Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

This article characterizes the varieties of four - dimensionalism and provides a critical overview of the main arguments in support of it.

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (shrink)

I demonstrate that the theory of persistence defended in Sider [2001] does not accommodate our intuitions about counting sentences. I develop two theories that improve on Sider's: a contextualist theory and an error theory. I argue that the latter is stronger, simpler, and better fitted to some important ordinary language judgments than rival four-dimensionalist theories of persistence.

Precis of my book by this title, for a symposium.

Four-dimensionalism is the thesis that everyday objects, such as you and me, are space-time worms that persist through time by having temporal parts none of which is identical to the object itself. Objects are aggregates or sums of such temporal parts. The main virtue of fourdimensionalism is that it solves—or does away with—the problem of identity through change.1 The main charge raised against it is that it is inconsistent with the thesis according to which there is change in the world.2 (...) If this charge could be sustained, then we would need compelling arguments in support of the view that things are four-dimensional, since the view that there is no change in the world conflicts with so many of our most well-supported common-sense beliefs. In what follows, however, I want to show that, contrary to what is usually believed, fourdimensionalism does not entail a changeless world. (shrink)

In "Does Four-Dimensionalism Explain Coincidence" Mark Moyer argues that there is no reason to prefer the four-dimensionalist (or perdurantist) explanation of coincidence to the three-dimensionalist (or endurantist) explanation. I argue that Moyer's formulations of perdurantism and endurantism lead him to overlook the perdurantist's advantage. A more satisfactory formulation of these views reveals a puzzle of coincidence that Moyer does not consider, and the perdurantist's treatment of this puzzle is clearly preferable.

Four-dimensionalism is the thesis that everyday objects, such as you and me, are space-time worms that persist through time by having temporal parts none of which is identical to the object itself. Objects are aggregates or sums of such temporal parts. The main virtue of four-dimensionalism is that it solves—or does away with—the problem of identity through change. The main charge raised against it is that it is inconsistent with the thesis according to which there is change in the world. (...) If this charge could be sustained, then we would need compelling arguments in support of the view that things are four-dimensional, since the view that there is no change in the world conflicts with so many of our most well-supported common-sense beliefs. In what follows, however, I want to show that, contrary to what is usually believed, four-dimensionalism does not entail a changeless world. (shrink)

Four-dimensionalism and eternalism are theories on time, change, and persistence. Christian philosophers and theologians have adopted four-dimensional eternalism for various reasons. In this paper I shall attempt to argue that four-dimensional eternalism conflicts with Christian thought. Section I will lay out two varieties of four-dimensionalism—perdurantism and stage theory—along with the typically associated ontologies of time of eternalism and growing block. I shall contrast this with presentism and endurantism. Section II will look at some of the purported theological benefits of adopting (...) four-dimensionalism and eternalism. Section III will examine arguments against four-dimensional eternalism from the problem of evil. Section IV will argue that four-dimensional eternalism causes problems for Christian eschatology. (shrink)

