Articles exploring God's attribute of self-existence and the challenge posed to God's unique aseity by Platonism, the view that there are mind-independent abstract objects.
Mary Leng, Mathematics and Reality (Oxford: Oxford University Press, 2010, 278 pp. ISBN 978-0-19-928079-7
This paper, presented before the C. S. Lewis Society in Oxford on the fiftieth anniversary of his death, surveys the options available to the theist for meeting the challenge posed by platonism to divine aseity and shows that Lewis anticipated a figuralist solution to the problem.
To the uninitiated, platonism, science, and Christianity might seem poles apart. Neither the average scientist nor the average Christian, after all, finds abstract objects to be relevant to his quotidian affairs. Appearances are in this case deceptive, however, for the principal argument for platonism today is that physical science requires the existence of abstract objects. This claim in itself demands careful scrutiny, since the very truth of science is at stake. But the importance of the issue is amplified for Christian theists because platonism is at the same time potentially a dagger in the heart of the Christian doctrines of divine aseity and creatio ex nihilo. In this article I shall first briefly introduce platonism and the argument for the reality of abstract objects based on their scientific indispensability; then I shall consider a series of responses that can be made to this argument and finally close with what I take to be a serious theological objection to platonism.
“God and Abstract Objects.” In The Blackwell Companion to Science and Christianity, pp. 441-52. Ed. Alan Padgett and James Stump. Oxford: Wiley-Blackwell, 2012.
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Peter van Inwagen argues that (1) there are uncreated abstract objects like properties and (2) the affirmation of the existence of uncreated abstract objects is consistent with the affirmation of the Nicene Creed that God is the creator of all things. I dispute both of these contentions. An examination of ante-Nicene and Nicene theology reveals that the Church Fathers opposed the postulation of any uncreated entity apart from God Himself, including such entities as properties and numbers, which they identified as ideas in the mind of God. Moreover, a detailed examination of van Inwagen’s argument for properties reveals a variety of nominalistic responses of which van Inwagen takes scant cognizance, thereby undermining his claim that one can’t get away with nominalism.
An abbreviated version of this article has been published as "Nominalism and Divine Aseity," Oxford Studies in Philosophy of Religion 4 (2011): 44-65.
Some platonists truly agonize over the ontological commitments which their platonism demands of them. But many others are remarkably insouciant about positing the existence of abstract objects, despite their unfamiliar nature. Why is that? An examination of various statements on the existence of abstract objects by the prominent platonists Bob Hale, Michael Dummett, and Burgess and Rosen suggest that some platonists may not believe that abstract objects really do exist. Hence, their insouciance.