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In philosophy, four-dimensionalism may refer to either eternalism or perdurantism. The former is a theory of time, while the latter is a theory about the identity of objects over time. Sider (1997), for example, uses the term four-dimensionalism to refer to perdurantism, the theory that objects (and people) are four dimensional (see below for explanation). Eternalism, by contrast, is the theory that the universe (but not necessarily its contents, e.g., objects and people) is four dimensional, with time being the fourth dimension. Nevertheless, both theories tend to be discussed together, as many philosophers hold the combination of eternalism and perdurantism, considering both as better theories than their counterparts, presentism and endurantism, respectively. Probably, nobody who accepts perdurantism rejects eternalism, and it is unclear if such a position would even be coherent.

Explanation

The term four-dimensionalism is often used without specification of exactly what is meant. Often, it is used in the context of the issue of personal identity over time. For example, Robinson stated that 'the m.o. view, as canvassed below, is not my first choice amongst approaches to fission cases. I prefer the four-dimensionalist account (itself an m.o. analysis) presented with exemplary clarity by David Lewis in 'Survival and Identity' '. Unfortunately, David Lewis, at least in the first edition of this book, does not appear to use the term four-dimensionalism at all! Muis offers an explanation of the terminology which (fairly) clearly equates four-dimensionalism with perdurantism (by using the term 'four-dimensional' in relation to perdurantism only), not eternalism, but does so in an opening paragraph that mentions all four -isms (i.e., eternalism vs. presentism, endurantism vs. perdurantism), stating that 'in analytical metaphysics, there are three, closely related, debates about time and the nature of change and persistence' , the third debate being A-theory vs. B-theory of time (see below). Therefore, it appears to be very difficult to disentangle the issues or work out any firm terminological distinctions. It is unclear if all the literature exactly follows the terminology of Muis .

Eternalism is a metaphysical/ontological theory about the nature of time, which has implications for the identity over time of people and other objects. According to this theory, past, present, and future all exist equally, as opposed to the view that only the present exists, the past exists no more, and the future is yet to exist (i.e. presentism). Some philosophers, such as Markosian , for example, defend presentism against objections, claiming it to be the "commonsense view", but this appears to be missing the point that, while it could be true, and while it certainly is the "commonsense view", as a theory presentism is a metaphysical "dead end". According to eternalism, by contrast, there is nothing "special" about the present. The present is merely the temporal analogue of "here", which can be thought of as the "spatial present". Being located in the present, as opposed to the past or the future, is just like being "here rather than there". In neither case does where you are located have any "special status" over and above the fact that it is where you are located. So, in essence, eternalism is just a theory of time which explains away the apparent special (fundamental) status of the present (but see below). All other things being equal, it is a better theory (=better as a theory) than presentism.

We tend to think that there is a fundamental distinction between objects and processes (events), for example, persons and their lives. We tend to think that objects, such as people, are wholly present at each moment at which they exist (endurantism). By contrast, only a stage (=temporal part) of a process can be present at any one moment, not the whole process. Endurantism is a metaphysical "dead end", and does not sit well with the doctrine of materialism. This may seem to threaten the everyday notion that objects and people persist (i.e., retain their identity over time). Perdurantism is an alternative to endurantism, according to which we must abandon the distinction between object and process, or, equivalently, reinterpret objects as processes. Effectively, a person is their life, with stages, and not wholly present at any one time. So, with the combination of eternalism and perdurantism, we can avoid the metaphysical "dead end" theories of presentism and endurantism, while retaining identity over time for people and objects.

It is hard to relate the difference between endurance and perdurance to any real life issue, but suppose that you are informed that tomorrow you will suffer the most horrendous torture. If you endure, then you will, in some sense, "find yourself" tomorrow being tortured. Better try to avoid it! But if you perdure, then you cannot "find yourself" anywhere tomorrow, for the stage of your life tomorrow is not intrinsically the "same one" (in the sense of numerical identity) as it is today, and tomorrow has no less reality today than today has! The person stage who gets told that tomorrow they will be tortured is "located in today", whereas the person stage who actually gets tortured is "located in tomorrow"! The significance of this is rather unclear, but there would seem to be far less rational reason to fear future pain if you perdure. Why should your "today stage" care about pain inflicted on your "tomorrow stage", except by way of sympathy/empathy? Issues of qualia are relevant here.

