Lowe - Substantial Change and Spatiotemporal Coincidence

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SUBSTANTIAL CHANGE ANDSPATIOTEMPORAL COINCIDENCE

E. J. Lowe

Abstract Substantial change occurs when a persisting object of some kindeither begins or ceases to exist. Typically, this happens when one

or more persisting objects of another kind or kinds are subjectedto appropriate varieties of qualitative or relational change, as whenthe particles composing a lump of bronze are rearranged so as tocreate a statue. However, such transformations also seem to result,

very often, in cases of spatiotemporal coincidence, in which twonumerically distinct objects of different kinds exist in exactly thesame place at the same time, such as a statue and a lump of bronze.

Various attempts to resist this way of describing the results of such

transformations are examined and found wanting and objectionsto the possibility of cases of spatiotemporal coincidence arerebutted.

Change comes in several species, which differ from one anotherin ontologically significant ways. Two familiar but quite different species of change that persisting objects can undergo are change of composition and qualitative change . The first sort of change occurs

when a composite object undergoes a change of its component parts. By a ‘component part’ of a persisting object I mean some-thing which helps to compose that object and which is thereforeitself a persisting object, capable in principle of existing inde-pendently of the object which it helps to compose. The secondsort of change – qualitative change – occurs when one and thesame object has numerically different qualities at numerically dif-ferent times. Of course, these two kinds of change are not entirely independent of one another. Sometimes, a change of the onekind brings about a change of the other kind. For example, if acomposite object acquires new parts possessing qualities that aredifferent from those of its old parts, the composite object itself may undergo a change of its qualities – as when a house changesin colour because new bricks of a different colour are used toreplace some of its old bricks. But a composite object can also

undergo qualitative change without undergoing any change of

© Blackwell Publishing Ltd. 2003, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350Main Street, Malden, MA 02148, USA.Ratio (new series) XVI 2 June 2003 0034–0006



composition – for instance, when its component parts are simply rearranged, with the result that the shape of the composite object as a whole changes. However, there is also a third species of

change that persisting objects can undergo, which is traditionally called substantial change . This is the kind of change which occurs when a persisting object either begins or ceases to exist. It is, thus,not exactly a kind of change which happens in or to an object, inthe way that qualitative and compositional changes are. Rather, it is a change of objects – a change with respect to what objects thereare in the world. This is aptly called ‘substantial change’, simply because persisting objects – things such as houses, apples, andplanks of wood – are traditionally called ‘individual substances’,or ‘substantial individuals’.

Most of the substantial individuals that we are familiar with –indeed, perhaps all of them – are composite objects. It is naturalto assume that there must exist some non-composite substantialindividuals, because it is natural to assume that hierarchies of com-position cannot be infinitely descending.1 That is to say, it is naturalto assume that although an object’s component parts may them-selves be composite objects, and the parts of these parts may againbe composite, there must eventually be an end to such a series of whole-part relations, the terminus being provided by objects whichare by their very nature simple or non-composite. The ‘atoms’ of Democritus played precisely this role in his ontology – ‘atom’meaning, quite literally, that which cannot be cut or divided intoany lesser parts. In modern physics, the so-called ‘elementary par-

ticles’, such as electrons and quarks, play a similar role – thoughin many other ways they are quite unlike Democritean atoms, sincethey are not conceived of as being perfectly hard and rigid bodies with precise geometrical shapes. Whether it is really metaphysically impossible for hierarchies of composition to be infinitely descend-ing is a difficult question, which I shall not attempt to answer here.Perhaps the most that we can safely say is that empirical evidencecurrently suggests that all material objects do in fact have ultimate

component parts of a simple or non-composite nature. However,since no macroscopic material object is non-composite as far as weknow and macroscopic objects will be our main concern in thispaper, we can effectively confine our attention in what follows tocomposite objects.

SUBSTANTIAL CHANGE AND SPATIOTEMPORAL COINCIDENCE 141

© Blackwell Publishing Ltd. 2003

1 See further my The Possibility of Metaphysics: Substance, Identity, and Time (Oxford:Clarendon Press, 1998), p. 158 and p. 171.



One way for a substantial individual to come into existence isfor certain other objects to be united together so as to form itscomponent parts. This is what happens when a house is built from

bricks or a ship is constructed from planks and spars. Another way, however, is for certain objects, which are already unitedtogether to form a composite whole, to be rearranged in such a

way that a composite whole of a new kind comes into existence.This is what happens when a mass of bronze is moulded into theform of a statue: a statue, we say, is created out of the bronze.Perhaps this is also what happens when a living organism, such as

a plant or animal, is created out of a mass of organic matter. Sub-stantial change of this kind raises some difficult metaphysicalproblems, however. Consider the case of the bronze and thestatue. We seem compelled to say that the mass or lump of bronzeis a numerically distinct object from the statue, because the lumpand the statue will ordinarily have come into existence at differ-ent times – the lump first and later the statue. Moreover, the lumpand the statue plausibly have different persistence-conditions – that

is to say, there are different kinds of changes that can and cannot be survived by the lump and the statue respectively. For example,the lump can survive a change in which it is flattened into theshape of a disc, but the statue cannot survive such a change. Con-

versely, the statue can survive the loss or replacement of some of the bronze particles that compose it, but the lump of bronzecannot: removing or replacing some of the bronze particles leavesus with a numerically distinct lump of bronze. However, if the

lump and the statue are numerically distinct substantial individ-uals, then they are ones bearing a seemingly strange relationshipto one another – for during at least part of their existences they exactly coincide with one another, occupying precisely the sameplace at the same time. Moreover, while this is the case, exactly the same bronze particles compose these two numerically distinct individuals, the lump and the statue – and we may wonder how this is possible.

