The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  This is Simple Bundle Theory:

  9.1T.1T.1A.2 Simple Bundle Theory. Substances correspond one-to-one to co-instantiated sets of universals; that is, a substance S exists if and only if some set of universals U is co-instantiated, and S exemplifies a universal F if and only if F is a member of U.

  BUNDLE THEORY AND INTRINSIC CHANGE The central problem with Simple Bundle Theory is accounting for change and the potentiality for change. Suppose that Jumbo changes from being placid to being angry. At one point in time, we have ELEPHANT, GRAY, and PLACID co-instantiated, and in the next moment it is ELEPHANT, GRAY, and ANGRY that are co-instantiated. If Jumbo simply corresponds to a single set of universals, then it cannot be identical to both of these sets, since the two sets are not identical to each other (one contains PLACID and not ANGRY, the other ANGRY and not PLACID). We have to say either that Jumbo is identical to the first set or to the second. If Jumbo is the first set, then Jumbo was annihilated when the change from PLACID to ANGRY occurred; if Jumbo is the second set, then Jumbo first began to exist when the change occurred. We seem to have lost the obvious and important fact that the change was a change in Jumbo, that Jumbo went from being placid to being angry.

  Thus, correlating particulars with sets of co-instantiated universals is too simple an account. It leaves out some crucially important facts about change and persistence. In response, Bundle Theorists can move in one of three directions:

  Nuclear Bundle Theory

  Four-Dimensional Bundle Theory

  Evolving Bundle Theory

  NUCLEAR BUNDLE THEORY First, Bundle Theorists could distinguish between nuclear co-instantiation and peripheral co-instantiation. Bundle Theorists could then identify particulars with nuclearly co-instantiated sets of universals, or ‘nuclei’ for short (see Simons 1994). A nucleus would correspond to those properties that some particular has at all times and cannot possibly lose, so long as it exists. In contrast to nuclei, a complete bundle is a peripherally co-instantiated set of universals. We will have to assume that each complete bundle contains exactly one nucleus (as a subset).

  Existence and Uniqueness of Nuclei. If x is a peripherally co-instantiated set of universals (a bundle), then there is exactly one subset of x, namely, y, such that y is a nucleus (a nuclearly co-instantiated set of universals).

  We thus get a third type of Classical Bundle Theory:

  9.1T.1T.1A.3 Nuclear Bundle Theory. Substances correspond one-to-one to nuclei of universals. That is, a substance S exists if and only if some set of universals U has the property of being nuclearly co-instantiated, and S exemplifies a universal F if and only if F belongs to some peripherally co-instantiated set (a bundle) that contains U.

  In addition to Nuclear Bundle Theory, which introduces a distinction between nuclear and peripheral co-instantiation, there are three close cousins of Nuclear Bundle Theory:

  One could claim that there are two kinds of universals, essential and accidental. The nucleus of a bundle would then just consist of all the essential universals in the bundle.

  One could claim that bundles have internal compositional structure. On that view, bundles can have sub-bundles. A nucleus could be any sub-bundle that contains no proper sub-bundle of universals. On this account, a bundle could have more than one nucleus.

  One could claim that every subset of the bundle that contains at least two universals is a nucleus. This would entail that any bundle with more than two universals will have multiple nuclei.

  On options 2 and 3, it would be possible for a bundle to have more than one nucleus. In such cases, we would have multiple coincident objects, objects that coincide at a moment by having exactly the same constituents and (consequently) exactly the same properties. However, the various coincident objects would have different persistence conditions. If a bundle had two nuclei, N1 and N2, then it would correspond to two distinct substances, S1 and S2, one with N1 as its nucleus and the other with N2 as its nucleus. If N1 survives but N2 does not, then S1 persists in existence, but S2 does not. If N1 and N2 come to be nuclei of two different bundles, then S1 and S2 will both have survived but will have separated from each other, no longer being coincident in constitution.

  On any version, Nuclear Bundle Theory and its cousins have a straightforward account of change and potentiality. When a particular changes, the nucleus changes from being the nucleus of one complete bundle to being the nucleus of a second, distinct bundle. To return to our simple example, let's suppose that Jumbo is the nuclear set {I, GRAY, ELEPHANT}, where ‘I’ represents some universal that uniquely picks out Jumbo among other gray elephants and that Jumbo could not have failed to exemplify (perhaps ‘I’ corresponds to Jumbo's having a particular origin in space and time). When Jumbo changes from being placid to angry, the set {I, GRAY, ELEPHANT, PLACID} loses its property of being peripherally co-instantiated (and so ceases to be a bundle) and the set {I, GRAY, ELEPHANT, ANGRY} gains the property of being peripherally co-instantiated. Meanwhile, the set {I, GRAY, ELEPHANT} continues to have the property of being a nucleus, and so Jumbo continues to exist, first as placid and then as angry.

  While Nuclear Bundle Theory seems to be able to handle the reality of persistence and change, it introduces a new primitive property or relation of nuclear instantiation. Further, Nuclear Bundle Theory must make some additional postulates involving this new relation. Finally, Nuclear Bundle Theorists must suppose that every bundle of universals contains exactly one nucleus. Thus, the increase in explanatory power that Nuclear Bundle Theory gains over Simple Bundle Theory comes at a not insignificant cost of decreased simplicity.

