Paul Gould’s Summary of the God & Abstract Objects Debate

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:

1. Abstract objects exist necessarily. [Platonism]
2. Abstract objects distinct from God are created (by God) and hence, dependent (on God). [common understanding of traditional theism applied to the Platonic horde]
3. If abstract objects exist necessarily, then they are either independent or uncreated. [Platonist assumption]

The answers:

1. Platonic Theism (the strong version rejects [2]; the weak version rejects [2] and [3]).
2. Theistic Activism and Divine Conceptualism (both reject [3]).
3. Nominalism (rejects [1]; there are no abstract objects]

Further problems:

1. Reject claim [1] and the problem of universals (or attribute agreement) emerges.
2. Reject claim [2] and the ultimacy problem emerges (God is dependent upon properties that exist apart from him for his nature).
3. Reject claim [3] 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).

The representatives:

1. Keith Yandell (Platonic Theism)
2. Richard Davis (Divine Conceptualism)
3. William Lane Craig (Nominalism)

Looks to be an interesting discussion!