1 Parsons, J. ‘Must a Four Dimensionalist Believe in Temporal Parts?’ The Monist 83 (2000) 399–418.CrossRefGoogle Scholar

2 I use ‘endurantism’ as synonymous with ‘three-dimensionalism.’

3 Thus x is an instantaneous maximal temporal part of y at instant t=df 1) x is part of y and 2) x exists at, but only at t and 3) x overlaps every part of y that exists at t. An extended maximal temporal part of y during temporal interval T is an object that exists at all and only times in T, is part of y at every time during T and at every moment in T overlaps everything that is part of y at that moment.

4 Sider, T. Four-Dimensionalism: An Ontology of Persistence and Time (Oxford University Press 2001), 65–8.Google Scholar Merricks, T. ‘Persistence, Parts and Presentism,’ Nous 33 (1999) 421–38;CrossRefGoogle Scholar M. Hinchliff, ‘The Puzzle of Change,’ Philosophical Perspectives 10, Metaphysics (1996) 119-33; Markosian, N. ‘The 3D/4D Controversy and Non-Present Objects,’ Philosophical Papers 23 (1994) 243–9.CrossRefGoogle Scholar

5 Inwagen, P. van ‘Four-Dimensional Objects,’ Nous 24 (1990) 245–55;CrossRefGoogle Scholar Haslanger, S. ‘Endurance and Temporary Intrinsics,’ Analysis 49 (1989) 119–25;CrossRefGoogle Scholar Johnston, M. ‘Is There a Problem about Persistence?’ The Aristotelian Society Supp 61 (1987) 107–35.CrossRefGoogle Scholar

6 Persisting objects A and B temporally overlap just in case there is some time t, such that at t, A and B materially coincide. Then for the perdurantist, A and B temporally overlap just if either A is a maximal temporal part of B, or B is a maximal temporal part of A.

7 M. Hinchliff, ‘The Puzzle of Change.’ Philosophical Perspectives 10, Metaphysics (1996) 119-133.

8 Perdurantists might think that they are identical to such regions, but set that aside for now.

9 Where an object O wholly occupies a region R just in case every part of O occupies a region of R, and no proper part of O occupies any region that is not a sub-region of R.

10 Parsons, J. ‘Must a Four Dimensionalist Believe in Temporal Parts?’ The Monist 83 (2000) 399–418.CrossRefGoogle Scholar

11 One might think there are four ways of persisting — counting the stage-view as a fourth alternative. Whether this amounts to a distinct way of persisting, i.e. by having temporal counterparts, or whether it amounts to a different semantics for four-dimensionalism is debatable.

12 I have elsewhere defended an account of non-mereological universalism that explicates this latter claim. See Miller, K. ‘Non-Mereological Universalism,’ European Journal of Philosophy 14 (2006) 427–45.CrossRefGoogle Scholar

13 There is no instant t that is in both T₁ and T₂.

14 Or, in a world where space-time is discrete, that a persisting object exists during each smallest interval, in virtue of some maximal part existing at that interval.

15 Then y is a fusion of the xs iff every one of the xs is a part of y, and no part of y fails to overlap at least one of the xs.

16 In fact, that outcome seems largely independent of whether we endorse universalism or a more restricted composition. Plausibly, whatever restrictions we place on composition will be consistent with there existing fusions of the xs at t where the xs at t all overlap a single persisting object at t.

17 Notice that as defined, these objects do not perdure, but so far, all we have said is consistent with them being three-dimensional objects: for these fusions could be strictly identical across time despite the fact that their parts are not.

18 I assume that a persisting fusion exists at a time just as long as it least one its parts exists at that time.

19 Where to spatially coincide is not simply to exist within the same spatial boundary, but to exist at all and only the same spatial points. Notice that we cannot define compilation in terms of material coincidence at a time on pain of circularity, since that is in turn defined in terms of parthood at a time.

20 Actually this is not quite right. Even if we set aside worries about deviant causal chains, if it turns out that P and P* have some sort of charge, then it might be the case that had P not existed at the relevant time and location, then although P* would still have existed, it would have existed at a slightly different location. In fact, this might even be nomologically necessary. Then there is no robust sense in which had P not existed at L at t, then P* would still have existed at L at t. Then to capture the sense in which P and P* are independent, we could say something like the following: P and P* are independent and distinct just if there is some world that is identical to our world up to time t, such that when at t, God makes it the case that P does not exist, it is still the case that P* exists at t at L. The idea here is just that at t, God could make it the case that P does not exist, yet P* would still exist at the same location. I thank David Braddon-Mitchell for this suggestion.

