Second, this solution means that Modular Substance Theorists cannot provide a metaphysical account of spatial location. Spatial location cannot correspond to a modifying trope, since this would result in an infinite regress or a vicious circularity. Location trope L would have to belong to substrate S only by being located in the same place as S, but this can happen only by L's belonging to S already. This version of Modular Substance Theory would have to be combined with an Extreme Nominalist account of spatial properties, resulting in another weird hybrid. If Extreme Nominalism is good enough for spatial properties, why not all properties?
In addition, Modular Substance Theory may also have a problem with thickening principles. Modular Substance Theory is asking us to imagine that substrates have substance-kind characteristics without having any sort of other characteristics. But here is another plausible thickening principle:
Substance-Kind Thickening. Every object that instantiates a substance-kind (like doghood) has some other characteristic (like a definite size and shape).
If Substance-Kind Thickening is true, then Modular Substance Theory must be false. However, the plausibility of this principle is not nearly as striking as that of the Color Thickening and Shape Thickening principles, especially in light of the reply considered in Section 8.2. There, we noted that Modular Trope Theorists ought to insist that these principles apply only at the level of ordinary objects, not at the level of tropes. We can add a further rejoinder to this reply at this stage. Color, for example, seems like the kind of thing that must spread over a certain physical area in order for it to be present at all, and such an area must be bounded in a certain way. The resultant boundaries will result in a color patch having a definite shape and size. This is one thing that lends enormous plausibility to the principle of Color Thickening, even at the level of tropes. Likewise the principle of Shape Thickening. Substance-kinds, on the other hand, do not seem to be connected to other features in this same way. At least the connections aren't quite so palpable and obvious. While it is indeed difficult to conceive of an unshaped object that exemplifies the substance-kind doghood, the connection seems much less necessary when one considers just the level of tropes. This is not the case with the connection between color and shape, for example. We leave it to the reader to consider this area in more detail.
Given the problem of Substance-Kind Thickening, defenders of Modular Substance Theory might consider going in a completely different direction. Perhaps the modular substrate is not an instance of substance-kind properties like being a human being or being an oak tree. We could instead think of them as instances of spatial extension properties, the property of having a certain definite shape and volume. The substance-kind property would then consist in a modifying trope that is contained by the modular substrate. We could then suppose that the modular substrate has one property in itself (its spatial extension) and many other properties (including its substance-kind) by virtue of containing (and being modified by) the appropriate modifying tropes.
This theory, the Quantitative Modular Substance Theory, might still face some thickening problems. We might worry that anything that has size and shape must have some qualitative properties to fill or occupy its volume. However, this isn't obviously true. The idea of an empty, qualitatively neutral spatial region doesn't seem self-contradictory, in the way that an oak tree without shape or a colored thing without size does. The Quantitative Modular Substrate Theory seems to be the most defensible version of Modular Substance Theory.
There is one more objection to any version Modular Substance Theory. Like other versions of Trope Nominalism, it is subject to the Hochberg-Armstrong objection. Two modular substrates will be both numerically distinct and exactly similar (with respect to their natural kind), and the only truthmaker for both truths will be the pair of modular substrates. In contrast, Bare Particular Theory is immune to this objection, since bare particulars are numerically distinct but not similar in any substantive way (see below). Similarity is grounded in the universals or tropes associated with the two bare particulars.
There is one view left to consider, namely, Bare Particular Theory:
9.1T.1A.2A Bare Particular Theory. Substrate Theory is true, and substrates have no properties in themselves.
Bare particulars are meant to be property-less, particular constituents of substances that both individuate and serve as the fundamental bearers of character. They are character-less character-havers, pure particulars without any features in themselves. In this way, they are analogous to Aristotelian prime matter, which for Aristotle was formless when considered in itself, was the principle of individuation of substances, and was the ultimate bearer of properties (‘forms’, in his terminology).
Wilfrid Sellars (1963) objected to the idea of bare particulars as self-contradictory.5 As we have seen, a bare particular is supposed to be something that bears properties (since it is a substrate modified by a modifying trope or universal), but it is also supposed to be completely without properties (since that is what makes it bare). How can something both have properties and lack them? We can put Sellars's objection in the present context in this way, given Classical Substrate Theory: one and the same universal may modify distinct bare particulars in such a way that the bare particulars are themselves made similar, and yet bare particulars are not supposed to be the sort of thing that can be similar to one another. If bare particulars are not similar to one another, then what exactly is the universal doing? In what is the universal grounding character?
In response, Bare Particular Theorists must insist that we distinguish between the substrate as bare and the substrate as modified by one or more universals or tropes. It is only the former that cannot be substantively similar to other (bare) particulars. Substrates cannot exist without exemplifying at least one universal, but we can still ask whether a pair of bare particulars are (by themselves and without its connections to those universals) collectively the truthmaker of a similarity proposition (like (10) above). Two bare particulars are similar only by virtue of their connections to one and the same universal. Hence, the truthmaker for the similarity claim must include that universal, while the truthmaker for the distinctness claim consists in the pair of bare particulars alone.
