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The Atlas of Reality

Page 22

by Robert C. Koons,Timothy Pickavance


  7.2.1.1 The Universal-Particular Distinction

  The first challenge a Realist faces can be put in the form of a question: What, exactly, is the distinction between universals and particulars? What is it, in other words, for something to be a universal rather than a particular (and vice versa)? Realists must commit to the following principle:

  6.2T Universal-Particular Distinction. There is a clear and coherent distinction between universals and particulars.

  The challenge is to find a way to uphold this principle.

  There are three popular candidates for making the universal-particular the distinction.

  7.2T.1 Aristotelian UP. Universals can be predicated of other things, while particulars cannot be predicated of anything.2

  7.2T.2 Russellian UP. Particulars are necessarily located in only one place at a time, while universals can be wholly present at many places at once.3

  7.2T.3 Wise UP. Any particular can coexist with another particular indiscernible from it, but it is impossible for any universal to be indiscernible from anything else.4

  There are some well-known problems with the Aristotelian UP and Russellian UP distinctions.

  Take Aristotelian UP first. Advocates of Aristotelian UP tend to start with the observation that predicates in natural languages “correspond” to universals, in the sense discussed at the beginning of this chapter. In at least a certain class of cases, something satisfies a predicate if and only if it exemplifies the universal that corresponds to that predicate. Aristotelian UP is an attempt to turn this mundane observation into an account of the universal-particular distinction. The thought goes like this: predicates in language are attached to subjects in a language via concatenation, and in an analogous way universals are “attached” to particulars via (so-called “ontic”) predication.

  Though there are a number of ways to try to execute this strategy, Frank Ramsey (1925) powerfully argued that this notion of (ontic) predication cannot be made sense of without presupposing a distinction between universals and particulars. Therefore, one cannot use predication as a basis for making that distinction. Instead, the distinction must be the basis for understanding predication. And even if one could understand predication independently of the universal-particular distinction, Ramsey argued that one would not be able to define the direction of predication. The only reason one has for thinking that it is universals, rather than particulars, that are predicated is an arbitrary linguistic distinction between subjects and (natural language) predicates. But natural languages needn't have had this sort of structure: we can develop languages such that the bits of language that correspond to particulars are the predicates, whereas the bits of language that correspond to universals are the subjects. In other words, Ramsey argued that the linguistic evidence is simply insufficient to support a robust universal-particular distinction. But that linguistic evidence is all the advocate of Aristotelian UP has to draw on.

  Consider now Russellian UP. It is not obvious that particulars cannot be multi-located. For example, if something is transported into its own past, it could occur twice over at the destination time. In addition, fission might enable one particular to exist in two places at once. But if it is possible that particulars be multiply located, then Russellian UP is false, since being possibly multiply-located would not be sufficient for being a universal. Further, if there are universals that only one thing can have, then those universals cannot be located in more than one place at once (unless particulars can, in which case there still is not the needed asymmetry). In this case, being possibly multiply-located would not be necessary for being a universal.

  We'll consider Wise UP in more detail. If Wise UP is correct, then particulars and universals must satisfy the following definitions, respectively:

  Def D7.1 Particular. Something is a particular if and only if it is possible for there to be two distinct but indiscernible duplicates of it.

  Def D7.2 Universal. Something is a universal if and only if it is not possible for there to be two distinct but indiscernible duplicates of it.

  One note before we begin our examination of these definitions in earnest: given that everything either is or is not such that it is possible that there exist two distinct but indiscernible duplicates of it, these definitions demand that everything that exists is either a universal or a particular. That is, there is nothing that is neither universal nor particular. It is an important question whether this is a reasonable assumption, but it is not a question we will explore here.

  Before we are able to ask whether these definitions are true, we must first understand their content, what they say. There is one issue, in particular, that will demand sustained attention, namely, the notion of indiscernibility. The idea is that two things are indiscernible if and only if they are qualitatively the same. As we have noted, things can be alike in various ways. This happens when things have the same properties. Things can also fail to be alike, by having different properties.

  We can thus begin a more careful examination with a simple-minded definition:

  Def D7.3 Indiscernibility. Things a and b are indiscernible if and only if a and b have the same properties.

  Given Def D7.3, we can understand Wise UP in another way. Gottfried Leibniz argued for two principles of identity:

  Indiscernibility of Identicals. If thing a is identical to thing b, then a exemplifies F if and only b exemplifies F.

  7.3T Identity of Indiscernibles. If (thing a exemplifies F if and only if thing b exemplifies F), then a is identical to b.

  The Indiscernibility of Identicals is almost universally accepted and has come to be known as ‘Leibniz's Law’. The Identity of Indiscernibles, on the other hand, has been much more controversial. Indeed, Wise UP amounts to the claim that some things, the universals, obey the Identity of Indiscernibles, while other things, the particulars, violate the Identity of Indiscernibles.

