The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  The epistemological puzzle is similar. If any number of distinct composites can have exactly the same parts at the same time, how could we ever tell how many of them there are? The most plausible answer to this question would be to appeal to relational structures as the ground for duplication (see Section 10.3 on structural universals).

  As explained in Koons 2014b, Aristotelian Compositional Reductionists can account for Strong Supplementation by appealing to the fact that the compositional structure of an Aristotelian universe will be linear: if x is not a part of y, and y is not a part of x, then x and y will not overlap at all. If two wholes did partially overlap each other, the entity constituting the overlap would have causal powers that are wholly grounded in two separate, independent sets of facts (facts about the two distinct wholes), which would happen only very rarely, if ever.

  Let's turn one last time to Composition as Identity. Is there a way to repair CAI in order to provide a foundation for Strong Supplementation (and, thereby, for Weak Supplementation as well)?

  We could try modifying the definition of completed plurality in this way:

  Definition of Completed plurality (2). The x's are a completed plurality if and only if

  (i) for every y such that y is one of the x's, if y = the z's, then each of the z's are one of the x's, and

  (ii) for every y such that there are some z's, y = the z's, the z's are a completed plurality, and each of the z's overlaps the x's, then y is one of the x's.

  If this were a workable definition, and if we defined composition and part-of in terms of completed pluralities (CAI 1.1 and 1.2), then we could show that Strong Supplementation would be valid. Clause (ii) would simply guarantee that any completed plurality x all of whose parts overlap some completed plurality y would have to be a part of y, which is exactly equivalent to Strong Supplementation.

  However, there is an obvious problem with this definition: it is viciously circular. We have to include the phrase ‘completed plurality’ in the very definition of that phrase, since we are restricting the part-of relation to wholes that are themselves completed pluralities (by CAI 1.2).2

  The only way around this problem is to make the definition recursive: which means that one must stipulate one or more base cases of completed plurality (such as: every pair of atoms is a completed plurality), and then use repeated applications of the definition above to generate additional cases. However, this will only work on the assumption that every composite thing is built up recursively from atomic parts, and so CAI theory would simply collapse into Reductive Compositional Anti-Realism.

  23.4 Parthood and Truthmaking

  Finally, let's turn to the question of the relationship between parthood and truthmaking. If x is a part of y, what is the truthmaker for this truth? Much turns on the essences of x and y. Is x essentially a part of y or is y essentially an encompasser of x or is neither the case? Let's define a ‘constant’ whole as one that contains all of its parts essentially and a ‘rigid part’ of something as something that is essentially a part of that whole:

  Def D23.5 Constant Wholes. x is a constant whole if and only if for all y, if y is possibly a part of x, then necessarily, if x exists then y is a part of x.

  Def D23.6 Rigid Parthood. x is a rigid part of y if and only if necessarily, if x exists, then x is a proper part of y.

  In the case of either constancy or rigidity, the parthood truths have a simple truthmaker. If x is a constant whole and y is a proper part of x, then x itself is the classical truthmaker for y's being a part of x. Similarly, if x is rigidly a part of y, then x itself is the classical truthmaker for x's being a proper part of y.

  Suppose that x is a proper part of y but not a rigid part, and y is not a constant whole. What then could the truthmaker be? It would seem that in such a case the parthood relation between x and y must be grounded in some further facts about x and y. In other words, it seems that we cannot then have a case of fundamental parthood. It seems that the fundamentality of parthood requires constancy or rigidity of some kind:

  Fundamentality Entails Constancy/Rigidity. If it is a fundamental fact that x is a proper part of y, then either y is a constant whole or x is a rigid part of y.

  We will return to the questions of mereological constancy and rigidity in Section 25.1, on persistence though a change of parts.

  Notes

  1. Of course, it can't be a fundamental fact about these fundamental things that they are simple (i.e., lacking in parts), since all facts about parts (including negative facts, like being simple or atomic), must be merely derived facts. Still, it seems to be coherent to suppose that there are fundamental things that are only derivatively atomic, since the proposed reduction of the part-of relation assigns them no parts.

  2. If we were to try to solve this problem by using a weaker restriction on the pluralities in clause (ii), by, for example, using the first definition of ‘completed plurality’, we would then run into problems of cardinality, i.e., problems with the absolute size of the pluralities involved. A weaker condition of that kind would in effect require a completed plurality to contain a distinct element for each of its non-empty, proper sub-pluralities, which is mathematically impossible for any plurality of greater than two elements (unless the members of the plurality form what mathematicians call a ‘proper class’, a fantastically large plurality).

