I should clarify what I'm trying to do; Grupp is right that my original comments are a bit cryptic in parts. I'm having difficulty seeing how his argument actually works, so my arguments shouldn't be considered categorically as attempts at refutation but rather as doubts or problems I'm having with the argument. They might, in the end, turn out to be refutations; but they might also turn out to be something else entirely. So I'm not going for a very strong claim with my arguments.
Grupp's argument (which can be found in the online articles) is that the positing of a Platonic exemplification tie introduces apparent contradictions having to do with the attachment of a located and an unlocated entity. Now, this is roughly the course the argument takes in the Dialogue article (as I summarized it in my original comments):
1. Suppose we have a wholly spatially located entity, L, e.g., a lion, and a wholly unlocated platonic universal, S, e.g., sublimity, which L exemplifies.
2. Since L is wholly spatially located, L only exemplifes n-adic properties, such as S, at x and nowhere else, because L is nowhere else but at x.
3. Therefore an exemplification not at x is an exemplification that does not have to do with L.
4. Since S is wholly spatially unlocated, it cannot fail to be spatially unlocated (Grupp calls this 'being at y'), S only involves a direct attachment to the exemplification tie at y, and nowhere else, because S is nowhere else but at y.
5. Therefore an exemplification not at y is an exemplification that does not have to do with S.
6. If L exemplifies n-adic properties only at x, if S involves a direct attachment to the exemplification tie only at y, and if the exemplification tie does not cross realms, since x is not y, L and S apparently cannot have any dealings with each other: for L to tie to S, S, which is wholly at y, must be at x, and thus be both located and unlocated, or L, which is wholly at x, must be at y, and thus both located and unlocated.
7. Therefore L and S cannot be tied by exemplification.
My first doubt about this was that the way Grupp has phrased the argument here gives it a superficial plausibility it does not strictly have. That is, the argument as it is put forward on p. 495 of the Dialogue article, makes the attribution of locatedness to the exemplification tie look parallel to the attribution of unlocatedness. L exemplifies S; L is wholly at x, so the exemplification must be at x; S is wholly at y, so the exemplification must be at y; hence the contradiction. However, suppose we grant that since L is located wholly at x, the exemplification tie must be at x. It does not follow from this that since S is unlocated, the exemplification tie must be unlocated. The cases are not parallel, although putting it in terms of 'being at x' and 'being at y' makes them look so. Grupp has given the Platonist no argument or reason to believe that she is committed to the exemplification tie's being unlocated, even if she agrees that she is committed to the exemplification tie's being located. In other words: Grupp claims that "A direct attaching with the exemplification tie that is not at y is a direct attaching that does not have to do with S" (p. 495), but this just means that an exemplification tie that is not unlocated can't have anything to do with S because S is unlocated. Now, it is by no means clear to me that a Platonic realist needs to accept such a claim without an argument. (Some might be committed to it, of course; but the question, I take it, is whether all positings of exemplification ties are committed to it.)
There is, I think, good reason to think that at least some Platonic realists would be inclined to deny such a claim. Two of the metaphors which Platonists of various stripes have occasionally used to describe the exemplification tie (or something analogous to it) are imitation and mental intention. Take imitation. Suppose we have an ectype, E, like a painting, and an archetype, A, like the person the painting depicts. E imitates A. Now E is wholly at x; and therefore the imitation of A is wholly at x. It has to be if E is an imitation of A, because E is wholly at x. But the imitation is of A. Now, it follows from nothing in this mix that the imitation tie has to be wherever A is. Or take mental intention or perception (e.g., Whitehead's ingression of eternal objects). P thinks about O. P is wholly at x; therefore the thinking about O is wholly at x. But it follows from nothing in this that the thinking about O is wholly wherever O is. And we can extend this to other properties besides location. So these sorts of metaphors suggest that we can conclude nothing about the exemplification tie as such directly from the properties of S. But this does seem to be what Grupp is trying to do in the argument.
