For theistically-minded philosophers, the problem of God and abstract objects has been heating up. The problem is motivated by an inconsistent triad of propositions, nicely formulated by Greg Welty:
1. Abstract objects (AOs) exist.
2. If AOs exist, they are dependent on God.
3. If AOs exist, they are independent of God. (81)
The first proposition is motivated by well-known arguments for the existence of abstract objects. The second is motivated by the theistic doctrines of creation and divine aseity: everything other than God must be created by God or depend on God. The third proposition is motivated by considerations suggesting that AOs, if they exist, are not the sorts of things that could be created or could depend on anything for their existence. Paul Gould’s edited book updates the state of play, and can serve as an excellent introduction to the debate for those of us who have not been following it closely. After Gould’s introduction, there are six major contributions, each followed by critiques from each of the other contributors and a final rejoinder from the main author of the section. We have “God and Propositions,” by Keith Yandell, “Modified Theistic Activism,” by Paul M. Gould and Richard Brian Davis; “Theistic Conceptual Realism,” by Greg Welty; “Anti-Platonism,” by William Lane Craig; “God with or without Abstract Objects,” by Scott A. Shalkowski, and “Abstract Objects? Who Cares!” by Graham Oppy.