The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  What we are butting up against here is a problem that is not unique to Classical Bundle Theory. Indeed, it is a problem for any Constituent Ontology that goes in for both universals without tropes and the Principle of Constituent Identity. To see the problem, recall the Hochberg-Armstrong objection to Resemblance Nominalism. Their objection was that Resemblance Nominalists have no way to account for the dual facts of resemblance and distinctness. That is, Resemblance Nominalists have trouble finding distinct truthmakers for (10) and (11) (from Chapter 8):

  (10) A and B are exactly similar fundamental particulars.

  (11) A and B are distinct fundamental particulars.

  What we have discovered is that Classical Bundle Theory faces a similar trouble, given PCI. Since only universals are constituents of substances, the facts explaining similarity are the same as those meant to explain distinctness. Since Constituent Ontologies with universals and without tropes provide a powerful account of similarity that is motivated independently of these theories of substance, what is apparently needed is a different account of what makes two things two, rather than one. This is the Problem of Individuation.

  RESPONSES TO THE PROBLEM OF INDIVIDUATION There are, broadly speaking, four responses to the Problem of Individuation: (i) primitive identity, (ii) fundamental relations of distinctness, (iii) Scotism, and (iv) Substrate Theory. We consider these in turn.

  PRIMITIVE IDENTITY The first response to the Problem of Individuation is to opt for primitive identity. Proponents of primitive identity assert that (11) is true simply because A and B exist. In truthmaker language, the truthmaker for (11) is just the pair, {A,B}. In this sense, A and B (and every other substance) are ‘self-individuating’:

  Def D9.1 Self-individuation. A pair of distinct things x and y is self-individuating if and only if the truthmaker for x's distinctness from y is the pair itself.

  We can thus characterize the primitive identity view in the following way:

  9.2T Primitive Identity. All pairs of substances are self-individuating.

  The trouble with Primitive Identity is that it seems to constitute a rejection of PCI, given Classical Bundle Theory. The reason is simple: the whole idea behind Constituent Ontology is to identify a substance with some combination of constituents. Given the Classical Bundle Theorist's commitment to universals, Primitive Identity offers no space for the Classical Bundle Theorist to identify a constituent that is unique to every substance. We have noted, however, that PCI is a constraint that most Constituent Ontologists accept. Thus it is no surprise that Robert Adams (1979) opts for Primitive Identity while explicitly denying Constituent Ontology.

  Moreover, Classical Bundle Theory (even without PCI) is still subject to a version of the Hochberg-Armstrong objection, namely, an appeal to One Truthmaker per Fundamental Property (see Sections 2.5.2, 3.4.3, and 8.1.3).

  PTruth 1 One Truthmaker per Fundamental Property. If p is the true predication of a fundamental property P to x1 through xn, and q is the true predication of a different fundamental property Q to the same things x1 through xn, then p and q have distinct truthmakers.

  If we have two bundles with the same universals as constituents, then the bundles are truthmakers for two, distinct natural relations: that of the co-instantiation of certain universals and that of the numerical distinctness of the bundles. Suppose, for example, that we have two bundles, B1 and B2, each comprising the same three universals (F, G, and H). B1 and B2 are individually and jointly a truthmaker for the proposition that F, G, and H are co-instantiated, but they are also jointly the truthmaker of the proposition that B1 and B2 are numerically distinct. Given One Truthmaker per Fundamental Property, we should look for some additional truthmaker for their distinctness.

  FUNDAMENTAL RELATIONS OF DISTINCTNESS The second response to the Problem of Individuation is to opt for primitive relations of distinctness, or fundamental distinctness nexuses. The idea is that the ground for the truth of (11) is a fundamental relation of distinctness that obtains between A and B, and more generally, between any two distinct substances. We can put the view in this way:

  9.2A.1 Fundamental Relations of Distinctness. For any distinct substances x and y, the truthmaker for x's distinctness from y is a fundamental distinctness nexus between x and y.

