Do Physical Objects Possess Temporal Parts?

president_baracl_obama_changeThe problem of qualitative change is how an object that has a particular property at one time can be numerically identical with an object that does not have that property at a different time without violating the principle of the indiscernability of identicals.[1] (This is distinct from the problem of mereological change: can object that has particular parts at one time be likewise identical with different parts at a different time?) There would be a very significant philosophical conclusion should we be unable to solve this, namely that we cannot make literally correct statements of the form ‘the banana changed from green to yellow’. Of course it is a very open possibility that all such statements are indeed false and that their efficacy is just that of a convenient shorthand where the fiction of persisting entities is used to make sense of a world whose constituents are in constant flux.[2]

The question of whether objects have temporal parts is not one that can be answered with any credibility here, since there are so many open metaphysical questions prior to it that must inform and shape our approach. An analysis of change depends, not only on one’s theories of identity and individuation, but also on “one’s theory of objects, one’s theory of time and one’s theory of properties.”[3] The aim of this essay therefore is merely to describe some of the considerations against temporal parts theory as a solution to the problem of change. It shall be claimed that while objects could consist of temporal parts, by its very nature that theory cannot explain the phenomena of qualitative change.

Pedurantism is based upon a four-dimensional object ontology, the fourth dimension being time. It holds thatfour-dimensional objects are bounded in four dimensions just as three-dimensional objects are bounded in three dimensions. In order to be extended along the fourth dimension such objects cannot be wholly present in a single moment.[4] It also holds that four-dimensional objects may be divided into temporal parts,just as three-dimensional objects may be divided into spatial parts.

So for Perdurantism all objects are in fact scattered objects. An object’s persistence is the continuation of its series of ‘time-slices’ across the temporal dimension, and it is these parts that are thepossessors of properties, rather than objects as wholes. Two consequences of this are first, that the theory depends upon a rough analogy between space and time in order to make sense of the idea of temporal parts. And second, that Perdurantism stands opposed to endurance theories of persistence. This is because Endurantism has a three-dimensional object ontology whereby persisting objects are wholly-present at every moment of time that they exist, and it is such wholes that are the possessors of properties. So while the endurantist can say that the champagne glass exists in at 2012 just as it existed at 2011, the perdurantist must describe the parts of the glass in a time indexed way- the glass exists from 2011 to 2012.[5]

The first question for Perdurantism then, is why would we think that there are temporally-scattered objects? There are theories that can support the existence of temporal parts, such as relativity in physics and determinism in metaphysics- and of course the B theory of time.[6] But there is no decisive reason for believing they exist, nor do the theories we have make them make them an adequate explanation of change. What then is the supposed advantage of this counter-intuitive theory? According to Mark Heller, Perdurantism solves the problem of change because the parts that possess contradictory properties are numerically distinct and therefore the principle of the indiscernability of identicals remains intact. But to argue in this way is merely to assume that objects over time are numerically distinct parts, when we could equally assume that they are identical and that we are using the principle incorrectly.[7] Indeed, as David Oderberg points out, the principle was always meant to refer to a number of entities at the same time.[8]

The second issue is how we are to understand the notion of a temporal part, seeing as no-one could directly experience one. Here Perdurantism faces a dilemma because it cannot stretch the analogy with spatial parts too far, but as it loosens it we lose what grasp we have on the notion. If the relationship between temporal parts and four-dimensional objects is the same as that between spatial parts and three-dimensional objects, then the theory faces the problem that its parts are only defined in terms of the objects they belong to, which is again to assume that, rather than to explain how, objects persist over time.[9]

Yet Heller himself admits that there are significant disanalogies between space and time, the most important of which is that time has a single direction.[10] Passing ‘through’ time is only ever the process of what was future becoming what is past. We have no experience of anything else, nor any explanation of why phenomena present themselves to us this way if the tensed aspect is illusory. If we as persons are four-dimensional worm-like objects why did we not develop in such a way as to perceive all of our spatial states ‘at once’ like the Tralfamadorians of Kurt Vonnegut’s novel Slaughterhouse-Five? For four-dimensionalism to be plausible, there should at least be a hypothesis enjoined to it that makes sense of these problems. All of this only detracts from our understanding of what temporal parts are; the notion therefore appears vague and contrived.

