From: "Kent Paul Dolan" 
Subject: Re: Robot Evolution
Date: Fri, 22 Dec 2006 01:08:57 -0500 (EST)

Phil Roberts, Jr. wrote:

> Godel demonstrated (1931) that for any formal
> (logical, mathematical, rule driven, etc.) system
> capable of simple arithmetic, there is at least
> one well-formed sentence or theorem, usually
> referred to as the Godel or G sentence, that
> cannot be proven in the system.  Interestingly
> enough, because of our ability to attach meaning
> to the symbols employed in such a proof, the G
> sentence is one that we humans can quite easily
> "see" to be true in that its semantic
> interpretation is simply: 'This sentence can not
> be proven in this system'.

But the fallacy in your, and your antecedents'
thinking, is right there and very obvious.

Goedel proved that there are well formed sentences
stating theorems that a computer cannot _prove_ to
be true _or_ to be false, within the same axiomatic
system of arithmetic that the theorem concerns.

In the _same terms in which Goedel worked_, NEITHER
CAN A HUMAN _prove_ that the theorem is true, or is
false, using only the axioms of the system of
arithmetic that the theorem describes.

That the human can "see" the truth or falsehood of
the theorem is an unrelated topic;

        [and arguably a fantasy as well; thinking
        you know something is not the same thing as
        knowing something; like a theisim, "knowing"
        something you cannot prove isn't "knowledge"
        at all, it's merely _faith_, the same trap
        into which theists so consistently fall]

the human is merely working in some other demesne
than the one in which Goedel's machine was working.

In particular, the human is not working in the
demesne of accomplishing that proof as Goedel
described that the proof must be accomplished.

Goedel was more than willing to admit that some
theorem unprovable in one system of arithmetic might
well be provable under a stronger set of axioms, but
he then showed that the stronger set of axioms would
form a system for which exactly the same sort of
unprovable sentence could again be written.

So, all you've proved is that the human mind _may_
employ a stronger set of axioms, not that it is
somehow different in kind.