properties Determine Sort

Burke begins his challenge with the claim that Angel and Clayton “are qualitatively identical. Indeed, they consist of the very same atoms. What, then, could make them different in sort?”^[25] 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 non-modal physical properties intrinsic to any time t determine its sort.

Objects that coincide at t are identical in their non-modal physical properties intrinsic to t.

\ It is impossible for objects to coincide and have different sorts.

But why should one think that a thing’s current physical properties would determine its sort?^[26] 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.”^[27] The tree and the coinciding quantity of cellular matter presumably provide a contrast case, for they are indistinguishable; therefore, runs the objection, what current properties could underlie something’s being the one rather than the other?

The pluralist can protest that the two are currently indistinguishable, but not indistinguishable simpliciter. The argument we are currently considering, though, claims that 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 garbage bin 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 line of reasoning underlying it, 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. 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’s intuition is an intuition that ‘multiple’ objects as individuated by temporally intrinsic properties cannot coincide and yet differ in sort — certainly a reasonable intuition — whereas the pluralist’s point is only that multiple objects as individuated by modal and temporally extrinsic properties can coincide and yet differ in sort.

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, for he quickly shifts to a separate argument. I suspect this argument we have examined plays a part in motivating his objection to pluralism, but perhaps I have merely constructed a straw man.^[28] In any case, understanding this first variation of the supervenience argument is important for understanding the variations to come.

Variation 2: Current Properties Determine Identity Through Time

In the same footnote in which Burke explains how monists can meet the explanatory challenge, he continues as follows:

In the extraordinary case in which the objects differing in sort are qualitatively identical (as in Peter Simons’ case of genuine bills and counterfeit bills . . . or the case of a statue and a qualitatively identical object produced by a volcano), the difference in sort is explained by differences in the manner or circumstances of their origin or, perhaps, by other differences in their histories.^[29]

But, adds Burke, though the monist can explain an object’s sort by its history, pluralists can not. The difficulty, according to Burke, is that the pluralist’s account of an object’s history, or cross-temporal identity, must appeal to the object’s sort, thereby making the account circular.

. . . 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 difference in sort.^[30]

Thus, the second major variation of the monist’s supervenience argument runs as follows:

Differences in the cross-temporal identity relations of objects are determined by differences in their 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, hence, it would be impossible for Angel and Clayton to coincide now but not later.

The argument tries to show that the pluralist cannot give a non-circular account of the history, or cross-temporal identity, of the statue and the lump of clay. Note, though, that as the problem is stated, the monist will likewise have trouble. According to Burke’s own account, the situation I have described as containing Angel and Clayton in fact consists of a single object, what is both a statue and a lump of clay, that is cross-temporally identical to the single object, what is both a statue and a lump of lead, that will sit on the mantle in one week.^[31] But we can consider a second situation that is the same as the first 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 beautiful winged woman when it rolled off the workbench. According to Burke’s account this second situation consists of a single object, what is a lump of clay but not a statue, that is cross-temporally identical with the single object, what is also only a lump of clay, that will sit in the garbage in one week and is not cross-temporally identical with the object, what is a lump of lead but not a statue, that will sit on the mantle in one week. How can Burke account for the difference in identity across time between what sits on the mantle in the first situation and what sits on the mantle in the second situation if not by appealing to their sorts? It seems his account fails his own challenge.^[32] But rather than a tu quoque, let me try to say what is wrong with Burke’s argument.

Burke’s argument centers upon the statue’s so-called ‘cross-time identity’. However, this is an ambiguous expression. By ‘cross-time identity’ Burke might simply mean identity. For the statue sitting here now is identical with the statue that will sit on the mantle next week. If identity is the relation intended by ‘cross-time identity’, then expressions describing the relata of this relation, such as ‘the statue that will sit on the mantle next week’, must simply be picking out an object, viz. the statue.

On the other hand, by ‘cross-time identity’ Burke might instead intend a relation not between a thing and itself but a relation between things that only exist at the times indicated. There are different ways to cash this out to get at the desired relation. The simplest way is to use talk of temporal parts. Thus, when Burke talks of a statue x existing at t and a statue y existing at t’ being cross-temporally identical, this can be rephrased as talk of the temporal slice at t of statue x and the temporal slice at t’ of statue y being temporal slices of a single thing. Or, in other words, this can be understood as talk of two temporal slices being co-slice related.

For those who deny the existence of arbitrary temporal parts we can instead speak of the properties intrinsic to t that are instantiated by the object. Thus, talk of the statue x at t and the statue y at t’ being cross-temporally identical can be rephrased as talk of the set of properties of statue x intrinsic to t and the set of properties of statue y intrinsic to t’ being sets of property instantiations of a single thing. We can ask the same question and give the same answer with or without talk of temporal parts, but because present concerns do not ride on the controversial commitments of temporal parts, I will continue to use temporal parts talk as a convenient shorthand.

When Burke asks the pluralist to explain the cross-time identity of the statue, and why it is different than the cross-time identity of the lump of clay, we can see now that there are two different things he might have in mind. On the one hand, he might be talking about identity and about the statue, asking for an explanation of why the statue (i.e., the one sitting here now) is identical to the statue (i.e., the one that will sit here next week) whereas the lump of clay (i.e., the one sitting here now) is not. But in this case, there is really nothing to explain. For identity is a two-place relation. 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.^[33] To the extent that there is something to explain, we can simply say that the statue is identical to the statue and the lump of clay is not because the statue has the same properties as itself whereas it has different properties than the lump of clay: among other differences, the one will be on the mantle next week while the other will not.

Burke argues that we cannot explain a difference in sort between two coincident objects by appealing to their ‘cross-time identities’ or ‘histories’ since the explanation of this would require appealing to their sorts. But, if we are to interpret Burke’s question of why the statue and the lump of clay have different ‘cross-time identities’ as a question about identity, then the explanation of why one thing is identical with itself and not with something else is 1) not an explanation of the objects’ differences in history, and 2) does not require appealing to their sorts.

