Re: NPR, Godel, Semantic Web

[John Cowan <cowan@mercury.ccil.org>]

Sam TH scripsit:

> > An example of what *might* be a Goedel sentence: nobody knows for sure.
> > If it is unprovable, it has to be true, because if it were false,
> > there'd be a counterexample, which would mean it wasn't unprovable.
> > Still, lots of people thought Fermat's Last Theorem was unprovable too.
> 
> That's only true in those cases where the idea of a counterexample
> makes sense.  For example, the continuum hypothesis [1], that the size
> of the set of real numbers is the smallest number larger than the size
> of the integers, is undecideable.  Yet Cohen, who proved the
> undecidability, believes the hypothesis to be false.  

Quite so.  But Goldbach, if it is going to be false, has to be false
by reason of some specific even number that is not expressible
as the sum of two primes.  It can't be the case that it is false even though no
counterexample exists!

-- 
John Cowan                                   cowan@ccil.org
One art/there is/no less/no more/All things/to do/with sparks/galore
	--Douglas Hofstadter