It is worth noting that Relational Ontologists also believe in bare particulars, in this sense. For Relational Ontologists, all ordinary particulars are bare in themselves. They take on qualities only by virtue of an external relation to universals or modifying tropes.
Bare particulars might perform as many as four distinct functions simultaneously:
(1) Bare particulars of two distinct substances are jointly the truthmaker for the distinctnessof those substances. This is the individuating or distinctness-grounding function.
(2) A bare particular is the truthmaker for the particularity (the concreteness and unre-peatability) of the substance to which it belongs. This is the particularizing function.
(3) A bare particular unifies the various properties that its substance possesses. This is theunifying or bundling function.
(4) The fact that several bundles contain (in succession) the same bare particular could bewhat makes those bundles successive stages in the history of one enduring thing. Thisis the persistence-grounding function.
In some metaphysical systems, including that of many medieval scholastic philosophers, these four functions are performed by three or four distinct entities. For example, for Thomas Aquinas, it is the prime matter that particularizes and grounds persistence (in some cases), the individual essence that unifies and grounds persistence (in other cases), and the spatial dimensions and location that individuate. If we accept One Truthmaker per Fundamental Property, it seems that we should look for distinct truthmakers for the four kinds of truths, rather than pressing a single category of things, bare particulars, to do all at once.
We have reached bare particulars through function 1, the distinctness-grounding function. If we adopt Wise UP, then whatever individuates will also be res
ponsible for particularization (function 2).
What about unification (function 3)? In particular, is it necessary that each particular contain just one bare particular? This is far from obvious if the only function of bare particulars is individuation. If particular P contains five bare particulars, and so does particular Q, and if P and Q contain the same universals, then it is the distinctness of the five bare particulars in P from the five bare particulars in Q that is responsible for the distinctness of P and Q. All that is required is that, if P and Q are distinct particulars, then at least one of the bare particulars contained in P be distinct from all of the bare particulars contained in Q or vice versa.
If a particular contains more than one bare particular, it would be natural to look for some correspondence between those bare particulars and the parts of the ordinary particular. Suppose that a particular P contains a set S of bare particulars {B1, B2,…, Bn}. If Q were a distinct particular that contains a subset of S, then it would be natural to suppose that Q was a part of P (in the language of formal mereology, a ‘proper’ part of P, since Q is not identical to the whole of P).
In fact, it could be that some bare particulars are proper parts of other bare particulars. Suppose that bare particular B contains parts B1, B2, and B3. If particular P contained bare particular B, it would also contain bare particulars B1, B2, and B3, and, if there are particulars Q1, Q2, and Q3 that contain (respectively) only B1, B2, and B3, it would be natural to suppose that Q1, Q2, and Q2 are proper parts of P.
In fact, it could even be the case that every ordinary particular contains an infinite number of bare particulars. Perhaps each bare particular contains an infinite number of bare particulars as proper parts. Bare particulars might turn out to be gunky (in the language of David Lewis). An entity is gunky if it contains proper parts, and all of its parts contain proper parts. A gunky thing contains no simple or atomic parts (parts without further proper parts). On one interpretation of Aristotle's metaphysics, prime matter might be composed of just such gunky bare particulars.
What about bare particulars and change (function 4)? Could an enduring, changing particular gain or lose bare particulars, just as it can gain or lose universals? There is a historical analogy for this possibility, namely, Locke's theory of personal identity through soul-substitution (in his Essay Concerning Human Understanding 1689, Book IV, Chapter 3, Section 6). Locke created a thought-experiment in which two people (e.g., a prince and a pauper) exchanged not only their bodies but also their souls (whatever that might be like). Locke argued that, so long as the new inhabitant of the pauper's soul and body had all of the memories, values, and intentions of the prince, the new inhabitant is in fact the same person (now) as the prince was (then). We could think of a changing particular substance as the analogue of Locke's persisting prince and the two bare particulars as the analogues of the souls.
Of course, bare particulars cannot change intrinsically, since they have no intrinsic features to change. Suppose that bare particulars do persist through time. Then it seems very natural to suppose that any substance that contains just one bare particular at one time must be identical to any substance that contains just that same bare particular at another time. That is, it seems natural to suppose that the inclusion of the same bare particular (or bare particulars) over time should be sufficient to ground the persistence of a substance.
However, it does not seem obvious that inclusion of the same bare particulars is necessary for the persistence of a substance. Return to Locke's story of personal identity despite soul-substitution. In much the same way, it seems that it would be possible, in some cases, for a substance to survive the substitution of its bare particular by another. We will take up these questions of persistence again in Chapters 24–25.
The results of this section are summarized in the Figure 9.1.
Figure 9.1 Theories of Substances
As we have seen, Realism can be divided into Relational and Constituent Ontologies. Relational Ontology has two principal drawbacks: it must posit a primitive instantiation relation, while Constituent Ontologists can make do with the part-of relation, and Relational Ontology faces the Extrinsicality Objection. Neither is decisive. Much depends on whether the Constituent Ontologists can make good on the promises of their program.
