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BLOCKING THE PATH FROM VAGUENESS TO

FOUR DIMENSIONALISM*

Kristie Miller

AbstractThere is a general form of an argument which I call the argumentfrom vagueness which attempts to show that objects persist by per-during, via the claim that vagueness is never ontological in nature

and thus that composition is unrestricted. I argue that even if wegrant that vagueness is always the result of semantic indeterminacyrather than ontological vagueness, and thus also grant that com-position is unrestricted, it does not follow that objects persist byperduring. Unrestricted mereological composition lacks the powerto ensure that there exist instantaneous objects that wholly overlappersisting objects at times, and thus lacks the power to ensure thatthere exists anything that could be called a temporal part. Even if we grant that such instantaneous objects exist, however, I argue

that it does not follow that objects perdure. To show this I brieflyoutline a coherent version of three dimensionalism that grants justsuch an assumption. Thus considerations pertaining to the natureof vagueness need not lead us inevitably to accept perdurantism.

1. Introduction

It is now well established that there are two main views about theway objects persist through time: four dimensionalism and threedimensionalism. Four dimensionalism is the view that persistingobjects are the mereological fusion of temporal parts: objectspersist by perduring. Three dimensionalism is the view that per-sisting objects have only spatial extension, and are wholly presentat each moment at which they exist: they endure. In his recentbook, Theodore Sider1 contends that the best argument in favour

of four dimensionalism is what he calls the argument from vague-ness. This argument has two parts: the first part seeks to establish

Blackwell Publishing Ltd. 2005, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350Main Street, Malden, MA 02148, USA.Ratio (new series)XVIII 3 September 2005 00340006

* Thanks to David Braddon-Mitchell and Mark Colyvan for useful discussion of theseissues.

1 Sider, T. (2001). Four-dimensionalism: an ontology of persistence and time. Oxford Uni-versity Press.


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that composition is unrestricted, that is, that any arbitraryarrangement of particulars composes some object. The secondpart seeks to show that if composition is unrestricted, then it

follows that persisting objects are composed of temporal parts,and thus that four dimensionalism is true.In general, the argument from vagueness is resisted by object-

ing to the first part of the argument, usually by denying that com-position can never be vague.2 In this paper though, I want toconcentrate on the less often considered second part of the argu-ment. I argue that even if we accept the first part of the argument,we are not led inevitably to accept four dimensionalism. For it is

perfectly coherent to agree both that vagueness is never onto-logical, and that composition is unrestricted, and nevertheless toembrace three dimensionalism. To show this I will briefly outlinea version of three dimensionalism and show how this view avoidsthe conclusion of the second part of the argument from vague-ness. Consideration of this view allows us more clearly to see thekey points at issue between the three and four dimensionalist, andto clarify just what it is for an object to be composed of temporal

parts. I conclude that even if one adopts the view that composi-tion is unrestricted, this alone provides no reason to prefer fourdimensionalism over three dimensionalism: considerations per-taining to vagueness are strictly orthogonal to the issue of themanner in which objects persist.

2. The argument from vagueness

The first part of the argument from vagueness owes its origins toDavid Lewis.3 Lewis argues that any attempt to restrict composi-tion in a way that is in-keeping with our intuitions about whichobjects exist, must necessarily be a vague restriction. For com-monplace objects all have imprecise temporal and spatial bordersand thus there is no determinate point at which, for instance,some atom A can be said to be part of some object x, or not partof x. But if composition itself is vague, then existence will bevague. It will be vague at exactly which moment an object comes

2 Cf. Koslicki, K. (2003). The crooked path from vagueness to four dimensionalism.Philosophical Studies, 114: 107134.

3 Lewis. D. (1986). On the Plurality of Worlds. New York Blackwell Press. pp. 212213.and Lewis, D. (1991). Parts of Classes. Oxford: Blackwell pp. 8081.


