> On Tue, 12 Nov 2002, Tyler Durden wrote:
>
> > As for "Godelian intractability", I didn't see that as necessarily an issue
> > of complexity. Godel showed that given any formal system, there are
> > statements that will certainly exist that are true but unprovable from
> > within that system (mathematical "truth" is often confused with
> > "provability").
Actually you have to include 'false' as well. The uncertainty is
symmetric. The point of differentiating 'truth' and 'provability' is to
recognize you can't prove them wrong either. 'Provability' is the ability
to answer definitively as compared to what the actual answer is. That is
the fundamental distinction. It's a sort of halting problem once you see
this (as compared to the actual state at the halt). Godel's simply states
in a different way that some things never stop, and you can't always tell
which ones they are.
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well....
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