#870 God and the Applicability of Mathematics

Dr. craig’s response

Let me take the second half of your question first, Gregg, as it reveals the deeper misconceptions. You seem to equate God’s possessing transcendent properties with God’s possessing no identifiable property or even no property at all. That’s not right.

Your questions have straightforward and meaningful answers:

I realize that there are many people who cannot conceive of the notion of a transcendent, unembodied Mind who is the Creator of all material reality. But such people are just conceptually impoverished. They need to stretch their minds!

So, of course, I don’t agree with your stated

Fact: If "something" has no known composition, no known location, and no known process of formation, then it is 100% consistent with "something" that is purely imaginary.

In the present case, a purely imaginary entity cannot be the cause of the mathematical structure of the universe. If God is the best explanation for the applicability of mathematics to the physical phenomena, then He cannot be purely imaginary, even if He is immaterial and transcends space and time. His causal relation to the world decisively rules out His being imaginary.

So the description of the uncanny effectiveness of mathematics as “a miracle” (Wigner’s word) is not subjective. Rather, in line with the usual definition of “miracle,” it is something for which there is no natural cause. In the video I explain at some length why naturalism is unable to provide a satisfactory explanation of the applicability of mathematics. But theism has the explanatory resources to make the applicability of mathematics perspicuous.

Now in the first part of your letter, you ask some interesting questions. “Are you saying it's a miracle we live in a universe where we can count things?” Not necessarily! Einstein considered it mysterious that even elementary arithmetic describes the physical phenomena. But Wigner, and I think most proponents of the puzzle, would disagree, saying that such operations hold with logical necessity. Rather, Wigner is talking about the sorts of elegant mathematics that are featured in high-level physics, like Heisenberg’s matrix mechanics or quantum electrodynamics. Wigner’s article is full of such examples.

You also ask, “At what point does the miracle happen? Does it happen when adding? Does it happen when subtracting?” I think your questions are misconceived. The point at which the miracle happens is the moment of creation, when the universe springs into being replete with a structure that is amenable to elegant mathematical descriptions. Rather, I think what you’re getting at is, “How sophisticated must the mathematics be in order to be truly puzzling?” I don’t know that there is a sort of cut-off line. But it’s easy to give examples of the fearsomely difficult equations of high-level physics that describe our universe and cannot be written off to logical necessity like the equations of elementary arithmetic. So the puzzle is genuine and one which no naturalist has been able to answer successfully.