Intrinsic Energy. Kinetic energy and momentum are intrinsic properties of moving things.
Energy a Function of Velocity. Kinetic energy and momentum are determined by and dependent on velocity.
The best strategy for At/At Theorists is to challenge Intrinsic Energy, arguing that the explanatory role of kinetic energy and momentum comes entirely from the fact that the fundamental laws of motion make reference to them, not to the metaphysical status of the properties as intrinsic features of moving things. This turns on a question that we took up in Chapters 4–6: are powers or the laws of nature more fundamental? At/At Theorists should be attracted to either a Nomism or Neo-Humeism, while Intrinsic Motion fits best with Powerism.
The At/At Theory is compatible with relativity theory. The At/At Theory doesn't presuppose the existence of absolute rest or motion or of a substantial space. It can be formulated in terms of Minkowski spacetime, with four dimensions (three of space and one of time). Intrinsic Motion, in contrast, is incompatible with relativity theory, since it entails that there is a real, intrinsic difference between bodies that are moving and those that are at rest. This is a serious drawback to Intrinsic Motion.
24.3.2 The At/At Theory vs. Intervalism
We can distinguish between moderately discontinuous and radically discontinuous motion. In the case of moderately discontinuous motion, every location-event belongs to a process of movement, but two such processes may be discontinuous, with the object undergoing a quantum jump in location from one place to a distant one at an instant. In the case of radically discontinuous motion, there are spatially isolated location events, events that do not belong to an extended process of motion, neither to the interior nor to an extreme boundary of such a process. In radically discontinuous motion, an object might undergo continuous motion up to time t, jump discontinuously to some distant location at time t, and jump immediately afterward, undergoing a second period of continuous motion after t at another distant location. The object's motion at t in such a case is radically discontinuous, unconnected to any continuum of motion both before and after.
There are two reasons for thinking that moderately discontinuous motion might be impossible. First, there is the problem of securing the persisting identity of the moving body both before and after the discontinuous jump. Second, any such jump would involve a kind of action at a spatial distance, with the condition of the body after t dependent directly on its condition at t, with a finite distance separating the two.
No Radically Discontinuous Motion. No body occupies a spatial position A at time t while also occupying positions at some fixed finite distance d from A at all times both before and after t.
Intervalism (19.1A) is a third reason for rejecting the possibility of radically discontinuous motion. If intervals rather than instants are metaphysically fundamental, then it would be impossible for a moving body to occupy a location at an instant when that location-event is not part of a temporally extended process of locomotion. This suggests that there is a third alternative, one disagreeing with both the At/At Theory and Intrinsic Motion. This third theory would agree with the At/At Theory by rejecting the view that motion is intrinsic to a thing at a moment, but it would differ from the At/At view by insisting that the fundamental truths about location are not truths about instantaneous location events but rather truths about extended processes of motion. This third position is Motion Intervalism, since it builds on the foundation of Intervalism:
24.5A.1A Motion Intervalism. The fundamental truths about locomotion are truths not about location events but about extended processes of motion.
Motion Intervalism is the position adopted by Aristotle and many of his successors. It has a simple answer to Zeno's paradox: the history of the arrow does not consist in a series of momentary states, but in one or more continuous processes of motion. During each of these metaphysically fundamental motion-processes, the arrow does not have a unique location, but rather an extended trajectory through space and time. At the same time, it can explain why radically discontinuous motion is metaphysically impossible, in a way that the At/At Theory cannot.
Notes
1. Note that Presentists don't have to be Endurantists. One can be a Perdurantist Presentist, though one would then be committed to denying Persistence. See the second argument for Endurantism, below.
2. Take our reference to vague and context-sensitive properties like coldness or bentness to be shorthand for picking out some specific, fundamental property (like having a precise temperature or exact velocity).
3. Quantum mechanics does not support the idea that motion can be discontinuous. We could say that a particle that is in a superposed state is simultaneously traveling along a very large number of different paths through space, but each of them is continuous.
