Theism, Platonism, and the Metaphysics of Mathematics

1 The Dilemma of the Theistic Platonist Theists generally hold that God is the creator of all there is distinct from himself. Traditionally, the scope of God's creative activity has extended across two disjoint realms: the physical, whose chief exemplars are ordinary middle-size objects, and the mental or spiritual, encompassing such things as angels and souls. Now, many theists are also platonists, or " metaphysical realists ". That is, in addition to the physical and mental realms, some theists also acknowledge the existence of a realm of abstract objects like numbers, sets, properties, and propositions. For such theists, the traditional understanding of creation presents a philosophical and theological dilemma. On the platonist conception, most, if not all, abstract objects are thought to exist necessarily. One can either locate these entities outside the scope of God's creative activity or not. If the former, then it seems the believer must compromise his view of God: rather than the sovereign creator and lord of all things visible and invisible, God turns out to be just one more entity among many in a vast constellation of necessary beings existing independently of his creative power. If the latter, the believer is faced with the problem of what it could possibly mean for God to create an object that is both necessary and abstract. Though not utterly incompatible with a robust theism, the first horn of the dilemma seems undesirable for the theistic platonist. God remains the greatest possible being, since, presumably, it is not possible for any being to exert any influence over abstract entities; but the platonist must put