  24

  Change and Persistence

  In the last couple chapters, we looked at the issues surrounding composite things: when do some things compose a whole, and what is composition? In this chapter and the next, we examine questions having to do with whether and how things persist through change. Is persistence possible? If things do persist, how do they do so? Are persisting things a kind of whole, made up of merely momentary pieces? If so, what unifies such instantaneous things into a single unified life? The issues in these chapters have profound ethical and existential implications, since we ourselves are among the world's persisting things. Is our identity over time something fundamental, or is it reducible to more basic facts? Is each of us truly one thing that exists through many moments, or a multitude of temporary things? Maybe more basically, is each of us really just a single thing or are we really a multitude of more or less coincident things?

  Two principal issues have occupied philosophers in this area. First, can objects persist through a change of properties, and if so, how? Second, can objects persist through a change of parts, and if so, how? We will take up the second issue in Chapter 25. With respect to the first issue, we will first consider (in Section 24.1) the question of whether things can change intrinsically at all. This is the dispute between Staticism and Kineticism. Next, assuming that intrinsic change does take place, we will examine in Section 24.2 two principal views about how things persist through change of intrinsic properties, Substratism and Replacementism. Substratists think that persisting things are fundamental, that one and the same fundamental object can have different properties at different times. Replacementists think that persisting things are not fundamental, that they are composed of a series of instantaneous temporal parts, and that a persisting thing has different properties at different times by having different parts that have those properties once and for all. Our final section on change (Section 24.3) will focus on the specific but very important case of motion, or change of location. Here there are three major theories: Intrinsic Motion, according to which motion is intrinsic at each moment to the moving thing; Bertrand Russell's At/At Theory, which defines motion simply as change in position over time; and an Aristotelian theory, Motion Intervalism, according to which motion is intrinsic to temporally extended processes.

  24.1 Does Anything Change? Does Anything Persist?

  Our experience of the world seems to present us with things that both change and persist, where a thing persists if it exists at more than one time. For example, objects in the external world, like people and dogs and computers and rocks, seem able to change and persist. When one reflects on oneself, one is al
so led to the view that one is capable of both change and persistence. For example, each of us seems to remember past actions and events in which he or she—the very person doing the remembering—once participated. Indeed, even our internal conscious states change and persist. Importantly, there are really two issues here, one having to do with change and another having to do with persistence through time. These issues are intimately interconnected, but for the most part we will focus on change. As we will see, views about change tend to drive views about persistence. At any rate, it is plausible to think that both Kineticism and Persistence are true.

  24.1T Kineticism. Some things change.

  24.1A Staticism. Nothing changes.

  24.2T Persistence. Something persists (has existed or will exist at more than one instant).

  Staticism commits us to counting the appearances noted above as illusory or misleading. One version of Staticism would be Solipsism of the Present Moment (20.1T.1A), according to which only one thing exists (one's own consciousness) and only for an instant. On this view, all memories of a so-called “past” and expectations for a “future” are simply illusory. Since we've already discussed this view in Chapters 13 and 20, we here assume that many things exist, and that there is some kind of real distinction among past, present, and future.

  How then, could one deny the reality of change? Clearly, different things happened in the past from what is happening now; dinosaurs once roamed the earth but do so no longer. And many things will happen in the future that have not happened yet, including, perhaps, human colonies on Mars. This is a question that will occupy us.

  To get at the real issue, we need to distinguish intrinsic change from mere Cambridge change. It is easier to give examples than to provide a clear and non-circular definition of these categories. When something changes its color or temperature, this seems to amount to some change in its intrinsic character or way-of-being. In contrast, when a woman's husband dies, her change in status from wife to widow need, in and of itself, involve no such change (of intrinsic character). The wife might not become aware of the husband's death for some time, and the same might be true of everyone with whom she interacts.

  Def D24.1. Mere Cambridge Change. Something undergoes a mere Cambridge change when it changes without changing intrinsically.

  24.1T.1T Strict Kineticism. Some things change intrinsically.

  24.1T.1A Moderate Staticism. Some things undergo mere Cambridge change, but nothing changes intrinsically.

  Democritus, Empedocles, and Descartes (if we focus on the physical world) advocated Moderate Staticism. All change consists of motion or, more precisely, locomotion: change in position. Locomotion, in turn, can be understood in two different ways: (1) as change in absolute position, that is, as moving from one place to another, or (2) as change in relative position, in a thing's distance from other things.

  Moderate Staticists must deny that there are composite things, things composed of atoms (like organic bodies or solar systems), since if there were such things, and if their constituent atoms were to move with respect to one another, then there would be intrinsic change (at the level of composite entities) after all. That is, Moderate Staticists must embrace Mereological Nihilism (22.6T.1T, 23.1A). They must also accept Spatial Relationism (17.1A), since if places exist, then locomotion would seem to involve either an intrinsic change in the places or in the place-occupiers. However, if spatial position consists entirely of relations to other things, and there are no composite things, then there would be absolutely nothing for locomotion to be intrinsic to. If a change occurs but is not intrinsic to anything, it would seem to be utterly unreal. Hence, Moderate Staticism seems an incoherent position.

