The Property Instantiation Approach

In what terms might one hope to supply a criterion of diachronic identity for something like a tomato? (The chosen example may seem to be a banal one: but its usefulness lies precisely in the ordinariness and familiarity of the kind of object in question.) I think that there are three general approaches that one might take, which I shall call the property instantiation approach, the temporal parts approach, and the substantial constituents approach, respectively. I shall argue that the first and second of these approaches are inadequate while the third, which is adequate, demands the existence of ungrounded identities. Hence, if no other approach is forthcoming, this may at least be taken as establishing the credentials of

the thesis that there are ungrounded identities. Later I shall advance a positive argument in its favour.

According to the property instantiation approach, the diachronic identity of a tomato is grounded in some spatiotemporal-cum-causal condition on the instantiation of tomatohood—the crudest version of the theory being that the identity is grounded simply in the spatiotemporal continuity of such instantiation.¹⁴⁹That is to say, what supposedly makes it the case that the tomato now sitting on the table is the same tomato as the tomato sitting on the table five minutes ago is that there is a spatiotemporally continuous sequence of place-times stretching from the place-time occupied by the tomato on the table five minutes ago to the place-time occupied by the tomato on the table now, such that tomatohood has been fully instantiated at each place-time in this sequence. (We have to say ‘fully instantiated’ so as to exclude, for instance, a case in which the original tomato is largely destroyed and a tomato is subsequently miraculously generated from the remnants: for in such a case one would rightly be reluctant to identify the later tomato with the earlier one.) Obviously, it is not important to this account whether or not our tomato has been removed from its table and then returned during the five-minute period—which is as it should be.

Now, one objection which might be raised against the foregoing account is that it rules out a priori the possibility of interrupted or intermittent existence for something like a tomato. I think that this sort of objection is probably correct, far-fetched though it may seem. But it would appear that it is not fatal to the property instantiation approach in general. For instance, one might, consistently with this approach, loosen the requirement on spatiotemporal continuity while at the same time adding a causal condition to distinguish between cases of the interrupted existence of the same tomato and cases of the annihilation of one tomato and its later replacement by another one created ex nihilo. The condition would be something to the effect that in order for later instantiations of tomatohood to ground the identity of the same tomato as earlier instantiations, the later instantiations have to be causally dependent on the earlier instantiations in certain appropriate ways. (Such a condition will arguably be needed in any case, so that its invocation here should not be seen as being merely ad hoc.)

But there is, I think, another far more serious objection of principle to

149 It may be wondered why I speak of the instantiation of tomatohood, as opposed to that of some cluster of non-sortal properties (such as size, shape, colour, and so on). My reason is that I do not believe that sortals are definable in terms of such properties: but anyone who thinks otherwise is at liberty to take my use of the term ‘tomatohood’ as merely abbreviatory.

the property instantiation approach. This begins to emerge once we ask what could possibly be meant by saying that tomatohood is ‘fully instantiated’ at a certain place and time. Just this, surely: that a tomato exists at that place and time.

In fact, matters are a little more complicated than this, but only in a way which makes things even more obviously difficult for the property instantiation approach. For that approach to stand any chance of success, it is crucial that talk of the ‘full’ instantiation of tomatohood at a certain place and time should be construed in such a manner that the possibility of multiple instantiations at that place and time is set aside. For otherwise the approach will not be able to handle, for instance, a case involving one tomato amongst a stationary bunch of contiguous tomatoes. In such a case, tomatohood is multiply instantiated within a certain region of space during a certain period of time. Now, the theory must be able to tell us what it is for a particular one of those tomatoes to persist throughout that period of time. But it won't do just to say that, between the place-time occupied by that particular tomato at the beginning of the period and the place-time occupied by it at the end of the period, there is a spatiotemporally continuous sequence of place-times at which tomatohood is ‘fully’ instantiated (even if it is additionally stipulated that these successive instantiations are causally related to one another in an appropriate way). For, evidently, the whole region occupied by the bunch of tomatoes has tomatohood ‘fully’ instantiated at it throughout the period in question, so that the proposal under consideration doesn't discriminate adequately between the persistence of the particular tomato in question and the persistence of the whole group of tomatoes. Thus, for the purposes of the theory, the ‘instantiation of tomatohood’ at a certain place and time has to be interpreted more accurately as meaning the ‘full and singular instantiation of tomatohood’ at that place and time. But this only serves to bring out more clearly than ever that what this talk of the (‘full and singular’) instantiation of tomatohood a certain place and time amounts to is just talk of the existence at that place and time of exactly one whole tomato. However, existential talk of the latter kind evidently presupposes—and hence cannot help to provide—an account of the identity-conditions of tomatoes. For to speak of the existence of exactly one tomato is to speak of the existence of one and the same tomato. (I am assuming here—I take it uncontroversially—that, in the terminology of Chapter 3, tomatoes are ‘individual objects’.)

To this it may be replied that all that is really being presupposed is an account of the synchronic identity-conditions of tomatoes, whereas what is now at issue is the question of their diachronic identity-conditions. My response would be to put pressure on the assumption that the synchronic and diachronic identity-conditions of things like tomatoes are independently

intelligible. Clearly, it is not an inessential property of tomatoes that they are things of a kind whose typical exemplars persist through time (even if we can make sense of the thought of this or that particular tomato having only a very short-lived existence). And so a synchronic identity criterion for tomatoes which failed to reflect this fact could not properly be represented as a criterion for the synchronic identity of tomatoes, as opposed, say, to qualitatively similar objects of a more ephemeral sort (such as, perhaps, the putative temporal parts of tomatoes with which we shall shortly be concerned). A synchronic identity criterion for tomatoes should tell us under what conditions we have to do with one and the same tomato—as opposed to two distinct tomatoes—at a certain time: and this cannot in general be a matter untouched by considerations of prior and subsequent existence, given the persistent nature of things that are of the tomato kind.

