Following on from my earlier discussion of Maverick's posts. Assume that a universal is either one thing or many things (an assumption which may be false). If it is many things, then we have an infinite regress. If Socrates' wisdom is numerically different from Plato's wisdom, and if all the wisdoms of many philosophers are many different things, just as the philosophers themselves are many different things, how do we explain the underlying common nature of all these wisdoms? Don't we need another universal to explain this common factor? And then I ask whether this common factor is one or many. If one, then eadem ratione standum fuit in primo: by the same logic we should have stopped with the original case and gone no further. If many, procedetur in infinitum, there is an infinite regress.
If by contrast it is one thing, we must suppose some relation between individual objects which are instances of the universal, and the universal itself. Socrates, who is wise, bears this relation to the universal wisdom. So does Plato. But Joe Stupid, who is not wise, does not. And so we can construct a predicate, e.g. '- has wisdom' which is satisfied by all wise people, and only wise people. But what is the common feature that explains why some individuals bear this relation to the universal, and some do not? Is this one or many? And so we have an infinite regress again.
I conclude that, if there are universals, they are neither one nor many. More later, and this may involve bringing Avicenna into it.