Some fine Daily Kos diarists, as well as the estimable Charles P. Pierce at Esquire, have highlighted the new article in Politico today called "**Taxpayers fund creationism in the classroom**"...

In addition to the now-customary attacks on biological evolution, the article refers to other domains of modern knowledge that are considered suspect by the religious, including areas of modern mathematics, and in particular, "set theory". Now I've seen this article linked on a few other lefty blogs I read in addition to Mr. Pierce, as well as by several friends on Facebook, and the usual response to the sentences about modern math are generally met with a comment like "Creationists are so dumb they probably still think Pi=3!". But the fact that the article specifically singles out set theory immediately jumped out at me, and for reasons which I would like to explore below the fleur-de-Kos, I think signifies something rather more *important* than many of us are giving it credit for. I would like to share directly with the DKos community something I wrote earlier on the Esquire piece...

I would like to offer an somewhat-informed opinion on the whole math & set theory thing, on the basis that if we are to be forced to debate these kinds of people, we should understand what it is they're *really* on about. I'm sure the creationist doesn't deny "carry the five" type arithmetic. Since the article specifically mentions set theory, allow me to posit something related to that which I have noticed cropping up a great deal in the modern Christian "apologetics" movement, particularly propounded by such folks as William Lane Craig (and I apologize but this comment is of necessity going to be kinda long)

Craig is the leading proponent of the so-called "Kalam Cosmological Argument" which uses some propositions based on formal logic and a lot of sophistry to deduce "therefore God did it." One of the supporting legs of this argument is the essential impossibility of a real infinity, and to explain this Craig uses a "thought experiment" known as Hilbert's Hotel (named for English mathematician David Hilbert)

The essence of Hilbert's Hotel is really an argument drawing from set theory, much like the following: take the "set" (or grouping) of normal positive integers (1, 2, 3, 4, 5, ... 10... 27 ... a billion...). It goes on forever, there are an infinite number of positive integers. Now consider the set of positive EVEN integers (integers evenly divisible by 2: 2, 4, 6, 8, 10, 12, ... a billion...). Are there fewer even integers than positive integers (even & odd)? There are an infinite number of members of both sets, but in some sense there's only "half as many" even integers... or alternately you could think of it as you get the set of evens by taking away the set of odds (1, 3, 5, 7, ... also an infinite set) away from the set of all integers. But in fact there are EXACTLY the same number of even integers as odd integers as all integers. How to prove it? You can map every single integer to every single even integer simply by doubling it: 1:2, 2:4, 3:6, 4:8, etc. In this way you can see that there must be one, and ONLY one, corresponding even integer to every member of the integer set we started with. Therefore the two sets must be exactly the same size.

But does this work for all real numbers? Real numbers include both integers and fractions and irrational numbers (numbers that can't be represented exactly as a fraction, such as Pi and the square root of 2). Is the infinity of real numbers the same size as the infinity of integers? As it turns out, no, it's not, it's a BIGGER infinity. Georg Cantor proved this again using this concept of mapping from one set to the other, and you CANNOT find a mapping which will include all possible real numbers. (check the links for the details or read the classic "Gödel, Escher, Bach" by Douglas Hofstader (where I was first introduced to these ideas back in college). Because of this difference the infinity of real numbers is not denoted by the familiar "sideways 8" character, but by the hebrew letter "Aleph".

Now how does this relate to Craig and creationism? Because the knowledge that there are higher order infinities which cannot be mapped in the simple way I described undermines the "Hilbert Hotel" argument, which is part of the underpinning of the Kalam Cosmological model which serves as a smart-sounding philosophical "proof" of the necessity of God.

I first came to understand this when I came upon a "William Lane Craig and Hilbert's Hotel" video on Youtube a while back, and tried to explain this in the comments: whereupon I was met with responses along the lines of "*Hurr Durr Infinity is the biggest there is you are stupid and Craig has a PhD*" before I was blocked from the channel.

I am far, far more annoyed and frightened by guys like Craig than I am by armies of Ken Hams (owner of the "Creation Museum" and recent debate opponent of "Bill Nye the Science Guy") and Roy Comforts (aka "Banana Man"). Those latter guys are never going to persuade anyone to creationism who wasn't already firmly in their camp to begin with. But Craig is different: he is a very smart sounding and soft spoken guy whose arguments sound very rational, even to the fairly educated. You won't understand the holes in them without knowing these kinds of fairly obscure branches of modern mathematics, philosophy, and so on. And that's why it's so easy for Craig to pull the wool over the eyes of otherwise smart people.

**I wanted to share this because I feel it's important for "Team Science" to understand the arguments of the enemy to successfully refute them in public. The reason they don't want kids to learn about set theory (among other things) is NOT because " It ain't in the Bible, that's good enough fer me" type yokel-ism (which is how I see this being characterized in a lot of the comments on this news on various websites), but because the vanguard of the assault on modern science (including guys like Craig) understand that knowledge of set theory undermines part of their pseudo-intellectual rationales for creationism; and if enough people learn about it, they won't be as easily able to get away with their intellectual chicanery.**

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