  There are at least three troubles for this account. First, insofar as this is a solution to the Problem of Individuation, it seems to follow that what makes a substance the substance that it is are these relations of distinctness in which that substance stands. But this means that it is part of the identity of that substance that it stands in those relations. For example, consider THP's dachshund, Elsie. A fundamental distinctness nexus obtains between Elsie and THP, between Elsie and THP's daughter Gretchen, and so on. If these nexuses jointly individuate Elsie, then part of what it is to be Elsie is to stand in these relations. This means that nothing that doesn't stand in these relations can be Elsie. However, Elsie existed prior to the beginning of Gretchen's life. Thus it is possible for Elsie to exist while the distinctness nexus between Gretchen and her does not. This contradicts the claim that this nexus individuates Elsie.

  Second, and relatedly, this account seems to get the order of explanation backwards. A relation is binary when it always holds between two things or between one thing and itself. A binary relation R is irreflexive if and only if the relation never holds between any thing and itself. If R is irreflexive and x stands in R to y, then x and y must be distinct. Any binary, irreflexive relation requires the existence of two distinct things in order for it to be instantiated. If so, then the distinctness of two things must be prior to their standing in any relation whatsoever, including the distinctness relation. This argument relies on the following metaphysical principle:

  Relata more Fundamental than Relations. The existence and distinctness of the relata of any relation cannot be grounded in or made true by the holding of the relation itself.

  Relata more Fundamental than Relations is a plausible principle. Ordinarily, we would take the grounding of the holding of a relation to include the existence and mutual distinctness of the relata, not the other way around. This is especially true when these relations hold only contingently, as we have seen that relations of distinctness do. Advocates of Fundamental Relations of Distinctness must reject the principle, however. This is a serious problem.

  Third, it seems reasonable to suppose that any relation of distinctness is intrinsic to any two distinct things. That is, if two things are distinct (and distinct in a fundamental way), then the two things are in and of themselves the truthmaker for the truth that they are distinct. We don't need to add a separate, third thing in such cases. However, that is just what the theory of fundamental distinctness nexuses does: it assumes that the distinctness of A and B is grounded in the existence of a separate, third thing, the distinctness nexus between A and B.

  There is, perhaps, a fourth objection to this account, a variant of Bradley's Regress. If we assume that it is never possible for two things to distinguish themselves, then the distinctness nexus N that is responsible for making A and B distinct can do so only by virtue of being distinct from both A and B. If N were identical to either one, then it would (by hypothesis) be incapable of grounding their distinctness. But this means that we have to posit two more distinctness nexuses N1 and N2 (each distinct from N) in order to distinguish N from A and from B. This would seem to lead to an infinite regress of such nexuses.

  SCOTISM The third response to the Problem of Individuation comes from John Duns Scotus. He proposed that we introduce universals which are uniquely instantiated by particulars and which ground the distinctness of each particular from all the others. Scotus called these universals ‘haecceities’, which is Latin for ‘thisnesses’ (‘haec’, pronounced ‘hike’, is the Latin word for ‘this’). A haecceity (‘hike-say-ity’) is a property that can, as a matter of metaphysical necessity, be instantiated by one and only one possible thing. It is impossible for two distinct things to instantia
te the same haecceity, either in the same or in different possible worlds.

  Def D9.2 Haecceity. If x is a substance, then the haecceity of x is a universal H(x) that exists necessarily, is instantiated by x, is necessarily instantiated by x if x exists, and is necessarily instantiated by nothing other than x.

  Scotism, then, is the view that haecceities exist and ground the distinctness of distinct objects, like Black's spheres.

  9.2A.2 Scotism. Substances have haecceities, and haecceities are natural properties.