25
The Persistence of Composite Things
In Chapter 24, we saw that Substratism (24.1T.1T.1T) and Replacementism (24.1T.1T.1A) are the two major contending accounts of intrinsic change. In this chapter, we turn to the interaction between composition and persistence, as the persistence of composite objects provides a critical test case for evaluating these two accounts. In particular, we are concerned with a question about the interconnection between composition and persistence: under what conditions do composite things persist through time? This question divides in two. First, can a composite thing survive the loss or the addition of parts? And second, can two distinct things come to share exactly the same parts at the same time, while retaining their distinct identities? These are, respectively, questions about mereological constancy and mereological coincidence. If a thing is mereologically constant, then it is incapable of gaining or losing parts over time; same thing, same parts. Some complex things, including organisms, seem to be mereologically inconstant, that is, capable of gaining or losing parts. In Section 25.1, we try to sort out whether inconstancy is possible, and if so, how. Two things are mereologically coincident at a time if they have exactly the same proper parts at that time. In Section 25.2, we look at arguments both for and against the possibility of coincidence. If coincidence is impossible, we would have the metaphysical law: same parts (at a time), same thing.
These two issues pose some challenging problems for both Substratism and Replacementism. For example, if Substratism is true, then we should expect diachronic survival to be a transitive relation: if A is the survivor of B at some point of time, and B the survivor of C at another time, then Substratists should assume that numerically the same substrate underlies A, B, and C at their various locations in time. Since numerical identity is transitive, so must be survival through time. However, as we shall see, there are a number of paradoxical situations that challenge the assumption that survival is transitive. In addition, Substratists have to cope with the possibility of intermittent existence. For example, if substrate x exists at time t1, ceases to exist at a later time t2, and then exists again at some still later time t3, Substratists must provide an account of what it means for a substrate to exist at some times and not at others. They will also have to explain why some substrates can survive certain kinds of changes and not others, and why some kinds of substrates can survive changes that other kinds cannot.
Replacementists are not bound to any assumption of the transitivity of identity, as we have already seen. Nonetheless, the task of accounting for the various paradoxes of survival for inconstant objects is still not trivial for the Replacemenist.
25.1 Mereological Constancy and Inconstancy
Can persisting things gain and lose parts? It would seem that quality objects, that is, dynamically first-class things that obey the fundamental laws of physics, cannot gain or lose parts. Such dynamically first-class things must satisfy the law of conservation of mass-energy, among other conservation laws. Such things are mereologically constant.
25.1T Mereological Constancy. Necessarily, everything that persists has exactly the same parts at all times at which it exists.
25.1A Mereological Inconstancy.
It is possible for a persisting thing to gain or lose parts over time.
Are there any mereologically inconstant things? Unstructured masses seem to be constant. So we have to look to structured things like natural formations (rivers, mountains), artifacts, and living organisms. All of these seem capable of surviving the gain and loss of parts. A river continues to exist, although it is constantly gaining new bits of water (as the rain falls on its watershed) and losing other bits (as they flow into the sea or evaporate from its surface). Artifacts can gain and lose parts, and it is obvious that living organisms do so all the time. But are any of these things fundamentally real? We've already established that they are not quality or dynamically first-class objects. That may provide some reason for doubting whether they are fundamentally real, but it is not all by itself a decisive reason. Why couldn't there exist real, fundamental things that do not themselves fall within the scope of the laws of physics? The laws of physics might apply only to a proper subset of the world's fundamental things.
Do we have any positive reasons for believing in mereologically inconstant things? Our common sense suggests that the world is filled with such things, as we've seen. Science might give us some reason for believing in the existence of unifying, continuous processes, like the flow of liquid water in a stream or of nuclear fusion in the heart of a star. In addition, we have strong Cartesian reasons for believing that each of us exists (see the discussion of the Cogito argument in Section 22.6.1), and each of us seem to be inconstant, since we are living organisms. In order to avoid that conclusion, we might suppose that we are immaterial souls that inhabit and animate our living bodies or even that we are each some small, special particle located somewhere in the brain.
