fun with Gödel

Originally published on Language and Philosophy, November 3, 2011

There’s an easy answer to this question, but if you replace c) 60% with 0%, then you get a liar paradox, a Gödel-type statement — it has no numerical answer and can only be evaluated outside its terms.

http://flowingdata.com/2011/10/28/best-statistics-question-ever/

Gödel, btw, once proved Anselm’s ontological argument, the argument that proves god exists. His version, so far as I can tell, removes all modality in Anselm’s argument, and I think that’s why it works. It’s a complicated version, but I think that even extremely simple, non modal versions work too, e.g., if “god” by definition is that which nothing is greater, then whatever is greatest is that thing. This version works for any model in which there is at least one object. So if nothing exists, then it doesn’t prove anything, but since something patently exists, we can safely assume that there is a greatest thing.

It’s been pointed out to me that there may be many notions of greatness. I think this is a problem in the logical semantics, not in the syntax, unless there is no such notion as “the greatest.” The only important of the many notions is the notion of “greatest of greatest things.” If that can’t be evaluated, then the designation of “god” is indeterminate, but not necessarily nonexistent. I mean, the argument is valid, so far as it goes; it just doesn’t tell you which notion of greatness is in fact the greatest.

There are a number of ways to treat this notion of greatness. Maybe the notion is inherently relative, like “good” — a good chess player might not be a good bricklayer. If so, then there is no idea of “the greatest.” But assuming there are such notions as “the good” and “the greatest,” I don’t see any contradiction within them. So one can assume there is such, without determining which.

I am fond of Anselm’s proof in part because it seems to make everyone nervous, non believers and believers alike. It makes non believers uncomfortable because they don’t want to admit they are wrong and they don’t want to believe in god. I’m not sure which is worse to them. It makes the believers nervous because the god it proves might not be the comfortable personal one they’ve been living with. They want to believe in their god, so it’s convenient that there is no logical proof of god that might be out of their control. And that is as it should be: the notion of god should be a #$%ing scary one, if you actually take it seriously for a moment. The Old Testament got that one right. People don’t take it as seriously as it should be. They should be crossing their fingers that there is no god.

If you look at the argument more closely, the character of the god that it proves is such a cipher, that it steals away all the personal comfort of the deity they want or need. That’s one reason Aquinas didn’t include it as one of his proofs. His proofs are all friendly ones like the order of the cosmos and its beauty. Nothing so cold as logical truth.

I delight in Anselm’s proof. What it says about god is utterly trivial — so I’m happy to live with it — and the argument strikes terror in everyone else. That’s almost as good as having a personal god working for you.

The logical positivists would have approved: the argument is true, but meaningless. So god exists in all his greatestness. So what? It’s no different than pantheism, which is basically indistinguishable from atheism.