[This is a graduate student paper from Sept., 1994. --mh]

An Argument against Nominalism

Here is an argument against Resemblance Nominalism: Consider all the red things in the world. All these objects could have been white. And consider all the (presently) white things in the world. It could have also been the case, at the same time, that these objects should have been red. In this case, where the (actually) red objects would be white and the (presently) white objects would be red, the same objects would exist, and the same objects would resemble each other, as do presently. Therefore, if resemblance nominalism is true, this alternate situation would be exactly the same as the way things are now. But this alternate possible world is certainly not how things are presently. Therefore, resemblance nominalism is false.

I'm going to elaborate this argument, see if it can be generalized to apply to other forms of nominalism, and consider replies to it.

Resemblance Nominalism, as I understand it, claims at least this: that the only things that exist are particulars and the relations of resemblance among them (but the latter category must be regarded as a redundancy, insofar as this is a form of nominalism). I think that it follows from this that if two worlds have the same particulars and the same resemblance relations, those two worlds are indiscernible (type-identical) -- that is to say, the way things are in the one world is exactly how things are in the other world.

Now let's suppose that there are only three white things in the world, a, b, and c. That this supposition is false, and that perhaps the resemblance nominalist would require there to be more than three objects in order to establish a type, will not be relevant, as we will be able to see the argument applies no matter how many white objects are supposed to exist (I restrict the number only for ease of exposition). Let's also suppose that all the red objects in the world are d and e. And now, to make things simple, let us imagine that a, b, c, d, and e are the only things in existence. Call the world in which all this is so W. Now it seems clear that there is another possible world,(1) V, in which a, b, c, d, and e are the only things in existence, but a, b, and c are red, while d and e are white. It further seems obvious that V is different from W -- i.e., that the situation posited in W is not the way things are in V. This is because, of course, things would be having different colors in V than they do in W. But, if resemblance nominalism is true, then the two worlds would have to be the same, since they have the same particulars and the same relations of resemblance.

I think this argument is correct. But the nominalist might try either of two replies at this point. First, he might say:

Your two worlds, W and V, are not identical, because they do not have the same resemblance relations. It's true that in V, a, b, and c resemble each other; and in W, a, b, and c resemble each other; but what makes you think that these two cases of resemblance are the same? They are both resemblances, but they are distinct instances of resemblance.

(Notice that the reply takes resemblances to be tropes, now.) One could question whether this last claim is true. It is not obvious that the resemblances among a, b, and c in W and V are (token) distinct, even if we believe that they are particulars. That is, it is unclear whether, or if so why, we are forced to posit distinct resemblances in the two worlds. I can stipulate that V contains the same individual objects, a, b, and c, as does W. Why can I not, likewise, just stipulate that V also contains the same individual tropes? It might be said that I cannot do this because, by stipulating that a, b, and c would be red in V rather than white, I already eo ipso stipulated that they had a different resemblance relation. It doesn't seem to me as if that was what I was doing, but then it didn't seem to me as if I ever posited any 'resemblances' whatever, so perhaps the nominalist defense at this point is successful in its own terms.

But the more fundamental counter-reply to make (that is, for the realist to make) would be to point out that my objection was against the implication that V and W were indiscernible, and the alleged fact that they contain distinct token relations has nothing to do with that. That is, even if possible worlds W and V contain different tokens of resemblance, it should remain the case that, on the nominalist theory, worlds W and V are type-identical, since they contain the same individuals in the same types of relations to each other. And, again, this result is highly counter-intuitive.

The second nominalist defense that might occur would involve just accepting that the imaginary worlds, V and W, are indiscernible; or else saying that what I purported to imagine is not really possible. I lump these two replies together both because I think they are pretty much equivalent and because I think the same thing should be said about both of them. If one says that V and W are indiscernible, then that seems to just entail that V does not, contrary to my stipulation, have a, b, and c being a different color from what they are in W; and so, in other words, my (attempted) stipulation about V is impossible. If one says that my two worlds are impossible, or that given W, V is not a possible alternative, it must be because one is saying that V could not be different from W (obviously V is possible if V=W), so that is just saying that the imaginary worlds are not distinct. That's why I say these are equivalent replies.

What ought to be said about this sort of reply is not very much, but just this: A philosopher ought to be prepared to accept in principle some way of defeating his position; at least, he ought to unless his position is self-evident and indubitable. I doubt (to say the least) that resemblance nominalism is simply self-evidently true. Now it seems to me that deducing a highly counter-intuitive conclusion from a philosophical theory is the most you can hope to do in philosophy (or in anything else, really), and I do not know what more reason to reject a theory you could want. If some philosopher stands ready to respond to objections against his view by simply swallowing any and all consequences of it, then I call that philosopher a dogmatist, and he is ineducable. It is as plain to me as any modal fact ever is, that it's logically possible, for instance, that the red things be white and the white things be red (taking "red things" and "white things" as rigid designators, of course). I will not attempt to prove it.

At this point, then, the reasonable philosopher should concede that Resemblance Nominalism is in serious trouble, and, unless some other reply than we have considered can be thought up, it is refuted.

But it is worthwhile to explore the objection further. Consider the following fairly obvious generalization on the argument, which applies to all versions of nominalism:

According to nominalism, the only things that exist or can possibly exist are particulars. It follows from this that any two worlds with the same particulars are exactly the same. They can differ in no way whatsoever; they can not differ, even, in what facts are true in them, since they have the same particulars, and particulars are supposedly all there is. If there are any facts in the world, the facts must be comprised of particulars in some way. But it is easy to imagine, what also certainly could have been the case, that the very same particulars as exist presently had had different characteristics, been in different states, and so on; and in this case, it is clear, the world would have been different. As the world would have been different, it must be that it would have differed in respect of something non-particular; that is, that it would have differed in respect of universals. Therefore, the world contains universals.

The simplicity of the objection may inspire suspicion. Surely the nominalists cannot be guilty of so obvious an oversight? Yet I can think of no reasonable defense against it.

One might try to lean on the type-token distinction, which I have been loose with in the exposition of the argument. When I say that two worlds could 'differ' while containing the same particulars, do I mean they could differ numerically, or qualitatively (that is, they could be type-distinct or token-distinct)? The answer is, I mean qualitative difference. At this point the suggestion might be pushed that the nominalist is not committed to worlds containing the same particulars being qualitatively identical. He says that the world is entirely composed of particulars. So he is committed, only, to the view that worlds containing the same particulars are numerically identical.

Why this does not work is, that the nominalist cannot treat qualitative difference as a primitive. Since he believes only in particulars, he must say either that there are no such things as qualities, or that qualities are particulars or in some manner composed of particulars (where the last alternative, "... composed of particulars", is really superfluous). So faced with the two apparently qualitatively different possible worlds, he cannot say that they just differ qualitatively ('differ in respect of some qualities') and stop there. He must say either that they do not differ qualitatively, perhaps because there are no such things as qualities and so no such things as qualitative differences, or that they differ in respect of what particulars are in them. For him to admit that the same particulars were present, and yet different qualities were present, would be to concede the realist case: that there are qualities and that qualities are not particular.


1. Or at least that there can be one, possibly depending on some details about W that I haven't specified. In other words, perhaps there could be some white objects a, b, and c with essential properties incompatible with redness; but it's clear that some example of the type I'm describing ought to exist.