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In philosophy, four-dimensionalism (also known as the doctrine of temporal parts) is an ontological position that an object's persistence through time is like its extension through space. Thus, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies, just like an object that exists in a region of space has at least one part in every subregion of that space.
Four-dimensionalists typically argue for treating time as analogous to space, usually leading them to endorse the doctrine of Eternalism. This is a philosophical approach to the ontological nature of time, according to which all points in time are equally "real", as opposed to the presentist idea that only the present is real. As some eternalists argue by analogy, just as all spatially distant objects and events are equally as real as those close to us, temporally distant objects and events are as real as those currently present to us.
Perdurantism—or perdurance theory—is a closely related philosophical theory of persistence and identity, according to which an individual has distinct temporal parts throughout its existence, and the persisting object is the sum or set of all of its temporal parts. This sum or set is colloquially referred to as a "space-time worm", which has earned the perdurantist view the moniker of "the worm view". While all perdurantists are plausibly considered four dimensionalists, at least one variety of four dimensionalism does not count as perdurantist in nature. This variety, known as exdurantism or the "stage view", is closely akin to the perdurantist position. They also countenance a view of persisting objects which have temporal parts that succeed one another through time. However, instead of identifying the persisting object as the entire set or sum (the "space-time worm") of the temporal parts which compose the object, the exdurantist argues that any object under discussion is a single stage (time-slice, temporal part, etc.), and that the other stages or parts which compose the persisting object are related to that part by a "temporal counterpart" relation.
Though they have often been conflated, eternalism is a theory of what time is like and what times exist, while perdurantism is a theory about persisting objects and their identity conditions over time. Eternalism and perdurantism tend to be discussed together because many philosophers argue for a combination of eternalism and perdurantism. Sider (1997) uses the term four-dimensionalism to refer to perdurantism, but Michael Rea (Forthcoming in The Oxford Handbook for Metaphysics), uses the term "four-dimensionalism" to mean the view that presentism is false as opposed to "perdurantism", the view that endurantism is false and persisting objects have temporal parts.
A-series and B-series
J.M.E. McTaggart in The Unreality of Time, identified two descriptions of time, which he called the A-series and the B-series. The A-series identifies positions in time as past, present, or future, and thus assumes that the "present" has some objective reality, as in both presentism and the growing block universe. The B-series defines a given event as earlier or later than another event, but does not assume an objective present, as in four-dimensionalism. Much of the contemporary literature in the metaphysics of time has been taken to spring forth from this distinction, and thus takes McTaggart's work as its starting point.
Contrast with three-dimensionalism
Unlike the four dimensionalist, the three dimensionalist considers time to be a unique dimension that is not analogous to the three spatial dimensions: length, width and height. Whereas the four dimensionalist proposes that objects are extended across time, the three dimensionalist adheres to the belief that all objects are wholly present at any moment at which they exist. While the three dimensionalist agrees that the parts of an object can be differentiated based on their spatial dimensions, they do not believe an object can be differentiated into temporal parts across time. For example, in the three dimensionalist account, "Descartes in 1635" is the same object as "Descartes in 1620", and both are identical to Descartes, himself. However, the four dimensionalist considers these to be distinct temporal parts.
Prominent arguments in favor of four-dimensionalism
Several lines of argumentation have been advanced in favor of four-dimensionalism, each of which will be discussed in turn below.
Firstly, four-dimensional accounts of time are argued to better explain paradoxes of change over time (often referred to as the paradox of the Ship of Theseus) than three-dimensional theories. A contemporary account of this paradox is introduced in Ney (2014), but the original problem has its roots in Greek antiquity. A typical Ship of Theseus paradox involves taking some changeable object with multiple material parts, for example a ship, then sequentially removing and replacing its parts until none of the original component parts are left. At each stage of the replacement until the last, the ship is presumably identical with the original, since the replacement of a single part need not destroy the ship and create an entirely new one. But, it is also plausible that an object with none of the same material parts as another is not identical with the original object. So, how can an object survive the replacement of any of its parts, and in fact all of its parts? The four-dimensionalist can argue that the persisting object is a single space-time worm which has all the replacement stages as temporal parts, or in the case of the stage view that each succeeding stage bears a temporal counterpart relation to the original stage under discussion.
Secondly, problems of temporary intrinsics are argued to be best explained by four-dimensional views of time that involve temporal parts. As presented by David Lewis, the problem of temporary intrinsics involves properties of an object that are both had by that object regardless of how anything else in the world is (and thus intrinsic), and subject to change over time (thus temporary). Shape is argued to be one such property. So, if an object is capable of having a particular shape, and also changing its shape at another time, there must be some way for the same object to be, say, both round and square. Lewis argues that separate temporal parts having the incompatible properties best explains an object being able to change its shape in this way, because other accounts of three-dimensional time eliminate intrinsic properties entirely by indexing them to times and making them relational instead of intrinsic.