  Def D7.3 turns out to be inadequate, but the reason for its inadequacy is instructive. What we are trying to capture with the notion of indiscernibility is what we might call “purely qualitative sameness”. We've talked above about objective similarities and are thinking about properties as something that might explain those similarities. But we also noticed a connection between properties and predicates. Connecting these to our discussion of indiscernibility, though, there seem to be predicates that won't correspond to a property that makes for objective similarity (if they correspond to a property at all—see the discussion of Russell's Paradox in Section 7.2.1.2).

  To see how this is so, consider the following:

  (1) Lyle is standing next to a tree.

  (2) Elsie is standing next to a tree.

  Suppose both (1) and (2) are true. If so, then both Lyle and Elsie satisfy the predicate ‘is standing next to a tree’. If there is a property of standing next to a tree, then Lyle and Elsie both exemplify it. But it seems quite strange to think that Lyle and Elsie objectively resemble or are objectively similar to one another just in virtue of standing next to a tree! Maybe they resemble one another in being mammals or in being alive or in being creatures or maybe even in that they are both standing. But their both standing next to a tree doesn't seem to be a sense in which they resemble each other.

  This apparent lack of resemblance can be emphasized if we consider a counterfactual case. Suppose Lyle walked away from the tree and stood instead next to a tractor. It is difficult to see how this would change the resemblance relations between Lyle and Elsie. If Lyle resembled Elsie while standing next to a tree, it doesn't seem that he would resemble her less just by moving next to a tractor.

  Returning to our discussion of indiscernibility, there are properties like that of standing next to a tree that seem to make it too easy for objects to be discernible, according to Def 7.3. Consider the property of being located at place p, for some definite p. (Let an appropriate substitution for p be a set of GPS coordinates.) This property, like that of standing next to a tree, doesn't seem to be the sort of property that ough
t to matter for whether things are indiscernible or not. But most things occupy different locations. If these location properties are relevant to indiscernibility, then we can use them to argue that things are discernible. But that seems wrong! A thing's location doesn't seem to be among its deep, qualitative characteristics.5

  There are other properties that seem to make things even worse. Take the property of being distinct from Elsie (which anything that satisfies the predicate ‘is distinct from Elsie’ has). Everything but Elsie has this property. But it doesn't seem that things ought to resemble just in virtue of sharing this property. It doesn't seem like a qualitative characteristic of a thing. And if properties like this, “properties of distinctness” we might call them, are relevant to discernibility, then it seems all too easy to show that two things are discernible. Suppose you have two things, Lyle and Elsie, for example. Given that Lyle and Elsie are two—that is, given they are distinct—they will exemplify different properties of distinctness. Lyle has the property of being distinct from Elsie, which Elsie lacks. And Elsie has the property of being distinct from Lyle, which Lyle lacks. Thus Lyle and Elsie are discernible (or fail to be indiscernible), by the lights of Def 7.3. This seems like the wrong way to argue that two things are discernible!

  What we need is to identify a restricted class of properties, a set of sparse properties (and relations), that are relevant to matters of discernibility. Notice that we have employed words like ‘deep’ and ‘qualitative’ in our discussion so far, and what we're looking for is a way to think and speak more clearly about these notions. David Lewis (1983, 1986a) described what he called “natural” properties, and these seem well suited to play the role we're hoping to occupy here.6 Natural properties are properties that are implicated in an account of the fundamental features of things in the world. According to Lewis, natural properties ground either resemblance or causal powers (or both). We believe that properties implicated in an account of the fundamental features of things will sometimes make for resemblance or causal powers, but we do not want to unduly limit our attention to just those sorts of properties. It may be that there are natural properties that do other things as well.

  It isn't easy to say exactly which properties are natural. One would like to have a list of the natural properties at the outset, but there is no such list. We will content ourselves to give a few examples of properties that are plausibly natural, to try to make some general remarks, and to consider each unclear case on its own merits. First, let's provide a few examples. The properties ascribed to very small physical objects are plausibly natural, like properties of spin and charge, for example. Biological kind properties like being a dog, being a human, being a mosquito, and so on, are also plausibly natural. So too simple mental properties like being in pain or having an itch. Properties of mass are plausibly natural, and to a lesser extent so are color and shape properties. On the relation side, relations of spatiotemporal distance are likely natural, as are simple logical and mathematical relations like entails and is greater than. Second, then, let's look at some tentative general observations, based on our earlier discussion. Logically complex properties are plausibly non-natural. Relational properties, including properties of identity and distinctness, are plausibly non-natural as well (though we'll consider a possible exception below).

  With that basic understanding of natural properties on the table, we can return to our discussion of indiscernibility. Given the troubles we had with Def 7.3 and the discovery of natural properties, we can offer the following, revised definition of indiscernibility:

  Def D7.3* Indiscernibility. Things a and b are indiscernible if and only if a and b have the same natural (monadic) properties.

  We can similarly modify the Identity of Indiscernibles, as follows:

  7.3T.1 Restricted Identity of Indiscernibles. If (thing a exemplifies F if and only if thing b exemplifies F), where F is a natural monadic property, then a is identical to b.