Background

As four-dimensionalism (understood as either eternalism or perdurantism) is a metaphysical theory, it is necessary to say something here about the aim of metaphysics. Like science, the aim of metaphysics is to understand as much as possible in terms of as little as possible. In other words, the aim is to reduce the number of fundamentals to a minimum, and understand everything else as if constructed in some simple way out of those fundamentals. If a theory of x maintains that x is a fundamental element of reality, then this is expressed in this article by saying that the theory is a metaphysical "dead end" theory (of x). The background assumption is that reduction of fundamentals will lead to a true picture of reality. If we can understand space in terms of fundamentals x, y, z, etc., then all the better if we can also understand time in terms of x, y, z, etc. Eternalism attempts to do just that. Time is understood as the fourth dimension, equivalent to the three dimensions of space. What we lose from this theory is any special status for the present, however special it might seem...

Temporal parts

The idea of a whole object being composed of smaller parts is not revolutionary. On the contrary, this notion is rather common. One instance of a whole object losing a part is the paradigm example of the Ship of Theseus. Another illustration is a familiar routine such as getting a haircut. Both of these instances provide an example of a whole object losing a part. For the four-dimensionalist, this does not represent the notion of parthood.

The notion of parthood for a four-dimensionalist allows one to speak of the parts of an object simpliciter. That is, without any criterion or condition, versus at any particular time such as t₁ or t₂. Within the framework of four-dimensionalism, one could say that his or her current temporal part is sitting at a computer, typing up a presentation on four-dimensionalism, wearing sweatpants and having tea. Therefore, a four-dimensionalist conceives of the parts of an object as an atemporal relation, or part of a larger spacetime worm. A spacetime worm is a four-dimensional object consisting of a three-dimensional object extending through the fourth dimension of time.

Furthermore, the notion of parthood allows a four-dimensionalist to account for change, in a basic and ordinary sense of the word. Change is what allows one to distinguish between different successive temporal parts. For example, one temporal part of a person may be typing at a computer, while another temporal part will be going to sleep. Still a third temporal part will be waking up to run errands and get prepared for work later in the evening.

Presentism vs. eternalism

Consider the proposition: there was an American president called Reagan. What are the truth conditions? According to presentism, we cannot say! According to eternalism, we can say the following: there is an American president called Reagan, in the past. We can only say that, if the past exists. How can Reagan exist in the past if the past doesn't exist? We can understand "was" in terms of "is" and "past", but only if the past exists. The past is understood as a time before the present. If you can understand the idea of someone existing in the present, and you understand the idea of a linearly ordered sequence (i.e., time), then you can understand the idea of someone existing in the past! It is just a simple set theoretic model of time. "Was" just means "is" at some point before the present (i.e., at some point before, or "less than", one's current coordinate on the time line). What is unclear, however, is that just because we can understand (model) time in this eternalist manner, does that mean that reality is really like that? Does the past really exist, and what does that mean, anyway? Or, is the model just a formal device which is useful to adopt for some theoretical purposes? Applying the model to the future does, however, seem to raise issues relating to determinism and free will.

A-series and B-series

J.M.E. McTaggart famously argues in his 1908 paper The Unreality of Time that time is necessarily unreal. McTaggart introduces three different types of ordered relations among events: the A-series, the B-series and the C-series. The A-series is “the series of positions running from the far past through the near past to the present, and then from the present to the near future and the far future.” The basic temporal distinctions of past, present and future are fundamental and unique to the A-series as well as essential to the reality of time. If the distinctions of past, present and future are not true of reality, then there is no reality in time. The A-series is championed by proponents of presentism.

The B-series is a series of positions that is ordered from earlier to later. Like the A-series, the B-series contains a direction of change. Unlike the A-series, the B-series does not define a present moment that separates past and future. Events are thought to exist earlier and later, rather than in the past or future. This distinction allows one to move away from the terminology employed in the basic conception of time.