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BLOCKING THE PATH FROM VAGUENESS TO FOUR DIMENSIONALISM 319


into existence, and vague at exactly which moment it ceases toexist: so for every object, there will be some time at which it isindeterminate whether that object exists or not. Since Lewis

thinks that vagueness is never ontological,4

but rather is the resultof semantic indeterminacy,5 he holds that existence cannot be amatter of degree, and thus he concludes that composition cannotbe restricted. Recently, Lewis argument for unrestricted compo-sition has been further refined by Sider.6 Expressed as a reductio,Siders argument is as follows.

Part I: from vagueness to unrestricted composition

1. Assumption: Existence is not vague: composition eitherdefinitely occurs or definitely does not occur.

2. Assumption: Not every arrangement of matter composes anobject.

3. So there must be a continuum of cases such that at one endof the continuum composition occurs, and at the other endcomposition fails to occur.

4. Each of the cases on the continuum is highly similar to theadjacent cases.5. So there is no principled way to draw the line between a case

where composition occurs and a case where compositiondoes not occur.

6. So there are cases where it is indeterminate whether com-position occurs or not.

7. So existence is vague.

As it stands, this argument requires the rejection of either (1)or (2). In general, arguments of this form have been resisted bydisputing the truth of (1).7 Hence Sider has constructed a

4 Lewis, On the Plurality of Worldsp. 212213.5 There is of course a large literature about the issue of whether all vagueness is purely

linguistic in nature or whether vagueness can be ontological. For discussion of these issuessee Evans, G. (1978). Can there be vague objects. Analysis 38: 208, Hyde, D. (1998).Vagueness, Ontology and Supervenience. The Monist81: 297312, Lewis, D. K. (1988).

Vague Identity: Evans Misunderstood. Analysis 48: 128130, Sainsbury, R. M. (1989).What is a Vague Object. Analysis49: 99103 and Tye, M. (1990). Vague Objects. Mind99: 535557.

6 Sider,Four-dimensionalism: an ontology of persistence and timepp. 120140, and Sider, T(2003). Against Vague Existence. Philosophical Studies, 114: 135146

7 See for instance Koslicki, The crooked path from vagueness to four dimensional-ism. Other advocates of the view that composition is not unrestricted, and vagueness isontological include Peter van Inwagen (1990). Material Beings. Cornell University Press.


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number of ancillary arguments that aim to bolster (1) and thuslead to the rejection of (2).8 In this paper, however, I want to focuson the second part of the argument from vagueness, namely that

part that moves from the falsity of (2) to the truth of four dimen-sionalism. Let us turn to this second part of the argument fromvagueness. Here is a reconstruction of Siders argument:9

Part II from unrestricted composition to temporal parts

1. Assumption: Composition is unrestricted.2. So there is a fusion of the members of any arbitrary set S

at time t, where x is a fusion of the members of S at t iffevery member of S is part of x at t, and each part of x at toverlaps at t some member of S.10

3. Objects persist through time, so we need a temporalisedversion of unrestricted composition.

4. An object x is a diachronic fusion of the members of setsS1, S2, and S3 at times t1, t2 and t3 if (i) x is composed of S1at t1, S2 at t2, and S3 at t3 and (ii) x exists only at the times

t1 t2 and t3.

11

5. Since composition is unrestricted, any sets of objects attimes has a diachronic fusion. Following Sider, call thisthesis U: Any arbitrary sets Sis and times tis has a diachronicfusion.12

6. Given U, it follows that for any y at t, there is some instan-taneous object x that (i) is the fusion of the members ofset y at t, and (ii) which exists only at t.

7. y is part of x at t and every part of x at t overlaps y at t (from(i) and the definition of fusion).13

8. With certain mereological principles we can then movefrom the claim that every part of x at t overlaps y at t, tothe claim that x is part of y at t.14

8 Sider, Against Vague Existence.9 This part of the argument can be found both in his book (pp. 134149) and in his

Against Vague Existence. I use the terminology from the latter, which differs slightly fromthat used in the former.

10 Defined by Sider, Against Vague Existence. footnote 2.11 Sider, Against Vague Existence, p. 135.12 Sider, loc cit.13 Sider, op cit p. 136 (x and y are transposed in this paper: Sider uses x to refer to

the set, and y to refer to the fusion of the members of x).14 Sider op cit. See footnote 4, p. 136.


