From: Scott R (jse885@spinn.net)
Date: Fri Apr 18 2003 - 02:23:17 BST
Platt,
> > > Is not Goedel's Theorem itself absolute? Has anyone been able to
> > > overthrow it?
> >
> > It is only "absolute" within the system based on the axioms of
arithmetic.
> > Change an axiom and it ceases to be a theorem.
>
> How do you change the axioms of arithmetic?
>
Well, when you do you no longer have arithmetic, so perhaps my wording needs
work. The point is that any mathematical theorem is a deduction from a set
of axioms, so it is only as "absolute" as the axioms which, from the formal
logician's viewpoint, are arbitrary. Recall that it turned out that Euclid's
Fifth Postulate could be replaced and one got different, but equally
powerful geometries.
- Scott
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