The Meaning of Mathematics

From the Journal of the American Scientific Affiliation 1 (January 1949):13-19

Finally I would like to say a word concerning the relationship existing between mathematics and the Christian idea of God. Since I believe with Professor Jaarsma in his paper entitled, “Christian Theism and the Empirical Sciences” that “the God of Christianity as the Creator is the unconditioned Conditioner of all things, including the very facts and conclusions of science,” I feel that even the thoughts of mathematicians have their ultimate source in God.

However to say, as some have said, “that the Great Architect of the Universe now begins to appear as a pure mathematician,” appears to me to belittle the idea of God. The pure mathematician is just a puny little man with a quite finite mind doing a small bit of purely human reasoning. If some of this reasoning does seem to aid us in delving into the mysteries of God’s creation, we should give more glory to His name for allowing us this privilege. But to put the infinite God, creator and sustainer of the universe, as well as savior of our souls, into this category seems to me to be quite a serious blunder.

May we then, as Christian men of science, make more use of the mathematical method in science, since it has proved so fruitful in leading us into a deeper understanding of God’s creation.

– Dr. H. Harold Hartzler

You can read the article in its entirety here.

I think Dr. Hartzler’s comments have some implications when thinking about the God of process theology. As I hope to explain in future blog posts as I work through my paper, much of process thought stems from developments in mathematics. In essence, process theology was seen as a solution to a perceived deficiency in the historical understanding of God; a “deficiency” that arose because of the havoc that Kurt Gödel’s Incompleteness Theorem wreaked on the philosophy of mathematics put forward by Bertrand Russel and Alfred North Whitehead (the credited founder of process thought).

To put it in a very small and awkward shaped nutshell (kind of like those peanuts at the bottom of the bag), Russell and Whitehead sought to demonstrate that logic could serve as a foundation and ultimate proof of all mathematical ideas. Gödel showed that any mathematical system depends upon axioms that cannot be proved within the system itself (remember that idea of belief being foundational, even in mathematics?).

Whitehead saw mathematical truths as being derived from the nature of God. Therefore any perceived lack in a mathematical system of thought was a perceived lack in the knowledge of God. The response of Whitehead was to modify the orthodox understanding of God, to the point where it no longer can genuinely be called Christian.

As Dr. Hartzler suggests, simply because our finite minds can comprehend something, or new proofs and mathematical ideas arise which change the understanding we thought we had, doesn’t make it ok to then modify our understanding of God. Theology should shape our mathematics, not the other way around.

Now that the malformed peanut has been digested, we can look forward to a fresh, tasty, symmetrical peanut in the future…. i.e. another blog post…. that’s what they call an extended metaphor, or something.

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