Another substantial issue is that Perdurantism’s ‘solution’ to the problem of change is in effect to insist that the problem is insolvable (of course this is a completely respectable response, so long as it is not misrepresented as a solution). On this understanding, because it is the parts and not the objects that possess intrinsic properties, qualitative change only ever takes place in a derivative, illusory sense.[11]

Related to this is the issue that Perdurantism may rest upon a category mistake. For the perdurantist all objects are ‘changing’ all of the time, whether or not their properties are. This means that objects are involved in events throughout their existence. Indeed it seems to say that objects are just events, which is extensionally equivalent with the view of process philosophers that our concept of substance (i.e. some thing which persists) is derivative of that of process/event. But as Brian Lombard points out, this cannot be true if “the very idea of an event is the idea of a change in some physical object.”[12] Jonathan Lowe calls this the category “mistake of treating persisting objects as if they were processes.”[13] Even so, process philosophy is a very underdeveloped research area and might not prove to be such a mistake after all. But until such time as a more coherent formulation of the doctrine can be given, or that we have a much better case for a four-dimensional ontology, the theory will remain too counter-intuitive to be accepted.

Oderberg claims that Perdurantism is not a theory of change but a theory of replacement of one thing by another, different thing.[14] He explains this is with the following illustration. For the perdurantist a four-dimensional worm-like object can be green at the far end and red at the near end (presumably this is the ‘textbook example’ of the ripening tomato). But there is no change from green to red since the respective sections of the worm are static and always retain those colour properties. Remaining partially green and partially red can hardly be equated with change, since nothing was wholly green nor is anything now wholly red.[15] This is because change is an inherently dynamic concept. As we saw above, time is very different from space in that it manifests such dynamism. The primary form of such dynamism is the motion that we experience in us and all around us. All qualitative change that we experience takes place through the vehicle of motion. And the processes of motion, by definition requires not only a spatial field but also the dynamics of temporality which temporal parts cannot possess.[16]

Another related dilemma for Perdurantism concerns the size of the most fundamental temporal parts. Katherine Hawley raises the common-sense objection, how“can instantaneous stages instantiate the properties and satisfy the predicates we associate with ordinary objects?”[17] Moreover, how such entities, given that they have zero duration, be sorts of things that could enter into relations with one another?Heller agrees with David Lewis that temporal parts each have a temporal duration. They abruptly begin to exist and cease to exist. Because they are so transient they cannot ‘do’ all of the things that people can do -far from it- any macroscopic event at all has to be composed of many stages.[18] But if the stages are not ultimately instantaneous but have a certain duration, how is it that time can pass within them? Since, as we have just seen, the passing of time is something essentially non-spatial which happens to spatial things, how can the endurantist understand time passing within temporal parts, modelled as they are upon spatial parts? Here we have the decisive point against Perdurantism: that the parts themselves cannot be capable of change, or else they would be subject to the same problem that is allegedly solved by their existence, which leads into a vicious regress.[19]

Having now dismissed Perdurantism, an alternative account should be proposed (only a brief sketch of which can be given here). Although this account is based on a three-dimensional object ontology, it is not endurantist because it shares with Perdurantism the denial that objects change with respect to their intrinsic properties. Rather than being a solution to the problem of change it is an alternative dissolution- in a broadly Wittgensteinian sense. This approach comes from Michael Jubien who recognises, as Hawley does, that “the root cause of these problems is the inflexible nature of the identity relation… it is the insistence on identity between objects wholly present at different times which gives rise to the problem of change”.[20] The account does not deny that objects are wholly present at different times. Instead it denies that the relation that holds between them before and after a change is one of numerical identity.