On the other hand, Burke might be talking about temporal slices that are co-slice related, asking for an explanation of why the current slice of the statue is co-slice related to the temporal slice next week of the statue whereas the current slice of the lump of clay is not. In this case we are asking about the difference in histories of the objects. But in this case we don’t get the asymmetry that Burke suggests. The current temporal slice of the statue sitting on the mantle is a slice 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 a slice of the same object as the future temporal slice of the statue that will sit on the mantle one week from now, because the current temporal slice of the statue just 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.

Burke’s argument draws upon a natural intuition that an object’s sort determines with which objects it is cross-temporally identical. If asked where ‘this’ will be next week, it seems that we can only answer the question once we determine whether ‘this’ is referring to the statue or the lump of clay. Thus, comes the conclusion, something’s sort determines its identity over time. However, I think this line of reasoning confuses metaphysical with epistemic determinations. As an analogy, consider the question of whether ‘this’, as I point to a spot on a plank of a ship, is identical across space with ‘that’, where I point to a spot on a different plank of the same ship, where context does not clarify whether ‘this’ and ‘that’ refer to the ship or to the planks of the ship. Does the referent’s sort explain whether ‘this’ is identical with ‘that’? In some sense, yes. Epistemically, I am unable to determine whether ‘this’ and ‘that’ are demonstratives referring to identical things unless I know the sort of the referents. But this is simply because I am unable to fix upon the referents without first coming to know their sorts. Metaphysically, however, whether ‘this’ and ‘that’ are identical is determined solely by the two referents, without any need to appeal to their sorts. If ‘this’ refers to one plank and ‘that’ refers to another, then ipso facto this and that are not identical; if ‘this’ and ‘that’ refer to the ship, then ipso facto this and that are identical.

Part of the intuitive appeal of Burke’s argument also comes from the suggestion that there is only one kind of ‘identity through time’, or ‘co-slice’, relation. Even Burke must allow that actually there are multiple types of co-slice relations since he thinks there are different sorts with different so-called identity conditions. If something can be a lump of clay and not a statue and something else be a statue, the conditions for two slices being slices of the same statue must be different than the conditions for two slices being slices of the same lump of clay. But this suggests that a single slice could bear one of these relations with one set of slices and bear the other to a different set of slices, i.e. be co-statue-slice related to some slices and yet co-lump-slice related to different slices. The problem is when we confuse these different co-slice 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’.

The conflation of the object with the temporal slice of the object is yet another symptom of the same conflation we saw earlier, that of sameness and absolute identity. Burke’s argument leans heavily on the fact that the statue and the lump of clay are composed of the same atoms, are coextensive with the same things, etc., but notice that these are tensed sentences talking about how the statue and the lump of clay are now. Thus, it is quite natural to slide into thinking of the statue now sitting on the mantle as characterized by all of the properties it has, i.e. has now. And, as suggested, this focus on the current properties is just what is needed when we want to talk about the relation of this temporal slice to a future temporal slice of the same object. But once we start thinking of the current temporal slice of the statue, then we cannot draw any inferences about the identity of the statue or, more generally, about things that depend upon how the statue is at other times.

In summary, when Burke asks how the statue can be identical across time with something to which the lump of clay is not identical across time, his question rides on two ambiguities, on whether ‘the statue’ means the statue or the temporal slice of the statue at t, and on whether ‘identity across time’ means identity or a co-slice relation.^[34]

My argument has largely been negative up to now, but I will briefly 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. for there to be a statue there must be a person with certain intentions towards that statue that precede its creation. But, this caveat noted, we can agree with Burke that a statue’s history explains its sort. But what then, asks Burke, 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 account of why the statue traces this particular historical path through space and time. This, though, is a question we just answered. Given this particular distribution of physical properties through space and time, and given what it is to be a statue, i.e. the identity conditions for statues, this temporal slice will be co-statue-slice related with these other temporal slices, the series of which traces 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 any particular thing is a statue or is a slice of a statue. Thus, pace Burke, there is no circularity.^[35]

Variation 3: Actual Properties Determine Sort

We started out with the challenge of accounting for an object’s sort in virtue of its physical properties intrinsic to the current moment. We found that this was an unreasonable challenge that neither the monist of Burke’s stripe nor the pluralist can meet. We then considered explaining the object’s sort by its history. We can see now that monist and pluralist alike are able to explain an object’s sort by ‘its history’, so pluralists seeking to defend coincidence have thereby met the challenge. Burke has charged that the pluralist who explains an object’s sort by its history would have to give a circular account, but his argument confuses an object with the temporal slice of the object, confuses identity with co-slice relations, and confuses the question of why there are these physical properties instantiated throughout what has turned out to be the history of the object with the question of why the object has this particular spatio-temporal path through history. If the job was to explain an object’s sort, the bottom line is that those who believe in spatially coinciding objects can do so just as easily as those who deny them.

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, or perhaps I should say spatio-temporal pluralists, say that the statue, call it Goliath, and the lump of clay, call it Lumpl, coincide spatio-temporally.^[36] 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.

We started out with the claim that an object’s sort is determined by its current properties, found this to be unreasonably stringent and thus retreated to the claim that an object’s sort is determined by the properties it has throughout its life. Thus, 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 make sense that an object’s sort could be determined by its modal properties as well.

At this point we come up against the third of the supervenience arguments. Heller, one of many who endorse this argument, believes that there are coincident objects but not objects, like Lumpl and Goliath, coincident throughout their lives. If there were spatio-temporally coinciding objects, he argues, they would have to have the same actual properties, and if they belong to different sorts, then they would have different modal properties. Yet this can’t be, he claims, because “There must be some non-modal basis for the modal differences between the lump of clay and the statue.”^[37] Thus the third variation of the supervenience argument:

An object’s actual physical properties determine its modal properties.

Objects that spatio-temporally coincide are identical in their actual properties.

\ Objects that spatio-temporally coincide have the same modal properties.