If this is so, then whatever one's particular view about whether the exemplification tie is where L is, at x, we have no reason to believe that any contradiction ensues from the exemplification tie's attaching a located with an unlocated entity. Some Platonic realists might be committed to something like such a contradiction, if they characterize the attachment of the exemplification tie in a certain way; but there doesn't seem to be enough here to regard it as a general problem for Platonic realists. Platonic realists in general do not appear to be committed to a view in which S's being unlocated has any implications for the characteristics of the exemplification tie; the only thing that is essential is that L's exemplification of S actually be of S. Grupp seems to assume that to be of S the exemplification has to be unlocated; but I see no reason why this would be plausible to most Platonic realists. If this is so, then the Platonic realist can agree with #1, #2, and #3 above; but deny that #4 and #5 are true (and hence #6 and #7).
My 'further thought' [i.e., in the original comments - ed.] on the topic is (on further further thought!) somewhat irrelevant to the argument as such. I do want to clarify it, though. I said:
S may be wholly unlocated in itself, as a Platonic universal, but it does not follow from this that S cannot be located in any way; particularly if you think 'being exemplified by' is one way something can be located somewhere. In this case, S would be wholly unlocated in itself, but located in L by L's exemplification of S.
Grupp responds to this:
The author of the Siris entry is discussing my work as if we can avoid the problems I outline in my article by merely maintaining that either the exemplification tie, or the property S, is located where physical particular L is located at. With respect to S, this however is not platonistic metaphysics and platonistic property possession, but, rather, some sort of minimalist realist or Aristotelian property possession (which I very briefly discuss earlier in my article).
The issue in my further thought is the 'with respect to S'. As I said, I've come to think that it's actually not relevant to Grupp's argument, strictly speaking. But I want to point out that Grupp's conclusion here ("this however is not platonist metaphysics and platonistic property possession, but, rather, some sort of minimalist realist or Aristotelian property possession") is not necessarily true. Again, perhaps my comment is a bit cryptic. Let's detour slightly to consider the case of action at a distance. Now, it is an old maxim that everything is in some sense present or located wherever it acts. If action at a distance is possible, then, with the maxim it would mean that objects capable of acting at a distance can be (in a looser sense) present or located in places where they are not (in a stricter sense) present or located. And this seems quite reasonable; it is not location in the strictest sense, but it is an entirely plausible way of thinking about the matter: acting-on-O is a way to be located where O is, in an extended sense of 'location'. It's the looser sense/ stricter sense that makes it irrelevant to Grupp's argument, since (I take it) the argument is only about location in the stricter sense, and wouldn't be concerned with the looser sense at all. But the thought still can serve a (small) function in the discourse by reminding us that even if a Platonic realist were to allow that S is in some sense located, they would not necessarily be committed to an Aristotelian view. For while S, as a Platonic universal, is strictly speaking unlocated (and necessarily so), there is nothing to prevent the Platonic realist from allowing that in a looser sense of location it can be located wherever it is exemplified. And this does have some small importance, beyond the purely semantic point, because of one reason for talking this way that I suspect would perhaps be somewhat plausible to anyone who found Platonic realism itself plausible. If location (in the strict sense) is a derivative property of some sort, and necessarily presupposes exemplification (it being impossible for something exemplifying no properties to be located anywhere), then the reason for the apparent plausibility of speaking of exemplification ties as in some way located would become very clear: all location presupposes exemplification, and (naturally) we find that universals are exemplified in the world largely (some might say wholly) in located things, so by a very easy metonymy we can shift between the two. And if this is the case, then it would seem that Platonic realists need not be committed to #2 and #3; i.e., the exemplification tie cannot be (and does not need to be) strictly characterized as located, because it is what location itself presupposes. But I only bring this up as a possibility. My point is that it is possible for a Platonic realist to allow that S is in some completely reasonable sense located even though (because he is a Platonic realist) in a strict sense he must say it is not; but, as I noted, this is not in itself relevant to Grupp's argument, so I'll leave the clarification of what I originally intended at that.
This is an interesting discussion, and I'd like to thank Grupp for picking my original comments up and responding to them. Even if I turn out to be way off base, I've already found it to be excellent mental exercise and quite thought-provoking; even to lose this argument would still leave me happy and heavily benefited by having engaged in it. I hope the above clarifies my position somewhat; it's still possible that I'm misunderstanding or missing something in Grupp's approach. (It's also possible, given that my own sympathies are Aristotelian, that I'm attributing things to Platonic realists that no Platonic realist would ever hold; but this is the less likely danger.) In any case, as I said, it's been an enjoyable conversation.
