Wednesday, August 08, 2012

Mathematical Set Theory, Please, Boing Boing

Maggie Koerth-Baker pens a very long post in Boing Boing to opine on what she thinks Christian fundamentalists have against set theory. She admits that her knowledge of set theory comes from classes in anthropological linguistics, which, the last time I looked, wasn't mathematics. It's mathematical set theory that the Christianists are opposed to, and Koerth-Baker cites the reason:

"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....A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory." —
She slogs through some of her old textbooks and struggles with the multiplicity of infinities and figures that infinity has something to do with God and all, so that must be what the Christianists deplore. But it's simpler than that.

Mathematical sets are nice neat little things, the finite variety anyway, and the infinite ones aren't much messier. But we can just look at the "arbitrary and relative" finite sets to see that their laws are not "a creation of God and thus absolute."

A mathematical set contains numbers or number-like objects and operations. The choice of both is (somewhat) "arbitrary and relative," in that you have a finite number of objects in the set, chosen by the set's maker (not God), unlike the infinite natural numbers and the infinite number of fractional and irrational numbers between integers. The operations are also chosen by the set's maker (not God). So you could construct a set in which 3 times 5 does not equal 5 times 3. It's all in the definitions.

So you have these odd little (and sometimes infinite) number systems in which things don't go according to intuition, presumably God-given and absolute in fundamentalists' minds. But sets show us the internal workings of mathematics, and they are useful for a variety of things, many pretty abstract. I've always looked at them as fun games and small laboratory experiments.

But definitely not God-given.

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