My argument again. The following formally expressed statements are inconsistent.
1. (E x) number(x)
2. (x) number(x) implies not created(x)
3. (x) God created x
If (1) some x is a number, then (2) that x was not created. But (3) for all x, God created x, so God created that x. Contradiction.
Given this, it doesn't help to say that existentially quantified statements such as (1) don't really express or imply existence, or that (1) has no 'ontogical commitment'. This is irrelevant. Even if (1) is true of some x's to which we have no ontological commitment, it still logically follows that (3) is true of all x's, and so (presumably) is true of x's to which we are not ontologically committed. This is no way out.
Azzouni argues that our criterion for existence should be 'ontological independence'. If an object's properties depend wholly upon us (as in the case of fictional objects) then that entity does not exist. If our method for establishing the truth about an object is trivial (as in the case of mathematics) then it is ontologically dependent upon us. Accordingly, mathematical objects do not exist.
This does not help with the theological problem above. Even if (1) is true of ontologically dependent objects, there is still a contradiction, because there is nothing to prevent the universal quantifier ranging over such objects. If God created all things, then he made ontologically dependent things. But according to (2) some ontologically dependent things (numbers) are not created. Contradiction.
And Azzouni's suggestion creates another problem. I can meaningfully ask whether there are such things as 'ontologically dependent' objects. If yes, then why does Azzouni say that such objects do not exist? If not, in what sense is Azzouni offering any kind of solution at all? More on this later.