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Re: NPR, Godel, Semantic Web

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On Mon, May 07, 2001 at 09:24:24PM -0400, John Cowan wrote:
> Mike.Champion@SoftwareAG-USA.com scripsit:
> > The first is a Semantic Web use case I remember from somewhere, and the
> > second is Goldbach's Conjecture, a (possibly) "true but unproveable"
> > assertion often used as an example of a "G?del sentence." =20
> 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. =20

[1] http://www.ii.com/math/ch/
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