Current formulations of Four-Dimensionalism may be objected to on grounds that they are too inflexible: the formulations do not seem to allow for enough variety in the views they are paired with. For instance, Kit Fine has noted that formulations of Four-Dimensionalism in terms of instantaneous parts may be too demanding for Four-Dimensionalists who believe nothing is instantaneous. And Trenton Merricks has argued that one can think something persists four-dimensionionally without taking it to have proper temporal parts, and claims that (...) our formulation of Four-Dimensionalism should be revised to allow for this. I will add my own worries to those of Fine and Merricks. I will note that current formulations of Four-Dimensionalism are not sufficiently neutral with respect to the structure of time, with respect to how liberally objects decompose into parts, and with respect to whether objects and the regions they fill match in mereological structure. I will show that we can formulate Four-Dimensionalism in a sufficiently neutral way, while still producing a view that can do the work we typically require of Four-Dimensionalism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Four-Dimensionalism and Identity Across Time: Henry of Ghent vs. BonaventureRichard CrossModern accounts of the identity of an object across time tend to fall roughly into two basic types.Let us say that something persists ıff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is (...) wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time.1On the first of these analyses, but not the second, a persistent object includes temporal parts, and persistent material substances are thus on this analysis four-dimensional objects. On the first analysis, but not on the second, time-indices are explicable in terms of temporal parts. I shall take this as the basic difference between the two views.2Both views allow us to talk of temporal order and temporal direction. I [End Page 393] shall follow the medievals and talk about succession to capture both of these claims: “The notion of succession formally consists in the notion of ‘before’ and ‘after,’”3 and I take it that talk of “before” and “after” entails both order and direction.4 Medieval accounts of identity across time are, however, in some ways more obscure than the two modern ones just described. The medievals tend to associate all temporal succession with temporal extension: an object x has temporal succession if and only if x is temporally extended (and thus includes temporal parts).5 The medievals also (correctly, I believe) tend to suppose that substances—unlike (say) processes—do not have temporal parts.6 Thus, by the end of the thirteenth century the schoolmen commonly [End Page 394] distinguish permanent objects from successive objects. Permanent objects do not, and successive objects do, have temporal parts.7 Successive objects are processes; the class of permanent objects was generally held to include not only God, but also angels, material substances, and static accidents (i.e., accidents which do not entail any sort of process).8Given these claims, there is a problem to be faced in giving an account of the identity of, say, a material substance across time. But it is not the problem we would face. Our problem, post-Hume, is to explain the relevant (explanatory) continuity requirements for identity across time. The medievals’ problem is rather different. They do not need to specify general continuity requirements, because for them there is a very real sense in which substances—and indeed all permanent objects—lack temporal extension and, therefore, any sort of temporal succession at all. The problem for the medievals is thus to explain how substances can persist at all, rather than exist merely fleetingly.9In what follows, I will examine two thirteenth-century solutions to this problem. The first is a radical one: simply to deny the standard claim that substances lack temporal parts. This view will thus bear some resemblance to what we would label four-dimensionalism. The second solution I will examine represents one of the more successful attempts to defend the standard thirteenth-century line that substances lack temporal parts. This solution goes some way towards allowing succession (and time-indexing) without appealing to temporal parts.To understand the debate, we need to keep in mind that the medievals—following Aristotle—talk of the temporality of an object in terms of its being [End Page 395] measured by time. Confusingly, they might speak of a substance’s being measured in one sort of way, and its accidental properties’ being measured in another. Thus, by the end of the thirteenth century it was often claimed that the duration of a substance is measured not by time but by the aevum—the durational measure of objects lacking temporal parts—while some of a substance’s accidental properties could be measured by time. (I will explain in detail below how time and the aevum were understood.) On this view, the temporality of an object’s properties is not sufficient cause for positing the temporality of the object. There are acceptable and unacceptable ways of understanding... (shrink)

Four-dimensionalists think that we persist over time by having different temporal parts at each of the times at which we exist. Eternalists think that all times are equally real. Deprivationists think that death is an evil for the one who dies because it deprives them of something. I argue that four-dimensionalist eternalism, conjoined with a standard deprivationist account of the evil of death, has surprising implications for what we should think about the evil of death. In particular, given these assumptions, (...) we will lack any grounds for thinking that death is an evil for some individuals for whom we would antecedently expect it to be an evil, namely those individuals who cease to exist at death. Alternatively, we will only have some grounds for thinking that death is an evil for certain individuals for whom we might antecedently be more inclined to think death is not an evil, namely those individuals who survive death, in the sense that they continue to exist after death. (shrink)

Anyone who endorses Universalism and Four Dimensionalism owes us an argument for those controversial mereological theses. One may put forth David Lewis’s and Ted Sider’s arguments from vagueness. However, the success of those arguments depends on the rejection of the epistemic view of vagueness, and thus opens the door to a fatal confrontation with one particularly troubling version of The Problem of the Many. The alternative for friends of Universalism and Four Dimensionalism is to abandon those currently fashionable arguments in (...) favor of others which are consistent with the epistemic view of vagueness and with the elegant solution it furnishes to that problem. (shrink)

