On Thu, 5 Dec 2002, Tim May wrote:
> On Thursday, December 5, 2002, at 06:50 AM, Peter Fairbrother wrote:
>
> > Jim Choate wrote:
> >
>
> > No he didn't. He proved Mathematics is incomplete, ie that there are
> > universally valid but unprovable statements within it.
> >
> > He proved that any system that contains Peano arithmetic (roughly, a
> > concept
> > of the natural numbers) is incomplete. Mathematics certainly contains
> > Peano
> > arithmetic.
> >
> > Go and lie down. Your brain is feverish. And stop posting nonsense.
>
> I believe you, Peter, are fairly new to the list. At least I have only
> been seeing a lot of posts from you recently.
Yada yada yada...usual bullshit from the CACL crowd...got a reference?
All you chuckleheads ever do is call names.
Let me quote from Godel's Incompleteness paper...-again-...
pp. 41 of Dover edition, pp 176 of the original publication
Footnote #14
The addition of the Peano axioms, like all other changes made in the
system PM, serves only to simplify the proof and can in principle be
dispensed with.
Bottom line....
The Peano axioms are -within- the system of PM and therefore can't be used
to -prove- anything about the completeness of PM. To do -that- you -must-
step outside of PM, Peano does -not- do that.
What you -can- do is prove that you can't prove it, which is what Godel
did.
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