This claim might, however, be challenged on the following grounds. A necessary and sufficient condition for the diversity of tomatoes at a given time, it may be said, is the diversity of their locations at that time, because no two tomatoes can occupy precisely the same place (nor even, indeed, partially overlapping places) at the same time. And this, it might seem, is a condition the satisfaction of which is untouched by considerations of prior or subsequent existence. However—while accepting, of course, the principle that tomatoes exclude one another from the same place at the same time¹⁵⁰—I do not accept that this principle does not rest upon assumptions concerning the diachronic identity of tomatoes, nor do I accept that it can be appealed to on its own as providing a criterion of synchronic identity for tomatoes: for, on the contrary, it seems to me that this is a principle which must, if anything, be seen to emerge from such a criterion rather than to constitute it. I shall take these two points in turn.

First we should appreciate that the capacity of an object to exclude another from the place it occupies is one that can only be exercised in the course of a finite period of time, not just instantaneously: so the ascription of such a capacity to an object actually presupposes that it is a thing of a persisting kind. (Certainly this is so if, as is clearly the case here, we are thinking of an object's capacity to exclude another from the place it occupies as a kind of impenetrability.) Secondly, however, we need to ask just what it is about tomatoes that confers upon them this special power of mutual place-exclusion—a power not possessed by objects of many

150 To accept this is not, obviously, to deny that a place (region of space) may contain a bunch of tomatoes, but only to imply that in such a case the place in question must be divisible into disjoint sub-regions each of which contains no more than one tomato. (It was, of course, in this uncontentious sense that I spoke earlier of the multiple instantiation of tomatohood at the same place and time.)

other kinds, such as shadows and beams of light. We can, after all, easily imagine two objects which look very much like tomatoes approaching one another and merging together; though the very fact of such a merger would disqualify these objects from being classified as tomatoes. Perhaps the most tempting answer is to say that what is distinctive about tomatoes is that they are material objects: different tomatoes are composed at any given time of different portions of matter—and different portions of matter themselves, it may be said, exclude one another from the same place at the same time. Impenetrability, after all, is often regarded as one of the essential properties of matter. (Recall here our discussion of material stuffs in Chapter 3—though there we had in mind putatively homogeneous stuffs.)

Now, this answer will certainly not do just as it stands, because it fails adequately to accommodate such mundane facts as that a quantity of water may seep through a piece of porous clay pot. (For this to happen, mustn't the water pass through the place occupied by the pot—since it must pass through the pot occupying that place?) Of course, one may refine what is meant by ‘existence in the same place’ so as to exclude such cases—stipulating, perhaps, that two things

‘exist in the same place’, strictly speaking, only if there is no spatial location within that place which is occupied by part of one of those things but not by part of the other. (The water, we suppose, can seep through the pot because parts of the water can occupy spatial gaps between parts of the pot.) But, what is more to the point, the answer we are now envisaging already presupposes some grasp of what makes for the identity and diversity of portions of matter and their persistence-conditions, from which a grasp of the exclusion principle for portions of matter must somehow be seen to emerge if it is finally to be endorsed at all. A grasp of that principle—the principle that different portions of matter exclude one another from the same place at the same time—cannot itself be constitutive of our putative understanding of the identity and diversity of portions of matter, for two reasons. First, because it is a mutual exclusion principle and hence, in the absence of a prior specification of what qualifies as a single and distinct portion of matter, it only tells us that one thing, of an as yet unspecified kind, excludes another thing of that kind from the same place at the same time.

Secondly, as I remarked earlier, only a thing of a persisting kind can exercise a capacity to exclude another thing from the place it occupies, so that the exclusion principle for portions of matter itself presupposes an account of the diachronic identity-conditions of portions of matter (their persistence-conditions) and hence an account of their synchronic identity-conditions too: thus it cannot itself constitute an account of those latter conditions.

So, even if we do accept the answer now being contemplated to the

question of what it is that confers the power of mutual place-exclusion upon material objects like tomatoes, we must clearly give up the thought that that power is what ultimately underpins the synchronic identity or diversity of such material objects. Moreover, to address the problem of persistence for things like tomatoes by simply taking for granted the persistence of matter is effectively to abandon the property instantiation approach as a general solution to the problem of persistence. I should add, however, that in fact I do not think that we ought to accept the answer now being contemplated in any case, because I am not convinced that a quite non-specific exclusion principle for matter in general is easily defensible. (It might be easier to defend for the hypothetical homogeneous stuffs discussed in Chapter 3, but is less so for matter as we find it constituted in this, the actual world, where it is ultimately composed of subatomic

‘particles’ capable of existing in states of quantum superposition.) But then it becomes clearer than ever that mutual exclusion principles for specific kinds of material objects—including tomatoes—must have the status of derivative truths relying for their appeal at least partially upon a prior grasp of the specific identity criteria appropriate to objects of the kinds in question.¹⁵¹

To sum up my main objection to the property instantiation approach, then, it seems to me that this approach to the diachronic identity of a persisting object such as a tomato tacitly presupposes the very phenomenon which it purports to account for, because its talk of ‘tomatohood’ being ‘instantiated’ at a sequence of place-times can only be understood in terms of an individual persisting tomato being located at the places and times in question, and this presupposes that we already understand what it is for an individual tomato to persist through time.