What do Christian fundamentalists have against set theory?

I've mentioned here before that I went to fundamentalist Christian schools from grade 8 through grade 11. I learned high school biology from a Bob Jones University textbook, watched videos of Ken Ham talking about cryptozoology as extra credit assignments, and my mental database of American history probably includes way more information about great revival movements than yours does. In my experience, when the schools I went to followed actual facts, they did a good job in education. Small class sizes, lots of hands-on, lots of writing, and lots of time spent teaching to learn rather than teaching to a standardized test. But when they decided that the facts were ungodly, things went to crazytown pretty damn quick.

All of this is to say that I usually take a fairly blasé attitude towards the "OMG LOOK WHAT THE FUNDIES TEACH KIDS" sort of expose that pops up occasionally on the Internet. It's hard to be shocked by stuff that you long ago forgot isn't general public knowledge. You say A Beka and Bob Jones University Press are still freaked about Communism, take big detours into slavery/KKK apologetics, and claim the Depression was mostly just propaganda? Yeah, they'll do that. Oh, the Life Science textbook says humans and dinosaurs totally hung out and remains weirdly obsessed with bombardier beetles? What else is new?

Well, for me, this is new:

"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." — ABeka.com

Wait? What?

First off, let's establish what set theory actually involves.

Sets are exactly what you think they are—groups of things. Prime numbers, unicorns, cats, whatever … you can make a set of it. Set theory is just a way of talking about what sets do and what they are like.

On the surface, this sounds pretty simple. For instance, most of what I learned about set theory when I was in college came through classes in anthropological linguistics. That's because sets, being made of anything you damn well please, have applications outside of pure math. Ted Sider, a professor of philosophy at Cornell University has some good examples of this in a set theory primer he's written:

In linguistics, for example, one can think of the meaning of a predicate, 'is red' for instance, as a set — the set of all red things. Here's one hint of why sets are so useful: we can apply this idea to predicates that apply to other predicates. For instance, think of 'red is a color'. 'Is a color' is a predicate, and it looks like it holds of things like the meaning of 'is red'. So we can think of 'is a color' as meaning a set containing all the colors. And these colors in turn are sets: the set of all red things, the set of all green things, etc. This works because i) a set collects many things into one, and ii) many sets themselves can be put together to form a new set.

So far, so good. In this basic form, sets are involved in lots of things. They come up in musical notation, they help define the way we communicate with computers, and they are the things that make Venn Diagram jokes possible.

But sets and set theory can also be a lot more complicated. For instance, you can make up sets that contradict themselves. The classic example is a set made up of barbers who shave everyone in town (including themselves) and who only shave the people who don't shave themselves. Oops. Another problem: Sets that are too broadly defined, so you don't know if you're actually putting the right stuff in there. A set made up of the favorite things of a tall person, say. Paradoxes like this are what really drive set theory, much of which centers on defining rules for sets and how they work so that we don't just go around assuming certain sets exist when they clearly can't—andso that we can still use the valuable logic and math of sets even when we can't prove that the stuff we're sticking into a set actually exists in the real world. Basically, set theory has a lot to do with creating rules and helping us apply a rule-based system in weird, hypothetical situations.

All of which turns out to be really important when you want to talk about the idea of infinity. Set theory actually has its origins in attempts to define infinity and deal with it in a concrete way in mathematics. Checking Wikipedia, you'll learn that this "modern" theory was actually established in 1874. Why 1874? Because that was when a guy named Georg Cantor proved that there are different infinities and that not all infinities are created equal.

Again, what?

This is really where set theory starts to sound like something you thought up while high and later forgot about.

You can have an infinite set of numbers, right? That makes sense. But, Cantor figured out that an infinite set of, say, whole numbers, is smaller than an infinite set of decimal numbers. They're both infinite. But they're not the same. This TEDEd video explains it really, really well:

So what does all of this have to do with Christian fundamentalists? I have to admit, when I first read that Mother Jones piece, I was stumped. I don't remember anybody disparaging set theory at the schools I went to. And, I'll be honest, I didn't remember enough about what set theory was to be able put the pieces together. (I was also somewhat disappointed to find that the Conservapedia entry didn't offer much help.)

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.

The second problem is a little more complex. Remember how the modern idea of set theory really isn't all that modern? That's because I'm pretty sure A Beka doesn't mean "modern" as in "recent", but "modern" as in "modernist".

