Motion's Metaphysics: Re-evaluating Four-Dimensionalism's Hegemony in Persistence Debates — Epoche C2
The thesis at issue, stated exactly Theodore Sider's four-dimensionalism is the thesis that every object that persists through time has, at each instant at which it exists, an instantaneous part located at that instant and at no other: persistence is a matter of having temporal parts strung out along the time axis, as a road persists across a county by having spatial parts strung out along it. David Lewis's terms for the two ways an object might last are the ones the literature uses. A thing perdures if it is extended in time and has different parts at different times; it endures if it is wholly present whenever it exists, so that the very same complete object is there at each moment. Four-dimensionalism is the claim that everything perdures; three-dimensionalism, or endurantism, is the denial. The received view is that the perdurantist has the better account of change, and in particular of motion, and that the endurantist's difficulty with an object that is here now and elsewhere later is the strongest reason for switching. This essay argues that the received view has the case almost exactly backwards. Motion is not where the endurantist is weak — the argument standardly cited on that point is about something else — and the one argument in the literature in which motion genuinely bears on the choice between the two ontologies runs the other way, against the perdurantist. The original claim of this essay, that four-dimensionalism's advertised ease with motion conceals a defect, is correct; the defect is a specific and named one, and the sections below identify it. A correction: the problem of temporary intrinsics is not about motion The argument that made temporal parts attractive to a generation of metaphysicians is Lewis's problem of temporary intrinsics (1986). Its statement is short and its scope is narrower than is usually remembered. An intrinsic property is one a thing has in virtue of how it itself is, irrespective of what else exists or how the thing is related to it. Shape is the standard example: being bent is a way I am, not a relation I stand in. Now, I am bent when seated and straight when standing. If I am wholly present on both occasions, then one and the same thing has two incompatible intrinsic properties, which is a contradiction. Lewis offers exactly three ways out: Deny that shapes are intrinsic — treat being bent as a relation between me and a time. Lewis rejects this on the ground that shapes are manifestly not relations to anything. Adopt presentism, holding that the only time at which anything has any property is the present, so that there are never two occasions to compare. Lewis rejects this because he takes past and future times to be as real as the present. Adopt temporal parts. The bent thing and the straight thing are two parts of me, each of which has its shape simpliciter and neither of which has the other's. The argument is valid, and it is the perdurantist's best weapon. But notice what it requires: the property that changes must be intrinsic . And spatial location is not intrinsic on anyone's account. Being in Cambridge is a relation between me and a place; it is the paradigm of what an intrinsic property is contrasted with. So a thing that is in Cambridge at $t_1$ and in Leeds at $t_2$ instantiates no incompatible intrinsic properties at all, and the trilemma has no purchase on it. The endurantist can say, without paying anything, that one enduring object stands in the located-at relation to two places at two times, exactly as one enduring object can be to the left of one thing and to the right of another. The earlier version of this essay accordingly misidentified the terrain when it credited four-dimensionalism with "effortlessly" resolving how a single entity can be in different places at different times, and treated the endurantist's answer as strained. There is nothing to resolve. The endurantist's real burdens lie elsewhere: with change in intrinsic properties, where Lewis's argument does bite, and with the puzzles of coincidence discussed below. Even on its own ground the argument is contested, and the state of the dispute should be reported. Haslanger (1989) replies that Lewis's first option is misdescribed. The endurantist need not turn shapes into relations; she can locate the time-dependence in the instantiation rather than in the property, holding that an object has a property at a time in a way that leaves the property itself monadic. Whether that is a genuine third position or a relabelling of Lewis's first is the live question, and Lewis's argument does not settle it, since it assumes that instantiation is not itself temporally qualified. Where motion does bear on the dispute: the rotating disc There is one argument in which motion is not incidental but essential, and it is the reason the original thesis of this essay is defensible. It concerns a perfectly homogeneous disc — a disc made of continuous matter, with no grain, no marks and no distinguishable parts, perfectly symmetrical about its axis. Consider two situations that are alike in every other respect. In the first the disc rotates uniformly about its axis; in the second it is at rest. The example is Saul Kripke's, from lectures he did not publish, and it entered the literature through discussions in the following decades. The two situations differ. A rotating disc has angular momentum, it will resist a torque, and it will fling off matter if it spins fast enough. But now ask what, in the four-dimensional distribution of matter, the difference consists in. At every point of the spacetime region the disc occupies, in both situations, there is matter of exactly the same kind with exactly the same local intrinsic character. Every instantaneous cross-section is a homogeneous disc of the same density. The distributions are identical. The perdurantist's account of persistence must therefore find the difference in some relation among the momentary stages: which bit of matter at $t_2$ i