Many philosophers think that it is fundamentally absurd tosuppose that the lump and the statue are two numerically distinct objects which exactly coincide with one another for a periodof time and are composed of exactly the same particles.2 They

142 E. J. LOWE


2 See, for example, Michael B. Burke, ‘Copper Statues and Pieces of Copper’, Analy- sis 52 (1992), pp. 12–17, Dean W. Zimmerman, ‘Theories of Masses and Problems of Con-stitution’, Philosophical Review 104 (1995), pp. 53–110, and Eric T. Olson, ‘Composition

and Coincidence’, Pacific Philosophical Quarterly 77 (1996), pp. 374–403.



complain that they cannot understand what would make theseobjects distinct at such a time. How could either object have any property which the other object lacked? Of course, it may be

replied that the objects could have different historical and modal properties – where an historical property of an object is one whichit has in respect of what has happened to it in the past and a modalproperty of an object is one which it has in respect of what could happen to it. We have already said, for instance, that the lumpand the statue may have come into existence at different timesand that there are different kinds of change that they can andcannot survive. However, it may be wondered how two objects which are, at a certain moment in time, exactly alike in their non-historical and non-modal properties could, nonetheless, differ inrespect of their historical and modal properties. And the lumpand the statue do appear to be exactly alike in their non-histori-cal and non-modal properties when they exactly coincide withone another. That being so, if this implies that they cannot, afterall, differ from one another in their historical and modal prop-erties, then Leibniz’s law (or, more strictly, the principle of theidentity of indiscernibles) would apparently compel us to judgethat they are in fact one and the same object, not two numerically distinct objects.

Faced with this apparent conundrum, philosophers haveresponded in a number of different ways, most if not all of whichseem to require some departure from everyday ways of thinking.One possibility is to question certain standard assumptions about

the nature of identity itself. Identity is normally thought of asbeing an absolute relation, in the following sense. Let ‘ F ’ and ‘G ’be certain sortal terms, that is to say, general terms denotingcertain sorts or kinds of substantial individual. Examples wouldbe the terms ‘tree’, ‘planet’, ‘tiger’, and, indeed, ‘statue’ and‘lump of bronze’. Then it is standardly assumed that if a and b are numerically the same F and are also both G s, then a and b arealso numerically the same G . It is easy to see, indeed, that

Leibniz’s law implies this, if we take the law to assert, in effect,that if, for some sortal term ‘X ’, a is the same X as b , then what-ever is true of a is also true of b . For then it follows that if a andb are the same F , then whatever is true of a is also true of b ; but if a is a G , then it is surely true of a that it is the same G as a , whence it is also true of b that it is the same G as a .3 But perhaps



3 See further David Wiggins, Sameness and Substance (Oxford: Blackwell, 1980), pp. 19–20.



this standard assumption – and with it the standard version of Leibniz’s law – should be questioned. Perhaps it makes sense,after all, to suppose that a and b may be the same F and yet not

the same G . This is what a proponent of a relative conception of identity maintains.4 According to this view, we cannot say of certain individuals a and b that they are, or are not, identical sim-

pliciter – that is, without further qualification. They may be iden-tical relative to one sortal characterisation of them, but distinct relative to another.

How might this help us with the case of the statue and the lump

of bronze? Simply as follows. We felt pressed to say, on the onehand, that the statue and the lump are two numerically distinct objects, because they differ in their historical and modal proper-ties. On the other hand, at least while the statue and the lumpexactly coincide with one another, we feel pressed to say that they cannot, after all, be two numerically distinct objects. The relativeidentity theorist may, however, diagnose our difficulties as arisingfrom a misconception that identity and distinctness are ‘absolute’

relations, when in fact they are sortally relative relations. Accord-ing to the relativist, we cannot intelligibly speak of the statueand the lump being, or failing to be, numerically identical objects ,because this is to attempt to speak of identity and distinctness

without relativising them to appropriate sortal characterisationsof the objects that we are referring to. Perhaps what we shouldsay – and what, according to the relativist, we can consistently say – is that the statue and the lump of bronze are one and the same

lump of bronze , but not one and the same statue . In order to makethis proposal a little more intuitively appealing, consider what wemight say if the lump of bronze were to be melted down againand formed into a different statue (perhaps the first statue was astatue of Napoleon and the second a statue of Wellington). Then,according to the relativist, we might say of the first and secondstatues that they are different statues but the same lump of bronze .But then, it seems, if the lump of bronze is a statue at the time at

which the first statue exists, it is not the same statue as the first statue. For, if it were, then, by the same token, the lump of bronze

would have to be the same statue as the second statue when that exists. But if the first statue were the same statue as the lump of bronze and the lump of bronze were also the same statue as the

144 E. J. LOWE


4 The locus classicus is P. T. Geach, Reference and Generality , 3rd edn (Ithaca, NY: Cornell

University Press, 1980): see p. 181.



second statue, then it seems that the transitivity of identity impliesthat the first statue would be the same statue as the second statue– which, we have agreed, it is not. So we must conclude that the

first statue and the lump of bronze are not one and the samestatue , even if they are one and the same lump of bronze . The attrac-tion of this account is that it explains why we are pulled in twodifferent directions concerning the statue and the lump of bronze, wanting to say both that they are distinct and that they are identical. Moreover, it even reconciles, in a way, the two judge-ments that we feel inclined to make, so that we are not compelledto surrender either in favour of the other: we can retain both judgements, provided that we qualify each in the way that therelativist recommends.

