Moderate Resemblance Nominalism with Concretism but without degrees of resemblance or a variably polyadic resemblance relation could handle all of the problems, but only at the cost of adding generic or determinable tropes and bare particulars. Generic tropes also bring a large number of brute necessities with them. For instance, every color trope has to be accompanied with a trope of some specific shade (hue and saturation), and every triangularity trope has to be accompanied with a trope of a specific triangular shape, like equilaterality.
8.2 Trope Theory
Let's return briefly to the extensionality problems for Class Nominalism. Suppose that Class Nominalists asserted that an ordinary object like the celestial body Pluto is actually a complex thing, a bundle of tropes. In other words, suppose Pluto is “built” from a number of tropes, each of which supplies Pluto itself with some sort of character. We could then identify shareable properties with classes of tropes. The property of being spherical, for example, would be a all the sphericality tropes. This is Trope Theory:
8.2T Trope Theory. Tropes directly ground the character of ordinary objects.
Those who reject tropes fall into two familiar camps, Nominalists and Realists:
8.2A.1 Extreme Nominalism. The character of ordinary objects is grounded neither in universals nor in tropes.
8.2A.2 Classical UP-Realism. The character of ordinary objects is grounded in universals and not in tropes.
To see how Trope Theory works as an account of attributes and similarity, recall RedSquare, RedCircle, and BlueCircle. Trope Theorists will say that RedSquare and RedCircle are similar because they each have a redness trope and that RedCircle and BlueCircle are similar because they each have a circularity trope. Further, Trope Theory offers a more serious account of character-grounding than does Extreme Nominalism, an account that mirrors Realists' in many ways. RedCircle is red because it is related to a redness trope. BlueCircle is circular because it is related to a circularity trope. It isn't difficult to see how these accounts of similarity and character-grounding can be generalized.
Trope Theory comes in two varieties depending on whether one plumps for universals. The difference concerns, as we have already seen, the sense in which distinct tropes are particularizations of the same shareable property. Trope Realists believe that tropes are related to universals in some way, and that these relations determine when tropes are particularizations of the same shareable property. Resemblance among tropes is a consequence of relations to universals. Moderate Resemblance Nominalists, on the other hand, take resemblance among tropes to be metaphysically fundamental and think of shareable properties as classes of exactly resembling tropes. (As we have seen, Trope or Moderate Resemblance Nominalism thus faces some of the extensionality problems for Class Nominalism, as well as the Hochberg-Armstrong objection to Resemblance Nominalism.)
More importantly, though, there are two different views of the nature of tropes themselves, and thus there are two types of Trope Theory that arise given different understandings of the nature of tropes.
Before we get to these distinctions, it is important to say a bit about why Trope Theorists think we need tropes in the first place. We have already seen one motivation, at least for Trope Nominalism: it is a way to do without universals while being more Realist about character-grounding. In this way, Trope Theory holds out hope for avoiding the difficult questions facing the postulation of universals while accruing some of Realism's benefits. Further, because of this more serious account of character-grounding, Trope Theory avoids the problem of co-extensive properties (the second extensionality problem discussed above). More generally, though, Trope Theorists have argued that we need tropes to make sense of causation, since tropes are plausible candidates to serve as the relata of causal relations. Relatedly, tropes can serve as the immediate objects of perception. What we see when we look, for example, at an apple, is this particular red, this particular shape, not redness in general or apple-shapedness in general. Finally, Trope Theory suggests an account of substances as bundles of tropes. We will return to these putative advantages in later chapters, but this should suffice to help make clear why believing in tropes might be initially attractive.
8.2.1 Two varieties of Trope Theory
There are two ways of thinking about tropes, ways that have not until recently been distinguished in the literature.2 We can get at the distinction by considering this question: Do tropes have the character they ground? If they do, then tropes are modular tropes. If they do not, then tropes are modifying tropes.
Def D8.5 Modifying Trope. A modifying trope is a trope that does not have the character it grounds.
Def D8.6 Modular Trope. A modular trope is a trope that does have the character it grounds.
An example may clarify the distinction. Consider again RedSquare. RedSquare, according to Trope Theory, is uniquely related to a redness trope and a squareness trope. Call these tropes, ‘r1’ and ‘s1’, respectively. Since tropes ground the character of ordinary objects like RedSquare, r1 grounds the redness of RedSquare, and s1 grounds the squareness of RedSquare. We might say, with many Trope Theorists, that r1 is the redness of RedSquare and that s1 is the squareness of RedSquare. If r1 and s1 are modifying tropes, then r1 is not itself red, and s1 is not itself square. Modifier tropes therefore ground character they do not themselves have. If, on the other hand, r1 and s1 are modular tropes, then r1 is itself red, and s1 is itself square. That is, modular tropes ground character they themselves have.
With this distinction between modifying and modular tropes in place, we get a two-fold distinction among types of Trope Theory:
8.2T.1T Modifying Trope Theory. Trope Theory is true, and tropes are modifying tropes.