  Nuclear Bundle Theory's cousins also come at a cost. Option 1, for example, requires a distinction between two kinds of universals, essential and accidental. This option may simply be equivalent to Nuclear Bundle Theory, since the most plausible way to make the distinction would be to stipulate that essential universals are the sort of universals that tend to cohere together in the nuclear way.

  Options 2 and 3 give up on the uniqueness of nuclei: one bundle can have many nuclei at the same time. This means that we can no longer simply identify substances and bundles, since the same bundle (if it has multiple nuclei) will correspond with multiple, coincident substances. Since we are working with a Constituent Ontology, this would seem to force us to identify substances with undivided nuclei, and not with the whole bundle. But then we can no longer attribute accidental properties to substances, since those accidental properties will no longer be constituents of the substances. In other words, options 2 and 3 seem inconsistent with the spirit of Constituent Ontology. At the end of the day, Nuclear Bundle Theory may be the only viable option in this family of views.

  In addition, Nuclear Bundle Theory faces an especially virulent form of the Problem of Individuation that we will examine below. It would seem natural to think that the essential properties of a thing (the properties it cannot lose) are those properties that make up its species or natural kind. If so, two members of the same species would have exactly the same nucleus—any two elephants, for example, would have the same essential properties and so the same nucleus. But this would mean that each species or natural kind can contain just one instance—there could be only one elephant, one molecule of water, and so on. In order to avoid this disastrous result, the Nuclear Bundle Theorists will have to include in each nucleus individuating properties sufficient to distinguish one member of the species from others. But what sort of properties could these be? Why couldn't two members of the same species be intrinsically exactly alike? It would seem that the Nuclear Bundle Theory would either have to add certain tensed properties (detailing the unique history of each member of the species) or it would have to include special properties or thisnesses whose only job is to distinguish individuals from one another. Either approach would mean abandoning Nuclear Bundle Theory for either Four-Dimensional Bundle Theory or Scotism (to be discussed below).

  FOUR-DIMENSIONAL BUNDLE THEORY AND EVOLVING BUNDLE THEORY A second way that Bundle
Theorists can cope with change is to deny that bundles change intrinsically at all. Instead, a bundle is an eternal object, extended in time, the fourth dimension. If the bundle constitutes an ordinary particular that changes over time, this is represented in the bundle by the fact that each of the properties contained in the bundle is somehow indexed or relativized to an instant of time. So, suppose we have an iron rod that is cold at time t0 and hot at a later time t1. This rod could correspond to a single, unchanging bundle that contains two universals, one corresponding to being cold-at-t0 and the other to being hot-at-t1. Clearly, this will involve some complexity in our theory of universals, as well as an infinite number of instants or moments of time. We will examine this sort of question in more detail in future chapters, including Chapters 19–21 (on time) and 24–25 (on change).

  The final way for Bundle Theory to cope with change is to deny the principle of Mereological Essentialism for bundles, allowing that a bundle can gain or lose parts (universals) while remaining one and the same bundle that it was before. What PCI forbids (on this interpretation) is the existence of two distinct bundles containing exactly the same universals at the same time.

  How can bundles evolve over time, gaining and losing universals? If a rod exemplifies COLDNESS at one moment and then exemplifies HEAT in the next moment, what can account for the identity of this bundle through time?

  Evolving Bundle Theorists might push back against this objection by postulating that each evolving bundle contains a single nature or essence universal, which governs the possible changes and non-changes which the bundle can undertake under various possible circumstances. This would correspond to Aristotle's idea of the form of a substance as the ultimate principle of rest and change for that substance. We will devote an entire chapter, Chapter 25, to the question of the persistence through time of composite objects (like bundles).

  THE PROBLEM OF INDIVIDUATION We have canvassed five different types of Classical Bundle Theory, and now move to a classic, powerful argument against Classical Bundle Theory as such. The argument's classic statement is found in Max Black (1952) but was extended by Robert Adams (1979), among others. Given our assumption that Classical Bundle Theory is committed to a sparse theory of properties according to which all universals are natural properties, it follows that Classical Bundle Theory, when combined with the Principle of Constituent Identity, entails that substances satisfy Restricted Identity of Indiscernibles:

  9.3T.1 Restricted Identity of Indiscernibles. If (thing a exemplifies F if and only if thing b exemplifies F), where F is a natural property, then a is identical to b.

  Black argued, however, that in fact substances can be indiscernible without being identical, contrary to Restricted Identity of Indiscernibles. His argument relies crucially on a thought-experiment. Black asks us to consider a possible world in which only two substances exist, perfectly homogeneous and symmetrical spheres of exactly the same shape, size, and composition. Imagine that the two spheres are co-eternal, and that they are forever revolving around their common center of gravity through a perfect vacuum. The world is characterized by perfect bilateral symmetry: whatever can be said truthfully about one sphere (using only general terms) can also be said truthfully about the others. The two spheres are thus perfectly indiscernible, unless we are allowed to assign names to each—let's call them ‘A’ and ‘B’—and make use of non-natural properties like being exactly such-and-such distance from A or being exactly such-and-such distance from B. If such a world is possible, then it is possible for two distinct particulars to be indiscernible. This possibility, if genuine, vindicates one half of Wise UP (7.2T.3), the half that says that particulars can be distinct yet indiscernible. But more important presently is the fact that if such a world is possible, Classical Bundle Theory must be false.

