From: Tim Tyler 
Subject: Re: Robot Evolution
Date: Thu, 28 Dec 2006 13:15:28 -0500 (EST)

Phil Roberts, Jr. wrote:
> Tim Tyler wrote:

>> John Lucas's 'Godel' argument has been much-criticized - and
>> Penrose's views in this area are essentially a variation on it.
> I concede that there is a clear majority who
> disagree with the Lucas/Penrose position.  On
> the other side of the equation, however, we have:
> a. Hofstadter, Dennett, Penrose, Clarke and Chaitin,
> in various ways acknowledging that Godel at least
> SUGGESTS a disconnect between formalism and
> mathematical reasoning.
> b. Little unanimity as to what exactly is wrong with
> the Godel argument, with dozens and dozens of different
> sorts of objections, many based on impenetrable
> confabulations.

Most of the ones I've seen present some
kind of variant of the view I cited:

The idea that humans can assert their own
Godel statement to be true means little -
because the Godel statement corresponding
to a human is going to be huge, complex and
incomprehensible to most mortals - so they
won't know if it is true or not - and humans -
even expert human mathematicians - are simply
not infallible truth-proving machines that never
emit incorrect statements in the first place.

Lucas was wrong and Penrose repeated his mistake.

The fallacy is neatly summed up by this sentence
from Penrose:

"The inescapable conclusion seems to be: Mathematicians
  are not using a knowably sound calculation procedure in
  order to ascertain mathematical truth. We deduce that
  mathematical understanding - the means whereby mathematicians
  arrive at their conclusions with respect to mathematical
  truth - cannot be reduced to blind calculation!"


Just because mathematicians are not following a
complete truth-finding procedure, it simply does
*not* follow that their (flawed and incomplete)
approach cannot be performed by a computing machine.

Tim Tyler