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 beween 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. Four Dimensionalism is an original and highly readable study of the metaphysics of time and identity. (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)

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)

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 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)

Both the multidimensional phenomenon and the polysemous notion of consciousness continue to prove resistant to consistent measurement and unambiguous definition. This is hardly surprising, given that there is no agreement even as regards the most fundamental issues they involve. One of the basic disagreements present in the continuing debate about consciousness pertains to its gradational nature. The general aim of this article is to show how consciousness might be graded and multidimensional at the same time. We therefore focus on the (...) question of what it is, exactly, that is or could be graded in cases of consciousness, and how we can measure it. Ultimately, four different gradable aspects of consciousness will be described: quality, abstractness, complexity and usefulness, which belong to four different dimensions, these being understood, respectively, as phenomenal, semantic, physiological, and functional. Consequently, consciousness may be said to vary with respect to phenomenal quality, semantic abstraction, physiological complexity, and functional usefulness. It is hoped that such a four-dimensional approach will help to clarify and justify claims about the hierarchical nature of consciousness. The approach also proves explanatorily advantageous, as it enables us not only to draw attention to certain new and important differences in respect of subjective measures of awareness and to justify how a given creature may be ranked higher in one dimension of consciousness and lower in terms of another, but also allows for innovative explanations of a variety of well-known phenomena (amongst these, the interpretations of blindsight and locked-in syndrome will be briefly outlined here). Moreover, a 4D framework makes possible many predictions and hypotheses that may be experimentally tested (We point out a few such possibilities pertaining to interdimensional dependencies). (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)

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

A review of Theodore Sider, Four-Dimensionalism: An Ontology of Persistence and Time, Oxford: Clarendon Press, 2001.

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.

We propose a new picture of nature in which there are only two fundamental universal constantsè ē (≡e/c) andh(≡ħ/c). Our theory is developed within the framework of a new four-dimensional symmetry which is constructed on the basis of the Poincaré-Einstein principle of relativity for the laws of physics and the Newtonian concept of time. We obtain a new space-light transformation law, a velocity-addition law, and so on. In this symmetry scheme, the speed of light is constant and is completely (...) relative. The new theory is logically self-consistent, and it moreover is in agreement with all previously established experimental facts, such as the “lifetime dilatation” of unstable particles, the Michelson-Morley experiment, etc. There is a difference relative to the usual theory, though, in that our theory predicts a new law for the Dopplerfrequency shift, which can be tested experimentally by measuring the second-order frequency shift. (shrink)

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)

This paper defends the view of continuants as 'four-dimensional worms' against an argument of Geach's. This is to the effect that if continuants are four-dimensional worms then their stages either do, or do not, fall under the very general terms satisfied by the continuants themselves (a stage of a man either is, or is not, a man); but that either alternative is untenable. I try to show how the former alternative may be defended by appealing to some of (...) Geach's own ideas about identity; then go on to defend the four-dimensionalist view from a criticism of it by Mellor, and finish with an account of the intuitive distinction between process and continuant terms. (shrink)

The process of a four-dimensional conversion and/or transformation strives in helping the leadership of an organisation, especially such as the church, with practical ways that may lead to the development of an effective leadership by observing the four important aspects of human spirituality as elaborated on in the article. The spiritual, intellectual, moral and socio-political dimensions of the transformation can be catered for so that the complete inner being of humans, as well as their social and political attitudes (...) and behaviours, can equally be transformed to maximum spiritual, personal and socio-political profitability. Mutombo-Mukendi demonstrates that the need for a spiritual leadership that can contribute to an effective transformation of Africa is dire, both for the church and the larger community. The real challenge is how to develop such leadership. This article provides intentional and practical ways that may lead to the development of the needed leadership. Four-dimensional transformation of people can be planned and carried out both in the church arena and in the surrounding communities. Skills development and transfer can also take place when skilled people from the church work with unskilled people from the community. (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)

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)

The paper argues that four-dimensionalism is incompatible with the existence of additively cumulative properties, including mass, volume, and electrical charge. These properties add up over disjoint objects: for example, the mass of a whole composed of two disjoint objects is a sum of the individual masses of the objects. The difficulty with such properties for four-dimensionalism stems from the way this theory makes persistence depend on the existence of disjoint objects at disjoint times. I consider various (...) possible responses to this difficulty and conclude that they all fail. (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.

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)

Multidimensional scaling of subjective color differences has shown that color stimuli are located on a hypersphere in four-dimensional space. The semantic space of color names is isomorphic with perceptual color space. A spherical four-dimensional space revealed in monkeys and fish suggests the primacy of common neuronal basis.

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)

I offer a clear conception of a temporal part that does not make the existence of temporal parts implausible. This can be done if (and only if) we think of physical objects as four dimensional, The fourth dimension being time. Unless we are willing to deny the existence of most spatial parts, Or willing to accept the possibility of coincident entities, Or accept something even more implausible, We should accept the existence of temporal parts.