  One crucial question is whether a Black world really is possible. It certainly seems to be. In particular, it is easy to imagine this sort of scenario, and there doesn't seem to be anything inherently contradictory about such a situation. To emphasize the plausibility, imagine a long series of possible worlds, where the first is exactly like ours, and each successive world in the series is more and more like the Black world. You can imagine, for example, that each successive world has one less object than our world, and makes one small change to some actually existing ball such that it becomes more like the spheres in the Black world. As we move through the sequence, then, we come to worlds containing two very but not exactly similar spheres. The last world in the series is just the Black world itself. Surely all of the worlds (except the last, so as not to beg questions!) is genuinely possible. What reason could we have for claiming that at some point in this sequence we move from a possible world to an impossible one? If there is no such reason, then it is hard to believe that the Black world is impossible, since there are perfectly possible worlds arbitrarily close to it in structure.

  As an alternative to Black's spheres, we can also imagine a temporally symmetrical world. For example, consider a world in which exactly the same cycle of events recurs over and over again without beginning or end. This is the sort of world imagined by Friedrich Nietzsche as the “myth of eternal recurrence”. Each event in each cycle could be distinct from the corresponding events in other cycles, even though all such events are qualitatively indistinguishable and bear exactly the same temporal relations to other events (qualitatively described). There would, in such a world, be indiscernible yet distinct particulars.

  Finally, it might be possible for there to be indiscernible thinkers. Can we imagine a Black world that contains, instead of two symmetrical spheres or eternally recurrent epochs, only two indistinguishable and disembodied minds? It is not clear whether such a scenario is really possible because we don't have direct experience of co-existing, disembodied minds. It is thus hard for us to judge what is or is not possible for these sorts of beings. Though we are inclined to think that such a situation is possible, we are less sure of it than in the other cases, so we don't rest anything on such a case.

  Further, we do have experience of our own conscious life, and we can, as the French philosopher René Descartes did, consider that conscious life as abstracted from the career of our physical body. Thus, we can imagine a Nietzschean world of eternal recurrence consisting of a single mind, eternally experiencing over and over (without beginning or end) the same cycle of experiences. In such a world, there would be distinct but indistinguishable mental events and actions, and these would be fundamentally real things. Given that these events and actions are particulars, we would here have another sort of Black-type world.

  Our defense of the possibility of a Black-type world appeals to two epistemological principles, Imagination as a Guide to Possibility (PEpist 1), along with its corollary, The Limit of Possibles Itself Possible:

  PEpist 1.1 The Limit of Possibles Itself Possible. If a series of scenarios is such that each represents a metaphysical possibility, and the series converges at the limit on a further scenario, then we have good reason to think that the latter scenario represents a metaphysical possibility.

  Both Imagination a Guide to Possibility and The Limit of Possibles Itself Possible are, as we intend them, defeasible principles. That is, they are true despite being subject to counterexamples. One might be able to imagine that Mark Twain and Samuel Clemens are different people, but this doesn't establish the possibility of their distinctness. Similarly, it is possible for a massive object to approach arbitrarily close to the speed of light, but it is impossible for one to reach the speed of light. Nonetheless, despite the possibility of exceptions, both principles are reliable guides to possibility. If one wants to reject an inference made on the basis of one of these principles, one must supply a reason why that particular inference should not be made.

  There are, however, several ways Classical Bundle Theorists could handle the possibility of Black worlds. First, they could suppose that each spatial location corresponds to a different universal. On this view, the two spheres are not r
eally indiscernible after all. They do correspond to different bundles of universals. This is a version of the Theory of Spatial Qualities (17.1T.1T), a theory we discuss at greater length in Chapter 17. We will see there that there are serious problems with this view of spatial location. It is inadvisable to rest one's theory of substance on such a controversial view of location.

  Second, as John Hawthorne (1996) has argued, Classical Bundle Theorists can embrace the possibility of a Black world, even if they reject the Theory of Spatial Qualities. Classical Bundle Theorists can suppose that it's possible for one and the same bundle of properties to be located simultaneously at two remote locations. Such a bundle could be x miles distant from itself. This isn't a problem for Classical Bundle Theorists, since they are already comfortable with the idea of universals being simultaneously located in many places at once. If individual universals can do so, why can't whole bundles? Notice that this strategy really amounts to embracing the claim that there cannot be distinct but indiscernible objects! Hawthorne's strategy simply rejects that possibility by insisting that there is really just one object with two locations. Thus, Hawthorne has not actually squared Classical Bundle Theory with the possibility of distinct yet indiscernible objects. Moreover, Hawthorne's suggestion would be of no help to those thought-experiments that don't use location, such as a world containing two indiscernible souls or two indiscernible particles in the same place at the same time.