  Finally, we can recast Wise UP as the claim that universals satisfy Restricted Identity of Indiscernibles, whereas particulars do not. That is, we read Def D7.1 and Def D7.2 as deploying this revised notion of indiscernibility.7 (Hereafter, we will use ‘Indiscernibility’ to mean Def D7.3*.)

  The question then becomes, do particulars run afoul of Restricted Identity of Indiscernibles while universals do not? We are going to leave an examination of the first part of that question, having to do with particulars, for the next chapter and our discussion of the Bundle Theory of substance. We turn presently, though, to the second half, the question whether universals satisfy Restricted Identity of Indiscernibles.

  For the sake of space, we will only suggest a few ways one might defend the claim that universals are identical if indiscernible. First, one might defend Causal Structuralism (6.1T.1T plus 6.2T.1), which has an implication that every property confers on the things that have it a unique set of causal powers. If, then, the properties of conferring such-and-such power (for the right such-and-such's) are natural, then it follows that each universal exemplifies a unique set of natural properties having to do with what powers they confer. Thus, it follows that universals satisfy Restricted Identity of Indiscernibles. Second, one might defend the claim that properties of identity (and/or distinctness) for universals are natural. For example, you might claim that the property of being the universal NEGATIVELY CHARGED is natural. If so, and since only the universal NEGATIVELY CHARGED can exemplify this property, then each universal exemplifies a unique natural property. Thus, universals satisfy Restricted Identity of Indiscernibles.

  Third, and maybe most promising, one might claim each universal has a unique set of categorial relational properties. What are categorial relational properties? Simply, they are relational properties that have to do with universals' categorial relations! Categorial relations, as we noted near the beginning of the chapter, are relations like being a determinable of and being a determinate of. Categorial relational properties, then, are properties that a universal exemplifies just in case it stands in one of these categorial relations to some specified other universal. Suppose, for example, that colors are universals, and that there is further a universal COLOR. Each color more determinate than the universal COLOR stands in the is a determinate of relation to COLOR, and thus each color more determinate than the universal COLOR exemplifies the categorial relational property of being a determinate of COLOR. Further, COLOR stands in the is a determinable of relation to each of these more determinate colors, so COLOR exemplifies, for example, the categorial relational property of being a determinable of REDNESS. REDNESS is, of course, a determinable of BURGUNDY, SCARLET, and so on, and so exemplifies the categorial relational properties of being a determinable of BURGUNDY, being a determinable of SCARLET, and so on.

  Plausibly, each universal exemplifies a unique set of such categorial relational properties. No other universal has just the determinates and determinables that COLOR does, no other universal has just the determinates and determinables that SHAPE has, no other universal has just the determinates and determinables that BURGUNDY has. Clearly this list could go on, and we can think of no examples of universals that don't fit the pattern. So, since each universal stands in a unique set of categorial relations, and since which categorial relational properties a universal exemplifies is determined by these sets, each universal exemplifies a unique set of categorial relational properties.

  Further, it is plausible that categorial relational properties are natural. Universals seem to be more or less similar to one another, and categorial relational properties offer a way to account for these similarities and dissimilarities. For example, colors are more similar to one another than they are to shapes, and this can be accounted for by noting that colors share more categorial relational properties (like the property of being a determinate of color) than they share with any shape. Since grounding resemblance is one telltale sign of naturalness, we have a reason to think that categorial relational properties are natural.

  The most o
bvious objection to this strategy is simple. We've seen that relational properties in general are bad candidates for being natural, and so we need some reason to think that categorial relational properties are unique among relational properties for being natural. We have already seen one such reason in the preceding paragraph. And another reason is not far to seek. It is part of what it is to be a certain universal that it stands in just the categorial relations it does to just the other universals it does. A complete description of the fundamental nature of universals cannot be complete without invoking categorial relational properties. This strongly suggests that such properties are natural.

  You might have the following thought. Can't one say the same thing about properties of identity and distinctness? Aren't they, too, relevant to a thing's being what it is? Though the case of properties of identity (and distinctness) is more complicated than many think (see Pickavance forthcoming), they aren't relevant in the same way. In particular, while it is the case that something can't be what it is without exemplifying the right property of identity, properties of identity seem to presuppose the identity in question. Take THP's dachshund Elsie. Elsie exemplifies the property of being identical to Elsie. But her doing so seems to presuppose that she stands in the identity relation to herself. Since one can't stand in relations to non-existent object, Elsie's exemplifying her property of identity presupposes her own existence!

  Think of it this way. A full description of the world needn't appeal to Elsie's identity property. Just mentioning Elsie herself is enough to convey that she is identical with Elsie. There is no need for an appeal to the property of being identical to Elsie. But this is not so with categorial relational properties. No full description of the universal ORANGE, for example, can fail to mention that ORANGE is a color. Thus, a full description of that universal invokes the property of being a determinate of COLOR.

 

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