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.

Math in Process

This semester I get to write a paper on the topic of my choosing. Here is the working title that I have submitted:

“Process Theology as a Departure from Orthodox Christianity and the Implications for the Philosophy of Mathematics”

I thought that was a rather awesome title.

I wanted to write a paper that brought together the two fields which most interest me: theology and mathematics. But not knowing exactly what to write on or exactly what topics might need to be addressed in these two fields, I turned to the Journal for the Association of Christians in the Mathematical Sciences and specifically to the letter from the founding editor. In that letter James Bradley lays out the framework for mathematics to be done Christianly. He also raises 14 areas in which he, as a mathematician and a Christian, believes more work needs to be done. Here are points 1 and 11:

1. What are the implications of the person and work of Jesus Christ for mathematics? If there are none, or if they are not central, what does this tell us about mathematics?

11. Some thinkers (perhaps influenced by process theology) have asserted the idea that God’s creation is not a finished work but that he creates new mathematical objects through mathematicians. Is this idea theologically sound? Is it helpful for our understanding of mathematics?

I believe both of these points can be addressed simultaneously and it is my intention to do so in this paper. Process theology deals quite thoroughly with how God relates to His creation and any discussion that revolves around creation from a Christian perspective cannot ignore the person and work of Jesus Christ. This is true because

In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things came into being through Him, and apart from Him nothing came into being that has come into being.

John 1:1-3

and

He is the image of the invisible God, the firstborn of all creation. For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities– all things have been created through Him and for Him. He is before all things, and in Him all things hold together.

Colossians 1:15-18

the latter verse being the influence for the subtitle of this blog.

For those of you unfamiliar with Process Theology, here it is in a nutshell: God is viewed as being dynamically involved in and with His creation. This God is bound to the present and relationally to creatures. He is seen through creative occasions through historical moments. He is always changing, hence the name of “Process.” This God is the process that carries forward the memories of the past and gives meaning to the present. This God does not condemn us or force us to do things, rather He sweetly persuades and simply hopes to convince you of the right choice. This is another way of saying that God is pure becoming (against the classical model which emphasizes being).

To read more on Process Theology and Process Thought in general from those who espouse it, you can visit the Center for Process Studies where you’ll find condensed summaries of their beliefs.

Here is what the paper boils down to: Process Theology is a very dangerous line of thought and (as the title suggests) should be viewed as a departure from the God of the Bible and what the church has historically defined as orthodoxy. Process Theology may be founded on good intentions, attempting to reconcile tough issues of faith, but to worship a God that differs from who He actually is and how He has revealed Himself is to commit idolatry.

Therefore any influence this theology has brought into the philosophy of mathematics should be heavily scrutinized, especially if we are attempting to do and think about mathematics Christianly.

I look forward to diving in to this topic and to providing you with some updates along the way.