S5, God, and Numbers

Res Cogitans 1 (1):63-78 (2010)
It has become somewhat ontologically fashionable for theists to embrace anti-realist views of abstract objects. I will argue that any theist who accepts the S5 ontological argument for the existence of God should also accept a parallel S5 ontological argument for the existence of abstract objects on pain of consistency. This is because the same ontological and modal inferences thought to demonstrate the existence of God can also be used to demonstrate the existence of numbers. I further argue that being ontologically consistent here might come at the price of being theologically unacceptable, as the argument for numbers would seem to vindicate a platonistic view of abstracta, and platonism is incompatible with the traditional concept of God. I conclude by suggesting what I see as the only way out of this dilemma, which is to embrace a view akin Augustine’s where abstracta exist “nowhere but in the very mind of the Creator.” Something like the Augustinian view of abstracta, therefore, can be seen as an indirect theological consequence of the S5 ontological argument for the existence of God.
Keywords Abstract Objects  Ontological Argument  Metaphysics  Philosophy of Mathematics  Conceptualism  Platonism
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