And this conclusion directly rules out cases like Lumpl and Goliath, as well as undermining the thought that there are any cases of spatio-temporal coincidence.

The third variation of the supervenience argument relies upon the intuitively appealing claim that the modal is grounded in the non-modal — that is, that modal properties must be a function of non-modal properties. And, Heller assumes, this means that any differences in the modal properties of Lumpl and Goliath must be rooted in differences in their non-modal properties. However, Sider and Rea have argued that the requirement that the modal is grounded in the non-modal does not necessarily mean that each object’s modal properties must be a function of its non-modal properties, i.e. mean that the modal strongly locally supervenes on the non-modal.^[38] Perhaps, they suggest, it only requires that the worlds alike in their distribution of modal properties be also alike in their distribution of non-modal properties, i.e. that the modal weakly globally supervenes on the non-modal. This would allow the existence of two objects that differ modally to share the same set of actual properties as long as any world with that one set of actual properties have two objects with those modal properties. However, while adopting this weaker supervenience relation would ‘allow’ the statue and the lump of clay to have different modal properties, prima facie it appears that this move does not explain the difference, for the problem still remains of how the actual properties could determine that the statue has certain modal properties while the actual properties determine that the lump has different modal properties, given that the statue and lump have identical actual properties.^[39] Thus, all agree that modal grounding is required, but monists have yet to show that the stronger sort of grounding is necessary, and pluralists have given little reason to think that the weaker sort of grounding is sufficient.^[40] In short, there seems to be a standoff awaiting a better understanding of what ‘modal grounding’ requires.

Answering the Challenge by Changing the Subject?

Heller argues that statues and lumps of clay do not really exist. And this means that there are not really modal properties of statues or lumps. There is only one sort of object, he says, and objects of this sort never spatio-temporally coincide. Other monists take similar, though perhaps less radical, eliminitivist stances, for example denying that the modal properties that we attribute to statues and lumps are correct. It may seem, as a result of this eliminativism, that if the intuition that the modal is grounded in the non-modal does require strong local supervenience, then Heller and other monists can easily satisfy the modal grounding intuition. However, the intuition that the modal is grounded in the non-modal is an intuition rooted in our dealings with what we take to be everyday objects such as statues and lumps of clay and therefore concerns the believed modal properties of these believed everyday objects. Thus, if Heller denies their existence and says that there are neither statues nor modal properties of statues but only talk of statues and their modal properties, then Heller has not in fact accounted for what needs explaining. He still must account for the grounding we intuit, but the intuition must instead be characterized as the requirement that the supposed modal properties of supposed statues are grounded in the supposed non-modal properties of supposed statues, or, perhaps better, that the accepted truth conditions of talk of modal properties of statues must be a function of the accepted truth conditions of talk of non-modal properties of statues.

In other words, even if someone shows that absolutely nothing exists, this does not mean they have thereby met the explanatory challenge laid down by the modal grounding intuition. We think the actual facts determine the modal facts, but even if there are no statues we still must explain our beliefs and inferences, whether there is a world which our statements describe or not. If I tell Julia about a statue in my car, we need to explain how she infers various modal claims about it, and we need to explain this whether or not there truly is a statue in my car. By denying spatially or spatio-temporally coinciding objects, monists do not thereby satisfy the challenge set down in the modal variation of the supervenience argument. They still have some explaining to do, and the only suggestion so far is that our beliefs of things’ modal properties are determined by our beliefs of their actual properties together with our beliefs of their natures or definitions, an explanation that succeeds whether or not the objects exist and whether or not they have those modal properties. In short, even if Heller is right and statues do not exist, to satisfy the modal grounding intuitions he must explain how our modal beliefs are determined by our non-modal beliefs, and it seems the only way to do this is by conceding that the means by which we believe the non-modal grounds the modal allows for objects that do coincide.^[41]

Exploring Theories of Modality

To fully settle the issue of what modal grounding requires, we would have to determine exactly how the modal is grounded in the non-modal. A straightforward consequence would be an answer to whether or not 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 provide prima facie evidence that coincidence is not ruled out by the requirement for modal grounding.

1. According to conceptualism, objects exist in virtue of our concepts. 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. According to one possible brand of conceptualism then, our concept of statues generates statues in those spatio-temporal regions having the appropriate non-modal properties. Similarly, lumps are generated in virtue of our concept of lumps. However, since the same spatio-temporal region can satisfy both concepts, and since our concepts attach different modal properties to statues than to lumps, it appears that the non-modal determines the modal — in virtue of our concepts — in a way that allows spatio-temporal coincidence.

2. As Lewis spells out linguistic ersatzism, something is possible iff some ersatz world represents it, where an ersatz world is a maximal consistent set of sentences.^[42] If the sentences describe the arrangement of fundamental property instantiations, then there must also be axioms that specify macrophysical conditions, such as when and where a statue exists, in terms of the fundamental properties. An ersatz world thus represents a statue by describing an arrangement of fundamental properties that satisfy the conditions specified by the statue axiom. But notice that these axioms allow spatio-temporally coinciding statues and lumps of clay having different modal properties. If there is this arrangement of fundamental properties, then, says one axiom, you thereby have a statue, i.e. a statue that would not have existed had there been an arrangement of fundamental properties not meeting the conditions specified by the axiom for statues.^[43] But another axiom says that with the same arrangement of fundamental properties you thereby have a lump of clay, a lump of clay that would not have existed under different conditions. 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.

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 by modal grounding, as Heller’s argument assumes, 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.

Heller’s Modal Properties

Heller is the one marshaling the modal variation of the supervenience argument, so it makes sense to see how his account escapes its consequences. Perhaps my argument has been tendentious in the choice of accounts to examine, so if there is another story of how the non-modal determines the modal, one more favorable to monists, it seems that Heller’s account is the natural place to look. As it turns out, the lessons we learn will generalize to other monist accounts as well.