  The trouble with Scotism is that haecceities do not seem to be natural properties because they do not ground either resemblance or causal powers. They cannot ground resemblance by stipulation, since haecceities in principle cannot be shared. But they also do not seem to ground causal powers, since the causal powers of a thing seem to be a consequence only of shared properties. In other words, it does not seem that there are causal powers unique to individual substances.3 Unfortunately, unless haecceities are natural properties, they cannot do the work needed by Classical Bundle Theorists, since only natural properties are constituents of substances.

  The fourth response to the Problem of Individuation is to adopt Substrate Theory.

  9.3.2.2 Substrate Theories.

  Substrate Theories are Constituent Ontologies according to which substances have a constituent other than their properties. This additional constituent is called a ‘substrate’.

  9.1A.1A Substrate Theory. Each substance has a constituent other than its characterizing properties, a substrate.

  A property is characterizing if and only if it is not a substrate. Substances, then, are metaphysically complex things containing some properties together with a substrate that is in a different fundamental category than those properties (see below for an explanation of why we don't just say that substrates are not properties at all).

  One motivation for Substrate Theory is to supply a solution to the Problem of Individuation besetting Classical Bundle Theory. As we have seen, Trope Bundle Theory has significant troubles in both its modifying and modular versions, while Classical Bundle Theory lacks the resources to account for the individuation of substances. Further, Modifying Trope Bundle Theory faced a problem of accounting for what, exactly, was being characterized by a thing's modifying tropes. Classical Bundle Theory faces a similar worry, since universals, like modifying tropes, have only formal character. That is, universals do not have the character they ground.4 Thus the Classical Bundle Theorist faces the challenge of saying what, exactly, universals are grounding the character of. Substrate Theories hold out hope for being able to solve that problem. Not only can substrates serve as an individuating constituent, they can also be the fundamental bearer of a substance's properties. Substrate Theory is, then, underwritten by this dual motivation.

  As with Relational Ontology and Bundle Theory, Substrate Theory comes in both a trope and a classical variety. Trope Substrate Theory insists that tropes ground character, while Classical Substrate Theory deploys universals in that regard:

  9.1T.1A.1T Trope Substrate Theory. Substrate Theory is true, and tropes ground character.

  9.1T.1A.1A Classical Substrate Theory. Substrate Theory is true, and universals ground character.

  Trope Substrate Theory faces troubles that have already, for the most part, been articulated. Modifying Trope Substrate Theory faces just the problem that Modifying Trope Relational Ontology faced (see Section 9.3.1 above, and note that the argument there didn't depend on the unique commitments of Relational Ontology). Thus, Modifying Trope Substrate Theory appears to be a quantitatively bloated version of Classical Substrate Theory. On the other hand, Modular Trope Substrate Theory, like Modular Trope Bundle Theory (see Section 9.3.2), faces a dilemma between character duplication and a violation of Existence of Thick-Characteredness. Classical Substrate Theory, therefore, seems the most promising option, at least at this stage.

  There is a second issue that Substrate Theorists must wrestle with, and though we will focus on Classical Substrate Theory in discussing it, Trope Substrate Theorists are faced with it as well. The question concerns many properties a substrate has in itself. That is, considered independently of the constitutive properties of the substance of which it is a part, does a substrate have character? If so, is that character merely one-dimensional or not?

  Before we name the views according to which substrates have zero properties or one property in themselves, we must dispatch with the possibility that substrates have two or more properties. The argument is a dilemma, one horn of which is a further dilemma. Suppose that substrates have two properties (the case of three or more properties goes in just the same way). The dilemma goes as follows. Either some properties ground the character of the substrate or they do not. If they do not, then substrates appear to be thickly charactered in just the way that Extreme Nominalists assert ordinary objects are. If that is right, then it's not clear why one shouldn't just adopt a more thoroughgoing version of Extreme Nominalism and avoid the discussion in this section entirely. On the other hand, if properties do ground the character of the substrate, then (and here's the further dilemma) either those properties are constituents of the substrate or they are not. If they are constituents, then one faces the problem of individuation for substrates. Given that one embraced Substrate Theory in the first place, one will need a substrate for one's substrate, and so on. A vicious infinite regress results. So a substrate's properties cannot be constituents of it. Suppose then that a substrate's properties are not constituents of it. Then one has abandoned one's commitment to Constituent Ontology. But Substrate Theory is explicitly a version of Constituent Ontology, and so one's view is incoherent.