I have tried to represent the relativist solution to our problemin as favourable a light as possible, but it is not without difficul-ties of its own. For one thing, in abandoning the standard versionof Leibniz’s law, it abandons what many philosophers and logi-cians would see as the most fundamental principle of identity, without which we effectively lose all real grip on the notion of identity. The ‘relativised identity relations’ of the relativist, it may be objected, are not really relations of identity at all, but some-thing else – relations of similarity, perhaps. Another problem isthat questions of identity are intimately bound up with questionsof existence : so that if one wants to relativise identity to sortal char-acterisations, one must be prepared to relativise existence tosortal characterisations also. This seems to have very strange

implications.

5

Suppose that the (first) statue is destroyed by melting down the bronze, but the bronze remains intact and socontinues to exist. Now, according to the relativist, the statue isthe same lump of bronze as the lump of bronze – and, as we have just said, the lump of bronze continues to exist. So, even after theprocess of melting has occurred, there still exists something whichis the same thing of some sort as the statue, according to the rel-ativist. This seems to imply that the statue does still exist, albeit

only ‘as’ the lump of bronze rather than ‘as’ the statue. But alsoit would seem that the relativist is not entitled to any ‘absolute’or ‘unrelativised’ conception of existence. So the relativist must judge that is wrong to say that the statue ceases to exist simpliciter when it is melted down – it only ceases to exist ‘as’ a statue.



5 See further my Kinds of Being: A Study of Individuation, Identity and the Logic of Sortal Terms (Oxford: Blackwell, 1989), pp. 56ff.



Perhaps this is not an absurd thing to say, but it certainly seemsto require a very big departure from common-sense ways of think-ing about existence and substantial change. We may have to give

up saying, for instance, that a piece of paper is simply destroyed when it is burnt to ashes, or even that a human being simply ceases to exist upon undergoing a fatal accident.

Suppose that we decide that the ‘absolute’ conception of iden-tity is too fundamental to be given up. How else might we handlethe case of the statue and the lump of bronze? Temporal- parts theories provide what may seem to be an attractive solution to our

problem. The temporal-parts theorist can say that, so long as they exactly coincide, the statue and the lump of bronze have exactly the same temporal parts, even though they may have different temporal parts before or after that period. This allows us to say that, considered as ‘four-dimensional’ wholes, the statue and thelump of bronze are indeed numerically distinct objects – and yet that, at any given time during their coincidence, just one tempo-ral part of an object exists in the place they occupy, because the

temporal part of the statue which exists at that time is numeri-cally identical with the temporal part of the lump of bronze whichexists at that time. This account, like the relativist one, bothexplains and to some extent justifies our inclination to say that the statue and the lump of bronze both are and are not identical

with one another during the time of coincidence. As temporally extended wholes they are not identical, but they are ‘partly’ iden-tical during the period of coincidence, inasmuch as they have

exactly the same temporal parts during that time.Naturally, this solution will only appeal to those who do not

consider temporal-parts theories subject to insuperable objec-tions.6 But even for someone who accepts a theory of temporalparts, coinciding objects can still present a problem. Consider acase in which a bronze statue is made from bronze which only comes together into a lump at the time when the statue is formedand which is dispersed or destroyed when the statue itself isdestroyed. In that case, the statue and the lump of bronze coin-cide throughout their entire existence, so that, according tothe temporal-parts theory, they have exactly the same temporalparts at all times and consequently are one and the same ‘four-dimensional’ whole. The trouble now is that we still want to

146 E. J. LOWE


6 I express my own doubts about temporal-parts theories in my The Possibility of Meta-

physics : see pp. 98ff, pp. 114ff and pp. 127ff.



say that there are changes which the statue could have survivedbut which the lump of bronze could not have survived and vice versa – in short, that they have different modal properties. But this

difference in their properties is enough, by Leibniz’s law, to imply that the statue and the lump of bronze are numerically distinct objects, even granting that they possess the same non-modal prop-erties throughout their respective existences and consequently donot differ in respect of any of their historical properties.

One possible response that the temporal-parts theorist cangive to this apparent difficulty is to say that, when we ascribe amodal property to an object, our ascription must be in a certainsense relativised to some appropriate sortal characterisation of theobject – and that one and the same object may possess a certainmodal property relative to one sortal characterisation of that object and yet lack it relative to another such characterisation.7

We shall have to say, for instance, that ‘as’ a lump of bronze a certain‘four-dimensional’ whole could have survived flattening, but that ‘as’ a statue it could not have survived this. This suggestion is,of course, reminiscent of what the relative identity theorist wasenvisaged as saying about the existence of objects – the differencebeing that, whereas the temporal-parts theorist need onlyrelativise judgements of what changes an object could survive tohow that object is characterised sortally, the relative identity the-orist has to relativise judgements of what changes an object actu-ally does survive to how that object is characterised sortally.However, one may well wonder whether, if one is going to have

to admit such relativisation in any case, it is not preferable toadopt the relative identity theorist’s position, since it doesnot require us to include in our ontology such seemingly strangeand obscure entities as the supposed temporal parts of persistingobjects. It is true that the temporal-parts theory allows us to retainthe standard, absolutist notion of identity and the standard version of Leibniz’s law, but perhaps a commitment to theexistence of temporal parts is too heavy a price to pay for this

advantage.Can we solve the problem of the statue and the lump of bronze without either relativising identity or adopting the doctrine of temporal parts? In particular, can we do so without having to say