Heller takes a rather radical stance, saying that chairs, atoms, cats, and all objects we normally think of, do not exist. Only four-dimensional hunks of matter exist, and these have their boundaries essentially.^[44] Thus, since there can be no spatio-temporally coincident entities and since there is only one sort of entity, the modal will strongly locally supervene on the non-modal. But let’s examine how these modal properties are determined. Heller tells us that these modal properties are “a function solely of the physical structure of the world.”^[45] How is this so? According to Heller, for a four-dimensional hunk of matter, its

boundaries are its defining characteristics. The material content of either a temporally larger or temporally smaller region of spacetime is, by definition, a different four-dimensional hunk of matter. It is because of the nature of a four-dimensional object that it has just those spatiotemporal boundaries and no others. Any hunk of a different size at this time would have had different spatiotemporal boundaries, and, hence, would have been a different hunk. Therefore, a four-dimensional hunk of matter, by its very nature, has its spatiotemporal boundaries essentially.^[46]

Finally, he adds: “The fact that four-dimensional hunks have their boundaries essentially follows from the very nature of the objects in question.”^[47]

So how do the actual properties of the world determine the modal properties of the world? Using the above reasoning, Heller supposedly comes to understand the nature of four-dimensional hunks of matter. Then, knowing the nature of hunks, it follows trivially where throughout space-time there is a hunk: every space-time boundary bounds exactly one hunk.^[48] Plus, knowing the nature of hunks we can infer what the modal properties are for any hunk: a hunk that has such-and-such a boundary necessarily has that boundary. Thus, knowing the nature of hunks, we can infer from the spatio-temporal distribution of basic physical properties both where hunks exist and what their modal properties are. So once one knows the nature of hunks, one can infer the function from the actual to the modal properties of hunks. And, as long as we assume that hunks are the only sort of thing that exists, something for which Heller provides an argument, this means that our knowledge of the nature of hunks shows us the function that takes us from any thing’s actual properties to its modal properties. In this way, then, we can see that the modal strongly locally supervenes on the actual.

But notice that this line of reasoning requires that hunks are the only sort of thing that exists. If any other sort of thing exists that might spatio-temporally coincide with hunks, then the modal would only weakly globally supervene on the actual. For example, if both hunks and statues exist, then our knowledge of the nature of hunks would tell us where, throughout the distribution of actual properties, each hunk exists and what its modal properties are, and our knowledge of the nature of statues would tell us where each statue exists and what its modal properties are. So according to Heller’s account, we do have reason to think the modal strongly locally supervenes on the non-modal but only because we have reason to think that no other sorts besides hunks exist which might coincide with hunks. Thus, the first moral I want to draw is that Heller’s account does not provide an argument for why we should think that the modal strongly locally supervenes on the non-modal, for such an argument would have to presuppose that there are not coincident objects, exactly what the modal supervenience argument is designed to show.

But there is also a second, stronger moral here. Heller’s account actually supports the case that modal grounding only requires that the modal weakly globally supervenes on the actual. Knowing the nature or definition of hunks, his account infers the existence and location of each hunk from the distribution of actual properties and infers the modal properties of each hunk from its actual properties and the fact that it is a hunk. But using this same line of reasoning, we can say that knowing the nature or definition for any sort we can infer the existence and location of any token of that sort from the distribution of actual properties and can infer the modal properties of each such token from its actual properties and from the fact that it is of that sort. The nature of the objects of any sort determines the function which takes you from the distribution of actual properties to the modal properties of every thing of that sort. And, more generally, knowing the nature of all sorts, you can determine the function which takes you from the totality of actual properties to the totality of all modal properties, but there will not be a function, in the general case, which takes you from the actual properties of any object to its modal properties. That is, using Heller’s line of reasoning of how the modal is determined by the actual, we can conclude that for an arbitrary number of arbitrary sorts, the modal will weakly globally, but not strongly locally, supervene on the actual.

Or, in other words, Heller’s account shows us how the modal is determined by the actual, and that way shows us how spatio-temporal coincidence is compatible with the requirement for modal grounding. Since for each sort the nature of that sort determines the function from the actual to the existence and location of all things of that sort and the function from the actual properties of each thing of that sort to its modal properties, this means that the modal is determined by the actual in a way that is fully compatible with spatio-temporal coincidence. If there are statues and lumps of clay, then knowing the nature of statues tells us that right there on the mantle is a statue and, because it has such-and-such actual properties it has this-and-that modal properties. And knowing the nature of lumps of clay tells us that at the same exact spot on the mantle is a lump of clay that, because it has such-and-such actual properties, has this-and-the-other modal properties. Just as with conceptualism and linguistic ersatzism, Heller’s account shows us a way in which the actual determines the modal that presents no problems for spatio-temporal coincidence.

Considering Objections

I have offered one explanation of the differences in sort between the statue and the lump of clay. What ‘makes’ one object a statue and the other a lump of clay, I have suggested, is their historical and modal properties. However, there are some natural objections to this view.

First, one may object that when they consider some object, such as this tree here, what makes this a tree is just the way it is, not the way it could or could not have been. Just by examining the bark, the leaves, the sap, etc. one can determine whether something is a tree. Thus, why would one think that we should appeal to modal properties?

This objection rides on the same conflation of sameness and absolute identity that we have seen before. The objection gets its intuitive appeal by focusing on an object, e.g. a tree. But what is being considered is an object as individuated by its temporally intrinsic actual properties. Individuated in this way, there is only a single thing standing in the field, and by examining only its actual properties, we can know that “it is a tree.” But if we’re individuating things by their temporally extrinsic and modal properties, then there are a multitude of coincident objects standing right here, and the only way to prize apart one from another is by appeal to their modal properties. So the natural thought that we need not appeal to modal properties to explain something’s sort comes from the natural way of individuating things by sameness. We say there is one thing here, and it is a tree, because we are individuating by temporally intrinsic properties and we’re supplying the most pragmatically useful answer as to its sort, i.e. what, given the context, we might call its ‘dominant kind’.^[49]

A second natural objection is the thought that I’ve got the order of explanation reversed. Something has certain modal properties, one might insist, because it is this sort of thing. The reason the tree cannot survive being cut into bits and distributed to the winds, whereas the quantity of cellular matter can, is because trees are just the sorts of things that cannot survive being scattered. There is something right about this objection, but I don’t think it counts against my claim that modal properties explain something’s sort. To see this, we need to distinguish different notions of explanation.

