From: Tim TylerNewsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Thu, 21 Dec 2006 13:23:11 -0500 (EST) Phil Roberts, Jr. wrote: >> Tim Tyler wrote: >>> My impression is that the only folk who reject the fundamentals >>> of the brain-computer analogy are people like Roger Penrose >>> and John Searle - i.e. those whose world view in the area is >>> totally muddled. [...] > > I have always thought the Godel argument constitutes a pretty > good ARGUMENT against a computational view of the mind. Where > I think Lucas went wrong was in his claim that Godel constitutes > a PROOF against computationalism. You can't prove empirical > assertions, you can only marshall evidence. That's why all > scientific theories are tentatively true until the next > revision. > > I can't recall to what > extent Penrose claimed Godel as a proof rather than an argument > against computationalism. But as an argument, I am definitely > in the Lucas/Penrose camp. Can you provide a brief overview of > why you consider Penrose "totally muddled" on this issue? John Lucas's 'Godel' argument has been much-criticized - and Penrose's views in this area are essentially a variation on it. Brief version of what's wrong: ``A mathematician often makes judgments about what mathematical statements are true. If he or she is not more powerful than a computer, then in principle one could write a (very complex) computer program that exactly duplicated his or her behavior. But any program that infers mathematical statements can infer no more than can be proved within an equivalent formal system of mathematical axioms and rules of inference, and by a famous result of Godel, there is at least one true statement that such an axiom system cannot prove to be true. "Nevertheless we can (in principle) see that P_k(k) is actually true! This would seem to provide him with a contradiction, since he aught to be able to see that also." This argument won't fly if the set of axioms to which the human mathematician is formally equivalent is too complex for the human to understand. So Penrose claims that can't be because "this flies in the face of what mathematics is all about! ... each step [in a math proof] can be reduced to something simple and obvious ... when we comprehend them [proofs], their truth is clear and agreed by all." And to reviewers' criticisms that mathematicians are better described as approximate and heuristic algorithms, Penrose responds (in BBS) that this won't explain the fact that "the mathematical community as a whole makes extraordinarily few" mistakes. These are amazing claims, which Penrose hardly bothers to defend. Reviewers knowledgeable about Godel's work, however, have simply pointed out that an axiom system can infer that if its axioms are self-consistent, then its Godel sentence is true. An axiom system just can't determine its own self- consistency. But then neither can human mathematicians know whether the axioms they explicitly favor (much less the axioms they are formally equivalent to) are self-consistent. Cantor and Frege's proposed axioms of set theory turned out to be inconsistent, and this sort of thing will undoubtedly happen again.'' - http://hanson.gmu.edu/penrose.html I see there's also this: http://www.paul-almond.com/RefutationofPenroseGodelTuring.htm As to what this has to do with evolution - if humans can do things no machine can do - or will ever be able to do - that may impact the hypothesis that machine-based organisms may replace humans as the dominant life form on earth over the next century or so. However, this particular argment for the qualitative superiority of humans is simply wrong - and (IMO) rather obviously so for anyone who knows anything about Godel's work. Tim Tyler