8.2T.1A Modular Trope Theory. Trope Theory is true, and tropes are modular tropes.
As it turns out, the distinction between modifying and modular tropes affects Trope Theory in some interesting and important ways. In particular, modifying and modular tropes have different sorts of intrinsic character and also ground character in ordinary objects differently. These differences mean that Modifier Trope Theory and Modular Trope Theory face different obstacles. We turn to some of these obstacles presently, and others will emerge in the next chapter. Along the way, we'll examine in more detail the differences between modifying and modular tropes.
8.2.2 Some troubles for Trope Theory
Trope Theory is thought by many to be a plausible theory of properties, but shedding light on the distinction between modifying tropes and modular tropes exposes new issues. For example, suppose tropes are modifying tropes. Then it isn't clear that tropes are able to be the relata of causal relations or the immediate objects of perception. To play those roles, a thing must actually exemplify the relevant property. Modifying tropes are no more fit to be causal relata or objects of sense perception than are universals. What is needed are tropes that have the properties they ground; that is, to play these roles Trope Theorists must go in for modular tropes.
But there is an even more serious worry, one that constitutes a sort of dilemma for Trope Theory. We can put the dilemma in roughly the following way. If tropes are modifying tropes, then Trope Theory is explanatorily identical to Realism but quantitatively less economical. Therefore, one ought to be a Realist. On the other hand, if tropes are modular tropes, then on pain of violating very plausible metaphysical principles, tropes are just the ordinary objects of Extreme Nominalism. Therefore, one ought to just be a Nominalist without tropes, like an Extreme Resemblance Nominalist, for example. The upshot of the dilemma is that Trope Theory is in danger of collapsing into Realism on the one hand or Extreme Nominalism on the other.
We turn presently to the modular trope horn of the dilemma; the modifying trope horn will be developed in the next chapter. Suppose, then, that Modular Trope Theory is true. Modular tropes, recall, have the feature they ground, but the idea nonetheless is that modular tropes have just one type of character. A redness modular trope is just red; a sphericality modular
trope is just spherical. Tropes, on this conception, are simply thinly charactered individuals. They are like the Extreme Resemblance Nominalists' ordinary objects except for having only one dimension of character.
To see why this conception of tropes is troubling, consider the following examples of “thickening principles” (see Garcia 2016):
Color Thickening. Every colored object has a definite shape.
Shape Thickening. Every shaped object has a definite size.
These principles are exceedingly plausible. But these principles entail that the redness modular trope of a red apple cannot be just red. That modular trope would, by Color Thickening, have to have some definite shape as well, presumably the shape of the apple itself. But then Shape Thickening would entail that our redness modular trope has a definite size as well, presumably again the size of the apple itself. Our redness modular trope seems to be transforming into the apple as it is conceived by Extreme Nominalists! That is, the redness modular trope is something that resembles things in various respects, has various features, and so on. These facts will need to be explained. Presumably the explanation will be in non-Realist terms, since Trope Theorists reject the Realist account of the redness of the apple. (Plausibly, even if one is a Modular Trope Theorist who plumps for universals, one doesn't think that the redness of the redness modular trope is a result of the trope's exemplifying the universal REDNESS. But if one did think that, then the redness modular trope begins to look, metaphysically speaking, like the apple as well!) The upshot of this is that it looks as though, given Modular Trope Theory, each object will have but one modular trope, in which case one wonders why one needs the trope and the object, rather than just the object itself.
The proponent of Modular Trope Theory could reply by saying that thickening principles apply only at the level of ordinary objects. In other words, they require only that every object with a color modular trope have a shape modular trope as well, that every bundle with a shape modular trope has a size modular trope, and so on. Intuitions about thickening were made for ordinary objects, not for tropes. While it may be hard to imagine an object that is colored but not shaped, it is equally hard to imagine certain things one finds in contemporary physics, like the 11-dimensional strings of string theory.
However, the reason why our cognitive powers give out in the string theory case is that the world of our experience is a three-dimensional one (four-dimensional if one counts time). We don't experience these other seven dimensions, even given that they exist. Since our conception of the spatiotemporal universe is plausibly derived from our experience of that universe, we have an easy explanation of why we cannot conceive of things that exist in more than three dimensions. But modular tropes are not this way. Our experience is sufficient to supply a conception of colored, shaped, and sized things. And those concepts seem irrevocably tied together, a tie that is captured by thickening principles.
The upshot of all this is that if one thinks that modifying tropes are unmotivated because they are unfit to be the relata of causal relations and the immediate objects of sense perception, then Trope Theory is already in serious jeopardy. For the very idea of modular tropes is, at the very least, seriously problematic. (We will consider a possible exception in Section 9.3.) Nonetheless, in the next chapter we will develop the other horn of the dilemma for Trope Theory, the one to do with modifying tropes.