7 See, for example, Harold W. Noonan, ‘Indeterminate Identity, Contingent Identity and Abelardian Predicates’, Philosophical Quarterly 41 (1991), pp. 183–93 and ‘Constitutionis Identity’, Mind 102 (1993), pp. 133–46.



that two numerically distinct persisting objects can exist in exactly the same place at the same time? Yes, we can, but only if we areprepared to give up some other common-sense assumptions. For

instance, we could deny that there are really any such things as‘statues’, holding that, although a lump of bronze may become‘statue-shaped’ for a certain period of time, this does not amount to the creation of any new substantial individual distinct from thelump itself. Alternatively, we could deny that there are reallyany such things as ‘lumps of bronze’, holding that, although anumber of bronze particles may become united together for a

certain period of time, this does not ordinarily amount to the cre-ation of any new substantial individual in addition to the many bronze particles themselves – but that when an intelligent agent deliberately imposes a specific form upon the particles, they thenbegin to compose a new substantial particular, such as a statue. If

we adopt either of these positions, we may have to admit that aplurality of different objects (the bronze particles) can togetheroccupy exactly the same place as some one object of a certain sort

– either a lump of bronze or a statue, as the case may be. But thisis obviously quite different from saying that some one object of acertain sort can exactly coincide with some one object of anothersort.

However, if we are prepared to entertain either of these posi-tions, it is not clear why we should not be prepared to combinethem, denying the existence of both statues and lumps of bronzeand accepting only the existence of bronze particles. But it is easy

to see where this train of thought is likely to lead, namely, to the view that, in reality, the only persisting objects that exist are simpleor non-composite ones, the most likely candidates being the so-called elementary particles of physics. The implication would bethat none of the assumed objects of common-sense ways of think-ing really exist, including not only artifacts, plants and animals,but even human beings ourselves (on the assumption that we, if

we are anything, are composite beings).8 Perhaps a case can bemade out for saying that living organisms are special in some way

148 E. J. LOWE


8 In point of fact, I do not myself believe that human persons or selves are compositebeings: see my ‘In Defence of the Simplicity Argument’, Australasian Journal of Philosophy 78 (2000), pp. 105–12 and my ‘Identity, Composition, and the Simplicity of the Self’, inKevin J. Corcoran (ed.), Soul, Body, and Survival (Ithaca, NY: Cornell University Press,2001). However, even if I am right, this does little to mitigate the paradoxical flavour of the claim that there are no composite objects.



and so really do exist, despite being composite objects.9 But that will certainly not be easy. It seems, then, that the position that weare now contemplating is potentially a paradoxical one, in which

we have to deny even our own existence in favour of the existenceof certain theoretical entities – the elementary particles of modern physics – whose status as ‘persisting objects’ is in anycase questionable, in view of the notorious ‘wave-particle duality’of quantum mechanical phenomena. The danger is that we shallhave to end up concluding that there are no persisting objects inthe world at all.

Some philosophers, it is true, consider that an eliminativist con-strual of our common-sense talk of composite objects is forcedupon us by causal considerations. They urge that a compositeobject can have no causal impact upon the world over and abovethe collective causal impact of its component particles, so that –on the assumption that causal efficacy is the mark of the real – we should not include composite objects in our ontology inaddition to the particles which supposedly compose them. Such anaddition, they suggest, amounts to double-counting and wouldonly be justified if there were an utterly implausible systematiccausal overdetermination of the effects of particles by the actionsof composite objects made up of those particles. However, thisline of argument is vulnerable, not least, to the objection that it rests upon an outmoded conception of particle physics. It is now widely accepted amongst philosophers of quantum physics that the properties of complex quantum systems do not simply super-

vene upon the properties and relations of their parts and that such systems therefore possess irreducibly holistic features,incompatible with the ‘bottom up’ style of causal explanationcharacteristic of classical physics.10 Nor should it be supposed that this fact has no bearing on what we say about the causal activitiesof macroscopic physical objects, for the domain of quantumphysics is not and cannot be restricted to the microphysical realm.I mention this as a caution to those philosophers who imagine



9 See, for example, Peter van Inwagen, Material Beings (Ithaca, NY: Cornell University Press, 1990), pp. 81ff. For discussion, see Joshua Hoffman and Gary S. Rosenkrantz, Sub- stance: Its Nature and Existence (London: Routledge, 1997), pp. 179ff.

10 See, for example, Paul Teller, ‘Relativity, Relational Holism, and the Bell Inequali-ties’, in J. Cushing and E. McMullin (eds), Philosophical Consequences of Quantum Theory: Reflections on Bell’s Theorem (Notre Dame, IN: University of Notre Dame Press, 1989) andTim Maudlin, Quantum Non-Locality and Relativity (Oxford: Blackwell, 1994), pp. 210–12.



that modern physics somehow lends support either to microre-ductionism or to macroeliminativism.