The typical Four-Dimensionalist metaphysics will posit the existence of many entities with thinking temporal parts. To determine which of these entities are persons, Hud Hudson relies upon an exclusion principle that withholds the label “person” from objects possessing any parts that don’t contribute to thought. Thus the human animal can’t be identified with the human person because it initially consists of mindless embryonic temporal parts. Since even normal adult human animals have parts such as hair and nails that don’t (...) appear to contribute to the production of thought, Hudson argues that the person is to be found “beneath the skin” of the animal. This chapter contests this claim of the non-identity of the human person and human animal while still operating with Hudson’s assumptions that we persist in virtue of temporal parts, that composition is unrestricted, and that there cannot be any persons embedded within larger persons. (shrink)

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)

Carroll shaped the corporate social responsibility discourse into a four-dimensional pyramid framework, which was later adapted to corporate citizenship and sustainability approaches. The four layers of the pyramid—structured from foundation to apex as economic, legal, ethical, and philanthropic responsibilities—drew considerable managerial attention. An important criticism of the economic foundation of the Carroll pyramid concerns the identification and ordering of the four dimensions, which are inadequately justified theoretically. The authors of this article propose an alternative approach that builds (...) on the public value concept, which integrates a microfoundation of psychological research into basic human needs. Drawing on their Swiss Dialogue process, the authors argue that a four-dimensional pyramid does have heuristic value for managers. The advantage of this alternative pyramid logic is that it may be contingently adapted to different cultural contexts, because it allows adaptive internal reordering. (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)

This book presents original translations and a penetrating analysis of hymns from the Rg Veda, the earliest literary document of the Indian tradition. For many years the Rg Veda has been a source of interest and inspiration to Western readers. Composed in the predawn of recorded history it narrates the struggle of the Aryans as they tried to unify the world around them by sharing a common vision.

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

This work is a two-division study of twentieth century philosophies of history in Europe. Fields engaged in the study are transcendental philosophy, speculative metaphysics, theology, historiographical theory, and intellectual history. The main question concerns the historical finitude of History and its temporal horizon. The work explores the unsolved consequences of G.W.F. Hegel's Phenomenology of Spirit (1807) and Martin Heidegger's Being and Time (1927) in twentieth-century German and French philosophies of History.

In a successful series of papers, Schroer and Schroer presented a reductionist narrative account of personal identity. They claimed that their reductionist account had advantages over traditional narrative theories. In this paper I intend to show that they were wrong. Although it is possible to defend a reductionist narrative account, the Schroers’ theory has a problem of circularity. And solving that problem will cause their theory to have much more problems than non-reductionist narrative theories. Consequently, they should either present a (...) new and improved reductionist narrative account, or accept that non-reductionist narrative theories are better suited to account for the problem of personal identity. (shrink)

This provocative book attempts to resolve traditional problems of identity over time. It seeks to answer such questions as 'How is it that an object can survive change?' and 'How much change can an object undergo without being destroyed'? To answer these questions Professor Heller presents a theory about the nature of physical objects and about the relationship between our language and the physical world. According to his theory, the only actually existing physical entities are what the author calls 'hunks', (...) four-dimensional objects extending across time and space. This is a major contribution to ontological debate and will be essential reading for all philosophers concerned with metaphysics. (shrink)

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors Ns, Nt and Ms, Mt, respectively, are given. The torques Ns, Nt (the angular momentums Ms, Mt), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\varvec{E,\,B,\,F,\,L,\,N}$ etc. and their transformations are objected from the viewpoint of the (...) invariant special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities. (shrink)

The structures of space and time associated with various four-dimensional symmetries are constructed and examined. It is interesting that some of these four-dimensional symmetries are compatible with the existence of an aether in the Einstein sense. There are two classes of infinitely many four-dimensional symmetries that cannot be ruled out by previous experiments. We discuss some laser experiments that test these two classes of four-dimensional symmetries. An interesting connection between the nonclassical aether and gravity through the (...) equality of inertial and gravitational mass is explored. (shrink)

This chapter presents a discussion of the manner many theories and models of human learning utilise sets of dimensions. The dimensionality of elements/aspects of learning is analysed to lay the basis for the introduction of a key conceptualisation of this book, that of a proposal to embrace a Four-Dimensional model of human learners, (Lifelong, Lifewide, Lifedeep and LifeTech) as a necessity for the twenty-first century Learning.

Following the ideas of Poincaré, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporatingcommon time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A (...) further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail. (shrink)

We explore the mathematical structure and the physical implications of a general four-dimensional symmetry framework which is consistent with the Poincaré—Einstein principle of relativity for physical laws and with experiments. In particular, we discuss a four-dimensional framework in which all observers in different frames use one and the same grid of clocks. The general framework includes special relativity and a recently proposed new four-dimensional symmetry with a nonuniversal light speed as two special simple cases. The connection between (...) the properties of light propagation and the convention concerning clock systems is also discussed, and is seen to be nonunique within the four-dimensional framework. (shrink)