This short note appears in Clark Butler's History as the Story of Freedom: Philosophy in Intercultural Context, editions Rodophi, 1995, pp. 94-95.
But Nominalism by no means has as easy a time of it as the foregoing might suggest.
First, that we sometimes intuit identities where they do not exist no more implies that such identities do not exist at all than the fact that we sometimes see trees where they do not exist (as in double vision) implies that trees do not exist.
Second, Hartshorne's view that no two things have the same color (or hue) implies that there are as many colors (or hues) as there are colored things. You only have to think for a moment about how many black, white, blue, etc. things there are to see how implausible that is. Are there really as many colors (or even hues) associated with, say, blackness as there are black things?
Just think of all the black words, letters, and spatially discriminable parts of letters, printed in all of the books, newspapers, libraries, newstands, recycling bins, dumps and storage areas in all the world at each point in time, or only in recent times. Can one seriously suppose that there are that many blacknesses or hues thereof--even if we disregard the billions of other black things (grains of sand, etc.) in the physical universe. But of course there must be, if Hartshorne is correct, and surely it amounts to a reductio ad absurdum of his view. The scientific theory of color of course indicates that there are thousands of different colors, but nothing like what would have to be the case if he were right.
Certainly no one has or can actually discriminate and specify more than a vanishingly small percentage of these billions and billions of alleged `blacknesses', `bluenesses', etc. This shows that Hartshorne is only following out his a priori assumption there there must be no genuine samenesses in all of the things that have a certain quality. But why must that be so? And does he not give his own case away with his statement that the many `qualities' are but determinations of the same determinable? At least he owes us a clarification of "same" that will avoid a universal determinable.
Third, the--admittedly rather strange--Platonic associations have nothing to do with the ontological issue of whether or not there are universals. The only point at issue is whether or not there is an identical constituent in all of the entities that are P--e.g., black, blue, triangular, two in number, human, etc. etc. That is, is there a constitutent in all of the entities that are P, such that all things true of that constitutent in one of those entities is true of the corresponding constituent in each of the others? (Note that what is in question here is being-P, not being called or said or thought to be P. In philosophy we require some pretty strong arguments to reduce being-P to being-called-"P" or being-regarded-as-P.) If there is such a constituent, then there are universals. And if there are such universals (one-in-manys) they can then serve to ground the unification of a class or term-extension of the objects which are blue, triangular, etc., over against the class or extension of those that are red, round, etc.
Fourth, Nominalism itself has to account for the obvious differences and groupings of objects (the blue ones, etc.) just as much as does any form of realism with respect to universals. It tries to do this in terms of a common name or noun that, allegedly, applies to all and only the entities in the given group. That is where it gets it name. "Nominalism" means "Nameism," as its etymology shows. Thus, what unites the group of blue enties, on its account, is the fact that they all have a relation to THE name or predicate "blue." But now of course `the' word "blue" is no more identical in all of its occurrences or embodiments, dispersed through space and time, than are the entities to which it applies. The unity of `the word' blue is as much in question as is that of the entities that are blue, over against those that are red. And the further question of why 'the' word "blue" applies to all and only the things it does requires an explanation, if we are not in a position to assume that its doing so is largely conditioned on the fact that all and only those entities to which it applies are blue in the sense of having an identical and therefore unifying constitutent.
D. M. Armstrong has provided a simply stated but strong case against the possibility of a coherent Nominalism in Chapter One of his Universals: An Opinionated Introduction. (Westview Press: Boulder, CO., 1989) Once disburdened of the Platonic associations, and formulated simply as a claim about the strict identity of certain types of constitutents of certain types of entities, realism is a theory of great explanatory significance, as Armstrong spells out in detail. It also proves very difficult to refute without simply presupposing that all entities must be individual, and hence begging the question at issue. But why do that?