  In addition, modern physics seems committed to the existence of intrinsic change. For example, some fundamental particles, like electrons and positrons, can undergo events of creation and annihilation. If an electron meets a positron, both particles are instantly annihilated, creating one or more new particles. Creation and annihilation are certainly cases of intrinsic change!

  Shortly, we will move to a discussion of two types of intrinsic change, change of property and change of part. First, though, we want to touch on one other issue about change.

  IS THERE AN ENDURING SUBJECT OF CHANGE? One important, and of late somewhat under-appreciated, dimension of change and persistence is whether change requires the existence of some enduring thing that underlies the change, something that exists both before and after the change, such that the intrinsic change is intrinsic to the enduring thing. To get at this issue, consider the following distinction between two kinds of change:

  Def D24.2 Qualitative Change. A thing undergoes qualitative change if and only if it changes intrinsically and exists both before and after the change.

  Def D24.3 Substantial Change. A thing undergoes substantial change if and only if it undergoes intrinsic change and either does not exist before the change (creation) or does not exist after the change (annihilation).

  It may be possible that a single change is both qualitative and substantial. The qualitative change of one thing (the enduring subject) might just be the creation and destruction of two additional things (some modes or attributes of the subject). A change is a case of purely substantial change if and only if it does not consist in the qualitative change of anything whatsoever. Using this distinction, we can distinguish two views about whether all intrinsic change requires an enduring subject, two versions of Strict Kineticism:

  24.1T.1T.1T Enduring Substratism. Fundamental things can undergo qualitative change, existing before, during and after the change.

  24.1T.1T.1A Replacementism. It is possible for something fundamental to undergo substantial change but not qualitative change.

  Replacementism asserts that the only kind of intrinsic change that is possible is purely substantial change, while Substratism affirms the possibility of qualitative change at the most fundamental level. If nothing fundamental persists through a change, then that change must consist in something's coming into existence (creation) or something's ceasing to exist (annihilation). Creation and annihilation are the two forms of substantial change. If a substantial change can occur even though nothing persists through the change, then it should be possible for everything in the world to be annihilated and replaced in an instant with a new set of things. Let's call such a global event ‘Global Replacement’.

  The possibility of Global Replacement follows from Replacementism assuming plausible patchwork principles. We have distinguished two patchwork principles:

  PMeta 5.1 Finite Patchwork. If an event or process of (intrinsic) type A is possible, as is an event or process of intrinsic type B, and if there is enough room in the history of the world to locate in it instances of both events (or processes) without overlap in time and space, then it is possible for events (or processes) of both types to occur together.

  PMeta 5.2 Infinite Patchwork. If T is a class of types of events or processes, and for each member of T, it is possible for an event or process of type T to occur, and there is enough room in the history of the world to locate within it instances of each of the types in T without overlap in space and time between the instances, then it is possible for all of the types in T to be realized together.

  The possibility of Global Replacement follows from an instance of the Infinite Patchwork Principle. If pure substantial change is possible in a single case, then it would be possible for such changes to fill all of space at the same time (since such changes wouldn't overlap in space and time).

  Tensers (20.2T) can use patchwork principles to build a simple argument for the necessity of an enduring substrate of change:

  Suppose that it was possible for some change to occur without any enduring thing.

  If this could happen once somewhere, then it could happen always everywhere. (Finite/Infinite Patchwork)

  So, if 1 and 2, then there could be a world containing time and change, but in which nothing persists for more than an instant.

&n
bsp; But such a world would be nothing but a pointillist mosaic of qualities extended over four dimensions, that is, an Eternalist (20.2A.2T) “block” universe.

  An Eternalist universe is one without any real change (as McTaggart argued) and so without time.

  Consequently, 1 must be false: every change must be accompanied by something that persists through the period of change.

  Anti-Tensers (20.2A) will reject premise 4. They could embrace a version of Russell's At/At Theory applied to change of properties, and they will deny that an Anti-Tensist, B-theoretic block universe is really devoid of change. So long as a thing has different properties at different times, they will say that there really is change in the world. Is there a version of the argument from Global Replacement that does not depend on Tensism?

  Suppose the world did undergo Global Replacement. This possibility would pose certain difficult problems, even for Anti-Tensers. First, what would make it the case that what is being described is really a change in a single world? Why not say that one world, with its one time-line, has simply been annihilated, bringing its time to an end, while another, entirely separate world has been created ex nihilo, with its own time beginning to exist for the first time. What is it that makes the last moment of the first world identical to the first moment of the second world, in such a way that the two time series together compose a single time series? It's not obvious that one can answer these questions in a principled way, or even distinguish between the two possibilities.