Re: Godel [was Re: qmail Re: freebsd - Re: recommended Virus Scanner?]
On Sun, Nov 30, 2003 at 07:01:16AM -0800, Tom wrote:
> On Sun, Nov 30, 2003 at 09:27:37AM -0500, Carl Fink wrote:
> > On Sun, Nov 30, 2003 at 12:00:05AM -0800, Tom wrote:
> >
> > > ... that in any sufficiently complex formal system there are no guarantees
> > > it won't grind out falsehoods ...
> >
> > But Goedel's Theorem actually says that in any formal system, there will be
> > true propositions that cannot be proved (without going outside the system).
> > Nothing I've seen about grinding out falsehoods.
>
> I thought it was neither complete (the doesn't capture all truths thing)
> nor consistent (may contain both a statement and its complement)[1].
> But I can look that up.
[The lack of consistency in arithmetic was shown by Skolem not Goedel]
>
> The Stanford prof told me the Lambda calculus (Lisp-ish stuff) almost
> proved one of the two. It looks like current metamathematics can have a
> set theory for intiutionists, one for computationalists, or other richer
> things, kind of like all the Non-euclidean geometries.
>
> I have many other things to say but this requires precision and this is
> OT. I'd love a crisp answer of "does this matter in everyday life."
>
> [1]-This was the assertion in "Illusion of Technique"
>
> > --
> > Carl Fink carl@fink.to
> > Jabootu's Minister of Proofreading
> > http://www.jabootu.com
> >
> >
> > --
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