Month: February 2010

The Meaning of Mathematics

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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

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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.

Pascal vs. Paulos, The Final Round: All Bets Are Off

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Previous Entries:

Pascal vs. Paulos, Setting the Stage

Pascal vs. Paulos, Round 1: Pascal’s Wager

Pascal vs. Paulos, Round 2: Paulos Ups the Ante

Here is a concise summary of the objections raised by Paulos that I plan on responding to (For a more thorough treatment of the objections Paulos raises against Pascal’s Wager, please see the previous post):

  1. The wager argument can be used to justify heinous acts by people who judge human penalties to be inconsequential in comparison to their heavenly rewards.
  2. The concept of “betting on God” is ambiguous and can be used by people of various faiths.
  3. The phrase “the probability of God’s existence” is nonsensical because the universe is a singularity.

I would also like to respond to Paulos’ comments on ethics. To be fair, Paulos notes that his discussion of ethics is being given as an aside and it is not the primary focus of the chapter. However, there is another chapter in the book in which his discussion does center around morality. So then, I will save the discussion of ethics, morality and mathematics for a future posting.

In regards to objection 1: I believe this comment ultimately stems from a misunderstanding of Pascal’s Wager. Pascal’s argument is given as a response to the question: “Supposing the evidence for God’s existence is inconclusive, then is it rational to remain in unbelief?” The premise of this question is crucial to understanding the argument. The Wager argument is only useful for a person who isn’t sure one way or the other that God exists. Pascal would openly say that if the evidence is indisputably in favor for God, then believe in God. If the evidence is indisputably in favor against God, then don’t believe in God (though Pascal himself would personally say that the evidence indeed favors God’s existence).

People who would use a line of reasoning similar to Pascal’s Wager in order to justify horrible acts of violence are certainly not people who are in doubt about God’s existence. They are people who are already 100% sold on his existence. They are also people who are 100% misinformed about the nature of God and the desires He has for His creation.

It is not my desire to go into great prose here in addressing the atrocities that evil people commit in the name of religion. Just because evil people perform evil acts in the name of some religion, it does not justify their actions nor does it make that religion inherently evil (since it seems to me that people in this category have largely warped the religion they claim). Similarly, it should be stated, just because evil people perform evil acts in the name of non-religion (atheists), it does not justify their actions nor do their actions alone make atheism inherently evil. All this line of argument does is show that people are evil. ALL people. All people, when left to their own devices, are at their core depraved. We are all in need of redemption and the grace of God.

In regards to objection 2: It is certainly true that with Pascal’s Wager alone you cannot arrive at an argument for the God of Christianity. But the fact remains, if the argument can succeed in persuading a person to simply theistic belief over atheism, then the leap to specific Christian belief is not nearly as great.

There also arises the question of what does it mean to “bet on God.” By betting on God, Pascal does not mean that you can make yourself believe. Salvation remains a work of the Spirit and not the will. Perhaps it is instructive to again quote here Pascal’s own understanding of any argument for God.

That is why those to whom God has given religious faith by moving their hearts are very fortunate, and feel quite legitimately convinced, but to those who do not have it we can only give such faith through reasoning, until God gives it by moving their heart, without which faith is only human and useless for salvation. (Pensees, 282)

What Pascal means by betting on God is that you can put yourself in situations that are more conducive to belief. For instance you can attend church, you can pray, and you can leave behind your present lifestyle. Putting yourself in those situations places you in a seemingly better position to be open to the working of the Spirit, though it is no guarantee of salvation.

And without faith it is impossible to please Him, for he who comes to God must believe that He is and that He is a rewarder of those who seek Him. (Hebrews 11:6, Italics mine)

We can be comforted in knowing that God rewards those who seek Him.

In regards to objection 3: While I certainly do not claim to have a complete understanding of statistics or the use of religious language claims, I see no reason why the phrase “the probability of God’s existence” should fail to make since simply because we cannot count the number of universes there are and how many of those universes have gods, or something along those lines (even if we could count the total number of universes in existences, the claim is still that there exists one God who is over all of them).

One of the more popular examples that statistics students bring to me is the infamous sock drawer. Questions read along the lines of: “You are getting ready for school and your sock drawer has four argyle socks, two polka-dotted socks, and one blue-striped sock (since you lost one). What is the probability that you select two socks that match?”

If there was only sock in the drawer, would it be nonsensical to ask “what is the probability of one sock existing in the drawer?” I hardly think so. The probability is either 1 (meaning there is absolutely one sock in the drawer), or it is 0 (meaning there is absolutely not one sock in the drawer).

To extend the metaphor, it would seem that Paulos believes “the probability of God” does not make sense because we cannot open the drawer (on his view) to see if God is really there. Either God exists or He doesn’t (but He does), so the probability is either 1 or 0 (but it’s 1). So then, the phrase “the probability of God’s existence” seems to me to make perfect sense.

In Summary: While this post has certainly not been exhaustive in the treatment of the topic at hand (though those of you are still reading at this point may disagree), my critique of Paulos essentially boils down to this: Paulos’ critiques of Pascal’s Wager stem from a restatement of the argument that Pascal never originally intended. Pascal simply intended to demonstrate through sound mathematical reasoning that if you aren’t sure whether God exists or He doesn’t, it makes more sense for you to believe in Him than to not so believe.

I don’t fault Paulos for this approach. I simply offer it up as evidence that the presuppositions we bring to a subject (in this case Paulos’ atheism) always affect the way we reason through an argument.