Anyone who endorses Universalism and Four Dimensionalism owes us an argument for those controversial mereological theses. One may put forth David Lewis’s and Ted Sider’s arguments from vagueness. However, the success of those arguments depends on the rejection of the epistemic view of vagueness, and thus opens the door to a fatal confrontation with one particularly troubling version of The Problem of the Many. The alternative for friends of Universalism and Four Dimensionalism is to abandon those currently fashionable arguments in (...) favor of others which are consistent with the epistemic view of vagueness and with the elegant solution it furnishes to that problem. (shrink)

Book Information Four-Dimensionalism: An Ontology of Persistence and Time. By Theodore Sider. Clarendon Press. Oxford. 2001. Pp. xxiv + 255. £30.

For those who think the statue and the piece of copper that compose it are distinct objects that coincide, there is a burden of explanation. After all, common sense says that different ordinary objects cannot occupy the same space at the same time. A common argument in favour of four-dimensionalism (or ?perdurantism? or ?temporal parts theory?) is that it provides the resources for a superior explanation of this coincidence. This, however, is mistaken. Any explanatory work done by the four-dimensionalist notion (...) of absolute parthood rests ultimately on notions equally available to the three-dimensionalist. Thus, a neutral explanation of coincidence is at least as good while avoiding commitment to temporal parts. ?Many thanks to David Christensen, Louis deRosset, Matti Eklund, and two anonymous referees for helpful comments. (shrink)

In 'Four-Dimensional Objects' Peter van Inwagen gives two arguments for the claim that proponents of four-dimensionalism have to be counterpart theorists. Recently Jack Copeland, Heather Dyke, and Diane Proudfoot, echoing in part points made by Mark Heller in this journal in 1993, have sought to rebut one of van Inwagen's arguments. In this paper I shall criticize their discussion and by implication certain points made by Heller. In so doing I shall also rebut a possible objection to van Inwagen's second (...) argument. While I shall conclude that Copeland et al . fail to make their case, I nevertheless argue that van Inwagen's argument can be resisted, provided that the four-dimensionalist is willing to adopt a certain conception of transworld identity. Moreover, I shall argue that to the extent that van Inwagen's paper highlights something problematic for four-dimensionalism in this particular conception of transworld identity, the paper highlights something equally problematic for three-dimensionalism. (shrink)

I argue that four-dimensionalism and the desire satisfaction account of well-being are incompatible. For every person whose desires are satisfied, there will be many shorter-lived individuals (‘person-stages’ or ‘subpersons’) who share the person’s desires but who do not exist long enough to see those desires satisfied; not only this, but in many cases their desires are frustrated so that the desires of the beings in whom they are embedded as proper temporal parts may be fulfilled. I call this the frustrating (...) problem for four-dimensionalism. In the first half of the paper I lay the groundwork for understanding the frustrating problem, and then in the second half, I will examine six possible responses to the frustrating problem on behalf of the four-dimensionalist, (i) the Parfit (1984) inspired claim that identity is not what matters, (ii) the personal pronoun revisionism of Noonan (2010), (iii) the indirect concern account of Hudson (2001), (iv) the sensible stages account of Lewis (1986), (v) a multiple-concepts account of desire satisfaction, and (vi) a No Desire View according to which subpersons have no mental states and thus no desires to frustrate. I argue that none of these solutions will help the four-dimensionalist; she does better to reject the desire satisfaction theory, while the defender of the desire satisfaction theory does better to reject four-dimensionalism. (shrink)

