From: Bob Kolker 
Newsgroups: 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