The basic objects of mathematics—namely, numbers and sets—fit very neatly into a theistic way of looking at the world—vastly better than into a naturalistic perspective. Perhaps this explains the strenuous efforts, on the part of Hartley Field and others, to ‘reinterpret’ mathematics in such a way as to make it possible for naturalism to accommodate it.Here again we see deep concord between theism and mathematics.
The objects of mathematics—numbers, functions, sets—are abstract objects. Abstract objects, so we think, differ from concrete objects in that they do not occupy space and do not enter into causal relations. The number 3 can’t cause anything to happen; it is causally inert. This is not a peculiarity of the number three; the same goes for all the other numbers—real, complex, whatever—and for sets, including functions. But this induces a long-standing puzzle.11 It seems sensible to think that the objects we can know about can causally affect us in some way, or at least stand in causal relationship with us. We know about trees; that is because we can perceive them, which involves light waves being reflected from trees into our eyes, forming an image on the retina; this induces electrical activity in the optic nerve, finally involving neural activity in the brain. We know something about distant galaxies, again, only because electromagnetic radiation from them reaches us. As I say, it seems sensible to think that a necessary condition of our knowing about an object or kind of object is our being able to stand in some kind of causal relation to that object or kind of object. If this is so, however, and if, furthermore, numbers and their kin are abstract objects, then it looks as if we couldn’t know anything about them.
Here again theism is relevant. According to classical versions of theism, sets, numbers and the like, as I argued above, are best conceived as divine thoughts. But then they stand to God in the relation in which a thought stands to a thinker. This is at any rate like a causal relation. If so, then numbers and other abstract objects also stand in a causal relation to us. For we too stand in a causal relation to God; but then anything else that stands in a causal relation to God stands in a causal relation to us. Therefore numbers and sets stand in a causal relation to us, and the alleged problem about our knowing these things disappears.
Excerpt: Plantinga, A (2011) Theism and Mathematics, Theology and Science 9(1)