The following quotation, from Frank Jackson, is the beginning of a typical exposition of the debate between those metaphysicians who believe in temporal parts, and those who do not: The dispute between three-dimensionalism and four-dimensionalism, or more precisely, that part of the dispute we will be concerned with, concerns what persistence, and correllatively, what change, comes to. Three-dimensionalism holds that an object exists at a time by being wholly present at that time, and, accordingly, that it persists if it is (...) wholly present at more than one time. For short, it persists by enduring. Four-dimensionalism holds that an object exists at a time by having a temporal part at that time, and it persists if it has distinct temporal parts at more than one time. For short, it persists by perduring. In the light of these comments, some readers will perhaps find the question that forms the title of this paper a little puzzling. They may have learned to use the terms ‘fourdimensionalism’ ‘perdurantism’ and ‘belief in temporal parts’ interchangeably; or perhaps even to define one in terms of the other. Such a usage, however, is inapposite. We might imagine a Flatland-like world of two spatial dimensions and one temporal, whose philosophers are divided between a theory of persistence on which they persist by having temporal parts, and a theory on which they persist by being wholly located in each of several times. This is just the same issue we face, but at least the label ‘four-dimensionalism’ seems inapposite: the four-dimensionalist Flatlanders believe in only three dimensions! (shrink)

Book Information Four-Dimensionalism: An Ontology of Persistence and Time. By Theodore Sider. Clarendon Press. Oxford. 2001. Pp. xxiv + 255. £30.

There are several faces of Four-Dimensionalism. Sometimes 4D-ism is formulated as the thesis that the material world is composed of spatial as well as temporal parts. Another version of 4D-ism states that persisting objects are extended over time in the same way that they are extended over space. Some Four-Dimensionalists defend the thesis that all objects persist by perduring i.e. by having different temporal parts at different times. Sometimes 4D-ism means the same as eternalism - the thesis that past and (...) future objects (and times) are just as real as currently existing ones. Finally it can mean the thesis that all objects are in fact four-dimensional i.e. they are in every case a filling of some subregions of space-time. The author examines some varieties of 4D-ism and tries to formulate both a precise meaning of those doctrines and an evaluation of them. (shrink)

There are several faces of Four-Dimensionalism (4D). Sometimes 4D is formulated as the thesis that the material world is composed of spatial as well as temporal parts. Another version of 4D states that persisting objects are extended over time in the same way that they are extended over space. Some Four-Dimensionalists defend the thesis that all objects persist by perduring i.e. by having different temporal parts at different times. Sometimes 4D means the same as eternalism - the thesis that past (...) and future objects (and times) are just as real as currently existing ones. Finally it can mean the thesis that all objects are in fact four-dimensional i.e. they are in every case a filling of some subregions of space-time. The author examines some varieties of 4D and tries to formulate both a precise meaning of those doctrines and an evaluation of them. (shrink)

This paper is about persistence of material objects through time and across possible worlds. It starts with the well-known argument from undetached parts, that is put as an objection to endurantism raised by four-dimensionalists who claim to have a nice treatment of it themselves. While it will be acknowledged that, indeed, four-dimensionalism has a good explanatory power here, and has an advantage over endurantism, we will then see a modified (modalized) version of the argument that will not be so easily (...) dismissed by the four-dimensionalist. To provide a solution to this second puzzle, a proposal will be made to use the four-dimensionalist's strategy in the case of modality and use this notion of perdurance across possible worlds to answer the modalized version of the objection. Finally, I examine some objections to this theory of modal perdurants, and try to answer them. (shrink)

This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between these two competitor (...) theories. I conclude that despite prima facie reasons to suppose that non-perdurantist four-dimensionalism might be a credible alternative to either other account of persistence, ultimately the view is unsuccessful. The reasons for its failure illuminate the sometimes stagnant debate between three-dimensionalists and perdurantists, providing new reasons to prefer a perdurantist metaphysics. (shrink)

Bonaventure is sometimes taken to be an ante litteram champion of the four-dimensional theory of persistence. I argue that this interpretation is incorrect: Bonaventure was no four-dimensionalist.