The A-series maintains that time is running from past to future while the B-series asserts that events are running from earlier to later, therefore both require a direction. The C-series, consequently, postulates that events have an order but that there is no inherent direction of time. McTaggart asserts that the order of the events does not necessitate change, a concept that he has already established to be necessary to the concept of time. Therefore, the C-series is atemporal and offers a plausible alternative to the conventional conception of time as well as a part of the concept of eternalism.

Comparisons to three-dimensionalism

The three dimensionalist view imagines time as being a unique dimension, 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 believes that objects can be differentiated based on their spatial dimensions, the same does not apply to time. Rather, the existence of temporal parts is a linguistic construct. For example, the person described by the phrase “Descartes in 1635” is objectively the same as the person described as “Descartes in 1620.” Temporal parts are not existent for the three dimensionalist. Therefore, change does not need to be accounted for. Accordingly, the only relation between these objects is that of identity. This helps to account for the paradox of change.

The four-dimensionalist view, by contrast, asserts that all objects occupying different time frames are inherently different versions of the same object. In order to account for these different versions, the notion of temporal parts is introduced. Differences among temporal parts are how a four-dimensionalist accounts for change. Thus, the temporal part described by the phrase “Descartes in 1635” is different from the temporal part described by the phrase “Descartes in 1620.” When combined, these parts form a spacetime “worm.”

See also

• Rietdijk–Putnam argument for an argument advocating this position.

References

1. Robinson (1985: 299-300)
2. Lewis (1976)
3. Muis (2005)
4. Muis (2005)
5. Markosian (2004)
6. ^ Cite error: The named reference Sider1997 was invoked but never defined (see the help page).
7. ^ "The Unreality of Time". Wikisource. Retrieved 2008-12-15.
8. ^ "Time". Stanford Encyclopedia of Philosophy. 2002-11-25. Retrieved 2008-12-15.

• Armstrong, David M. (1980). “Identity Through Time.” In Peter van Inwagen (ed.), Time and Cause, 67-68 Dordrecht: D. Reidel.
• Hughes, C. (1986)). “Is a Thing Just the Sum of Its Parts?” Proceedings of the Aristotelian Society 85: 213-33.
• Heller, Mark (1984). “Temporal Parts of Four Dimensional Objects.” Philo-

sophical Studies 46: 323-34. Reprinted in Rea 1997: 12.-330.

• Heller, Mark (1990). The Ontology of Physical Objects: Four-dimensional Hunks of Matter.

Cambridge: Cambridge University Press.

• Heller, Mark (1992). “Things Change.” Philosophy and Phenomenological Research 52: 695-304
• Heller, Mark (1993). “Varieties of Four Dimensionalism.” Australasian Journal of Philosophy 71: 47-59.
• Lewis, David (1983). “Survival and Identity.” In Philosophical Papers, Volume 1, 55-7. Oxford: Oxford University Press. With postscripts. Originally published in Amelie O. Rorty, ed., The Identities of Persons (Berkeley: University of California Press, 1976), 17-40.
• Lewis, David (1986a). On the Plurality of Worlds. Oxford: Basil Blackwell.
• Lewis, David (1986b). Philosophical Papers, Volume 2. Oxford: Oxford University Press.

• Lewis, D. 1976: Survival and identity. Pp. 17-40 in Rorty, A.O. (ed.) The identities of persons. Berkeley: University of California Press. Google books
• Markosian, N. 2004: A defense of presentism. Pp. 47-82 in Zimmerman, D.W. (ed.) Oxford Studies in Metaphysics, Volume 1. Oxford: Oxford University Press. Google books
• Muis, R. 2005: Four-dimensionalism: an ontology of persistence and time. By Theodore Sider. Ars Disputandi, 5 ISSN: 1566-5399 PDF
• Robinson, D. 1985: Can amoebae divide without multiplying? Australasian journal of philosophy, 63(3): 299–319. doi:10.1080/00048408512341901

External links

• Rea, M. C., "Four Dimensionalism" in The Oxford Handbook for Metaphysics. Oxford Univ. Press. Describes presentism and four-dimensionalism.
• "Time" in the Internet Encyclopedia of Philosophy

• Philosophy of time
• Philosophy of physics
• Spacetime