On Wednesday, January 9, 2002, at 12:58 PM, Marcel Popescu wrote:
From:
Maybe I'm oversimplifying, but it seems to me that Godel's theorem follows trivilaly once you've heard of Cantor's diagonal slash. As I understand it, Godel's theorem says in essence that in any system complex enough to include the irrational numbers there must be statements which are true in that system but which cannot be proven in that sytem. But since there are uncountably many irrational numbers, there are uncountably many statements of the form A=A which are true but which cannot be expressed with a finite number of symbols.
I think you're oversimplifying. The theorem doesn't say "there are statements which can't be written", but "there are statements (implicitly writeable) which can't be proven".
What Godel spent most of his proof doing was formalizing "statements" and what it means to write them. The "hand-waving version" of Godel's proof is related to Cantor's diagonalization proof, but didn't fall out of it trivially. --Tim May "Dogs can't conceive of a group of cats without an alpha cat." --David Honig, on the Cypherpunks list, 2001-11