21 Notice that clause (iii) is required in order to prevent its being the case that, for instance, fusion xy compiles at t₂ some non-fusion O₂ that has spatial part x as an improper part at t₂.

22 For a defense of something like this position see K. Miller, ‘Thing and Object’ Acta Analytica (forthcoming). One might worry that if enough ‘contextual’ or ‘conventional’ sorts of features are included in the definition of a non-fusion, this might lead us to eliminativism about ordinary objects. The idea, perhaps, is that ordinary objects only really exist if their properties are independent of our conventions. It seems to me that this is a controversial claim about what is required to vindicate realism, and certainly not one that a realist must endorse. Something might count as a work of art only if certain artistic conventions hold. So the existence of a work of art might in part supervene on the existence of these conventions. But, as I see it, conventions are perfectly real thing themselves — they supervene on the behaviours of persons and institutions over time — they are not, in most cases, mere decisions of fiat. So it is not clear why having conventions in this sense in the supervenience base for the existence of objects ought to lead us to be eliminativists about those objects. Of course, I cannot argue for this here, and since for the remainder of the paper I do not include such features in the definition of a non-fusion, we can set the issue aside. After all, this worry is really orthogonal to whether terdurantism is true.

23 One might be tempted to say something else. Namely, that the appearance of strong part loss is just that, mere appearance. Perdurantists might seem to be making that claim. After all, perduring objects are mereological fusions of temporal parts, and hence, do not strongly lose any parts. But some perduring objects are ordinary objects. So if the perdurantist can have ordinary objects without strong part loss, maybe the terdurantist can too. In that case, the terdurantist might not need nonfusions in her ontology.

But this will not work. Why does it seem as though ordinary objects strongly lose parts if perdurantism is true? Well, consider a perduring object O that exists at t₁ and t₂. It is the fusion of temporal parts O-at-t₁ and O-at-t₂. It never gains or loses these parts: it has them both tenselessly. O-at-t₁ has spatial parts: P₁ and P₂. O-at-t₂ has spatial parts P₂ and P₃. O-at-t₁ never loses any spatial part, and neither does Oat-t₂ (obviously, since they have no duration in which to lose anything). But there is some sense in which O does lose a part, namely P₁. And this is not a mere ‘seeming.’ Suppose P₁ persists. The temporal part of P₁ that is part of O-at-t₁ does, not exist at t₂. This is why, strictly speaking, O does not lose a part: because there is no wholly present object that exists at t₁ and is part of O at t₁, and which exists at t₂ and is not part of O at t₂.

But when we say that O loses a part we can plausibly be held to be making the following claim. If perduring object O has perduring object P₁ as a (spatial) part at some time (and hence O-at-t has P₁-at-t as a part simpliciter), then O counts as strongly losing P₁ if P₁ exists at a time other than t₁ in virtue of a t_n part existing at tn, such that the t_n part of P₁ is not a part of any temporal part of O. The point is just that ordinary talk about part loss has to be reconstrued as talk about perduring parts. Once understood that way, then perduring objects are such that at one time some perduring object is part of them, and at another time that perduring object is not part of them. This is what makes ordinary talk about part loss true.

Now, more to the point, the terdurantist cannot tell any such story. To put it another way, because the perdurantist has access to instantaneous or short-lived temporal parts, for any ordinary object I describe, such that I claim that that object has different parts at different times, the perdurantist can ‘construct’ a perduring object that has just those parts at just those times, by being composed of the relevant temporal parts at those times. If I say that O has P at t₁ and loses P at t₂, then the perdurantist will say that O is a fusion of parts that includes P-at-t₁, and does not include P-at-t₂. But the terdurantist does not have the apparatus to do this. If P is a non-perduring object, then any fusion that includes P will always include P, so there is no sense at all in which a fusion can lose P. Whereas if P is a perduring object, then a fusion can include P-at-t₁, but not P-at-t₂ and hence the perdurantist can make sense of an object like O, whereas the terdurantist cannot. At least, she cannot if O is supposed to be a fusion.

