The Atlas of Reality
Page 88
If we adopt Presentism, then we must believe that persisting things are metaphysically fundamental. A persisting thing could not be a logical construction from a collection of instantaneous things spread out over time, since Presentists deny the existence of anything that does not exist in the present. There cannot be any instantaneous things that do not exist in the present moment, and so there cannot be any logical constructions of such things. Similarly, Presentists cannot take there to be fundamental spatiotemporal or genidentity relations, since the relata of such relations do not exist at the same time, and so are never in existence together.
If we have embraced Strong Powerism (4.4A.3), then we have some reason to embrace Enduring Substratism as well. The possession of passive and immanent powers both presuppose that the bearer persists through time, since to have a passive power is to have the ability to be affected (now or in the future) in a certain way, and to have an immanent power is to have the power to evolve through time in accordance with a certain pattern. If there are fundamental truths about such powers, there must be fundamental truths about the persistence of their bearers. This is especially true if some of the fundamental powers involve continuous activity over intervals of time (such as the passive capacity to acquire inertial motion through absorbing kinetic energy or such biological activities as respiration, metabolism, sensation, and voluntary motion). For similar reasons, Strong Nomism (4.4A.2) may provide support for Substratism, so long as the fundamental laws are laws about the interactions of persisting things.
GENERAL ARGUMENTS FOR REPLACEMENTISM As we have noted, the paradox of intrinsic change is often taken by Replacementists to support their view. Indeed, it is sometimes touted as the main reason to be a Replacementist (cf. Lewis 1986a). Here are two other arguments for Replacementism.
An argument from Instantism (19.1T). If temporal instants are fundamental and all temporal intervals are mere sets or pluralities of instants, then it would be natural to conclude that persisting things are likewise mere sets or pluralities of instantaneous parts. However, this argument isn't airtight. Substratists could believe that both instants and persisting things are fundamentally real.
Replacementism is very attractive from the perspective of Ockham's Razor (PMeth 1), especially if one adopts Spatial Pointillism (18.1T), Anti-Tensism, and Neo-Humeism (4.4T). On this combination of views, there is only one kind of fundamental thing, namely, a thing that occupies a single point of time for just an instant. Each of these things has one or more pure qualities (non-powers) during its brief moment of existence. All of the other facts that make up the world are facts about the temporal and spatial distances between these instantaneous, point-sized entities. The world is just a four-dimensional mosaic of pure qualities, and nothing more. (Couple this view to Concretism 14.1T.1T, and you have, in broad strokes, David Lewis's metaphysical system. See Lewis 1986a.)
24.2.1 Replacementism: reducing the persistent to the instantaneous
Replacementists, as we have noted, think of persistent and changing things as composed, in some way or another, of temporal parts. We turn now to a more detailed exploration of this view.
FROM PLENITUDE TO RAMSEY-LEWIS-SIDER PERDURANTISM Replacementists imagine a world that is literally filled with instantaneous objects, each fundamental and each existing only for a moment. Since we are assuming that there are persisting things, we must suppose that these instantaneous objects sometimes form persisting wholes that persist for some finite period of time. Replacementists must ask an analogue of the Special Composition Question (from Chapter 22) applied to temporal parts and wholes: when do some instantaneous things compose a persisting thing? One possible and very simple answer is: Always. This is Temporal Plenitude:
24.3T.1 Temporal Plenitude. For every set S of instantaneous temporal parts of things, containing exactly one instantaneous object for each instant in some finite interval T, there is a persisting thing that persists throughout T with exactly the members of S as its instantaneous temporal parts.
Temporal Plenitude can be expressed in the language of spacetime worms. We could say that Temporal Plenitude asserts the existence of arbitrary spacetime worms, one worm for each set of instantaneous temporal slices of things, containing exactly one time-slice for each instant in some interval T. Adopting Temporal Plenitude would force us to recognize all kinds of strange objects, such as things that are squirrels before midnight and battleships after midnight or car-like objects that go out of existence whenever a car is driven out of a garage and that are generated whenever a car is driven into a garage. Any successive chain of time-slices, however different and however discontinuously scattered about space, would constitute a persisting object, according to Temporal Plenitude.
A somewhat restricted version of this thesis would posit only the existence of arbitrary continuous worms, worms whose trajectory through time and space is continuous, without any jumps or discontinuities.
Def D24.6 Spacetime Worms. S is a spacetime worm over interval T if and only if S is a set of instantaneous things, containing exactly one instantaneous thing for each instant in T.
24.3T.2 Continuous Arbitrary Worms. For every spacetime worm S over interval T, if the spatial locations of the members of S form a continuous trajectory through spacetime, there is a persisting thing that persists throughout T with exactly the members of S as its instantaneous temporal parts.
