Self-exemplification and contingency in abstracta

The Argument from Sets is a really nifty argument that tries to ground the existence of sets in the mental activity of God. This is a really interesting way of looking at abstract objects, since their existence is actually contingent; they could have not existed!

An upshot of this argument is that it opens the door for grounding the contingency of other abstracta in the mind of God. For example, the property of "being an abstract object" exemplifies itself. So, some abstract objects exemplify the property of self-exemplification. But, does the property of self-exemplification exemplify itself? This is not the paradox of the property of non-self-exemplification. With that paradox, both affirming and denying that non-self-exemplification exemplifies itself entails a contradiction. However, with self-exemplification, it can either exemplify itself or not without contradiction. So which is it? And what's the explanation for why it stands in the relation to itself which it does in fact stand in? A theist can ground the property of self-exemplification in the will of God, and maintain that whether or not self-exemplification exemplifies itself is up to the free will of God. Coolio.