From: Bob KolkerNewsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Fri, 5 Jan 2007 12:19:03 -0500 (EST) Phil Roberts, Jr. wrote: > > Stripped to its bare bones, I suspect the Godel argument > amounts to something like: > > a. We have reason to believe that Peaono arithemtic is > consistent. > b. Therefore we have reason to believe that its Godel > sentence can not be proven within the system. > c. Therefore we have reason to believe its Godel is > "true". It is true that the consistency of arithmentic implies its incompleteness. It is also true that the consistency of arithmentic cannot be proven within a first order logic with the axioms of arithmentic added. These two true statements completely torpedoed Hilberts program of establishing the correctness of mathematics by purely formal methods. Bob Kolker