This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between these two competitor (...) theories. I conclude that despite prima facie reasons to suppose that non-perdurantist four-dimensionalism might be a credible alternative to either other account of persistence, ultimately the view is unsuccessful. The reasons for its failure illuminate the sometimes stagnant debate between three-dimensionalists and perdurantists, providing new reasons to prefer a perdurantist metaphysics. (shrink)

In his excellent book, Four-Dimensionalism: An Ontology of Persistence and Time (Sider, 2001), Theodore Sider defends a version of four-dimensionalism which he calls the ‘stage-theory’. This paper focuses on Sider's argument from vagueness and argues that, due to the problematic nature of the argument from vagueness, Sider’s case in favor of four-dimensionalism is in the end not successful.

I argue that two competing accounts of persistence, three and four dimensionalism, are in fact metaphysically equivalent. I begin by clearly defining three and four dimensionalism, and then I show that the two theories are intertranslatable and equally simple. Through consideration of a number of different cases where intuitions about persistence are contradictory, I then go on to show that both theories describe these cases in the same manner. Further consideration of some empirical issues arising from the theory of special (...) relativity lead me to conclude that the two theories are equally explanatory, and thus finally that they are metaphysically equivalent. (shrink)

The claim that selves are narratively constituted has attained considerable currency in both analytic and continental philosophy. However, a set of increasingly standard objections to narrative identity are also emerging. In this paper, I focus on metaphysically realist versions of narrative identity theory, showing how they both build on and differ from their neo-Lockean counterparts. But I also argue that narrative realism is implicitly committed to a four-dimensionalist, temporal-parts ontology of persons. That exposes narrative realism to the charge that the (...) narratively constituted self, on the one hand, and the self that is the object of much of our everyday self-reference and self-experience, on the other, can't be the same thing. This conclusion may well force narrativists to abandon metaphysical realism about narrative selves—which, in turn, may leave the invocation of ‘narrativity’ as identity-constituting somewhat under-motivated. (shrink)

Four-Dimensionalism is a thorough, lively and forceful defence of the claim that “necessarily, every spatiotemporal object has a temporal part at every moment at which it exists” (59). The standard four-dimensionalist view is perdurance theory, according to which everyday things like boats are temporally extended. But Sider rejects perdurance theory, nicely disparaging it as the “worm view”, and he argues for the “stage view” version of fourdimensionalism instead. According to the stage view, everyday things like boats are instantaneous, and claims (...) about the history of the Anstruther lifeboat are made true or false by the boat’s past counterparts. Sider reserves the term “four-dimensionalism” for these two views of persistence; he also defends a tenseless B-theory of time. The book develops, extends and systematises work which Sider has published over the last few years, and it makes a compelling and readable whole. I am sympathetic with many of the conclusions, but I will take issue with some of the arguments. (shrink)

The claim that selves are narratively constituted has attained considerable currency in both analytic and continental philosophy. However, a set of increasingly standard objections to narrative identity are also emerging. In this paper, I focus on metaphysically realist versions of narrative identity theory, showing how they both build on and differ from their neo‐Lockean counterparts. But I also argue that narrative realism is implicitly committed to a four‐dimensionalist, temporal‐parts ontology of persons. That exposes narrative realism to the charge that the (...) narratively constituted self, on the one hand, and the self that is the object of much of our everyday self‐reference and self‐experience, on the other, can't be the same thing. This conclusion may well force narrativists to abandon metaphysical realism about narrative selves—which, in turn, may leave the invocation of ‘narrativity’ as identity‐constituting somewhat under‐motivated. (shrink)

The claim that selves are narratively constituted has attained considerable currency in both analytic and continental philosophy. However, a set of increasingly standard objections to narrative identity are also emerging. In this paper, I focus on metaphysically realist versions of narrative identity theory, showing how they both build on and differ from their neo‐Lockean counterparts. But I also argue that narrative realism is implicitly committed to a four‐dimensionalist, temporal‐parts ontology of persons. That exposes narrative realism to the charge that the (...) narratively constituted self, on the one hand, and the self that is the object of much of our everyday self‐reference and self‐experience, on the other, can't be the same thing. This conclusion may well force narrativists to abandon metaphysical realism about narrative selves—which, in turn, may leave the invocation of ‘narrativity’ as identity‐constituting somewhat under‐motivated. (shrink)