The challenge has been to explain a statue’s sort. The most common kind of explanation gives the causal history of something. Ramin died because Mary forgot to turn the gas off. Jan received an A because she bribed the proctor. A thing’s sort is clearly not to be explained causally since a thing has its sort necessarily, with certain properties being constitutive of having that sort. However, there is, it seems, a derived sense of ‘explains’ in which we say that X explains Y and mean by this that one’s knowledge of X causally explains one’s knowledge of Y. It is in this epistemic sense that we might say that a postulate explains a theorem, that the postulate is prior to the theorem. In this epistemic sense of ‘explains’, the sort of an object (and, again, here I mean a temporally and modally individuated object) often does explain its modal properties. Typically the context of a conversation makes clear the sort of an object, and only in virtue of knowing the sort are the intended object’s modal properties known. If someone expresses interest in the object on the mantle and asks what we are planning to do with it, it is only through the context that we would know how to answer the question. If the statue is intended, then we might respond that we think it is beautiful and hope to keep it on the mantle forever. If the lump of clay is intended, then we might say that we’ll be throwing it out soon. Of course, this sort of epistemic priority is not an absolute priority since one can learn things in almost any order. Knowing the theorem, one can deduce the postulate. Learning that the thing on the mantle to which Ramin is referring will be a round ball next week, we thereby learn it is not a statue but a lump.

Another sense of ‘explains’ deals with conceptual priority. Our concept of being a bachelor ‘contains’ the concepts of being unmarried and being male. It is in this sense that prior concepts, or component concepts, explain composed concepts. One doesn’t have the concept of a statue unless one understands the identity conditions for statues, i.e. the necessary properties of a statue. Part of what it is to be a statue is not being able to survive flattening. In this sense the property of not being able to survive flattening explains what it is, in general, to be a statue. And, in a derivative sense, part of what explains why this particular object is a statue is the fact that it has the property of not being able to survive flattening.

I suspect part of the difficulty in answering the question of what it is that explains an object’s sort has come from the confusion of these different notions of explanation. Causal explanation, the predominant kind of explanation, does not apply to an object’s sort. In the derived epistemic sense of ‘explains’, we usually would explain an object’s modal properties by its sort, though there is not an explanatory asymmetry here, since in a different context we can explain an object’s sort by its modal properties. Conceptually, though, there is an asymmetry, with something’s modal properties being prior, and thus explaining, its sort. Even here, though, confusion is likely to creep in lest we keep in mind that we are talking about modally individuated objects, that we are not talking about the thing on the mantle and merely explaining its dominant kind.

Rea’s Explanation

Rea has provided an alternative response on behalf of pluralists.^[50] He too claims that a weaker grounding relation is sufficient to satisfy the requirement of ‘modal grounding’ and takes up the challenge laid down by monists like Zimmerman, Burke, and Heller to explain an object’s sort. Rea claims that the explanation for the differences in objects’ sorts is to be found in the fact that objects of different sorts supervene on different types of events.^[51] That is, for any sort, there is associated with that sort a set of microphysical properties, P, upon which the macrophysical properties of objects of that sort supervene. Thus, the property of being a person supervenes on the set of microphysical properties associated with persons, while the property of being a lump of tissue supervenes on another set, the set of microphysical properties associated with lumps of tissue, even though objects of these two sorts can be composed of the same microphysical particles. And, claims Rea, not merely sortal properties, but all properties had by an object will supervene on the set of microphysical properties associated with that object’s sort. If only one of a multitude of coincident objects has a property, then that property will supervene on the set of microphysical properties associated with that object’s sort but not on the sets of microphysical properties associated with the other objects’ sorts. For example, the property of thinking, which, says Rea, belongs to a person but not to the coincident lump of tissue, will supervene on the set of properties associated with persons but not on the set associated with lumps of tissue. Similarly, properties had by multiple coinciding objects, such as the property of weighing 100 kilograms, which can belong to both a person and the coincident lump of tissue, will supervene on multiple sets of properties. Thus, says Rea, we can explain why coincident objects like persons and lumps of tissue can have different properties.

But are there in fact sets of properties that can do the job Rea is asking? I think not. First, I’d like to argue that it is unnecessary, and perhaps misleading, to appeal to the properties and relations of the microparticles. According to Rea’s account, what explains why something is a lump is the fact that it supervenes on the contiguous arrangement of the microparticles of which it is composed. But is it a lump in virtue of being composed of microparticles? Couldn’t a lump consist of atomless gunk or, at the other extreme, of a single large malleable atom? This suggests that it is better to view the explanation as consisting in the property of the lump rather than in the property of its microparticles. What makes something a lump is not its comprising microparticles that are related to each other by the ancestral of contiguity; rather, what makes it a lump is the fact that it is contiguous.^[52] Granted, given that this lump here consists of molecules, it is in virtue of these molecules being contiguous that they compose a lump. But just as we do not explain why something is tall by appealing to its parts, though we could, so too should we not explain why something belongs to a certain sort in virtue of its parts. I can explain why something is a lump, or understand or see that something is a lump, without making any appeal to what sorts of parts it comprises or even if it comprises (proper) parts. Rea begins with the intuition that “the intrinsic qualitative properties of macrophysical objects supervene on the intrinsic properties and relations exemplified by their microphysical parts,” what he calls the doctrine of microphysical supervenience.^[53] But we do not violate this doctrine by explaining something’s sort by its properties, for its properties will, in turn, supervene on the properties and relations of whatever parts it comprises.

