From: Tim TylerNewsgroups: sci.bio.evolution 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!" - http://www.cs.bham.ac.uk/~mmk/papers/05-KI.html 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