_ABSTRACT_ A relevant part of the literature about the metaphysical problem of persistence of concrete particulars exhibits, I believe, too much freedom as far as the use of terms like “Four-Dimensionalism”, “Perdurantism” and “Doctrine of temporal parts” is concerned. This attitude clashes against the rigorous and valid arguments of many four-dimensionalist views and it is mainly due to a lack of precision on the four-dimensionalist side. In this work I analyse Parsons’ attempt to clarify the content of these notions. His (...) clarification, based on the postulation of a difference between temporal parts and temporal extent, is aimed at demonstrating that Four-Dimensionalism and Perdurantism have not the same content and are not tied by any apriori connection. I endorse Parsons’ clarification as legitimate from a logical and semantic point of view, but I maintain that, despite his useful distinction between Perdurantism as a theory of persistence and Four-Dimensionalism as a theory of extension, these doctrines are ultimately equivalent, when it comes to formulating a general view about material objects. Indeed, I argue that objects extended four-dimensionally necessarily persist by perduring, and perduring objects necessarily extend four-dimensionally in space-time. (shrink)

In his article 'The Evil of Death' (henceforth: ED) Harry Silverstein argues that a proper refutation of the Epicurean view that death is not an evil requires the adoption of a particular revisionary ontology, which Silverstein, following Quine, calls 'four-dimensionalism'.1 In 'The Evil of Death Revisited' (henceforth: EDR) Silverstein reaffirms his earlier position and responds to several criticisms, including some targeted at his ontology. There remain, however, serious problems with Silverstein's argument, and I shall highlight five major ones below. I (...) conclude that Silverstein has not shown that an appeal to four-dimensionalism facilitates a refutation of Epicurus, although a consideration of some of Silverstein's points helps to indicate the limited scope of the Epicurean thesis. (shrink)

This is a critical notice of Theodore Sider's book, _Four-Dimensionalism_.

Ted Sider’s book makes a beautifully presented and compellingly argued case for four dimensionalism. Most of the arguments for four dimensionalism to be found in the literature seem to me to be uncompelling. Ted’s argument from vagueness, given in the last section of chapter 4, is a notable exception. After discussing that argument I will respond to his objections in section 5 chapter 5 to my own temporary identity view.

The view that human beings begin to exist at fertilization (namely conceptionism) faces a serious challenge from the twinning argument, that identical twins coming from the same zygote must be numerically distinct from the zygote and so did not exist at fertilization. Recently, some philosophers have claimed that the twinning argument rests on a particular metaphysical theory of persistence, namely endurantism, on which a human being, for example, is wholly present at every moment of her existence. And we can easily (...) refute the argument, they claim, by employing perdurantism or exdurantism, according to which a human being is a temporally extended entity with temporal parts or a momentarily existing stage who has other momentarily existing stages as counterparts. I argue that such claims are mistaken. The twinning argument does not rest on endurantism and can be formulated in terms of perdurantism to provide a good reason for perdurantists to reject conceptionism. And exdurantism does not have any advantage in defending conceptionism either, for it already concedes more than what the twinning argument aims to show. (shrink)

How do the familiar concrete objects of common sense persist through time? The four-dimensionalist argues that they perdure, that is, they persist through time by having temporal parts at each of the times at which they exist. The three-dimensionalist, on the other hand, holds that ordinary concrete objects endure; they lack an additional temporal dimension and persist, instead, by being “wholly present” at each of the times at which they exist.

I argue that medieval solutions to the limit decision problem imply four-dimensionalism, i.e. the view according to which substances that persist through time are extended through time as well as through space, and have different temporal parts at different times.