You might recall a few weeks back I had a post on “Aseity and Abstract Objects” hinting at some of the problems that arise if we grant that
(1) God has a nature–a property or group of properties that He has essentially and that are distinct from Him.
(2) God exists “a se”–God depends on nothing distinct from Himself for His existence.
I had planned on a follow-up post looking at another facet on the problem of God and abstract objects, namely, the question of divine sovereignty. Imagine my delight when I found that Simon recently commented on the very subject, doing a far better job than I would have. Check out his post yourself. Let me just add my 2 cents however:
Suppose we define Sovereignty thus:
(3) Whatever is distinct from God depends on God for its existence
How does this square with the Platonic thesis of necessarily existing abstract entities? After all, if such things are necessary (that is to say, their non-existence is impossible), how can they depend on God for their existence? It would seem, as Plantinga wonders, that their existence isn’t “up to God.”
Moreover, consider the very character of such abstract entities. Take for example, the property omniscience. Its character is such that whatever entity, x, has it, for every true proposition p, x knows that p. But it does not seem that this characteristic of omniscience is “up to God.”
So then how should we understand divine sovereignty if it seems that the existence and character of abstract objects are not “up to God?”