Thus, we might want to say that being a lump supervenes on a set of properties that includes being a contiguous mass, while being a mere quantity of material supervenes on a set of properties which does not include being a contiguous mass. However, Rea claims not merely that sortal properties will supervene on this set of properties, but that all properties of things of that sort will supervene. For example, Rea tells us that thinking is a property that will supervene on the supervenience base associated with human beings, whereas it will not supervene on the supervenience base associated with lumps of tissue. And this, he says, explains why there are not multiple coincident thinkers, but only one as intuition suggests. Unfortunately, though, one set of properties for each sort can’t do the two jobs he intends, i.e. determine an object’s necessary properties such as its sort and its contingent properties such as its weight. Consider the property of being a contiguous mass. It would be quite counter-intuitive to say either that quantities of clay never have such a property or that lumps of clay never have such a property. So for both quantities of clay and lumps of clay, the supervenience base, whether a set of microphysical or macrophysical properties, must include those properties that determine whether something will be a contiguous mass. On the other hand, it is such properties as being a contiguous mass that will distinguish lumps of clay from mere quantities of clay, and therefore such properties must appear in the supervenience base associated with lumps but not in the supervenience base associated with mere quantities. Moreover, we can see that this will be a problem in general. If, as Rea claims, a single set of properties associated with each sort explains both the essential and contingent properties of objects of that sort, an essential property of one object could never be a contingent property of a coincident object. And yet such cases are ubiquitous, at least if common sense is to guide us.^[54]

Given the previous discussion of the temporal relativity of ‘the same’, though, we can see that part of Rea’s project is unnecessary. Besides trying to explain how coinciding objects can have different sorts, he is also seeking a resolution of two problems that Zimmerman presents as being related. Rea wants to explain 1) why the person and the coincident lump of tissue can both weigh 100 kilograms and yet not together weigh 200 kilograms; and 2) why the multiplicity of coincident objects doesn’t commit him to the absurd claim that there are multiple thinking things standing where a person stands, each thinking, e.g., that she is a person, even though only one of these beliefs could be true since only one of the coincident entities is a person. However, if pluralists are only claiming that there are multiple coincident objects as individuated by their temporally extrinsic and modal properties, then this multiplicity should never pose a problem for the summing of weighs, for weight is a temporally intrinsic property, and individuating things by their temporally intrinsic properties, there are not multiple coincident objects. Similarly, there is no need to deny that the lump of tissue thinks. I, at least, find it quite intuitive to say that lumps of tissue sometimes do think — viz., whenever they are arranged human-wise. But, again, saying that the person thinks and that the lump of tissue thinks does not commit us to the everyday claim that there are two thinking things since the person is the lump of tissue, at least as individuated by temporally intrinsic properties. Once we disambiguate the temporally relative and the absolute senses of ‘the same’, we see that Zimmerman’s puzzles dissolve and need no explanation.

But let’s consider whether Rea can succeed with half of his project, i.e. if he can get sets of properties that will explain differences in sort. I have argued that the appeal to properties of the microparticles making up an object is unnecessary, so let’s consider a macrophysical supervenience base, i.e. a set of macrophysical properties of the object on which the object’s sort supervenes. Could there be such a thing? Yes! However, talk of supervenience only obfuscates what is going on in such a case. To say that A supervenes on B is to say that necessarily A is a function of B. What is important for present concerns is that this is claiming a necessary connection between the A’s and B’s. So can we find a set of properties on which an object’s sort will supervene? Of course! The set of essential properties for any sort can serve as the supervenience base to be associated with that sort. Whenever something has the essential properties of a statue, then it is, of course, a statue — likewise for lumps of clay, quantities of clay, and so forth. In other words, we can explain a statue’s sort by saying that it supervenes on the essential properties of statues, but what we are doing in this case, under disguise, is explaining something’s being a statue by its having various properties necessarily. In other words, Rea is explaining something’s sort by its modal properties!

I, of course, have no qualms with this, for this is the strategy I myself endorse. I doubt, however, that Rea himself would agree with my characterization of what I have retained of his account. His appeal to supervenience relations and to properties of the microparticles suggests that he does not think of himself as explaining an object’s sort by its modal properties.^[55]

In summary, Rea offers an alternative explanation, an explanation that is intended to explain not only differences in coincident objects’ sorts, but also differences in their other properties as well. I have argued that a set of properties associated with a sort cannot do both jobs but this poses no problem since coincident objects never differ in their contingent properties.^[56] I have also suggested that we should not appeal to properties of microparticles to distinguish sorts, as Rea claims, but that the properties of the whole will do the same job more directly. Finally, once we have gone this far, any talk of supervenience relations can be cast aside and replaced with less tortuous talk of essential properties — in short, we can explain an object’s sort by appealing to its modal properties.

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 ‘cross-time identity’ and ‘the statue’. Heller offers a modal supervenience argument, but it presupposes that modal grounding requires a stronger relation than current accounts of modality suggest is reasonable to expect. Perhaps, then, coincidence is not so strange after all.^[57]

^[1] The terminology is Kit Fine’s (in conversation).

^[2] And, likewise, statements can predicate sameness at past or future times even if they identify the relata in terms of properties they have at other times: “My uncle, who is now in Chicago, was the person who called you yesterday.”

^[3]Myro, “Identity and Time”; Gallois, “Occasional Identity”; Gallois, Occasions of Identity.

^[4] According to Gibbard, who claims that identity is contingent, “For two things to be strictly identical, they must have all properties in common. That means, among other things, that they must start to exist at the same time and cease to exist at the same time.” Apparently, for Gibbard part of the meaning of ‘identity’ requires that temporal properties be shared by identical things, but it is not part of the meaning of the term that modal properties be shared. Rather than seeing this as a substantive debate about the nature of the identity relation, I am suggesting that there are multiple equivalence relations which we might pick out with ‘identity’. Thus, until we say enough to determinately pick out one relation rather than another, it makes little sense to talk about ‘the’ relation of identity. Gibbard apparently has one relation in mind, while Gallois and Myro have another. Since I think most philosophers mean by ‘identity’ a relation that obeys Leibniz’s Law for temporally extrinsic and modal properties, I am defining ‘absolute identity’ accordingly. The names mean nothing, so my same point will remain if someone else calls my relation ‘false identity’ and their own relation ‘true identity’.