24 There are two rather distinct worries here. One is that fusions turn out to be more ontologically basic than objects rather than the other way around, and the other is that the fusions there are, are very unlike any of our ordinary objects. I think it is the combination of these two claims that is unattractive. While it is no part of perdurantism that fusions are ontologically more basic than objects, some perdurantists do hold this additional thesis. This perdurantist thesis about the direction of fundamentality is that parts are more fundamental than wholes, and hence that temporal parts are more fundamental that persisting objects. This is a rather different claim to the claim the terdurantist makes about the direction of fundamentality, which is that fusions, one kind of object, are more basic than nonfusions, a different kind of object that supervenes on the former. But one might think that the terdurantist is no worse off in making her claim about the direction of fundamentality than is the perdurantist in making her somewhat different claim. I think the force of the objection, though, lies first in the fact that the perdurantist claim about fundamentality is purely optional, whereas the terdurantist claim about fundamentality is not, and second, that even for perdurantists who accept the fundamentality claim, at least some of the parts they take to be fundamental are pretty ordinary. If mereological universalism is true, then some fusions are odd, and there's no getting around that. But temporal parts of ordinary objects are pretty ordinary — they are things that look just like ordinary objects at a time. This is not the case for the terdurantist: she has nothing in her fundamental ontology of fusions that looks like an ordinary object. All fusions turn out to be odd, gerrymandered or scattered entities, and only non-fusions are like ordinary objects. Perhaps it is controversial the extent to which this is a cost of terdurantism, but certainly there are very real differences between terdurantism and perdurantism to be found here.

25 I use scare quotes here to remind the reader that a slice is not an instantaneous temporal part of a persisting object.

26 One helpful referee has pointed out that what at the beginning of the paper I called ‘weak’ terdurantism is consistent with being able to reduce the instantiation of properties of a non-fusion at a time, to the properties simpliciter of the fusion that compiles it at that time. Weak terdurantism does not guarantee that one can do this, since all weak terdurantism allows is that there might exist shorter-lived objects that wholly coincide with terduring fusions at times, but are not parts of those fusions. It does not guarantee that this is the case, nor certainly guarantee the stronger claim for every temporal interval and instant at which a fusion F exists, there is some fusion F* that exists during, or at, just that time and coincides with F at or during those times. A weak terdurantism with ‘insufficient’ coinciding fusions would still have problems because there might not be a coinciding object that exists at the relevant time or during the relevant interval, that has the relevant property simpliciter. So while weak terdurantism might have some advantages here, I have focused exclusively on strong terdurantism throughout because weak terdurantism is generally unattractive, at least as an alternative to perdurantism, insofar as it allows that there exists entities that are very much like temporal parts, albeit that they are not parts of persisting objects but are merely entities that coincide with those objects at times.

27 This terminology is from Lewis, D. On The Plurality of Worlds (Oxford: Blackwell 1986), n. 55Google Scholar, on 76.

28 I use the locution of objects ‘existing at regions’ as neutral terminology between objects being identical to the regions at which they exist, and occupying the regions at which they exist.

29 Simons, P. ‘Extended Simples: A Third Way Between Atoms and Gunk,’ The Monist 87 (2004) 371–85.CrossRefGoogle Scholar Simons’ GCP is phrased slightly differently, in terms of objecting having parts corresponding to the parts of the region the object occupies. I prefer this version, since it is neutral between monism and dualism.

30 This is not to say that they must agree that there is exact synchronic mirroring. Those who reject the doctrine of undetached arbitrary parts with respect to objects but not regions will deny that the mirroring is exact. Those who hold that simples are not only four-dimensionally extended, but extended in space as well will also deny that the mirroring is exact.

31 There is a difference here between an atomistic terdurantism and a gunk terdurantism. The former can accept that there is an exact synchronic mirroring, while the latter cannot. But all terdurantists deny that there is exact diachronic mirroring. Gunk terdurantists deny that there is diachronic mirroring, because they hold that some of the occupied sub-regions of any four-dimensional stream of gunk are not parts of that gunk, though they are, presumably, parts of the region that the gunk occupies. Atomistic terdurantists deny that there is diachronic mirroring, because they hold that for any extended simple S, there are sub-regions occupied by that simple that are not parts of the simple, though those sub-regions are parts of the region occupied by the simple.

32 Sider, for instance, rejects it on the grounds that an appeal to counterpart theory and contingent identity allow us to say that though the very same things are picked out by the designation ‘object’ as by ‘space-time region’, nevertheless each of these designations have attached to them different sets of counterpart relation — regionrelations and object-relations — such that not all of the region-counterparts are also object-counterparts and vice versa, thus explaining why objects and regions have different modal properties despite being identical. T. Sider, Four-Dimensionalism, 110-13.

33 P. Simons, ‘Extended Simples,’ 371-85; P. Van, Inwagen ‘The Doctrine of Arbitrary Undetached Parts,’ Pacific Philosophical Quarterly 62 (1981) 123–37;Google Scholar Markosian, N. ‘Simples, Stuff and Simple People,’ The Monist 87 (2004) 405–21.CrossRefGoogle Scholar In the case of Simons and Markosian, this is at least in part motivated by a particular view about extended simples.