​(That said, I agree that Aquinas would probably not countenance disjunctive relations.

I would have to check, but I seem to recall my argument against disjunctive universals being one Armstrong gives against a view that (among other people) Wittgenstein held. You aren't letting dear old W. intrude on your Thomism, are you Greg-o? 
(Just having some fun, of course.)

 My first tendency here was to deny that the instantiation relation is metaphysically fundamental on the Aristotelian view. One could elaborate that by saying that if there is an instantiation relation, then it's disjunctive.)

Fair enough. If you want to adopt a nasty Armstrongian doctrine, you could perhaps say that the disjunctive universal is an "ontological free lunch".

John West wrote:

Neither, I think. The way Armstrong uses “strict identity” (which is the same as “absolute identity”), something is strictly identical if and only if it's both numerically and qualitatively identical.

I see. Thanks. That suffices for my purposes. Even the medieval non-nominalists, on my reading, want to qualify or reject the claim that a universal is numerically identical in each of its instances; a fortiori, they want to qualify or reject the claim that a universal is strictly identical in each of its instances.

John West wrote:

The reason that it's a truism that each universal is strictly identical in each of its instances is that the whole idea behind positing universals is that they account for sameness among different things by the fact that each of the different things have exactly the same entity as a constituent or ontological “part”.
...
Medieval authors used “universals” in two ways. They use it in the sense of whatever can be present in many things (i) wholly, (ii) simultaneously, and (iii) in some appropriately metaphysically constitutive way, or in the sense of whatever is naturally able to be predicated of many (Spade).

​Yes, that is the definition (or near to it) that Boethius gives in his sophistical argument against universals: "common in such a way that both the whole of it is in all its singulars, and at one time, and also it is able to constitute and form the substance of what it is common to" (Spade's translation). His solution to the problem of universals is a qualification of that definition, though. He claims (obscurely) that a universal is the likeness (which he also calls a "nature" and a "form") of numerically distinct things, when thought. The likeness in question is "universal in one way, when it is thought, and singular in another, when it is sensed in the things in which it has its being." He accepts his sophistical argument's premise that nothing is common to many wholly, simultaneously, and constitutively. He wants to get around the problem by arguing that what have universality in thought are, as they are in singulars (wholly and constitutively), not common to many.

​And I think that each of Abelard, Avicenna, and Aquinas agree that there is nothing common to many individuals wholly, simultaneously, and constitutively. (I am not familiar with the contemporary discussion of universals, but it seems to me that the goal of contemporary realists is to get something which the medievals generally agreed was not to be had.)

John West wrote:

Boethius's argument, if it's the argument I'm thinking of, fails because he thinks of universals as substances rather than as ways things are.

The sophistical argument takes the prime examples of universals to be genuses and species, which are secondary substances in the sense of the Categories. In Boethius's positive view, a universal is a likeness or form or nature as it is thought (which turns out to be a species, if it's a likeness of individuals; a genus, if it's a likeness of species).

John West wrote:

This is literally one of Armstrong's arguments against irreducible natural kinds. I think, at the very least, that the believer in them is going to have to assume that men and horses are identical in respect of something that is going to seem like a “mysterious ingredient” to some.

Yeah, in Thomism, and in the Thomist reading of Aristotle, the genus-species relation is not, in general, what subsequent philosophers have called additive​; differentia is not always specifiable independently of genus.

​As one case of this, consider rationality. Rationality and intellectuality are not the same thing on Aquinas' view. Rationality is the human or animal way of having an intellect, but it is not adequate to identify "the" powers associated with having an intellect and to define humans as animals with those powers. There is not a common ingredient, in that sense, in humans and angels. What differentiates humans from mere animals is suffused with animality. Thus we return to our hylomorphic-dualist theme.

​Anscombe's Intention​ can be read as arguing, among other things, that the same is true of action and of intentional action. It is not possible to define additively an action as an event that is such-and-such or an intentional action as an action that is such-and-such. (And many of Wittgenstein's arguments about language and mind can be read as arguing that meaning, understanding, rule-following, perceiving, thinking, etc. cannot be given additive definitions.)

​And I think that each of Abelard, Avicenna, and Aquinas agree that there is nothing common to many individuals wholly, simultaneously, and constitutively. (I am not familiar with the contemporary discussion of universals, but it seems to me that the goal of contemporary realists is to get something which the medievals generally agreed was not to be had.)

Yes, I think this is right. (Somehow, my eyes glided over it the first time I read your comment.)

Well, I'm going to tie off my part in this thread with this comment.