^[5]“Sameness without Identity.”

^[6]Wiggins, Sameness and Substance; Johnston, “Constitution is not Identity”; Thomson, “The Statue and the Clay.”

^[7]Lewis, “On the Plurality of Worlds,” p. 218; Lewis, “Survival and Identity,” p. 63; Robinson, “Can Amoebae Divide Without Multiplying?”

^[8]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. 148-9)

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)

^[9]On the Plurality of Worlds, p. 218.

^[10]“On Being in the Same Place at the Same Time,” p. 3. Wiggins is here reporting a common view, though not his own.

^[11]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)

^[12]The Ontology of Physical Objects, p. 14. Cf. Lewis, “Many, but Almost One,” pp. 177ff.

^[13] Of course, a temporal part theorist would disagree with my reasoning by insisting that temporal parts are parts, thus locating the partial identity of the statue and the lump of clay with the temporal slices at the time in question and their partial distinctness with slices at other times. The way I am suggesting we reconcile the common sense dictum with pluralism is, in effect, similar to this sort of appeal to temporal parts in that we both disqualify putative counterexamples by claiming that they are not ‘two wholly distinct’ things since they are identical in all ways intrinsic to the time in question. However, temporal parts theorists will claim that the putative counterexamples are cases of two things that are not ‘wholly distinct’, while I claim that they are not ‘two’ things in the relevant sense, i.e. the sense intended by the common sense claim that two things cannot occupy the same place at the same time. See The Ontology of Physical Objects, pp. 14-15.

^[14]“Things Change,” p. 695.

^[15] Heller claims that physical objects have their boundaries essentially. It therefore appears that he in fact is not identifying objects with the material content of a region, at least as we ordinarily individuate material content. And it therefore seems that Heller cannot capture the common sense dictum. It is conceivable that two people or two quarks, e.g., could pass through each other, such that they both occupy the same exact spatial region at the same time, though retaining their own identities throughout. This explains why we picture ghosts passing through walls and why we wonder if magicians can make a coin pass through a piece of wood. That is, I take it that common sense takes itself to be making a contingent claim in saying that two things cannot occupy the same place at the same time. Yet if we cash out the dictum using Heller’s hunks, the claim becomes tautologous: two hunks that occupy the same space at the same time ipso facto are partially identical. (See also the later section in this paper, “Heller’s Modal Properties.”)

^[16]Material Beings, p. 126. Similarly, Sosa seeks to eschew views according to which, “The barest flutter of the smallest leaf creates and destroys infinitely many things, and ordinary reality suffers a sort of ‘explosion’.” See “Existential Relativity,” p. 133.

^[17]“The Statue and the Clay,” p. 150.

^[18]“Theories of Masses,” p. 87.

^[19]Lewis, On the Plurality of Worlds, p. 252-3.

^[20]On the Plurality of Worlds, p. 218.

^[21]“Constitution and Kind Membership,” p. ? Johnston, using the same line of thought, comments that with mereology “we seem to have a powerful tool for arguing to identities. Exhaustively enumerate the ‘parts’ . . . of x and of y. If they have just the same parts ‘they’ are identical.” (“Constitution is Not Identity,” p. 48 of Rea.) See also Robinson’s “Re-Identifying Matter,” p. 323.

^[22]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. 78-82; Heller’s The Ontology of Physical Objects, pp. 30-32; and Bennett’s “On Differing Modally”. See also Levey, “Coincidence and Principles of Composition”.

^[23]“Copper Statues and Pieces of Copper,” pp. 14-15.

^[24]“Theories of Masses,” p. 87.

^[25]“Copper Statues and Pieces of Copper,” p. 14.

^[26]By ‘current properties’ I mean non-modal 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.

^[27] “Copper Statues and Pieces of Copper,” p. 14n4.

^[28] Why would Burke see the appeal to the object’s history as necessary only in ‘the extraordinary case’ if the line of reasoning I have given is not at least underlying Burke’s thinking? As an analogy, consider the following: We can explain the difference between any objects x and y by appealing to their differences in properties. Admittedly, only in the extraordinary case need we appeal to anything other than the differences in the exact times they exist, but it would be strange to mention this unless one thought that times of existence were somehow special in determining the difference between objects.

^[29]“Copper Statues and Pieces of Copper,” p. 14n4.

^[30] “Copper Statues and Pieces of Copper,” p. 15.

^[31] See his “Preserving the Principle of One Object to a Place”.

^[32] Burke’s challenge consists of a single situation which, according to the pluralist, contains two objects; thus Burke asks for an account of the difference in the identity across time of the two objects. My challenge in response consists of two situations, each of which, according to Burke’s account, contains a single object; thus I ask for an account of the difference in the identity across time of these two objects. Because Burke’s challenge involves two objects in a single situation, an explanation of their differences in identity across time can only appeal to differences in the objects themselves. My challenge, in contrast, involves two situations, leaving open the possibility that the differences in the objects’ identity across time might instead be due to differences in the situations other than differences in the objects. However, the point of the similarity between the two situations is that their only differences lie in the past. Thus, Burke might respond by saying that he can explain the difference in identity over time between the two objects by appealing to the different circumstances surrounding the shaping of the two objects. But the idea behind Burke’s challenge seems to be that if this now is identical across time with that then, but something else now is not, then the explanation of the difference must come from facts about what obtains now. In short, I don’t see how Burke can take advantage of the fact that my challenge involves two situations rather than one.

^[33]See Lewis, On the Plurality of Worlds, pp. 192-3. Sider also makes this point in “Global Supervenience and Identity across Times and Worlds.” Cf. Lowe, “What is a Criterion of Identity?”, esp. pp. 12-13; and Jubien, “Identity Conditions”.