Is there any way in which we can, without adopting either rel-

ative identity theory or the doctrine of temporal parts, acknowl-edge the real existence of macroscopic composite objects such asstatues and lumps of bronze and still deny that two numerically distinct objects can exactly coincide? The answer is still that, yes,

we can, provided that we are prepared to abandon yet anotherfeature of common-sense ways of thinking about objects and theirpersistence. What we could say in the case of the statue and the

lump of bronze is that when the lump of bronze is formed intothe statue, bringing the latter into existence, the lump of bronzeitself ceases to exist. We may still want to say that a lump of bronzeexists after the statue has been created, but it is open to us to deny that this lump of bronze is identical with the lump of bronze from

which the statue was formed. We can say instead that this new lump of bronze is simply identical with the statue itself and thuscame into existence when the statue did.11 There is nothing log-

ically inconsistent about this combination of judgements. But it can hardly be said to respect our common-sense ways of thinkingabout the persistence of objects. For its implication is that merely by imposing a certain shape upon a lump of bronze – the kind of shape that is necessary to form it into a statue of a certain sort –

we bring it about that that lump of bronze ceases to exist. Why should that be so? How could a lump of bronze cease to exist merely for this reason? Our common-sense notion of a lump of

bronze is the notion of something which precisely can undergoany manner of change in its overall shape, provided that it con-tinues to be composed of the same bronze particles unitedtogether into a mass. I conclude that there is very little prospect for an acceptable solution to our problem along these lines.

Having considered every other alternative that seems evenremotely plausible,12 let us now consider again the view that the

150 E. J. LOWE


11 See Michael B. Burke, ‘Preserving the Principle of One Object to a Place: A Novel Account of the Relations Among Objects, Sorts, Sortals, and Persistence Conditions’, Phi- losophy and Phenomenological Research 54 (1994), pp. 591–624. I discuss Burke’s view in my ‘Coinciding Objects: In Defence of the “Standard Account” ’, Analysis 55 (1995), pp. 171–8.

12 I exclude as not remotely plausible André Gallois’s ‘Occasional Identity Thesis’,according to which we may say that the statue and the lump of bronze are numerically identical while they exactly coincide but are numerically distinct at other times: see hisOccasions of Identity: The Metaphysics of Persistence, Change, and Sameness (Oxford: ClarendonPress, 1998). I raise some objections against Gallois’s view in my review of his book, Mind

109 (2000), pp. 354–7.



statue and the lump of bronze are numerically distinct persistingobjects which exactly coincide with one another for a certainperiod of time. As I have already indicated, an apparent difficulty

with this view is that the statue and the lump of bronze seem tobe indistinguishable from one another at such a time: we cannot tell them apart by the minutest scrutiny, or so it seems. However,much depends on what precisely is understood by ‘indistin-guishability’ in this context. It certainly seems to be true that thestatue and the lump of bronze are empirically indistinguishableduring the period of their coincidence, at least in the sense that during that time they do not differ from one another in respect of any perceptible property – say, of shape, colour or weight. But persisting objects may – and, in fact, must – possess many otherproperties in addition to their perceptible ones, if by a ‘percep-tible property’ one means a property whose possession by anobject at a time can in principle be discovered by observation of that object at that time. We have already mentioned certain kindsof property which are clearly not perceptible in this sense – thehistorical and modal properties of objects. Of course, many ofthe historical properties of objects can be detected empirically,although not simply by observing the objects at the time at whichthey possess them. A man may, as an empirically detectable matterof fact, possess the historical property of having worn a beard ten years ago, but no observation of him now can be expected toreveal this fact about him. As for modal properties, consider suchso-called dispositional properties as elasticity and solubility.13 Elas-

ticity is a modal property, because it is the property an object hasof being able to return to its original shape upon being stretched. An empirical test can certainly reveal whether or not an object has this property: one can simply attempt to stretch the object and see whether it returns to its original shape. But such a test takes time to perform, so it does not provide an empirical meansof detecting, at a certain time, that an object is elastic at that time .This is why elasticity is not, strictly speaking, a perceptible prop-

erty of an object, in the sense I have just defined. By contrast, wecan very often detect an object’s colour or shape at a certain timesimply by observing it at that time, which is why colour and shape



13 I am in fact doubtful about the distinction that is standardly drawn between ‘dispo-sitional’ and ‘categorical’ properties: see my ‘Dispositions and Laws’, Metaphysica 2 (2001),pp. 5–23. But I set aside such doubts for present purposes. In any case, the account of theontological ground of dispositions that I favour reinforces, if anything, the positiondefended in the present paper.



are, in this sense, perceptible properties. These considerationssuggest that although it may be the case that the statue and thelump of bronze are empirically indistinguishable during the time

of their coincidence, this still leaves scope for them to possess dif-ferent properties from one another during that time and henceto be ‘distinguishable’ in a broader sense. However, it remains tobe seen whether, and if so how, this possibility can be exploitedby the advocate of spatiotemporal coincidence.

Earlier, I suggested that some philosophers find it difficult tounderstand how two numerically distinct objects could be exactly

alike in respect of their non-historical and non-modal propertiesat a certain time and yet differ from one another in respect of their historical and modal properties – particularly if, as is sup-posedly the case with the statue and the lump of bronze, the twoobjects in question are composed of exactly the same materialparticles. Now, it may be true that the statue and lump of bronzeshould not be expected to differ from one another in respect of their physical dispositional properties during the time of coin-

cidence. If the bronze is electrically conductive and soluble insulphuric acid, then so too, it seems, will be the statue. This isbecause it seems that such dispositional properties are groundedin, or ‘supervene upon’, the properties and relations of the mate-rial particles composing the statue and the lump of bronze(setting aside any doubts on this score arising from the quantummechanical considerations discussed earlier). However, not allmodal properties are like such dispositional properties in this

respect. Some of an object’s modal properties arise not fromits material constitution but from its persistence-conditions , whichdetermine what sorts of changes the object can and cannot survive – and this is a matter of what kind of object the object is.

A statue, for instance, is a kind of object which, unlike a lump of bronze, cannot survive much change to its shape. Conversely, alump of bronze is a kind of object which, unlike a statue, cannot survive any change to its material composition.

