But Nominalism by no means has as easy a time of it as the foregoing might
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
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
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?