There are two problems with such attempts to identify human beings with constant objects. First, many of our ethical and interpersonal beliefs and practices presuppose that we are composite, mereologically inconstant, (at least partly) material objects, and not mere souls. We treat rape and torture as violations of the person, and not as on a par with vandalizing a person's property. We believe that we see and touch other people and not merely material things animated by other people. Second, if there were no mereologically inconstant things, then we would have no bodies. All that would exist would be atoms and souls (and mereologically constant sums of these). If one's body does not exist, then there would be a very severe problem explaining how one (a pure immaterial soul) would be able to interact in a regular way with the physical universe. Mental/physical interaction is a hard enough problem for dualists. Denying the existence of a persisting, living body makes the problem insoluble. What would tie each soul to some congeries of particles if there is no enduring human body to serve as the locus of interaction?
25.1.1 Objections to inconstant things: Paradoxes of intransitive persistence
Even though the existence of inconstant things seems to be part of our common-sense view of the world, philosophers have long been aware of the fact that inconstant objects give rise to a number of difficult puzzles and paradoxes. Many have used these paradoxes as an argument for rejecting the real existence of inconstant objects, especially when Substratism is taken for granted.
If something really persists from time t1 to time t2, then there is something existing at time t1 that is identical to something existing at time t2. We have cases of diachronic (cross-time) identity. It is a basic principle of logic that identity is transitive:
The Transitivity of Identity. Necessarily, if x = y and y = z, then x = z.
We have also seen in Section 24.2.2.1 that there is a strong argument (made by Kripke) for thinking that identity and distinctness are eternal. Once distinct, always distinct, and once identical, always identical. Consequently, if x = y at any time and y = z at any time, then x = z at all times.
However, if there are inconstant things, then there are cases in which we want to say that x (something existing at time t1) is identical to y (existing at time t2), y is identical to z (existing at time t3), and yet x is not identical to anything existing at time t3. In other cases, we want to say that x (existing at time t1) is identical to y (at time t2) and also identical to z (at time t2), even though y and z are not identical to each other.
PARADOX 1: THE SHIP OF THESEUS The ship of Theseus is an ancient puzzle about the persistence of material objects through time. We are to imagine a ship whose planks of wood are taken out, one by one, placed in a warehouse, and replaced by new planks. Eventually, all of the ship's wood has been replaced, and a second ship is constructed from the planks stored in the warehouse. Which ship is the original? It is tempting to say that both ships are identical to the original, but this leads to a conflict with the transitivity of identity, since it is obvious that there are two distinct ships at the end.
If we reject the existence of artifacts and other inconstant objects, we can avoid the problem by simply denying that there ever was or is a ship at all. All we can say is that there is ship-ping going on here-ishly and there-ishly. The question of which ship is identical to the original ship of Theseus cannot be properly posed.
PARADOX 2: TIB AND TIBBLES Suppose there was a rabbit that putatively survived the loss of its left foreleg. Let's call the rabbit before the removal of the leg ‘Tibbles’, and let's call the rabbit minus its leg ‘Tib’. It seems that both Tib and Tibbles exist before the leg is removed. At that point in time, Tib is a proper part of the rabbit (all of the rabbit except for its left foreleg). It seems clear that Tib and Tibbles are not identical, since Tibbles has a left foreleg and Tib does not. However, after the leg is removed, the rabbit is identical to Tib, since the rabbit itself now lacks a left foreleg. So, we seem to be saying that, at t1, Tib and Tibbles were not identical, and the rabbit and Tibbles were identical. At the later time t2, the rabbit and Tib are identical. So, the rabbit was once not identical to Tib, and then later it is identical to Tib. (This problem is related to the problem of the many introduced in Section 22.4.1, but applied across time rather than merely at a single time.)