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9. Now consider the definition of an instantaneous temporalpart: x is an instantaneous temporal part of y at instantt= df(a) x is part of y at t (b) x exists at, but only at t and

(c) x overlaps at t everything that is part of y at t.15

10. The diachronic fusion x meets the definition of an instan-taneous temporal part (from 7, 8, 9 and 10).

11. Since all diachronic fusions exist (see 6) it follows thatevery persisting object is composed of these instantaneousobjects.

13. So four dimensionalism is true.

Siders argument then, is that every diachronic fusion exists,

and that these fusions count as temporal parts. If this argumentis successful, then it is surprising, for we might have thought thatthe issue of when composition occurs, and thus which objectsexist, is orthogonal to the question ofhowobjects persist.

3. Mereology and composition

Let us grant part I of the argument and consider only part II. Thefirst thing to notice is (2), the claim that given unrestricted com-position, there will exist the fusion of the members of any arbi-trary set S at time t, where x is a fusion of the members of S at tiff every member of S is part of x at t, and each part of x at t over-laps at t some member of S. Now unrestricted mereological com-position only tells us that given that we have some particulars, wecan fuse those particulars. It does not tell us that there exist any

instantaneous basic particulars that can be fused to compose aninstantaneous object. So it does not tell us that any members ofS are instantaneous. But suppose S has three members, particu-lars P, P1 and P2which persist through T. We cannot assume theseparticulars perdure. But if they endure, their fusion just is anenduring object that persists through T: there exists no instanta-neous object that is the fusion of P, P1 and P2 at t in T, for thereexists no object P-at-t.

Now Sider attempts to bypass this problem by talking (in 2) ofthe fusion of the members of S at t. The problem is that (2) isambiguous between the claim that x is a fusion-at-t ofthe members of S, and that x is a fusion of the members of S-at-t.

15 Sider,Four-dimensionalism: an ontology of persistence and time, p. 60.


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Construed as a fusion-at-t, (2) involves some additional mereo-logical axiom that allows for the fusion-at-a-time of particulars which exist at other times, and it is difficult to see why the

endurantist need accept such an axiom. Construed as a fusion ofthe members of S-at-t, (2) looks like a tricky way of smuggling intemporal parts by the back door. After all, what is S-at-t if not atemporal part?

For the sake of argument however, let us grant what theendurantist almost certainly will not, either that basic particularsare instantaneous and thus that there exists any arbitrary fusionof these particulars, or that there exist instantaneous fusions-at-

times of particulars. Thus we grant that there exists some arbi-trary fusion of the members of S at t. Now let us consider whetherSiders argument establishes that such objects count as temporalparts. The crucial step in Siders argument is premise 8, whichrelies on the mereological principle that licenses the move fromevery part of x at t overlaps y at t to x is part of y at t.

To clarify this step a little, we need to be a little clearer aboutthe move from premise 7 to 8. Siders idea, I take it, is that we

begin with some persisting object y. At some arbitrary time t, y iscomposed of some things. Now consider the set y whose membersare all of those things that compose y at t. The argument is a littleconfusing because Sider uses y to refer both to the persistingobject, and to the set whose members compose y at t. I retain thisterminology because ultimately it allows us to see how the argu-ment goes wrong. So given that composition is unrestricted, wecan fuse all of the members of that y at t, and call this fusion x.Then we conclude that the instantaneous object x, is part of thepersisting object y. We derive premise 7 from the definition offusion, combined with the fact that x is the fusion of the membersof y at t. If x is the fusion of the members of y at t, then we knowthat every member of y at t is part of x at t, and x at t overlaps att some member of y. So 7 should more properly read:

7. Every member of y is part of x at t and every part of x at toverlaps some member of y at t.

Then in premise 8 we move from every part of x at t overlapsy at t to x is part of y at t. This should instead read: every partof x at t overlaps some memberof y at t. And it is not obvious thatx is part of y at t follows from this claim, even if we accept therelevant mereological principle. For presumably the y in x ispart of y at t, refers to the persisting object y at t: for only if x was


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part of this object, could it be said that we have shown four dimen-sionalism to true. Moreover, since no fusion is ever part of a set,(since sets do not have parts, they have members) it could not be

that x is part of y at t, where y at t is a set at a time. In order toshow that x is part of y at t, we need to note that every part of yat t overlaps some member of the set y at t, and every member ofset y at t is part of y at t. It then follows that x is part of y at t.