8.3 Conclusion
The most viable form of Nominalism would seem to be Resemblance Nominalism. We have seen the competition reduced in effect to two competitors: Resemblance Nominalism and UP-Realism. Deciding between these two is not an easy matter. Each theory has one basic relation: instantiation in the case of Realism, and resemblance in the case of Resemblance Nominalism. Nominalists have a slight advantage in terms of quantitative economy, since they do not have to acknowledge the existence of universals. At the same time, Realists have an account of the essential laws of resemblance that Nominalists must take as brute facts. As we have seen, in order to meet the problems of imperfect community, co-extensive properties, and companionship, Nominalists must replace the simple, binary relation of resemblance with a variably polyadic relation of collective, comparative similarity that seems a great deal more cumbersome than the Realist's binary instantiation relation.
The next chapter, in which we consider theories of the constitution of particulars, may provide further considerations both for and against Realism to add to the balance.
Notes
1. Gonzalo Rodriguez-Pereyra (2002) solves the problem while keeping resemblance as a binary relation. However, he allows the relation to connect not just two particulars, but also two pairs of particulars, or two pairs of pairs of particulars, or two pairs of pairs of pairs, and so on. However, the relation's holding between two pairs is never logically entailed by its holding between the members of those pairs, so it is still (metaphysically speaking) a relation holding between variable pluralities of particulars.
2. The material about these two varieties of Trope Theory, both in this chapter and the next, derives from work by Robert Garcia (2015, 2016). We thank him for permission to use his arguments here and for many helpful conversations.
9
Particulars and the Problem of Individuation
9.1 Introduction
In the last two chapters we have been considering some important questions about the nature of properties, including their relations to the powers of things. In this chapter, we turn our attention to the question of the relation of properties to particulars. We consider, first, facts (the shorter Section 9.2) and, second, substances (the longer Section 9.3). In Section 9.2, we will consider three theories of facts: as tropes, as states of affairs, and as nexuses between particulars and universals. We note that in each case, facts turn out to be particulars of a kind. This raises a question about how to understand the ordinary particulars of everyday life and science: are they constituents of facts or facts of a certain kind or some third thing? These ordinary particulars are richly charactered and potentially changeable things—things known as ‘substances’ in ancient and medieval philosophy.
Investigating the question of substances will take up Section 9.3, where we consider two accounts about the relationship between substances and properties, namely, Relational and Constituent Ontology. According to Constituent Ontology, properties are literally parts of substances they characterize. According to Relational Ontology, in contrast, properties are separate things, extrinsically related to their instances. After considering the Extrinsicality Objection to Relational Ontology, we will examine two versions of Constituent Ontology, Bundle Theory (according to which substances are mere “bundles” of properties) and Substrate Theory (according to which substances have both properties and some fundamental particular as parts).
The questions that we will be investigating in this chapter presuppose a set of possible answers to the questions about properties that we investigated in Chapters 7 and 8. Those who embrace Extreme Nominalism, whether in its Ostrich or Reductive (e.g., Resemblance) forms, need not worry about the internal metaphysical structure of things. On those views, all substances and facts (if there are such things as facts) are metaphysically simple. In contrast, those who believe either in tropes or universals (or both) will have to confront the issue about the relationship between those properties and particulars.
9.2 Facts
The notion of a fact has already played an important role in our discussion. The most natural view of truthmakers is that they are facts. Simple subject-predicate sentences seem to be made true by a fact that some particular instantiates some property. Further, tropes seem closely allied to facts, since many facts seem to be simply a particularization or an instance of a property. This can be seen most clearly in causal statements. The fact that the vase was fragile caused it to break when it hit the ground. Trope Theorists, recall, say that tropes are the fundamental relata of causal relations. In our example, ‘the fact that the vase was fragile’ must then denote
a trope, namely the glass's fragility trope. But Realists seem to have space for property instances as well, though on that view property instances will be complex objects composed of a universal and some particular. If facts, or anyway some facts, are just property instances, can we make any headway toward settling the dispute between Trope Theorists and Realists by considering the nature of facts?
A question thus arises: exactly what sort of thing is a fact? There are three popular answers, two of which have already emerged in our brief discussion.
A fact is a trope or individual accident like the particular whiteness of a particular snowball. This must be a non-transferable trope or accident, one that could not possibly be the accident of any other particular. If the whiteness trope of this snowball could be transferred to another object, like an icicle, then it wouldn't be a classical truthmaker for the proposition that this snowball is white, since its mere existence would not be sufficient for the truth of that proposition. If tropes are non-transferable, then the whiteness trope of this snowball exists if and only if this snowball is white. The greenness of the snowball, for example, simply doesn't exist, and as a consequence, it is not true that the snowball is green.
A fact is a complex state of affairs, something made up of at least one particular (the snowball) and at least one property or universal (the property of being white or WHITENESS). The combination of the particular and the property exists only if the corresponding sentence (the one predicating the property of the particular) is true. If the sentence is false, then the individual parts (particular and property) may exist, but their combination or union into the relevant state of affairs does not. If we adopt Totality Fact Maximalism (2.1T.3), then the basic facts are complexes built up from properties and those individuals that make up the totality of its instances.
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