This problem can be dissolved by rejecting Mereological Inconstancy. There are two persisting things: Tib and Tibbles. Before the operation, Tibbles is a rabbit and Tib isn't (Tib is just part of a rabbit), and after the operation, Tib is a rabbit and Tibbles isn't (since Tibbles is now a scattered object). There simply is no such thing as the persisting rabbit. No rabbit ever persists: all that persist are mereologically constant objects like Tib and Tibbles. Defenders of Mereological Inconstancy can dissolve the paradox in another way: by denying Mereological Universalism (22.3T.1). This at least makes it possible to deny (though it does not entail that) there is no such thing as Tib prior to the loss of the leg, and no such thing that includes the leg after the loss.
PARADOX 3: THE KAFKA PARADOX The Kafka Paradox is similar to the ship of Theseus, except that we focus on the career of a single inconstant object. Suppose that a living organism, like a human being, can always survive the removal or addition or replacement of a single particle. We start with a human being, like Franz Kafka, and we gradually transform Kafka into a cockroach, one particle at a time. It seems clear that a human being cannot persist if all that remains is a cockroach. Human beings cannot become cockroaches, since cockroaches lack many of the essential features of humanity. However, each stage of the transformation seems to be genidentical to the next, and we have good reason to believe that genidentity is transitive.
PARADOX 4: FISSION AND FUSION Suppose that a human being could survive the loss of one-half of his body, including one-half of his brain. Now suppose that a human being is cut in half, and each half is reconstituted into a whole human being through the addition of transplanted organs. Call the original person ‘Alpha’, and the two fission-products ‘Beta’ and ‘Gamma’. Since Alpha could have survived as Beta, and Alpha could have survived as Gamma, it seems that the successful production of both Beta and Gamma should not negatively affect Alpha's survival. In addition, let's suppose that the entire operation was perfectly symmetrical,
so we have no reason for saying that it is Beta, rather than Gamma, that is the best candidate for being the continuation of Alpha, or vice versa.1 Thus, we should say that Beta is Alpha and that Gamma is Alpha. However, it is clear that Beta and Gamma are not identical. They are located in different places, doing different things. Over time, Beta and Gamma could become different in many ways, including their memories, personalities, and legal status. Once again, since identity is eternal and transitive, we seem forced to say both that Beta and Gamma are identical and that they are not identical.
The possibility of fusion provides similar problems for inconstant objects. Suppose we take the organs and brain parts from two people Alpha and Beta and fuse them together, Frankenstein-style, into a single human being, Gamma. Have both Alpha and Beta survived? Was Gamma once two different people? To think so is to violate the eternity of identity. And yet it seems that Alpha and Beta have both in some sense survived, and that Gamma has had some sort of past existence.
25.1.2 Objections to inconstant things: Vagueness and conventionality
THE VAGUENESS OF IDENTITY Suppose that there once was a restaurant in Philadelphia called “Bookbinders''. The restaurant is moved and subsequently changes owners and menus. Is it still the same restaurant or a different one? There will be borderline cases in which we feel that either answer is legitimate. It is hard to believe that there is a real, fundamental fact of the matter. We can make sense of this fact if inconstant objects like restaurants are just useful fictions.
THE CONVENTIONALITY OF IDENTITY: EXOTIC OBJECTS Eli Hirsch (1992, 1993) asks us to imagine a community with very exotic ideas about the persistence conditions of certain objects. For example, they do not believe in cars, but they do believe in incars and outcars. An incar consists in what we would call a car while and insofar as the car is inside a garage. An outcar is a car outside a garage. Let's call the members of this conceptually exotic community ‘Hirschians’. When we back a car out of a garage, Hirschians would say that an incar is gradually shrinking until it vanishes, and an outcar comes into existence, first as a part of the rear bumper and gradually growing into a complete outcar. Hirschians don't believe in persisting cars. They think that the only really persisting things are incars and outcars. If you drive your outcar into a garage, you have destroyed it and replaced it with a new entity, an incar. There are similarly exotic objects that could be constructed out of natural formations. For example, we could consider Sunday-rivers. A Sunday-river is a river-like entity that comes into existence on midnight at the beginning of one Sunday and ceases to exist at the end of the next Sunday.
The Atlas of Reality Page 90