So has Sider shown that given the truth of unrestricted com-position, it follows that four dimensionalism is true? If we grant(2), he has shown that there exists a plethora of instantaneousobjects that wholly overlap persisting objects at a time, and which

are part of those objects at that time. Isnt that just to say that fourdimensionalism is true? To answer this question we need to con-sider the persisting object y. What is y? If persisting objects arediachronic fusions, then y is a diachronic fusion. Now recall thatan object is a diachronic fusion of the members of sets at times,if it is composed of those sets at those times, and exists only atthose times. What is it to be composed of the members of a set ata time? According to Sider, some object x is composed of the

members of set S at t, iff every member of S is part of x at t, andeach part of x at t overlaps at t, some member of S.16 So x is com-posed of the members of S at t, just if x is the fusion of themembers of S at t. Call the fusion of the members of a set at atime a synchronic fusion. Adiachronicfusion, then, is the fusionof two or more synchronic fusions.

A synchronic fusion is an instantaneous object that has asspatial parts, each of the members of the set that it fuses. Adiachronic fusion is a persisting object composed of the fusionsof members of sets at times. So at each time at which it exists, adiachronic fusion has the spatial parts of the synchronic fusionthat exists at that time. But in addition to these spatial parts, adiachronic fusion has as parts, all of the synchronic fusions of

which it is composed. Diachronic fusions not only have spatialparts, they have synchronic fusions, or instantaneous objects, asparts. So diachronic fusions are the mereological fusion of instan-taneous objects: they are four dimensional objects.

So if y is a diachronic fusion, then it follows that y is a fourdimensional object, and that x is an instantaneous temporal partof y. And if all objects are either synchronic or diachronic fusions,

16 Sider, Against Vague Existence. footnote 2.


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then it follows that four dimensionalism is true. But no threedimensionalist will concede that persisting objects are diachronicfusions, nor need she understand unrestricted composition as the

claim that every synchronic and diachronic fusion exists. For thegeneral claim that any arrangements of matter at any differenttimes composes some persisting object, need not be understoodas the claim that every diachronic fusion exists. For there isnothing in three dimensionalism per sethat prohibits the threedimensionalist from holding that there exists any enduring objectcomposed of arbitrary combinations of things at times. Even ifthe three dimensionalist accepts that there exist instantaneous

objects (fusions-at-times), she need not concede that persistingobjects are the fusions of these objects. She could instead holdthat for every synchronic fusion, there is some enduring object xthat is constituted by those fusions at those times. Call such anobject a diachronic object.

A diachronic object is an enduring object: it is wholly presentwhenever it exists. So too a synchronic fusion is wholly presentwhen it exists. At any time at which any diachronic object exists,

there will be some synchronic fusion that wholly overlaps thatobject at that time. At that time, these two objects are related bythe constitution relation. The constitution relation is the relationthat holds at a time, between any two objects that are materiallycoincident at that time.17 So if x and y are related by constitutionat t, then x is an improper part of y at t, and y is an improper partof x at t.18

Now let us suppose that y is a diachronic object, and consideragain the question of whether or not this object is composedof instantaneous objects. Well if what it is to be composed ofcertain objects is to be the fusion of those objects, then nodiachronic object is composed of instantaneous objects, for nodiachronic object is the mereological fusion of instantaneousobjects. Rather, there exist instantaneous objects, and enduringobjects (diachronic objects) both of which are wholly present whenever they exist, and where these diachronic objects are ateach time at which they exist, constituted by some instantaneous

17 As defined, the constitution relation is symmetrical, though the definition could betightened so that the relation is asymmetric.

