Russell's The Problems of Philosophy was published in 1912; but he published the short paper, "On the Relations of Universals and Particulars," in Proceedings of the Aristotelian Society in the 1911-12 edition. In what follows, I'm going to give a very brief sketch of the argument he presents there. The conclusion of the argument is that there is a fundamental distinction between two radically different sorts of thing: universals and particulars. (The article's title, as we shall see, involves a bit of word-play, as "relations" play a fundamental role in Russell's argument for universals.) I will proceed mostly without commentary, attempting to illustrate the bare bones of the argument.
I. Some approximate distinctions.
Russell begins by reviewing some distinctions to orient us toward the distinction he is trying to get at. The first three are psychological or metaphysical, and the last two are logical.
1. Percepts and concepts: These are the different objects of two different mental activities: perceiving and conceiving. Percepts (what he calls "sense-data" in Problems) are (one sort of) particular, while concepts are (one sort of) universal.
2. Time--Entities which exist in time and entities which do not: Garden variety example of the former would be physical objects (cars, pens, books, planets, etc.). What would the latter include? Presumably concepts (though the whole area is obviously tendentious), but also numbers, ideal shapes, and perhaps things like mathematical laws.
3. Space--(a) entities which are not in any place (e.g. relations); (b) entities which are only at one place at any one time (physical bodies or unities); and (c) entities which are in many places at once (e.g. colors and perceived shapes). Russell has a complex notion of space, depending on the vantage point from which it is described. So he recognizes, e.g. visual and tactical space (spaces of sense data), as well as physical space (the existence of which we can infer but not experience directly).
4. Relations and non-relations: This doesn't neatly map onto our prior distinctions. Relations can relate particulars as well as universals and other relations. (So "Dallas is north of Austin," "Squares have more sides than triangles.")
5. Verbs and substantives: Strictly, Russell is referring to the objects denoted by verbs and substantives. Here he provides some help. Recall that he often thinks in terms of sentence structure. Take a simple example: "Desdemona loves Cassio." Russell analyzes this as a complex in which the relation love relates the two non-relations, Desdemona and Cassio. Take another: "Othello believes Desdemona loves Cassio." Here "believes" relates Othello to our former complex fact of Desdemona loving Cassio. Russell tends to think that at least most verbs are relational in this sense. This distinction is important because it gets at how Russell thinks about universals and particulars. If the two are fundamentally distinct sorts of things, it will at least be the case that particulars cannot do the work of relations or predicates. So universals would just consist of the objects denoted by relations and predicates.
[This basic distinction traces back to Aristotle, who argued, in effect, that substances have to be fundamentally different from qualities. The best way to see this is to consider proper nouns. You can't predicate "is Socrates" of anything. (You can, of course, say, "The annoying pale snub-nosed fellow is Socrates," but this sentence states an identity, and not a subject-predicate combination.]
II. The Common-Sense Notion of Things and Qualities
By the "common-sense" view, R has in mind the bundle theory of the early empiricists, according to which, e.g. an apple consists of a bundle of sensible qualities coexisting in a single perceived space. Russell thinks it rests on the confusion of thinking of actually different sensory spaces as combined. As Hume might say, we are habituated to think of the apple and apple flavor and scent as all occupying the same "space," but they are each different modes of sense perception, so the "common space" is a useful fiction. The apple isn't the same as our senses of it, nor are our senses of it common to one another. He uses this to make a very interesting dilemma, which deserves quotation:
"Realists who reject particulars are apt to regard a thing as reducible to a number of qualities co-existing in one place. But, apart from other objections to this view, it is doubtful whether the different qualities in question ever do co-exist in one place. If the qualities are sensible, the place must be in a sensible space; but this makes it necessary that the qualities should belong to only one sense, and it is not clear that genuinely different qualities belonging to one sense ever co-exist in a single place in a perceptual space. If, on the other hand, we consider..."real" space...then we no longer know what is the nature of the
qualities, if any, which exist in this "real" space."
III. Three Theories
Very broadly, there are three possible stances about universals and particulars (assuming that one or the other exists):
1. Universalism: Only universals exist. There are no particular things, just universal qualities existing in multiple places at different times. To call out a "particular" patch of red is only to indicate its place, not to name a separate kind of entity. To call out two distinct but identically colored patches of red is just to indicate one thing in different places. The position here is more or less that the addition of particulars is unnecessary, since whatever role particulars are supposed to play can be handled by qualities and relational properties.
2. Nominalism: Only particulars exist (Berkeley and Hume). There are no abstract ideas or universals, only particular things--so no general "yellow," but only particular shades; no generic triangle, but only particular representations of triangles.
3. Realism: Both universals and particulars exist.
Russell's general strategy is to offer refutations for 1 and 2, and go on to consider, in some detail, strategies for arguing for 3.
Refutation of Nominalism
The strategy for refuting nominalism is the same one he uses in Problems. Recall that Berkeley and Hume get around positing universals by claiming that there are only particular sense data, say, different patches of white. This poses a problem for them, though: how are we able to recognize different patches as being, in some sense, the same? (Note that this problem exists both for distinct patches of white in a single experience, and for novel experiences of white things. For convenience, let us refer to a single experience of diverse white things as "Case 1" and later recognitions of white things as "Case 2.")
Nominalists typically solve this by saying that the diverse particulars that we give the same labels (like "white") are similar to one another. So, of two patches of the same color in one visual field, the nominalist claims that the two are exactly similar, and that that relation of exact similarity is logically fundamental insofar as it cannot be further analyzed into different predicates (e.g. beige, cream, lighter or darker white, etc.). Similarly with a new patch which we recognize as white. Our new patch bears the same relation of exact similarity to our memory of a color patch which we have baptized "white."
Now, the basic refutation is this: Even on the most simple terms, the nominalist has to recognize at least one relation, that of exact similarity. (If they're forced to grant one universal, why not more?) The harder problem, though, is that this solution doesn't look very plausible, at least insofar as we learn to reliably use quality terms very flexibly. Somewhat worse, if we take it's analysis seriously, it appears to generate a vicious regress. These problems help to illuminate one another.
The Regress: The nominalist claims that we learn how to use color terms by spotting different instances of exact similarity (our Case 1). Let us imagine a simple case of two white patches in our visual field, a and b. We recognize "a is white" and "b is white" are true because aRb, that is, where R denotes the relation, "is the exactly similar color as." (Remember that they can't be the same, because that would imply having a single thing in multiple places.) On this analysis, the predicate white just consists in the likeness relation that a bears to b. How, then, does Case 2 work? Imagine two novel white patches, c and d. Given that Case 1 defines "white," we must say that c bears some relation of color likeness to something else, but note that that something else cannot be a or b alone, since white is defined by reference to the relation between them. The obvious recourse would be to say that c's relation to a is exactly similar to a's relation to b. The regress is vicious because it means that we shall have to explain every novel instance of a quality by providing a higher-order relation of exact similarity to past similarities. This pretty obviously wrecks the nominalist's thesis that the similarity relation has to be basic and not analyzable into more than terms applying to particular bits of sense data. Given our flexible use of predicates of predicates like "white" or "round", it looks like nominalists need to accept some recourse to higher-order relations of similarity between different type-similarity relations.
The Lesson: Even if the nominalists accept only relations of exact similarity, they are forced to recognize universals. Further, Russell takes this to demand their recognition of: concepts (rather than merely percepts, since "similarity" is not a further item on our inventory of sense data); things which do not exist in time (since relations are not on a par with objects--objects can instantiate relations, but they appear to be fundamentally different from them in kind).
The most interesting part of the argument comes next, but I'm exhausted, so I'll leave it there for now. :)
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