Re: (probably stupid) question on Fermat decidability

From: Dave Seaman (dseaman_at_no.such.host)
Date: 11/20/04 

Date: Sat, 20 Nov 2004 00:08:36 +0000 (UTC)

On 19 Nov 2004 15:40:20 -0800, Mike Ferenduros wrote:
> I was reading Simon Singh's book on Fermat's last theorem, and got a
> big confused by one passage - he mentions the possibility that the
> theorem was undecidable (although obviously it turned out not to be).

> What confused me was this: The theorem couldn't be false but
> undecidable, since falsehood implies the existance of a definite
> counter-example. So if it's undecidable then it must be true, which
> contradicts it being undecidable. So you get a contradiction,
> therefore it cannot be undecidable.

In what way does that contradict it being undecidable?

> Would anyone care to point out where I'm going wrong here?

The Goedel sentence is an example of a statement that is true but
unproveable (hence undecidable) within the system under consideration. 

-- 
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>