These modal properties of the objects in question are evidently not to be explained by reference to the properties and relationsof the material particles which compose statues and lumps of bronze respectively. Indeed, such modal properties are not really empirical properties at all. They are, rather, a priori ones that aregrounded in categorial distinctions of a metaphysical nature. Itis an a priori truth that what is required for a lump of bronze

to persist over time is for certain bronze particles to be united

152 E. J. LOWE




together for a period of time, without any of them being sepa-rated from the rest or being replaced by any new particles.Equally, it is an a priori truth that what is required for a bronze

statue to persist over time is for sufficiently many bronze particles– but not necessarily the same bronze particles – to be unitedtogether for a period of time while constantly exhibiting a certainoverall shape. The concepts of a lump of bronze and of a bronzestatue are precisely the concepts of persisting objects of kindsgoverned by the foregoing persistence-conditions. The conse-quence is that one cannot in principle tell, simply by examiningan object empirically at a certain moment of time, that it is abronze statue or a lump of bronze. For whether or not somethingqualifies as an object of one of these kinds at a certain moment of time is partly a matter of what is the case at earlier and latermoments of time. If, by chance, a large number of bronze parti-cles were to come together for just a moment in the shape of astatue, immediately to be dispersed again a moment later, that would not imply that either a lump of bronze or a bronze statuehad existed for that moment – for no persisting object composedof those particles would have been created. In this respect, theproperties of being a lump of bronze and being a bronze statueare similar to the property of being in motion.14 Whether or not an object is in motion at a certain moment of time cannot beestablished simply by an empirical examination of the object at that time, because it is partly a matter of what is the case at earlierand later moments of time – namely, whether the object is in a

different position at earlier and later moments of time. We now have to hand the materials with which to answer theobjections that have been raised against the notion of the spa-tiotemporal coincidence of persisting objects, such as the statueand the lump of bronze. It is true that, at any given moment of their coincidence, the statue and the lump of bronze do not differin respect of any property whose possession by them is deter-mined solely by what is the case at that moment of time, without

any reference to what is the case at earlier or later moments of time. This is why the statue and the lump of bronze are indistin-guishable in respect of their perceptible properties at any moment of their coincidence. It may also be true that the statueand the lump of bronze do not differ, at any moment of their



14 See further my The Possibility of Metaphysics , pp. 198–9.



coincidence, in respect of any of their physical dispositional prop-erties – understanding these to be those of their dispositionalproperties that are grounded in the properties and relations of

the material particles composing them. However, it can still betrue to say that the statue and the lump of bronze differ, at any moment of their coincidence, in respect of many of their modaland historical properties: for their possession of these propertiesis not determined solely by what is the case at the times at whichthey possess them, nor are these properties grounded in theproperties and relations of the material particles composing the

statue and the lump of bronze.Here it is important to appreciate that modal and historicalproperties, quite generally, are only ascribable to objects in virtueof the fact that certain appropriate persistence-conditions areassignable to those objects. Clearly, we cannot properly say of acertain presently existing object that something befell it in thepast, or that it would behave in such-and-such a way in the futureif it were to be acted on in a certain fashion, unless we can say, in

principle, what is required for that very object to exist both now andin the past, or both now and in the (actual or possible) future.One consequence of this is that the statue and the lump of bronzecan in fact differ from one another, during the time of their coin-cidence, even in respect of certain of their dispositional properties– the implication being that not all of their dispositional proper-ties are simply grounded in the properties and relations of thematerial particles which compose them.15 For example, we may

say of the statue that it is disposed to cast a shadow of a certainshape, implying that if it were to be set on the ground andexposed to sunlight, a shadow of that shape would be cast on theground at its foot. But we cannot say of the lump of bronze , without qualification, that it is disposed to cast a shadow of any particularshape. For, whereas the statue, so long as it exists, must retain acertain constant shape, this is not true of the lump of bronze –these facts being consequences of the respective persistence-conditions of the statue and the lump of bronze. Of course, wecan say of the lump of bronze that, so long as it retains any given

154 E. J. LOWE


15 A similar point is made by Sydney Shoemaker in his ‘Self and Body’, Proceedings of the Aristotelian Society , Supp. Vol. 78 (1999), pp. 287–306: see pp. 297ff. However, Shoe-maker makes the point in the course of defending the view that a human person is con-stituted by his or her body, which is a view of embodiment that I reject: see my ‘Identity,

Composition, and the Simplicity of the Self’.



shape , it is disposed to cast a shadow of a corresponding shape:but in saying this we are by no means saying the same thing as weare saying of the statue, when we say of the latter that it is, without

qualification, disposed to cast a shadow of a quite specificshape.

Reflection on the foregoing point leads me, indeed, to modify my earlier concession that the statue and the lump of bronze may not differ, at any moment of their coincidence, in respect of what I called their ‘physical’ dispositional properties, such as electricalconductivity and solubility in sulphuric acid. This is true if we con-ceive of the statue as being something that is essentially composedof bronze. But if we allow that this very statue could come to becomposed of material particles of some other chemical nature,such as particles of stone or of gold, then we shall have to deny that the statue is, without qualification, disposed to conduct elec-tricity or to dissolve in sulphuric acid. Instead, we shall only beable to say that, so long as it remains composed of bronze , the statue will conduct an electrical current that is applied to it or will dis-solve in sulphuric acid in which it is immersed. In contrast, wecan say of the lump of bronze, without qualification , that it willbehave in these ways in the circumstances in question, becausethere can be no circumstances in which this very lump of bronzecan exist and yet fail to be composed of particles of bronze.