- Sider, Theodore (April 1997). "Four-Dimensionalism" (PDF). The Philosophical Review. Duke University Press. 106 (2): 197–231. JSTOR 2998357.
- Kuipers, Theo A.F. (2007). General Philosophy of Science: Focal Issues. North Holland. p. 326. ISBN 978-0-444-51548-3.
- Alyssa., Ney,. Metaphysics : an introduction. OCLC 870919144.
- Hawley, Katherine (2010). "Temporal Parts". In Edward N. Zalta. The Stanford Encyclopedia of Philosophy (Winter 2010 ed.).
- Sider, Theodore (1996-09-01). "All the world's a stage". Australasian Journal of Philosophy. 74 (3): 433–453. doi:10.1080/00048409612347421. ISSN 0004-8402.
.. This view is variously called "four-dimensionalism", "perdurantism", or "the doctrine of temporal parts". Some think that four-dimensionalism understood as the denial of presentism implies four-dimensionalism understood as perdurantism. But whether or not that is true, the important thing to recognize is that these are two very different views. To avoid confusion, I will in this paper reserve the term "four-dimensionalism" exclusively for the view that presentism is false, and I will use the term "perdurantism" to refer to the view that objects last over time without being wholly present at every time at which they exist.— MICHAEL C. REA, FOUR DIMENSIONALISM, Forthcoming in The Oxford Handbook for Metaphysics
- Presentism and the Space-Time Manifold by Dean Zimmerman, p. 7
- "Time: The 3D/4D Controversy". Stanford Encyclopedia of Philosophy. 2002-11-25. Retrieved 2008-12-15.
As in the case of the disputes between A Theorists and B Theorists, on the one hand, and Presentists and Non-presentists, on the other hand, the 3D/4D controversy is part of a general disagreement among philosophers of time concerning the degree to which time is dissimilar from the dimensions of space. That general disagreement has been an important theme in the philosophy of time during the last one hundred years, and will most likely continue to be so for some time to come.
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- Lewis, David (1983). "Survival and Identity", in Philosophical Papers, Volume 1, 55-7. Oxford University Press. With postscripts. Originally published in Amelie O. Rorty, editor (1976) The Identities of Persons University of California Press, pages 17-40.
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- McTaggart John Ellis (1908) The Unreality of time, originally published in Mind: A Quarterly Review of Psychology and Philosophy 17: 456-473.
- Lewis, D. (1976) "Survival and identity", pages 17-40 in Rorty, A.O. editor, The identities of persons. Berkeley: University of California Press. Google books
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- Rea, M. C., "Four Dimensionalism" in The Oxford Handbook for Metaphysics. Oxford Univ. Press. Describes presentism and four-dimensionalism.
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T Sider - 2003 - arsdisputandi.org, Four-dimensionalism: An ontology of persistence and time, Cited by 744 http://www.arsdisputandi.org/publish/articles/000200/article.pdf. In analytical metaphysics, there are three, closely related, debates about time and the nature of change and persistence. The first is about what there is. Presentists believe that only present things exist, whereas eternalists think that also past and future things exist, even though ...
- MICHAEL C. REA- The Oxford handbook of metaphysics, 2003 - books.google.com, Four-dimensionalism,
CHAPTER 9 FOUR-DIMENSIONALISM i. INTRODUCTION. Cited by 48 . FOUR-DIMENSIONALISM, as it will be understood in this chapter, is a view about the ontological status of non-present objects. Presentists say that only present objects exist. There are no ...
- K Koslicki - Philosophical Studies, 2003 - Springer, The crooked path from vagueness to four-dimensionalism. Cited by 37 
How do the familiar concrete objects of common-sense – houses, trees, people, cars and the like – persist through time? According to the position known as 'four-dimensionalism' or 'the doctrine of temporal parts', ordinary concrete objects persist through time by perduring, i.e., by ...
- Markosian - Philosophy and Phenomenological Research, 2004 - Wiley Online Library
2, Two Arguments from Sider's Four‐Dimensionalism, Cited by 19 . The Argument from Vagueness Sider's argument from vagueness for Four-Dimensionalism is adapted from his reconstruction of David Lewis's argument for the following conclusion about fusions.2 ... The Principle of Universal Fusions (PUF): Every class of objects has a fusion.
- Miller - Erkenntnis, 2005 - Springer, The metaphysical equivalence of three and four dimensionalism. Cited by 15 . ABSTRACT. 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 inter- translatable and equally ...