From: "Phil Roberts, Jr."
Newsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Wed, 10 Jan 2007 13:37:54 -0500 (EST) Tim Tyler wrote: > 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 that its Godel >> sentence is "true". > > That doesn't mention human beings or machines - and > thus is not the argument under discussion. > > Stripped to its bare bones, the Godel argument amounts to: > > * Machines have limits on their truth determining capabilites - > in particular they cannot consistently assert the truth of > their own Godel sentence. > > * Humans do not have any such limit. > > * Therefore, humans can do what machines cannot - so > they are not equivalent to machines. > This could serve as a caricature of the Lucas argument that "minds are DIFFERENT FROM machines". But I have been assuming that your disagreement has been with Hofstadter who I quoted as someone who had offered "one of the most lucid statements of the Lucas/Penrose PERSPECTIVE". Here is a repeat of what started the whole ruckus, and in which I have taken the liberty of including some of Hofstadter's rationale: [quote] The only way to explain G's [G = Godel sentence] non-theoremhood is to discover the notion of Godel-numbering and view TNT [or Peano arithmetic] on an entirely different level. It is not that it is just difficult and complicated to write out the explanation on the TNT-level; it is IMPOSSIBLE [my emphasis]. Such an explanation simply does not exist. There is, on the high level, a kind of explanatory power which simply is lacking, in principle, on the TNT-level. G's non-theoremhood is, so to speak, an INTRINSICALLY HIGH-LEVEL FACT. It is my suspicion that this is the case for ALL undecidable propositions, that is to say: every undecidable proposition is actually a Godel sentence, asserting its own nontheoremhood in some system via some code. Looked at this way, Godel's proof suggests -- though by no means does it prove! -- that there could be some high-level way of viewing the mind/brain, involving concepts which do not appear on lower levels, and that this level might have explanatory power that does not exist -- not even in principle -- on lower levels. It would mean that some facts could be explained on the high level quite easily, but not on lower levels AT ALL. No matter how long and cumbersome a low-level statement were made, it would not explain the phenomena in question. It is analogous to the fact that, if you make derivation after derivation in TNT [or Peano arithmetic], no matter how long and cumbersome you make them, you will never come up with one for G [the Godel sentence] -- despite the fact that on a higher level, you can SEE that G is true. What might such high-level concepts be? It has been proposed for eons, by various holistically or "soulistically" inclined scientists and humanists that CONSCIOUSNESS is a phenomenon that escapes explanation in terms of brain-components; so here is a candidate at least. There is also the ever- puzzling notion of FREE WILL. So perhaps these qualities could be "emergent" in the sense of requiring explanations which cannot be furnished by the physiology alone. ('Godel, Escher, Bach', p. 708) [endquote] I like this, because it presents a view compatible with my own view (one based on the premise that 'feelings of worthlessness' are a maladaptive byproduct of the evolution of rationality) that reasoning is not so much a matter of following rules as a matter of COGNIZING rules (e.g., "from outside the system") and with it, the capacity to TRANSCEND those rules on those occasions deemed reasonable given the appropriate context (e.g., Parfit's example of rational irrationality and its implication that rationality may have a holistic element). I also like it because it's coming from someone with sufficient authority on the subject that trying to argue that this is just another one of those boneheads who doesn't understand the theorem is going to be a bit of a hard sell, although so far it hasn't seemed to slow you down all that much. :) The relevance to biology, as I mentioned previously, is because it opens the door to the possibility of an inverse correlation between 'being cognizant' or 'being rational' and 'being determined', and as such offers a new way out of the theoretical impasse we have reached in our attempt to develop a biological explanation of the benevolence and malevolence extremes we find in human nature -- "the central theoretical problem of sociobiology" to quote E. O. Wilson. Another way of saying this is that it opens the door to entertaining the possibility that, with the introduction of rationality into nature, psychodynamic mechanisms may have begun to usurp the older mechanics of natural selection, much as Dawkins has implied with his introduction of the term 'memetics' to serve as a placemarker to help keep us all reminded of the explanatory abyss we are currently staring into. I am occasionally accused of having backtracked on memes; of having lost heart, pulled in my horns; had second thoughts. The truth is that my first thoughts were more modest than some memeticists, including perhaps Dr. Blackmore. For me, the original mission of the meme was negative... The original didactic purpose of the meme was the negative one of cutting the gene down to size. I became a little alarmed at the number of my readers who took the meme more positively as a theory of human culture in its own right -- either to criticize it (unfairly given my original modest intention) or to carry it far beyond the limits of what I then thought justified. This was why I may have seemed to backtrack. (Dawkins). PR Why We Turned Out Like Captain Kirk Instead of Mr. Spock The Psychodynamics of Genetic Indeterminism http://www.rationology.net