Right. And I assume we're talking about this logically, not psychologically. An account of, I guess, properties, rather than how we come to learn them, or think them up, and so on.
A theory of universals presumably has something to offer, is supposed to explain how something works or what something means. I haven't thought about universals in a long time (having gotten accustomed to predicates and such) but it would appear to be in the neighborhood of where you started, two numerically distinct objects both being red, for example.
We have to first see how this is a problem, right? The objects are distinct. Anything you pick out to describe a concrete object is a bit of that object, is that object minus almost everything about it except some particular aspect you've chosen. (Passing over how we do that, for the moment anyway.) At least, that's how I presume abstraction works.
So you take a ball and you imaginatively delete its location, its mass, the texture of its surface, everything but the light it radiates and you call that its color. (This is no good, of course, since it needs to be a propensity or a disposition, but we don't know whether we need to bother yet.) We do the same thing with some other object, maybe a car. If this is how we 'create', as it were, colors of things, by taking a particular and leaving out everything else, we still end up with just a partial particular.
What you get is still two numerically distinct abstract objects rather than concrete ones, yes? No matter how similar the abstract objects are, they are distinct. What could possibly entitle us to say that they are in any sense the same thing?
Now we might think — identity of indiscernibles to the rescue! And now that we come to it, how did we imagine the sort of partial particular I described being a numerically distinct entity? It's not, after all; it's only an aspect of a 'genuine' concrete entity. Not even a part of it, but something that, obviously it seems, cannot exist on its own, but only as an aspect of something concrete.
No problem; we knew that as soon as we said we were creating an abstract object (the red of this ball) from a concrete object (this ball). But if it's no real objection that these things can't exist on their own, then we can't rely on their individual existence to underwrite their being numerically distinct. Maybe abstract objects can be numerically distinct, but if they can it's not the way regular concrete objects are.
Which leaves us where? We want to head toward saying these two abstract objects are the same or similar, but now it's not even clear in what sense they are objects at all, or whether they can be distinguished in order to be compared or identified. If these are objects, it's not clear what use they can be to us. We're in a muddle.
Abstraction looked so straightforward, but it seems to leave us nowhere.
So what do you think? We want an account of properties of objects, and we expect to be able to say that two objects have the same property, or that they have properties that are similar but not identical. But how do we fix our account of properties? Was my account of abstraction all wrong? Or are we in a better position than it seems?