I remember seeing this argument in my undergraduate metaphysics class. I don't remember where it came from originally, or specifically what conception of universals it was against. So, this post has two points (i) to present the problem, and hopefully encourage discussion, and (ii) to ask where to find this (or the cleaned-up version of this) argument.

We postulate universals to make our claims like "The blue car and the blue pen have something in common" true. What the car and the pen have in common is the universal blueness.

So, the argument takes the form of a dilemma:

Either blueness instantiates itself (is blue), or it does not.

If blueness instantiates itself, then we can make a true claim like "The blue car and blueness have something in common". What does blueness have in common with the blue car? It seems weird to say that it is blueness itself. So, it must be super-blueness. But then, we can ask if super-blueness instantiates itself. If it does, we get the same problem. If it doesn't, we get the second horn of the dilemma at the 'super' level.

If blueness doesn't instantiate itself, then presumably neither does redness. So, there is something that blueness and redness have in common, namely non-self-instantiation. So, we can ask: does the property of non-self-instantiation instantiate itself? Now, we get a Russell's Paradox.

Here are three quick replies:

(i) Bite the bullet and say that what blueness and a blue car have in common just is blueness.

(ii) Hold that universals themselves do not instantiate universals.

(iii) Allow universals to instantiate other universals, but claim that non-self-instantiation is not a genuine universal. Perhaps you can point to the fact that it leads to a paradox as reason to make this claim.

Thoughts?