Why do philosophers find it natural to talk of spacetime “worms” in this context? Imagine a dog walking a mile down the street. The path of the dog is worm-like: very narrow at each moment in time (less than a yard wide, tall or deep), but very long over the interval of the walk (several hundred yards long). In addition, if the dog takes 15 minutes to walk the mile, then the corresponding spacetime worm is 15 minutes long along the time dimension. We can convert time into space and vice versa by using the natural ratio given by the speed of light. A second of time would be equivalent to a light-second of space (186,000 miles). Consequently, a 15-minute walk is very long in the time dimension and narrow in the three spatial dimensions.
The main advantage of Continuous Arbitrary Worms over Temporal Plenitude is that the latter lends support for the impossibility of discontinuous motion.3 That is, it provides support for Continuity of Motion:
PNatPhil 3 Continuity of Motion. It is impossible for any material thing to move discontinuously through spacetime.
There is, however, another serious problem with Continuous Arbitrary Worms, one explored by Hawthorne (2006: 111–144). In fact, Hawthorne isolates two related problems: the restriction problem and the collapse problem. To satisfy the restriction problem, Replacementists must somehow explain which continuous worms correspond to quality or dynamically first-class objects, that is, objects that obey the fundamental laws of physical dynamics. Many continuous worms obviously do not satisfy those laws. For example, suppose that two neutrinos with different velocities were to meet at a point in space and pass through one another without effect. The history of each particle corresponds to a continuous spacetime worm. However, there are also two other worms, one made up of the pre-collision history of particle 1 and the post-collision history of particle 2, and the other made up of the pre-collision history of particle 2 and the post-collision history of particle 1. These two spacetime worms correspond to fictional or junk objects. Call these junk objects particle 1-2 and particle 2-1. Particle 1-2 might suddenly speed up at the meeting point and simultaneously change directions, while particle 2-1 slows down and makes a mirror-image change in direction. The two junk particles might well violate the laws of conservation of energy and momentum. They might even violate other laws, such as the conservation of spin.
A slight variation in the same thought-experiment also illustrates the collapse problem. Suppose for example that two identical particles actually collide and ricochet off one another. In such a case, there are actually four continuous spacetime worms. Let's use A and B to represent the paths of the two particles before the collision, and C and
D to represent the two paths after the collision. Particle 1 follows the trajectory A+C and particle 2 follows the course B+D. In addition to these two, there are two additional spacetime worms: A+D and B+C. These two worms represent the case in which the two particles pass right through each other without deflecting or being deflected from their original, straight-line trajectories. Common sense tells us that there are two distinct possibilities here, one in which there is collision and ricochet and a second in which the particles pass through one another without effect. The doctrine of Arbitrary Continuous Worms would force us to say that there is just one possibility here, one that can equally well be described in either way. There would be no real fact of the matter as to which happened, a result that seems quite paradoxical.
Another set of thought-experiments involves motion in absolutely continuous and homogeneous substances. Examples of this sort have been offered by C.D. Broad (1925: 36–7), Saul Kripke (discussed by Shoemaker 1984: 242–247), and David Armstrong (1980). We could imagine an infinitely long river of homogeneous stuff. Imagine that we've reduced friction to zero, and the river is not undulating or pulsating in any way. We can't tell whether the river is moving at all or how fast it is moving or in which direction, simply by looking at the changes in qualities at various spatial locations, since there are no qualitative changes of this kind. A similar thought-experiment involves a sphere of homogeneous stuff that is spinning (cf. Zimmerman 1999). Again, its spinning in a certain direction doesn't correspond to any pattern of qualitative or quantitative change. The sphere maintains its shape and position, and its interior remains homogeneous in quality, density, and chemical composition. How can we distinguish the quality objects from the junk objects if the only fundamental things are instantaneous?
Take a sphere of fluid in the homogeneous river. We could build a spacetime worm of such spheres corresponding to a northward movement at 10 mph. We could build an equally good worm corresponding to a perfectly stationary sphere. In fact, there are infinitely many such spacetime worms, all coinciding with a given sphere at a time, all moving in different directions and at different speeds, and all perfectly consistent with the uniform distribution of qualities. (As Hawthorne pointed out, the qualitative uniformity isn't essential to these thought-experiments. Even if the river varied in quality over time, we would still have to ask whether it is a stationary fluid that is changing in its qualities at various places or whether it is a qualitatively constant fluid that is moving around.)
The homogeneous movement thought-experiments also illustrate the collapse problem. Replacementists seem to be forced to say that there is no fact of the matter as to whether the fluid or the sphere is moving. There is just one possibility that can be described in infinitely many different ways, each equally true. Intuitively, this is simply wrong. There is all the difference in the world between a stationary disk and a spinning one, or a disk spinning in one direction and one spinning in the opposite direction.
Replacementists might hope that the laws of nature or facts about causal connections could help sort out both of these problems. Suppose, for example, that there is a law of nature to the effect that whenever the paths of two particles meet, they must collide and ricochet off one another. That would rule out one of the two possibilities in the case of the colliding particles thought-experiment. However, Replacementists had better be careful here. If the laws of nature are fundamental truths, and those laws make reference to persisting things, like particles, then it would seem that the persisting things are also fundamental and irreducible.
