From: "Phil Roberts, Jr."
Newsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Fri, 12 Jan 2007 12:46:17 -0500 (EST) Tim Tyler wrote: > Phil Roberts, Jr. wrote: > > > 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: > > > > I had been wondering how on earth you had managed > to conclude that Hofstadter, Dennett and Chaitin > were remotely on the same side as Penrose on > the issue of potential cognitive capacity of > machines. :) In hindsight, I added to this confusion by quoting from Lucas and Penrose in response to various objections raised by yourself and others. But on the other side, I really did make quite a fuss about the fact that I was not viewing Godel as a proof or a formal argument that minds are different from machines, but rather more like a controlled experiment, or as Hofstadter puts it, as a SUGGESTION when "looked at this way". This is a much softer stance than that of Lucas and Penrose, and one which I have tried to buttress with evidence from other spheres of experience, some of which I have yet to present, and which is a considerably different approach from the one taken by either of my esteemed (by me at least) allies (Lucas and Penrose). Here is a little more of the Hofstatder rationale that preceded the passage I have already quoted: Godel's proof offers the notion that a high-level view of a system may contain explanatory power which simply is absent on the lower level. By this I mean the following. Suppose someone gave you G, Godel's undecidable string, as a string of TNT [or Peano arithmetic]. Also suppose you knew nothing of Godel numbering. The question you are supposed to answer is: "Why isn't this string a theorem of TNT?" Now you are used to such questions; for instance, if you had been asked that question about S0=0 [successor of 0 = 0], you would have a ready explanation: "Its negation, ~S0=0 [no successor of 0 = 0] is a theorem." This, together with your knowledge that TNT is consistent, provides an explanation of why the given string is a nontheorem. This is what I call an explanation on the TNT level... Now what about G? The TNT-level explanation which worked for S0=0 does not work for G, because ~G is NOT a theorem. The person who has no overview of TNT will be baffled as to why he can't make G according to the rules, because as an arithmetical proposition, it apparently has nothing wrong with it. In fact, when G is turned into a universally quantified string, every instance gotten from G by substituting numerals for the variables can be derived. 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]. > > Those guys normally have their heads screwed on - > and Hofstadter and Dennet are AI proponents, well > known for advocating the opposite viewpoint. > Yes. And in fairness, Hofstadter continues with a paragraph in which he seems to be holding out hope that the higher level explanation issues might themselves be addressed without necessarily abandoning the assumptions of the AI advocates: But it is important to realize that if we are being guided by Godel's proof in making such bold hypotheses, we must carry the analogy through thoroughly. In particular, it is vital to recall that G's nontheoremhood DOES have an explanation -- it is not a total mystery! The explanation hinges on understanding not just one level at a time, but the way in which one level mirrors its metalevel, and the consequences of this mirroring. If our analogy is to hold, then, "emergent" phenomena would become explicable in terms of A RELATIONSHIP [my emphasis] between different levels in mental systems (Douglas Hofstadter, GEB, p. 708) Or, in the words of Hofstadter's cohort, D.C. Dennett, "And then a miracle happens." :) PR