18 Some three dimensionalists in part define constitution as the relation that holdsbetween objects that are improper parts of each other at a time. Cf. Thomson, J. J. (1998)The Statue and the Clay. Nous32: 149173.


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object. Moreover, since every diachronic object exists, each instan-taneous object will constitute more than one diachronic object ateach time at which it exists: for there will exist diachronic objects

that wholly overlap for some period of time. Just as an instanta-neous temporal part will, if unrestricted composition is true, bea part of more than one four dimensional object, so too for thethree dimensionalist, these instantaneous objects will constitutemore than one enduring object at the time at which they exist.

4. Diachronic fusions and diachronic objects

But is there any real difference between the view I am describing,and four dimensionalism? Well the debate between the three andfour dimensionalist is not a debate about whether or not objectscan have other objects as parts at times: for no one need denythat. Nor is it a debate about which objects exist. For there isnothing about four dimensionalism that prescribes that oneaccept unrestricted composition. Crucially, four dimensionalism

is the view that persisting objects are temporally extended: that is,that at every time at which they exist, some of their parts are notpresent at those times. An object does not have a temporal partin virtue of having some improper spatial part for a period oftime. An object O has a temporal part P if it is true that O has Psimpliciter.

For the four dimensionalist, P is part of O is true at every timeat which O exists, even if P is not present at the time of utterance.So a four dimensional object that is the mereological fusion ofinstantaneous objects is an object that has each of these instan-taneous objects as parts simpliciter. For the three dimensionalistthough, these instantaneous objects are not parts simpliciter ofthe diachronic object that they constitute at a time. The threedimensionalist will say that the instantaneous object x that existsat t, is an improper part of the diachronic object O at t, but is notpart of O simpliciter. This version of three dimensionalism, there-fore, is not simply a way of accepting that there exist ersatz tem-poral parts. For it involves rejecting the idea that objects aretemporally extended, and thus rejecting the idea that there is any-thing answering to the description of temporal part.

We can further clarify this distinction if we consider how Sidersargument would proceed with respect to extended temporalparts. Consider daisy*. Daisy* is a diachronic fusion of the fusions


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of the members of sets C at t, C1 at t1, C2 at t2 and C3 at t3. Letssay that at t, every member of C is part of some other object Daisy,and every part of Daisy at t overlaps some member of C at t. So

too with C1 at t1 and so forth. Daisy is a cat, and therefore existsat many times at which daisy* does not. So is daisy* an extendedtemporal part of Daisy? To answer this, consider the followingdefinition, due to Sider, of an extended temporal part.

ETP: x is an extended temporal part of y during T iff (1) xexists at, but only at, times in T, (2) x is part of y at every timeduring T, and (3) at every moment in T x overlaps everythingthat is part of y at that moment.19

Daisy* exists through times t to t3. Call this duration T. So daisy*exists at and only at times in T. Daisy* is part of Daisy at everytime during T, and at every moment in T, daisy* overlaps every-thing that is part of Daisy at that moment. So we can concludethat daisy* is a temporal part of Daisy. All well and good since thethree dimensionalist denies that daisy* exists.

But now let us consider the diachronic object snowy*. Snowy*

is an object that is constituted by the fusions of the members ofsets D at t, D1 at t1, D2 at t2 and D3 at t3. At each of those times,the fusions of those sets also constitute Snowy the dog, who is fiveyears old. Both snowy* and Snowy are enduring objects that arewholly present whenever they exist: snowy* is not, for the threedimensionalist, a temporal part of Snowy. When we look to Sidersdefinition of an extended temporal part, however, we run into dif-ficulties. For snowy* exists only during T. Snowy* overlaps at everymoment in T, everything that is part of Snowy at that moment,and snowy* is part of Snowy at every time in T. So by Sidersdefinition of an extended temporal part, snowy* is a temporalpart of Snowy.

What is snowy*? Snowy* is simply a persisting object that existsbetween and only between certain times, and which happens tooverlap another object, Snowy, at the times at which it exists. Noneof this precludes snowy* (and Snowy) from being wholly presentat every time at which each exists. For consider a more familiarexample: the statue and the lump of clay. A statue and the lumpof clay that composes the statue are materially coincident at

19 Sider, op cit. Note this definition is also accepted by Markosian in Markosian, N.(1994). The 3D/4D Controvery and Non-Present Objects. Philosophical Papers23: 24349.


