The new Philosophia Christi came the in mail yesterday and it has a symposium dedicated to the issue of the "God and Abstract Objects" debate. Paul Gould has a helpful summary of the debate:
The question: how does God relate to abstract objects like universals, properties, propositions, numbers, and sets?
The problem:There is an inconsistent triad:
- Abstract objects exist necessarily. [Platonism]
- Abstract objects distinct from God are created (by God) and hence, dependent (on God). [common understanding of traditional theism applied to the Platonic horde]
- If abstract objects exist necessarily, then they are either independent or uncreated. [Platonist assumption]
- Platonic Theism (the strong version rejects ; the weak version rejects  and ).
- Theistic Activism and Divine Conceptualism (both reject ).
- Nominalism (rejects ; there are no abstract objects]
- Reject claim  and the problem of universals (or attribute agreement) emerges.
- Reject claim  and the ultimacy problem emerges (God is dependent upon properties that exist apart from him for his nature).
- Reject claim  and the dependency problem emerges; i.e how can God be the creator of his properties without depending on a property such as being able to create a property).
- Keith Yandell (Platonic Theism)
- Richard Davis (Divine Conceptualism)
- William Lane Craig (Nominalism)
Looks to be an interesting discussion!