Re: Godel [was Re: qmail Re: freebsd - Re: recommended Virus Scanner?]
On Sun, Nov 30, 2003 at 07:07:18AM -0800, Tom wrote:
> 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]
Here is my concrete answer:
What is new is merely that a full set of purely formal rules for such
proofs cannot be specified once and for all. In proving genuinely new
results one must always be ready in principle to countenance steps which
are not in accordance with the previously acknowledged rules of
inference
*That's* the practical impact of it. I always said, nothing much needs
to change in practice... But unless you are ready to do this, boom!
Last word....
>
> >
> > 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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> > >
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