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certain times. But suppose that the statue is squashed, and thusceases to exist at some time, while the lump persists for some timelonger. It surely does not follow merely from the fact that the

statue and the lump wholly overlap for some period of time, andthat the statue exists during and only during that period of time,that the statue is a temporal part of the lump. The same is truefor the relation between snowy* and Snowy.

The problem lies in Siders definition of an extended tempo-ral part. For on this definition, something is an extended tem-poral part of y if it completely overlaps y for some period of time,and exists only during that period of time. Once we accept,

however, that three dimensionalists can coherently accept a version of unrestricted composition, then this definition of anextended temporal part is seen to be lacking. For given unre-stricted composition, a three dimensional diachronic object canoverlap another such object during and only during some periodof time T. But nothing about this suggests that one of thosediachronic objects is a part simpliciter of the other. Specifically,nothing about snowy* shows that it is part of Snowy simpliciter.

At each time at which snowy* exists, snowy* is an improper partof Snowy at that time. But there is no timeless sense in whichsnowy* is part of Snowy, because neither Snowy nor snowy* aretemporally extended.

The problem with Siders ETP definition of an extended tem-poral part is that clause (2) is couched in terms of parthood attimes, rather than atemporal parthood. This was an attempt toaccommodate the three dimensionalist, who rejects the idea ofatemporal parthood. The difficulty is that clause (2) does not dis-tinguish between a case where we have a diachronic object suchas snowy*, where snowy* is an improper part of Snowyat each timet in T, and the case where we have a diachronic object daisy* thatis part of Daisysimpliciter. For if daisy* is part of Daisy simpliciterthen it is also true that daisy* is part of Daisy at each time in T,though the reverse is not the case. But only if daisy* is part ofDaisy simpliciter, does it follow that Daisy is a temporally extendedobject, of which daisy* is an extended temporal part. Siders atem-poral version of ETP achieves just this:

AETP: x is an extended temporal part of y during T iff (1) xexists at, but only at, times in T (2) x is part of y and (3) atevery moment in T, x overlaps every part of y that exists at thatmoment.


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Considering again clause (2), we can see that in the case ofdaisy* and Daisy, it is true that daisy* is a part of Daisy, and thusthat daisy* is an extended temporal part of Daisy. In the case of

snowy*, however, since both snowy* and Snowy are wholly presentat each time at which they exist, there is no atemporal sense in which snowy* is part of Snowy. While there are some times at which snowy* is part of Snowy, there are other times at whichsnowy* is not part of Snowy. So (2) is not true of snowy* andSnowy, and thus snowy* is not an extended temporal part ofSnowy.

This brings us back nicely to the question of why the second

part of the argument from vagueness does not show that thefusion of the members of y at t, namely x, is part of the persistingobject y. Recall that Sider employed a mereological principleaccording to which we can move from the claim that every partof x at t overlaps y at t, to the claim that x is part of y at t. I earlierconceded that Sider had shown that x at t is part of y at t, wherey is a persisting object. We can now see why conceding this wasnot conceding that x is a temporal part of y. For consider again

snowy* and Snowy. Snowy* at t overlaps Snowy at t. So by themereological principle, we can conclude that snowy* at t is partof Snowy at t. Even having shown this, however, we have not shownthat snowy* is a temporal part of Snowy. To show that, it needs tobe the case that we can move from the claim that snowy* at toverlaps Snowy at t to the claim snowy* is part of Snowy. Forthe three dimensionalist does not deny that at t, snowy* is part ofSnowy: snowy* is an improper part of Snowy at t. Rather, shedenies that snowy* is part of Snowy simpliciter. So while the mere-ological principle is sound, applying this principle to two whollyoverlapping persisting objects that exist for different durations,tells us only that at each time at which both exist, each is animproper part of the other. There is a further question as towhether one is a part of the other simpliciter. Only if this latter isthe case, can we conclude that one is a temporal part of the other.So all Siders earlier argument shows is that x at t is part of y at t.It does not show that x is part of y simpliciter, and thus does notrule out the possibility that y is a diachronic object, and not adiachronic fusion.

