Godel's Theorem

Tim May tcmay at got.net
Wed Jan 9 14:17:22 PST 2002


On Wednesday, January 9, 2002, at 12:58 PM, Marcel Popescu wrote:

> 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".
>

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





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