Saturday, July 21, 2007

On Goedel

Jacob says Goedel, Escher, Bach convinced him of a reductionist view of the universe. The book is beautiful, but that's not what I got out of it. I was skimming Hofstadter's I am a Strange Loop: he complained that nobody seemed to get what he said in GEB, which I take it is something about consciousness.

I admit, I missed that too. I found the book a clever exposition (with frequent divergences) of the Goedel proof. But so far as consciousness being a mirage, which is Hofstadter's view--I missed the argument. This, incidentally, reminds me a lot of what I've read of Dennett: he tends to refer to some powerful argument he's made, but when I go back and read what he's written, I don't see it.

I don't see it with Hofstadter either. I understand why a materialist view of the universe would compel thinking consciousness was either a hallucination, as with Hofstadter, or simply doesn't exist, with Dennett, but so much the worse for materialism, eh? Either way--nothing about Goedel seems to imply materialism. After Lucas and Penrose, the opposite seems the obvious conclusion--though I'm not sure that argument works.

But Goedel isn't even necessary to disprove materialism. Even if you want to be a thoroughgoing materialist, you've got to come up with your own web of axioms to validate the data you receive. Now, there's nothing wrong with that, but supposing you believe your materialism to be true, you need some kind of means to call those axioms you've picked true. But you can't appeal to your beginning axioms to prove themselves (but this starts to sound Goedelian all over again, doesn't it?).

You have a fork here. You either submit to some kind of radical skepticism where you admit the impossibility of knowledge, or you appeal to some notion of reasonableness, some means with which you identify the true axioms.

But what is reasonableness? It's not material. It floats.

I talked to an absolutely gorgeous girl today. Inspiring.

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