I have taken considerable pains to defend the view that twonumerically distinct persisting objects can coincide because,although it may superficially seem peculiar, any alternative view

seems to have still more peculiar consequences. Perhaps the view seems peculiar, in part, because it may be confused with another,much less easily defensible view – namely, that two numerically distinct persisting objects of exactly the same kind can coincide. Theidea that two statues , or two lumps of bronze , could exist in exactly the same place at the same time, seems very strange indeed –although, remarkably, some accounts of objects and their persist-ence require us to say precisely this.16 The view that I have

defended restricts cases of spatiotemporal coincidence betweenpersisting objects to ones in which the objects in question possessdifferent persistence-conditions and are consequently objects of quite different kinds. If one were to ask an ordinary member of



16 See, for example, Christopher Hughes, ‘Same-Kind Coincidence and the Ship of Theseus’, Mind 106 (1997), pp. 53–67. My sympathies lie, then, with the position of DavidS. Oderberg, ‘Coincidence under a Sortal’, Philosophical Review 105 (1996), pp. 145–71.



the public whether or not two different objects could exist in thesame place at the same time, one might well receive an emphatic‘No’ for an answer – but that, I think, is only because the respon-

dent would not have in mind the kind of case that we have beendiscussing. This point also helps to explain the spurious appealof the objection, sometimes raised against the view that a statueand the lump of bronze composing it are two distinct but exactly coinciding objects, that, since each of these objects weighs, let ussay, fifty pounds, their combined weight ought to be doublethat amount, one hundred pounds – which it plainly isn’t.17

Clearly, two distinct lumps of bronze , each weighing fifty pounds, would have a combined weight of one hundred pounds, becausetheir combined weight is the sum of the weights of all of thebronze particles composing one or the other lump – and the twolumps are composed by entirely different particles. But the statueand the lump of bronze are composed by exactly the same parti-cles, so that although their combined weight is again the sum of the weights of all of the bronze particles composing one or the

other of them, this is just the same as the weight of the lump of bronze.If we accept that the statue and the lump of bronze are two

numerically distinct objects even when they coincide, a questionstill remains concerning their relationship to one another whenthey coincide: if that relationship is not one of identity, what thenis it? A standard answer would be to say that the relationship isone of ‘constitution’: the lump of bronze constitutes the statue

during the period of their coincidence.18 Constitution is under-stood to be an asymmetrical relation: that is to say, if a constitutesb , then b does not constitute a . The statue, for instance, doesnot constitute the lump of bronze. But how do we decide whichconstitutes which? That question can perhaps only be answeredsatisfactorily by providing an analysis or definition of the consti-tution relation, which is no easy matter. I shall not attempt tosettle finally upon such an analysis here, though I do want tomention one quite promising proposal. The proposal assumes,as seems reasonable, that the relation of constitution only ever

156 E. J. LOWE


17 See, for example, Zimmerman, ‘Theories of Masses and Problems of Constitution’,pp. 87ff. More recently, Zimmerman has come to doubt the force of the objection: see his‘Criteria of Identity and the “Identity Mystics”’, Erkenntnis 48 (1998), pp. 281–301, espe-cially pp. 293–4.

18

See David Wiggins, Sameness and Substance , pp. 30ff.



obtains between persisting objects which are composite objects,as are the statue and the lump of bronze. And the proposal isthis: that one composite object, a , constitutes another composite

object, b , at a time t just in case a and b exactly coincide at t andevery component part of a at t is a component part of b at t , but not every component part of b at t is a component part of a at t .This definition has the desirable feature of implying that consti-tution is an asymmetrical relation. But it may be wondered how it is satisfied in the case, say, of the statue and the lump of bronze.The answer is that while it is plausible to say that every compo-nent part of the lump of bronze is a component part of the statue– for example, each particle of bronze is – it is also plausible tosay that there are certain parts of the statue which are not com-ponent parts of the lump of bronze. I am thinking of such partsof the statue as its head, arms, legs and so forth. Each of theseparts of the statue, it seems right to say, is constituted by a part of the lump of bronze, but is not identical with that part of the lumpof bronze, for the same reason that the statue itself is not identi-cal with the lump of bronze as a whole – namely, because a part of the statue such as its head has different persistence-conditionsfrom those of the part of the lump of bronze which exactly coin-cides with that part of the statue. This helps to explain why it def-initely seems wrong to say that the head of the statue is a part of the lump of bronze as a whole.19 However, a full defence of thisproposal would require much more discussion, so I offer it heremerely as an illustration of how one might attempt to analyse the

relation of constitution.

20

Our discussion of spatiotemporal coincidence would not becomplete without consideration of another kind of case whichthreatens to be, in some ways, even more troubling that that of the statue and the lump of bronze. I have in mind the notoriousproblem of Tibbles, the accident-prone cat.21 Tibbles, like any normal cat, has a tail, which we can call, quite simply, ‘Tail’. Tail



19 See further my ‘In Defence of the Simplicity Argument’ and my ‘Identity, Composi-tion, and the Simplicity of the Self’.

20 Judith Jarvis Thomson offers a different and much more complicated definition of the constitution relation in her ‘The Statue and the Clay’, Nous 32 (1998), pp. 149–73: seepp. 155ff. However, she makes it part of her definition – quite implausibly and unneces-sarily, to my mind – that if x constitutes y at t , then x is part of y at t and y is part of x at t .

