From: "Phil Roberts, Jr."
Newsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Thu, 21 Dec 2006 13:23:10 -0500 (EST) firstname.lastname@example.org wrote: > Phil Roberts, Jr. wrote: > >>I have always thought the Godel argument constitutes a pretty >>good ARGUMENT against a computational view of the mind. > > How? Godel demonstrated (1931) that for any formal (logical, mathematical, rule driven, etc.) system capable of simple arithmetic, there is at least one well-formed sentence or theorem, usually referred to as the Godel or G sentence, that cannot be proven in the system. Interestingly enough, because of our ability to attach meaning to the symbols employed in such a proof, the G sentence is one that we humans can quite easily "see" to be true in that its semantic interpretation is simply: 'This sentence can not be proven in this system'. Since machines (computers) can prove theorems, but cannot prove the Godel sentence without a logical contradiction, Godel's theorem has served as the basis for an argument, originally championed by J. R. Lucas (1961) and more recently by the physicist, Roger Penrose (1989, 1994), that "minds are different from machines" (Lucas). Interestingly enough, one of the most lucid statements of the Lucas/Penrose perspective comes from Douglas Hofstadter (1979), who himself is perhaps one of its most vocal critics: [quote] 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 [Peano arithmetic], no matter how long and cumbersome you make them, you will never come up with one for G -- despite the fact that on a higher level, you can see that [the Godel sentence] 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). [unquote] > > [moderator's note: And how does this relate to evolutionary > biology? Keep it on topic, people. - JAH] > Because if one assumes, as I do, that 'feelings of worthlessness' are a maladaptive byproduct of the evolution of rationality, then they can be construed as an empirical vindication of the Lucas/Penrose perspective on Godel's theorem, i.e., the assertion that Godel constitutes an argument that rationality can not be constrained (captured in its entirety) within a formal (e.g., mechanical) system and therefore that "minds are different from machines" (Lucas). Another way of saying this, is that they can be construed as evidence that Dawkins was right in maintaining that: Darwinism is too big a theory to be confined to the narrow context of the gene.... As presented in my paper, 'Feelings of Worthlessness' (see URL below), my assertion that 'feelings of worthlessness' constitute an empirical vindication of Lucas/Penrose is based on the following assumptions: 1. That human beings have been programmed by natural selection to survive. 2. That human beings do not survive by blindly responding to stimuli with no understanding of the overall objective such mechanisms have been "designed" to achieve, as is likely the case with most other species, but as the result of a conscious intention to survive often involving long range planning. 3. That the basis of the conscious intention to survive, at least when not under the influence of fear, anger, pain, etc., is the value the organism places on its own existence, i.e., its self-value. 4. That 'feelings of worthlessness' constitute evidence that humans are beginning to question the value of their existence and therefore are beginning to question the objective of nature's most basic program. 5. That the same capacity for "standing outside the system" (Lucas) that allows us to "see" that the Godel sentence is "true" is what is responsible for our ability to stand outside of nature's program and question (in the guise of 'feelings of worthlessness') whether it is one worth completing. 6. That rationality cannot be constrained (captured in its entirety) within a formal system, not even by Mother Nature herself. [quote] So even if mathematicians are superb cognizers of mathematical truth, and even if there is no algorithm, practical or otherwise, for cognizing mathematical truth, it does not follow that the power of mathematicians to cognize mathematical truth is not entirely explicable in terms of their brain's executing an algorithm. Not an algorithm for intuiting mathematical truth - we can suppose that Penrose has proved that there could be no such thing. What would the algorithm be for, then? Most plausibly it would be an algorithm -- one of very many - for trying to stay alive... (Dennett, 1989) [unquote] Oops! Sorry! Wrong program, old bean! [My response to Dennett's failure to notice that, in man, self-worth maximization often trumps the program "for trying to stay alive".] [quote] I have often felt as though I had inherited all the defiance and all the passions with which our ancestors defended their Temple and could gladly sacrifice my life for one great moment in history (Sigmund Freud). [unquote] -- Phil Roberts, Jr. Feelings of Worthlessness An Annotated Outline of a Theory of Emotional Instability http://www.rationology.net