Set Theory, Now? [EvolutionBlog]

During my time in New York, I had lunch with some friends from England. We were discussing evolution and creationism, and religious fundamentalism more generally. Somewhere along the line I mentioned that creationists routinely use mathematical arguments in their writing, and one of my friends relied that he had heard that some fundamentalists even have a problem with set theory.

I stared at him. I thought I was up on the latest in pseudomathematics, but this one was entirely new to me. But with a few taps on his phone he showed me what he was talking about. He was referring to this paragraph, from the website for A Beka Book. They are a fundamentalist Christian publisher whose materials will now be supported by taxpayer dollars in Louisiana.

Unlike the “modern math” theorists, who believe that mathematics is a creation of man and thus arbitrary and relative, A Beka Book teaches that the laws of mathematics are a creation of God and thus absolute. Man’s task is to search out and make use of the laws of the universe, both scientific and mathematical.

A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory. These books have been field-tested, revised, and used successfully for many years, making them classics with up-to-date appeal. Besides training students in the basic skills needed for life, A Beka Book traditional mathematics books teach students to believe in absolutes, to work diligently for right answers, and to see mathematical facts as part of the truth and order built into the real universe.

Of all the crazy things! What could possibly be wrong with set theory?

Maggie Koerth-Baker tries to help us out.

But after re-acquainting myself with this stuff, I think I see a couple of things happening that would make set theory problematic for some Christian fundamentalists.

First: Some of these folks get very touchy about the idea of infinity. Mark Chu-Carroll is a software engineer at foursquare and a math blogger. Unlike me, he was already aware of the fundamentalist objection to set theory, because he’s actually had people show up in his comment section railing about how the theory is an affront to God. Particularly the part about multiple infinities. Chu-Carroll told me that one commenter explained the problem this way: “There is only one infinity, and that is God.” Basically, this perspective looks at set theory and Georg Cantor and sees humankind trying to replace the divine with numbers and philosophy.

I think this is right. Indeed, Georg Cantor, a pioneer in set theory, faced precisely this objection to his original work. People get weird when you start talking about infinity. They think you’re talking about God and religion and whatnot.

This, of course, is the sheerest madness. Mathematicians rarely talk about infinity in the abstract. We mostly talk abut infinite sets, and when we do we have in mind a rigorously defined abstract construction no different from anything else we study. To say that there are more real numbers than positive integers, for example, is just to say that the set of real numbers cannot be placed into one-to-one correspondence with the set of natural numbers, but the positive integers can be placed into one-to-one correspondence with a proper subset of the reals. That’s just true as a matter of logic. Nothing about God, or even the real world, for that matter.

The A Beka paragraph quoted above also refers to the laws of mathematics being absolute and God-given. That’s one I have heard before, as I describe in the first chapter of Among the Creationists. At a home-schooler’s convention in Richmond, VA, I heard a speaker going off on how she hated math in high school, because her teachers never told her that math was about learning God’s laws for the universe. It is because of God’s faithfulness and constancy, she told us, that we can be sure that 1+1 will always equal 2. Seriously.

After the talk I met a math professor from Liberty University. That’s Jerry Falwell’s outfit, you might recall. He rolled his eyes at the speaker. He also told me that at Liberty they have a college-wide faculty meeting at the start of every year to discuss how the curricula of the different academic units will contribute to the religious mission of the school. He then told me that usually they just skip right over the math department. So I guess this sort of thing is just too crazy even for some fundamentalists.

Interestingly, I heard something similar when I met a mathematician from Brigham Young University. This particular professor was Jewish. A group of us had dinner with him, and someone asked him what it was like to teach at a Mormon university. He replied that almost no one in the math department was a Mormon. As far as the school was concerned, the math department existed because a school that wants to be taken seriously must have a math department. But the department was entirely separate from the religious mission of the school. So they actually have a pretty good deal. The school leaves them alone, and they don’t challenge the religious mission of the school.

I hope the A Beka folks don’t start giving them ideas.

Anyway, Koerth-Baker’s article has a lot of other good stuff, so go read the whole thing.