Online research in philosophy

Here are two ways space might be (not the only two): (1) Space is “pointy”. Every finite region has infinitely many infinitesimal, indivisible parts, called points. Points are zero-dimensional atoms of space. In addition to points, there are other kinds of “thin” boundary regions, like surfaces of spheres. Some regions include their boundaries—the closed regions—others exclude them—the open regions—and others include some bits of boundary and exclude others. Moreover, space includes unextended regions whose size is zero. (2) Space is “gunky”.1 Every region contains still smaller regions—there are no spatial atoms. Every region is “thick”—there are no boundary regions. Every region is extended. Pointy theories of space and space-time—such as Euclidean space or Minkowski space—are the kind that figure in modern physics. A rival tradition, most famously associated in the last century with A. N. Whitehead, instead embraces gunk.2 On the Whiteheadian view, points, curves and surfaces are not parts of space, but rather abstractions from the true regions. Three different motivations push philosophers toward gunky space. The first is that the physical space (or space-time) of our universe might be gunky. We posit spatial reasons to explain what goes on with physical objects; thus the main reason..

In a recent paper, Stephen Barker and Phil Dowe (2003)1 argue that multilocation is impossible. An object enjoys multi-location just in case it is wholly present at more than one (distinct) space-time region (106). One popular view that is committed to multi-located objects is endurantism, the doctrine that objects persist through time by being wholly present at each time they are located.2 So if Barker and Dowe are right, endurantism is in big trouble.

In the exuberance that followed Einstein’s discoveries, philosophers at one time or another have proposed that his theories support virtually every conceivable moral in ontology. I present an opinionated assessment, designed to avoid this overabundance. We learn from Einstein’s theories of novel entanglements of categories once held distinct: space with time; space and time with matter; and space and time with causality. We do not learn that all is relative, that time in the fourth dimension in any non-trivial sense, that coordinate systems and even geometry are conventional or that spacetime should be reduced ontologically to causal, spatio-temporal or other relations.

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.

The ‘friends of temporal parts’ and their opponents disagree about how things persist through time. The former, who hold what is sometimes called a ‘4D’ theory of persistence, typically claim that all objects that last for any period of time are spread out through time in the same way that spatially extended objects are spread out through space — a different part for each region that the object fills. David Lewis calls this manner of persisting ‘perdurance’. The opposing, ‘3D’ theory has it that at least some objects do not persist in this manner; they ‘endure’ through time by ‘being wholly present at more than one time’.1 A related dispute pits ‘presentists’ against ‘non-presentists’. Presentists hold that the only things that really exist are those that exist now, at the present moment; and nonpresentists believe in something like a ‘block-universe’ in which non-simultaneous objects and events nevertheless co-exist (in a tenseless or non-temporal sense). Of late, the relations between these four positions have come under considerable scrutiny.2 As Ned Markosian has pointed out, it would be surprising if commitment to a perdurance or endurance theory of persistence automatically foreclosed one’s options in the presentism—non-presentism debate. But, says Markosian, that is just what the standard formulations of the perdurance and endurance theories imply.3 David Lewis has set the terms of the debate; in his usage, someone who thinks that all persisting objects endure would be said to hold the following.

Under the eternalist hypothesis that objects or events exist temporally, but independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in (space-)time, and persisting objects perdure if they are singly located by having numerically different temporal parts. In the framework of the special theory of relativity (SR), the metaphysics of persistence is confronted with peculiar difficulties. Things persist by being “wholly present” at more than one time; but what are times within a temporally non-separated spacetime? Things persist by having different temporal parts at different times; but what are the temporal parts of a four-dimensional object in Minkowski spacetime? Recently, several authors have argued that SR favours perdurantism over its endurantist rival. In this paper, I intend to show that the purported arguments are only those against endurantism. The first simply fails, but the second, more convincing one, is such that with a similar strategy we should argue against perdurantism as well: Enduring and perduring entities are hence both in conflict with SR which undermines the eternalist hypothesis.

Four-dimensionalism, as I’ll use the term, is the doctrine that reality is spread out in time as well as space.1 Just as objects that are located at multiple regions of space contain parts confined to those regions of space, so objects that are located at multiple regions of time contain parts — temporal parts — that are confined to those regions of time. (Or better: an object that occupies an extended spatiotemporal region R has parts confined to the various subregions of R; but I’ll ignore this complication henceforth.) Most who accept this ontology of perduring objects, as they are often called, identify the continuants of our everyday ontology with “space-time worms” — mereological sums of stages from different times. Elsewhere (1996) I have proposed a different version of four-dimensionalism, which identifies continuants with the stages themselves, and which analyses de re temporal predication with a temporal version of modal counterpart theory (Lewis, 1968, 1971). On this view, a current assertion of ‘Clinton was indiscreet’ is true iff the (current) referent of ‘Clinton’ — a stage — has an indiscreet temporal counterpart in the past. The temporal counterpart relation is the same “genidentity” or “unity” relation used by the worm theorist to unify the successive stages of continuing space-time worms. In my 1996 I supported this view by appeal to its ability to resolve various philosophical puzzles, including the paradoxes of material constitution and Derek Parfit’s (1971) puzzle about identity and what matters; the purpose of the present note is to mention one other line of argument. A widely discussed contemporary argument for temporal parts is David Lewis’s argument from temporary intrinsics, according to which only the fourdimensionalist can explain the phenomenon of intrinsic change.2 I am now straight-shaped, but will fail to be straight-shaped in the future. There is an..

Four-dimensionalism, as I’ll use the term, is the doctrine that reality is spread out in time as well as space.1 Just as objects that are located at multiple regions of space contain parts con ned to those regions of space, so objects that are located at multiple regions of time contain parts — temporal parts — that are con ned to those regions of time. (Or better: an object that occupies an extended spatiotemporal region R has parts con ned to the various subregions of R; but I’ll ignore this complication henceforth.) Most who accept this ontology of perduring objects, as they are often called, identify the continuants of our everyday ontology with “space-time worms” — mereological sums of stages from different times. Elsewhere ( ) I have proposed a different version of four-dimensionalism, which identi es continuants with the stages themselves, and which analyses de re temporal predication with a temporal version of modal counterpart theory (Lewis, , ). On this view, a current assertion of ‘Clinton was indiscreet’ is true iff the (current) referent of ‘Clinton’ — a stage — has an indiscreet temporal counterpart in the past. The temporal counterpart relation is the same “genidentity” or “unity” relation used by the worm theorist to unify the successive stages of continuing space-time worms. In my I supported this view by appeal to its ability to resolve various philosophical puzzles, including the paradoxes of material constitution and Derek Par t’s ( ) puzzle about identity and what matters; the purpose of the present note is to mention one other line of argument. A widely discussed contemporary argument for temporal parts is David Lewis’s argument from temporary intrinsics, according to which only the fourdimensionalist can explain the phenomenon of intrinsic change.2 I am now straight-shaped, but will fail to be straight-shaped in the future. There is an..

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 (Jackson 1998, p. 138). 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!

Worlds, Lewis says this: Let us say that something persists iff, 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. Perdurance corresponds to the way a road persists through space; part of it is here, and part of it is there, and no part is wholly present at two different places. Endurance corresponds to the way a universal, if there are such things, would be wholly present wherever and whenever it is instantiated. Endurance involves overlap: the content of two different times has the enduring thing as a common part. Perdurance does not.1 Lewis's remarks suggest the following formulations of the two views in the 3D/4D controversy.2..