The only reason we call an object which undergoes a change the same object is that the majority of its original features remain unchanged. So shouldn’t we be more concerned with the persistence of particular properties rather than with objects? We are misled by our everyday reference to ‘the’ object at t1 and ‘the’ object at t2 into thinking that they are strictly identical, but there ultimately is not an adequate philosophical explanation for how that can be. When we perceive qualitative change the object at t1 and at t2 are two different objects- its identity does not survive the change, but they still have features in common. In addition, new properties are instantiated only as the old object ceases to be and a new object comes into existence. According to Jubien, the relation that holds between the two such objects is one of ‘relevant similarity’ rather than identity. For Jubien, there is a particular form of this relation for what we ordinarily term ‘persisting objects’ (but aren’t really), namely the ‘same-o-as’ relation (where ‘o‘ is the type of object).[21]

Although objects typically persist through time, nothing actually endures a change in its intrinsic properties. Although we are not able to identify matter when it is independent of form, we have no reason to suppose that the constituent matter of the object at t1 is destroyed and/or replaced with new matter in the object at t2. So the matter probably survives qualitative change in a loose sense, and the new object usually instantiates some of the same properties as before (some properties will be essential to the object’s identity as an object of a particular type).

To sum up, we have identified numerous problems with Perdurantism, only one of which is shared by my interpretation of Jubien’s account, namely that its ‘solution’ to the problem of change is in effect to insist that the problem is insolvable– an object does not retain its identity through qualitative change. The problems with Perdurantism include the following: attempting to use it as a theory to explain qualitative change leads into a vicious regress (there would have to be temporal parts of temporal parts ad infinitum); the notion of temporal parts is overly vague and contrived; it is extensionally equivalent with the (probably) incoherent doctrine of process philosophy; it is unlikely anything of brief enough duration to function as a temporal part could instantiate the necessary properties or bear the necessary relations; and there aren’t even any good arguments for believing that objects could be divided up into temporal parts. Given that Jubien’s account has at least as much explanatory scope and power as Perdurantism, and that the latter has all these additional problems, on standard philosophical grounds the former theory is to be preferred. In conclusion therefore, at least insofar as the problem of change, we have no reason to believe that material objects possess temporal parts. Whether such entities will be more decisively suggested by the progress of science and by research on process theories remains open for the philosophers of the future.


Hawley, Katherine, [2002], ‘Selections from How Things Persist‘, In: Haslanger, S. & Kurtz, R. M. (eds.), Persistence: Contemporary Readings, (2006), Cambridge (MA), Bradford Books, pp. 119-33

Heller, Mark, [1990], ‘Temporal Parts of Four-Dimensional Objects’, From The Ontology of Physical Objects, Cambridge University Press, Ch. 1; Reprinted in: Metaphysics: An Anthology, (1999), Kim, Jaegwon, & Sosa, Ernest (eds.), Oxford, Blackwell, pp. 312-26

Jubien, Michael, (1997), Contemporary Metaphysics, Oxford, Blackwell

Lowe, E. J., (2002), A Survey of Metaphysics, Oxford, Oxford University Press

Kim, Jaegwon, & Sosa, Ernest (eds.), (1991), The Blackwell Companion To Metaphysics, Oxford, Blackwell

Oderberg, David, S. (2004), ‘Temporal Parts and the Possibility of Change’, Philosophy and Phenomenological Research, 69, (3), pp. 686-708


[1] Lowe, (2002), p. 41; the principle that for two things to be identical they must be alike in all their properties.

[2] This is the general position taken in the tradition of Process Philosophy, of which the most notable representatives are Heraclitus and Whitehead.

[3] Smith, Quentin, ‘Change’, In: Kim & Sosa, (1991), p. 84

[4] Heller, [1990], p. 314; cf. Lowe, (2002), p. 49

[5] Heller, [1990], p. 314, p. 314

[6] The B theory of time states that tensed statements cannot be true because time does not ‘flow’. It is often said this is supported by the theory of relativity because that involves conceiving of time as a static, extra dimension of space.

[7] Oderberg, (2004), p.690; cf. Lowe, (2002), p. 42

[8] Oderberg, (2004), p.691

[9] Lowe, (2002), p. 54

[10] Heller, [1990], p. 314

[11] Lowe, (2002), p. 46

[12]Lombard, L. B., ‘Event Theory’, In: Kim & Sosa (eds.), (1991), p. 142

[13] Lowe, (2002), pp. 52-3

[14] Oderberg, (2004), p. 702

[15] Oderberg, (2004),p. 706

[16] Oderberg, (2004), pp.707-8

[17] Hawley, [2002], p. 124

[18] Heller, [1990], p. 312

[19] Lowe, (2002), pp. 46 & 52

[20] Hawley, [2002], pp. 120-1

[21] Jubien, (1997), p. 74

Identity and Change


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