The best way (and perhaps the only way) out would be for the Replacementists to adopt Neo-Humeism, reducing laws to patterns of particular fact by means of the Ramsey/Lewis Theory of laws (see Section 5.2). As Sider (2001: 230–236) explains, we could then extend the Ramsey/Lewis Theory to an account of persisting things as well. The account would go roughly like this: a spacetime worm corresponds to the existence of a persisting thing if and only if the simplest and most powerful scientific theory of the actual world assigns the worm to a single persisting thing as its trajectory. This view is Ramsey-Lewis-Sider Worms:
Def D24.7 Worm/Thing Correspondence. If x is a spacetime worm and y is a persisting thing, then x corresponds to y if and only if x and y have exactly the same instantaneous parts.
24.3T.3 Ramsey-Lewis-Sider Perdurantism. A spacetime worm S over interval T corresponds to the existence of a derived thing persisting through T if and only if the simplest and most powerful scientific theory of the actual world assigns a persisting entity to S.
If Ramsey-Lewis-Sider (R-L-S) Perdurantism is combined with Neo-Humeism, we end up with a version of Replacementism according to which the existence of persisting things is reducible to the more fundamental facts about instantaneous things and their qualities and spatiotemporal relations. R-L-S Perdurantism is one way of providing an account of genidentity as a non-fundamental or derived relation:
Def D24.8 Genidentity. Two instantaneous things x and y stand in the genidentity relation if and only if there is a single persisting thing z (either fundamental or derived) such that x and y are time-slices of z.
For Substratists, the genidentity relation depends on the real, fundamental existence of persisting things. For Replacementists, this cannot be so. Replacementists have two options: they could add genidentity as a new, fundamental relation (resulting in Classical Genidentity Theory) or they could try to reduce genidentity to other relations, such as causal, nomic, and temporal ones. R-L-S Perdurantists take the second course. (We'll take up Classical Genidentity Theory in the next section.) For R-L-S Perdurantists, whether two instantaneous things stand in the genidentity relation to one another depends on whether the simplest theory of the world treats them as time-slices of the same thing.
How does R-L-S Perdurantism help with the problem of the spinning homogeneous sphere or the flowing infinite and homogeneous river? It can help if the sphere and the river have a more interesting history and if they are embedded in a world in which a variety of things happen. Suppose that someone started the sphere's spinning by striking it in a certain way, and suppose that the simplest and most powerful scientific theory in that world is one in which striking things in that way causes them to spin. For example, there may be many other cases of bumpy and heterogeneous spheres that are made to spin in certain ways in that world. In the case of the river, perhaps the whole river is under the influence of a gravitational field that causes all liquids to flow downhill at a certain rate of acceleration, whether they are homogeneous or not. Under such hypotheses, there could be a definite matter of fact as to whether a given sphere is spinning or a given river flowing.
PROBLEMS WITH R-L-S PERDURANTISM: SMALL POSSIBLE WORLDS Dean Zimmerman (1999) points out that R-L-S Perdurantists will have residual problems with small worlds, a point that Lewis himself conceded (Lewis 1999b). Suppose that the entire universe is filled with a single, uniform substance and that the laws of the world in question make it impossible for there to be any vacuums and impossible for there to exist any matter of any other kind. In such a world, any law of motion would be superfluous. The simplest system of laws would require the fluid to be essentially stationary. We would have to say that it is metaphysically impossible for any locomotion to exist in such a universe, which is surely an incorrect result. We could easily imagine that there are eternally recurring eddies and vortexes within the fluid, any of an infinite variety of kinds of motion.
Sider (2001: 233–234) considers a particular simple world that is very troubling for his theory, namely, a world consisting at all times of a single, spinning, homogeneous sphere, with a velocity vector field attached to the material points within the sphere. That is, the simplest laws of nature require us to assign vectors to each point in the sphere, a vector of the kind that we normally assign to moving things in our world. As Sider recognizes, there are at least two equally good candidates for the best system of laws in such a world:
(1) Each material point locat
ion-event with a velocity vector is always genidentical to some later material point location-event that is located in the direction toward which the original velocity vector was pointing. (The sphere is rotating in the direction indicated by the velocity vectors.)
(2) A material point location-event with a velocity vector is always genidentical to some later material point location-event that is located in exactly the same place as the first location-event. (No motion at all. The velocity vectors all point in some direction, but they are not nomologically connected with any locomotion.)
Sider admits that he cannot decide in a principled way between these two candidates. So he must give up the intuition that there could be any fact of the matter about whether such a sphere is rotating or not.
Sider recognizes that R-L-S Perdurantists face this difficulty, but, as he points out, it is a difficulty afflicting the Ramsey/Lewis Theory of the laws of nature, not one specific to the Replacementist component of R-L-S Perdurantism. Sider puts it this way, “The defender of best-system accounts is already accustomed to biting similar bullets” (Sider 2001: 234) To our mind, these small world counterexamples to the Ramsey/Lewis Theory of laws are about as devastating as things get in metaphysics.