I can tell you from experience that A Beka (and Bob Jones University Press) are stridently against modernism in all its forms. (I'm assuming they're against post-modernism, too, but you have to understand that the opinions and perspectives this sort of Christian fundamentalism has about society and culture were formed between the late 1920s and early 1970s and, because of this, the culture wars that they are fighting often come across as confusingly antiquated. Thus, the ongoing obsession with the imminent threat of Communism. See also: Why I sat through multiple sermons on the evils of rock n' roll in the late 1990s.)

If you associate modernism primarily with abstract art, Scandinavian furniture, and houses made out of glass, then all of this is probably just as confusing as set theory, itself. But art isn't really what the fundamentalists are thinking about when they think about modernism.

Instead, they see modernism as the opposing worldview to their own. They are all about tradition (or, at least, what they have decided is traditional). Modernism is a knee-jerk rejection of tradition in favor of the new. Obviously, they think a very specific sort of Christian God should be the center of everything and all parts of society, public and private. Modernists prefer ideas like secular humanism and think God is something you should be doing in private, on your own time. They believe strongly in the importance of power hierarchies and rules. Modernism smashes all of that and says, "Hey, just do your own thing. Nobody's ideas are any better or worse than anybody else's. There's no right and wrong. Go crazy, man!" [Insert obligatory bongo drumming session]

I am hamming this up a bit, but you get the picture. Modernism, to the publishers of A Beka math books, is sick and wrong. The idea is that if you reject their specific idea of God and their specific idea of The Rules, then you must be living in a crazy, dangerous world. You could kill people, and you would think it was okay, because you're a modernist and you know there's really no such thing as right and wrong. Basically, they've bumped into a need to separate themselves from the almost inhuman Other on a massive scale, and latched on to modernism as a shorthand for how to do that. It doesn't matter what you or I actually believe, or even what we actually do. They know what we MUST believe and what we MUST be like because of the tenets of modernism.

More importantly, they know that we are subtle, and use sneaky means to indoctrinate children and lure adults into accepting modernist values. So the art, the literature, the jazz—probably the Scandinavian furniture, too, though I never heard anyone mention that specifically—are all just traps. They're ways of getting us to reject to One True Path a little bit at a time. (I should note that, up to this point, I am basing my analysis on what I was taught in Baptist school. After this, I'm speculating, and attempting to connect the ideas I know are present in this subculture with set theory.)

Set theory, particularly the stuff about infinity, has a bit of that wibbly-wobbly, timey-wimey flavor to it. It doesn't make sense on the level of "common sense". It's dealing with things that aren't standard, simple numbers. It makes links between nice, factual math and floppy, subjective philosophy. If you're raised in Christian fundamentalist culture, all of that—every last bit—absolutely reeks of modernism. It's easy to see how somebody at A Beka would look at set theory and conclude that it's really just modernist propaganda. To them, set theory is just a step on the road to godless atheism.

Add in the historical fact that Georg Cantor's ideas weren't terribly popular at first, and they can easily create a narrative where true math is being suppressed so that false, modernist math can corrupt the minds of children.

If this sounds crazy … you're right. It's pretty crazy. In fact, it's this kind of thinking, and my realization that it was based fundamentally on lying about everybody who wasn't a member of your religious tribe, that led me away from religion to begin with. Ironically. But there is a coherent thought process going on here, and I want you to understand that. If all you do is point and laugh at the fundies for calling set theory evil, then you are missing the point. This isn't about them being stupid. It's about who they think you are.


Mother Jones on the wacky things you can find in Christian school textbooks

Wikipedia on set theory; some interesting history, but not great for helping you understand this stuff.

Ted Sider, a philosophy professor at Cornell, has a pdf document that is a must-read if you are starting from scratch and Wikipedia's set theory explanation makes your brain hurt.

• A link to the TEDEd video embedded in this story, which explains some of the weirdness with infinite sets quickly and simply.

• Vanderbilt University math professor Eric Schechter has a page about the Axiom of Choice, one of the rules in set theory that allows you to play with hypothetical sets and overlaps with some of the problems of infinity. Includes links to other great resources.

• Mark Chu-Carroll's math blog Good Math, Bad Math

Image: Venn Diagram, a Creative Commons Attribution (2.0) image from scottjacksonx's photostream