^[34] Again, these points do not depend upon the existence of temporal parts. For those who believe temporal parts do not exist, or who believe they do but they are not parts, we can rephrase these ambiguities as 1) whether ‘the statue’ means the statue or the property instantiations of the statue that are intrinsic to t, and 2) whether ‘identity across time’ means identity or a relation among sets of property relations that holds whenever both sets of properties are instantiated by a single thing (of sort X).

^[35] We explain this statue’s sort by its history but not its history by its sort, i.e. by whether it has this sort vs. another. As an illustrative analogy, we explain why 1) this molecule is a water molecule (or, better yet, why “this molecule is a water molecule” is true) by explaining 2) that these two atoms are hydrogen atoms, 3) that that atom is an oxygen atom, 4) that the three atoms are bonded together and to none others, and 5) that what it is to be a water molecule just is to be two hydrogen atoms and an oxygen atom bonded together and to none others. One might then ask for an explanation of this molecule’s ‘identity across space’, i.e. ask why these three atoms and none others are part of the same molecule. Again you would appeal to the same facts: (5) specifies conditions under which you have a whole, and (2), (3), and (4) show that these conditions are satisfied, so you thereby have a whole, something which has these three atoms as parts. Nowhere here does the explanation appeal to what sort this molecule is. Given (2), (3), (4), and (5), you thereby learn both that these three atoms are a whole and of what sort it is.

One who charges that the appeal to (5) is circular is confusing the fact that this is an X with what it is to be an X. An explanation of why something is an X must rely upon the knowledge of what it is to be an X lest the explanation invite the question, “But what do those conditions have to do with why this is an X?”

^[36]“Contingent Identity,” p. 96 in Rea.

^[37]The Ontology of Physical Objects, p. 31.

^[38]The idea originates in Zimmerman, “Theories of Masses and Problems of Constitution,” p. 88. Zimmerman credits an anonymous referee with this point. Rea supports the idea in “Supervenience and Co-Location.” Sider pursues the point in “Global Supervenience and Identity across Times and Worlds,” §§ 1 & 3.

A set of properties A strongly locally supervenes on a set B =_df there is a function f which, for any possible individual, maps that individual’s B properties to its A properties. Following Sider and McLaughlin, worlds W and V are X-isomorphic =_df there is a one-to-one mapping of the individuals of W to the individuals of V such that an individual is mapped to another only if they have exactly the same X properties. Then, A weakly globally supervenes on B =_df for any pair of worlds which are B-isomorphic, there is a mapping of the individuals of one world to the other in virtue of which they are both A-isomorphic and B-isomorphic. (This is a somewhat stronger definition of weak global supervenience than the one proposed by Sider and by McLaughlin, though I think it is perhaps more intuitive.) See Sider’s “Global Supervenience and Identity across Times and Worlds” for a full discussion of the relevant supervenience relations.

^[39] This, very roughly, is the line that Zimmerman takes in “Theories of Masses and Problems of Constitution.”

^[40]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) Rea, in “Supervenience and Co-Location” attempts just such an explanation. I examine Rea’s explanation in the upcoming section, “Rea’s Explanation.”

^[41] Heller spends considerable time in The Ontology of Physical Objects explaining our ordinary beliefs about objects, beliefs which he sees as mistaken. He appeals to convention to explain the acceptability of our talk and how we reason about objects (or, rather, about what we mistakenly take to be objects). Thus, Heller does provide the sort of explanation I am demanding. However, if he adequately explains how we can infer different modal properties of objects that spatio-temporally coincide, prima facie he has met his own challenge and explained how the modal can be grounded in the non-modal while still allowing coincidence. Heller, of course, has arguments based upon arbitrariness intended to show that these believed objects can not in fact be objects, but it is this denial I am questioning.

^[42]On the Plurality of Worlds, pp. 142-157.

^[43] See Lewis, On the Plurality of Worlds, pp. 155-156.

^[44]Heller informs me (in correspondence) that only regions filled with matter are hunks. Apparently, then, the idea is that having particular boundaries and being filled with matter are the essential properties of hunks of matter.

^[45] The Ontology of Physical Objects, p. 53.

^[46]The Ontology of Physical Objects, p. 53.

^[47]ibid.

^[48] More precisely, every space-time boundary filled with matter bounds exactly one hunk.

^[49] I am gesturing at the ‘Dominant Kinds’ account offered by Burke and Rea, suggesting that the intuition underlying such an account relies upon our consideration of objects as individuated by sameness. See Burke’s “Preserving the Principle of One Object to a Place” and Rea’s “Constitution and Kind Membership.”

^[50] “Supervenience and Co-Location.”

^[51] Rea often talks of objects supervening on events: “an event consisting of some matter exemplifying a certain property, and the object in question supervenes on that event” (p. 371). Supervenience is normally expressed as a relation between sets of properties, the instantiations of which are modally related in certain ways. Rea also explains his thesis at times in this way. But, talk of supervenience relations among properties is talk of events, and talk of the property of being an object is talk of an object. Thus, there are two closely related notions of supervenience at play. I see no harm in sliding between the two, though I will couch my arguments simply in terms of properties.

^[52] I am wielding two notions of contiguity, one a relation between things that are touching, the other a property of a single thing. Something has the property of being contiguous iff it is not the case that it consist of parts, none of which are contiguous (the relation) with each other. Thus, something can be contiguous without having any proper parts at all.

^[53] “Supervenience and Co-Location,” p. 367.

^[54] In fact, Rea says that “the stuff filling the region occupied by Socrates is arranged both humanwise and lumpwise.” (“Supervenience and Co-Location,” p. 371.) But if we are to admit stuff as a sort, then there will be an object, viz. Socrates, which essentially has a humanwise arrangement, and another object, viz. the stuff composing Socrates, which contingently has a humanwise arrangement.

^[55] See “Supervenience and Co-Location,” p. 375n17.

^[56] Rather, spatially coincident objects can differ in their temporal properties, but we can explain these by their ‘histories’.

^[57]I wish to thank Michael Burke, Troy Cross, Kit Fine, Brian McLaughlin, Tim Maudlin, Ted Sider, and Ernie Sosa for their many useful comments on earlier drafts.