21 For earlier discussions of this and similar problems, see Harold W. Noonan, Objects and Identity (The Hague: Martinus Nijhoff, 1980), pp. 22ff, my Kinds of Being , pp. 84ff, andMichael B. Burke, ‘Dion and Theon: An Essentialist Solution to an Ancient Puzzle’, Journal of Philosophy 91 (1994), pp. 129–39.



is clearly a component part of Tibbles. But now consider the rest of Tibbles – the whole of Tibbles apart from Tail – and let us callthis ‘Tib’. Whether there really is any such object as Tib is a debat-

able matter, as we shall see, but for the time being let us assumethat there is.22 Then Tib would also appear to be a component part of Tibbles. Clearly, Tibbles and Tib are not identical with oneanother, for Tibbles has Tail as a part whereas Tib does not.However, cats can survive the loss of their tails. So suppose that Tibbles loses Tail, perhaps in an accident. Since Tail was no part of Tib, the loss of Tail can apparently have no bearing on the exis-

tence or non-existence of Tib. So when Tibbles loses Tail, it seemsthat Tib must still exist. If so, however, then it is now the case that Tibbles and Tib exactly coincide with one another. And the ques-tion is: how is it possible for them exactly to coincide and yet toremain numerically distinct from one another?

One’s initial thought might be that this is not really any dif-ferent from the case of the statue and the lump of bronze: we cansay that, after the loss of Tail, Tib constitutes Tibbles – and consti-

tution is not identity. However, it is not clear that such an answeris in fact available to us in this case, because it is not clear that Tib and Tibbles are objects of different kinds, in the sense of pos-sessing different persistence-conditions from one another. Tib isnot like the lump of bronze in being something which cannot undergo a change of its material composition. Nor does it appearthat we can plausibly say, after the loss of Tail, that Tibbles hasany component part which is not also a component part of Tib,

as well as vice versa. So the definition of the constitution relationthat I offered a moment ago would not seem to permit us to say that Tib constitutes Tibbles after the loss of Tail.

As usual, several other solutions to this problem, of varyingplausibility, can be suggested. A proponent of the doctrine of tem-poral parts can say that, after the loss of Tail, Tibbles and Tib haveall their temporal parts in common, so that they are ‘four-dimen-sional’ objects which exactly coincide with one another after, but not before, a certain moment of time. Another possibility is to say that Tib does, after all, cease to exist when Tail is lost.23 Yet

158 E. J. LOWE


22 For doubts about the existence of objects such as Tib, see Peter van Inwagen, ‘TheDoctrine of Arbitrary Undetached Parts’, Pacific Philosophical Quarterly 62 (1981),pp. 123–37.

23 This is Burke’s solution in his ‘Dion and Theon: An Essentialist Solution to an Ancient Puzzle’.



another possibility is to say that no such object as Tib ever existed– and perhaps no such object as Tail, either.24 But any putativesolution to the problem should take into account its full ramifi-

cations. If a solution defends the view that, after the loss of Tail,Tib and Tibbles are two numerically distinct objects which exactly coincide with one another, then it must also defend the possibil-ity of there being any number of such exactly coinciding objects.This is because we can easily imagine a succession of losses of partsof a cat, each one of which would generate an addition to thenumber of exactly coinciding objects. For instance, after the lossof Tail, Tibbles and Tib might suffer the loss of Ear, so that now three objects exactly coincide – Tibbles, Tib and the part of Tiband Tibbles that did not include Ear.

I think there may be something to be said for the suggestionthat Tib does exist prior to the loss of Tail, but ceases to exist thereafter. But this will require us to say that Tib does not, afterall, have the same sort of persistence-conditions as Tibbles the cat does. However, once we do say that, then it perhaps becomesmore questionable whether we should admit the existence of Tibat all. Tib’s existence would be awkward to deny if that commit-ted us to denying also the existence of Tail, because it is an articleof common sense that cats have tails amongst their component parts. However, it may well be possible to deny that the existenceof Tib and that of Tail stand or fall together. Tail certainly has aclaim to being a genuine component part of Tibbles – that is, tobeing something which helps to compose Tibbles because it is

identifiable independently of Tibbles and, indeed, could con-tinue to exist even if Tibbles were to cease to exist. (Recall heremy characterisation of ‘component parts’ in these terms at thebeginning of the paper.) But it is very doubtful that the same canbe said for the putative object Tib. For Tib was only introducedto us as ‘the rest of Tibbles apart from Tail’ – that is, as the ‘dif-ference’ between two other objects, Tibbles and Tail. It is not clear, then, that we are provided with any way of identifying the

putative object Tib independently of Tibbles and Tail – and sonot clear that Tib, even if it exists, could qualify as a genuine com-ponent part of Tibbles. (Certainly, it is hard to see how Tib couldcontinue to exist even if Tibbles were to cease to exist, in the way that Tail plainly could.) But once we deny Tib this role, it becomes



24 This is van Inwagen’s solution in his ‘The Doctrine of Arbitrary Undetached Parts’.



questionable why we should acknowledge Tib’s existence at all. And if we deny Tib’s existence, of course, there is no question of Tib exactly coinciding with Tibbles after the loss of Tail: the

problem is dissolved.25

Department of Philosophy University of Durham

Durham DH1 3HN UK

160 E. J. LOWE

25 I am grateful for comments received when this paper was presented at the Sympo-sium on Current Issues in Ontology , held at the University of North Carolina at Greensboro,March 31–April 2, 2000, directed by Joshua Hoffman and Gary S. Rosenkrantz. I would

especially like to thank the directors and the commentator on my paper, David Robb.

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