Constituent Ontology divides into Bundle Theory and Substrate Theory. The most serious problem for Bundle Theory is that of individuation, making room for the possibility of distinct but indiscernible particulars. Substrate Theory solves that problem by positing substrates whose ontological job is to ground distinctness. Bare Particular Theory has the added advantage of immunity to the Hochberg-Armstrong objection, as well as avoiding the weird combinations of modular tropes with modifying tropes or universals that are required by the alternative, Modular Substance Theory. In the next chapter, we consider how Bare Particular Theory, as well as Ostrich Nominalism and Resemblance Nominalism, fare as accounts of relational facts.
Notes
1. Somewhat surprisingly, David Armstrong is a Realist who believes in states of affairs and not nexuses, and yet who takes the second option. He does so by distinguishing two kinds of part-whole relations: mereological composition (resulting in wholes composed by every collection of things) and non-mereological composition (resulting in the special entities, states of affairs). He never explains what makes a whole of the first kind into a whole of the second kind if not the presence of a nexus.
2. PCI corresponds closely to the assumption of Strong Supplementation in the theory of classical mereology (see Section 23.1).
3. Cf. Pickavance (forthcoming).
4. This is a matter of some dispute, but we have not taken the question up here. Aristotle's Third Man argument is, famously, an argument against Plato's claim that universals are self-exemplifying.
5. For discussion, see e.g., Alston (1954), Anscombe (1964), Moreland (1998), Pickavance (2014), Sider (2006).
10
Relations, Structures, and Quantities
In this chapter, we will examine four special problems involving properties (whether universals or tropes). First, in Section 10.1, we will look at various accounts of relational facts, facts that involve properties relating two or more particulars. Then, in Section 10.2, we will examine an important special case of relational facts: those that involve non-symmetric or ordering relations. In Section 10.3, we turn to structural properties, those relational properties that enable many things to form a single structure, like a group or a team. Finally, we take up the problem of measurable quantities in Section 10.4.
10.1 Accounts of Relational Facts
All Realists (7.1T) must answer this question: are there relational universals, in addition to qualitative ones? Trope Nominalists (8.1T.4.1A) have to answer a similar question: are there relational modifying tropes or modular tropes? Each of the following propositions attributes a relation to a pair of things:
(1) Dallas is to the north of Austin.
(2) John loves Mary.
(3) Texas is next to Oklahoma.
(4) Particular P instantiates universal U.
(5) Universals U1 and U2 are co-instantiated (or bundled).
(6) Modifying trope A resembles modifying trope B exactly.
(7) Modular trope C resembles modular trope D exactly.
Are there universals corresponding to the relational property of being to the north of or loving? If so, must UP-Realists (7.1T.1T) recognize the universal INSTANTIATION? Must Classical Bundle Theorists (9.1T.1T.1A) treat BEING BUNDLED itself as a universal?
Similarly, Modifying Trope Theorists (8.2T.1T) must consider whether there is a relational modifying trope connecting Dallas and Austin, a modifying trope that makes (1) true? For Modular Trope Theorists (8.2T.1A), is there a single modular trope, something to the north of the other, and if so, is this modular trope a part of both Dallas and Austin or a part of some whole that contains Dallas and Austin as parts? Are there modifying tropes of resemblance or merely-resembling modular trope
s?
In each case, to answer Yes is to run the risk of a version of Bradley's Regress. Consequently, many UP-Realists, Classical Bundle Theorists, and Trope Nominalists have restricted their accounts to monadic (non-relational or one-place) properties. Doing so still provides all of these theories with an advantage in terms of economy over Ostrich Nominalism (7.1A.1A), since Ostrich Nominalists will have to recognize the same number of fundamental relational kinds as do the others, while the others will have far fewer fundamental monadic kinds.
One extreme position that such anti-relational theorists could take is simply to deny that there are any fundamentally relational truths at all. Such a theory was proposed by Leibniz, who called his unrelated substances ‘monads’. Hence, we say that Monadism is the view that all relational truths are grounded in the intrinsic character of substances taken individually:
10.1T Monadism. There are no fundamental relational truths.
10.1A Anti-Monadism. There are some fundamental relational truths.
Monadists must reject the existence of all external or non-internal relations. We defined internal relations in Chapter 2:
Def D2.2 Internal Relation. R is an internal relation if and only if, necessarily, for every x and y, whether R holds between x and y depends only on the intrinsic properties of x and of y.
The expression ‘depends on’ as we used it in this definition was intentionally ambiguous. It could simply mean that the holding or non-holding of the relation weakly supervenes on the intrinsic properties of the two relata (so that it is impossible for two situations to be the same with respect to those intrinsic properties and yet different with respect to the holding of the relation), or it could mean that the relation's holding is wholly grounded in the intrinsic properties of the two relata. Let's call these two more precise notions ‘weakly internal’ and ‘strongly internal’, respectively:
The Atlas of Reality Page 33
