Godel's Theorem

[Marcel Popescu]

From: <georgemw at speakeasy.net>

> 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".

Mark