Re: Godel's Incompleteness and Nonmonotonic Logic

From: Stephan Lehmke (Stephan.Lehmke_at_ls1.cs.uni-dortmund.de)
Date: 08/26/04

  • Next message: Stephan Lehmke: "Re: Godel's Incompleteness and Nonmonotonic Logic" 
    Date: 26 Aug 2004 11:55:31 GMT

    In article <2p47gfFgp0b4U1@uni-berlin.de>,
            me@privacy.net (Jamie Andrews; real address @ bottom of message) writes:
    >
    > This *completeness* result does not extend to arithmetic
    > because no *finite* set of axioms characterizes arithmetic.
    > Induction on the integers is an axiom *schema*, not a single axiom.

    I think it's exactly the other way round: `Formalizing' arithmetic
    with an axiom schema which stands for a (countable) infinity of axioms
    leads to a first order `formalization' which does not axiomatize the
    naturals up to isomorphism.

    The formalization leading to incompleteness is the second order one
    with a single (second order) axiom.

    regards
    Stephan

  • Next message: Stephan Lehmke: "Re: Godel's Incompleteness and Nonmonotonic Logic"

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