Re: MD Undeniable Facts

From: Scott R (
Date: Fri Apr 18 2003 - 02:23:17 BST

  • Next message: Scott R: "Re: MD Undeniable Facts"

    > > > 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
    > > 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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