So it is hardly surprising that it is the atemporal, and only theatemporal version of the definition of an extended temporal partthat permits us to draw the distinction between diachronic objectsand diachronic fusions. For showing that some object is a tem-


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poral part of another object involves more than just showing thatthe former is at some times an improper part of the latter, itinvolves showing that the former is part of the latter simpliciter,

and the temporal definition of an extended temporal part isunable to accomplish this. Thus what it ends up defining is not atemporal part at all.

5. Unrestricted composition and fusions-at-times

But why would a three dimensionalist accept that there exist any

such instantaneous objects at all? Perhaps most wouldnt. Thiswould not preclude the endurantist from accepting unrestrictedcomposition and its attendant advantages. As we noted previously,that composition is unrestricted does not entail that there existinstantaneous objects that could count as instantaneous temporalparts. The fusion of materially coincident enduring particulars isan enduring object. But suppose there exist two basic particularsP1 and P2. P1 endures through T, and P2 endures through T*,

where T and T* are non-contiguous intervals. Given unrestrictedmereological composition, there exists a fusion of P1 and P2, callit P, and P appears to be a four dimensional object in that it hasP1 and P2 as parts, albeit enduring parts. So while P1 is whollypresent through T, P is only partly present during T.

Although this would not be disastrous for the endurantist (it would certainly not be typical perdurantism) the endurantistmight want to understand unrestricted composition not in mere-ological terms, but rather, in the same non-mereological terms asdoes the endurantist who accepts the existence of instantaneousobjects as constitution at a time. Thus she might contend thatany arbitrary combination of enduring particulars constitutessome persisting object, and thus that P is constituted by P1 duringT, and constituted by P2 during T*. Hence P is wholly present

whenever it exists. Thus unrestricted composition would beunderstood as the claim that for any arbitrary arrangement ofparticulars, there is some enduring object that is constituted bythose particulars at times.

Still, if empirical discovery revealed that basic particulars areinstantaneous, I do not see that this would entail the truth of fourdimensionalism, rather, it would entail something like the threedimensionalist view I have been considering according to whichenduring objects are constituted by instantaneous objects at


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times. So too there are certain advantages for the three dimen-sionalist in accepting Siders idea of a fusion-at-a-time. Forinstance, if there exist instaneous objects that constitute endur-

ing objects at times, then the endurantist can make sense of theidea that in some sense enduring objects can have properties sim-pliciter: an enduring object O is red at t just if O is constituted att by some object that is red simpliciter. The instantaneous objectsthat constitute enduring objects can play much the same explana-tory role as temporal parts do for the four dimensionalist, withoutthe need to claim that objects are only partly present wheneverthey exist.

6. Conclusion

What all this shows is that even if one endorses part I of the argu-ment from vagueness, this does not compel one to accept fourdimensionalism. The endurantist can still reject the idea thatbasic particulars are instantaneous, or that there exist fusions-at-

times, and can thus reject the idea that enduring objects arediachronic objects constituted by shorter lived objects at times.On the other hand, even if one grants Siders contention thatsuch instantaneous objects exist, it does not follow that persistingobjects perdure, for it does not follow that persisting objects arethe fusions of these instantaneous objects. Thus the argumentfrom vagueness provides no reason to prefer four dimensional-ism to three dimensionalism.

University of QueenslandBrisbane, QueenslandAustralia [email protected]

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sophical Studies114: 107134.Lewis, D. (1991). Parts of Classes. Oxford: Blackwell. (1988). Vague Identity: Evans Misunderstood. Analysis48: 128130. (1986). On the Plurality of Worlds. New York Blackwell Press.


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Sainsbury, R. M. (1989). What is a Vague Object. Analysis49: 99103.Sider, T. (2003). Against Vague Existence. Philosophical Studies114: 135146

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