  Therefore, substrates must have either zero properties or one property in themselves. If one says substrates have one property, then one is a Modular Substance Theorist, while if one says they have no properties, then one is a Bare Particular Theorist:

  9.1T.1A.2T Modular Substance Theory. Substrate Theory is true, and substrates have one property in themselves.

  9.1T.1A.2A Bare Particular Theory. Substrate Theory is true, and substrates have no properties in themselves.

  According to Modular Substance Theory, a substance's substrate is simply a modular trope. We've called the view Modular Substance Theory, though, in order to evince the idea that the substrate is thinly charactered in an irreducibly substance-kind oriented way. That is, you can think of a Modular Substance Theory substrate as thinly charactered in a dog-like way, a human-like way, a oak-tree-like way, and so on. Substrates, on this view, are merely dogs, humans, oak trees, and so on.

  Why couldn't substrates be thinly charactered in the way that modifying tropes are? The reason is just that which plagued Modifying Trope Bundle Theory. Substrates are meant to be ultimate bearers of character, but modifying tropes are meant to be only formally charactered. Substrates must be people, turtles, electrons or whatever else in themselves. Modifying substrates cannot have such intrinsic character. They are thus unfit to play one of the roles substrates are meant to play. Modular substances must be modular tropes.

  Modular Substance Theory, in order to avoid troubles with character duplication and the general problem of thickening principles, ought to think of characterizing properties as either modifying tropes or universals. Thus we see that substrates will be of a different fundamental kind from characterizing properties, even if substrates are properties. On this view, a substance is a bundle consisting of one modular trope (the substrate) and many modifying tropes or universals. The result is a weird hybrid of Trope Theories: modular tropes for the substance-kind properties, and modifying tropes or universals for the accidental properties.

  The Realist version of Modular Substance Theory is also a weird hybrid of two incompatible theories: Relational Ontology and Constituent Ontology. The modular substance does not contain any property as a part. Consequently, it does not contain its substance-kind universal as a part. Either there is no substance-kind universal at all, in which ca
se the Modular Substance Realists would have to give some Nominalistic account of substance-kinds (by, for example, appealing to fundamental resemblance relations) or there is such a universal but the modular substance stands in an extrinsic instantiation relation to that universal. However, if such an extrinsic instantiation relation is fine in this case, why not abandon Constituent Ontology altogether and suppose that substances stand in that same instantiation relation both to substance-kind and to accidental universals?

  Let's suppose, then, that Modular Substance Theorists think of substances as composed of a modular substance-trope and a number of modifying accident-tropes. What holds this bundle of tropes together? It must be a relation between the modifying tropes and the modular substrate. In fact, this relation would seem to be exactly the relation that Relational Ontologists call ‘instantiation’. It would be simpler to simply replace the modifying tropes with universals, resulting in Classical Relational Realism. What good is achieved by multiplying accidental properties into a large number of indistinguishable modifying tropes?

  There is one plausible response to this objection, but it is a response that will get Modular Substance Theory into further trouble. Modular Substance Theorists could argue that what unifies modifying tropes and modular substrates is not the instantiation relation but spatial location. A substance is unified by the fact that its modular substrate and its modifying tropes are all located in the same place at the same time.

  This solution generates two difficulties. First, it makes it impossible for two substances with different properties to share the same location at the same time. If they are in the same place at the same time, then the modifying tropes present there would belong equally to both substances. However, it seems possible for two things with different properties to exist in the same place at the same time. Photons and neutrinos, for example, can do this.