Re: Godel's theorem

Bill Hamilton (hamilton@predator.cs.gmr.com)
Mon, 18 Mar 1996 16:05:22 -0500

At 1:11 PM 3/18/96 -0500, jeffery lynn mullins wrote:
>Are logic
>professors misusing Godel when they do not talk about the arithmatic of
>the natural numbers, but rather of axiomatizable systems of extensional
>logic?

I don't believe so. My understanding is that Goedel's original theorem
applied to the natural numbers. Later it was extended to systems of axioms
(I'm not sure whether Goedel or someone else made the extension) As I said
in an earlier post, Hofstadter, in "Goedel, Escher Bach..." has a fairly
rigorous but still readable proof of the axiom version based on encoding
sentences and formulating a legal sentence which contains a contradiction.
Turing proved the theorem using Turing machines, I believe, and Penrose
repeats the proof (or one very similar) in "Shadows of the Mind".

Bill Hamilton | Chassis & Vehicle Systems
GM R&D Center | Warren, MI 48090-9055
810 986 1474 (voice) | 810 986 3003 (FAX)
hamilton@gmr.com (office) | whamilto@mich.com (home)