From: "Phil Roberts, Jr."
Newsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Fri, 5 Jan 2007 01:57:11 -0500 (EST) Tim Tyler wrote: > > The argument from Godel's theorem really is totally dead. > > If you don't see why, I recommend consulting the numerous > refutations of the argument on the internet until you > understand exactly what is wrong with it. > > There /may/ be other reasons for thinking machines > cannot match the computational powers of humans - > but the argument from Godel's theorem is simply defunct. > > It was been dead since the moment it was proposed - and > only continues its zombie existence in the minds of those > who don't understand it :-( 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 its Godel is "true". d. Since the machine is restricted to formal proofs, we can "see" something that is "true" that can not be proven by the machine. This is certainly not a proof, not even a formal argument. "Minds are different from machines" (Lucas) is an empirical assertion. One does not prove empirical assertions, one marshals evidence. Its also why I am a bit skeptical of Dennett's assertion about Penrose PROVING that mathematicians are not employing a knowably sound algorithm. I see what I have referred to as 'the Godel argument', for lack of a better term, as more analogous to a controlled experiment in which, under certain conditions, it is possible to observe something interesting in nature in clearer relief than is common. In this case an occasion in which it appears that reasoning can actually go beyond logic, or perhaps employ the same logic at a higher level, and for that very reason avoid inconsistency. This suggests that in addition to an internal form (e.g., classical logic), rationality may have holistic properties that, before Godel, were not so easily noticed. Here is a quote from one of my papers in which I suggest something similar to the Godel thingy above only in the realm of practical rationality. [quoting my paper] On pages 13 and 14 of Reasons and Persons, Derek Parfit offers a hypothetical scenario in which there is a significant likelihood that a robber will inflict grave harm on someone's family irrespective of whether the individual conforms to the robber's demands or not, and in which, given the specific circumstances, far and away the best alternative would be to take a "special drug" that causes one to become temporarily irrational: "While I am in this state, I shall act in ways that are very irrational. There is a risk that, before the police arrive I may harm myself or my children. But, since I have no gun, this risk is small. And making myself irrational is the best way to reduce the great risk that this man will kill us all. On any theory of rationality, it would be rational for me, in this case, to cause myself to become irrational. An acceptable theory about rationality can tell us to cause ourselves to do, what in its own terms, is irrational."(Parfit) I would argue that what Professor Parfit is actually consulting here, is not any of the current theories of rationality, many of which would indeed sanction rational irrationality in the above scenario and thereby qualify as self-defeating (i.e., false), but rather a shared implicit theory in which being rational' is simply a matter of 'being objective', and in which no objective is rational in any but a relative sense of the term. This would explain how he could get away with asserting a logical contradiction that none of us finds cognitively dissonant, in that underlying the absolutist terminology (rational vs. irrational) would be the shared understanding that in the above scenario the individual would actually be opting to become relatively less rational for a time as a means to a relatively more rational end (protecting his family), and in which the temporary reduction in rationality is merely an extension of the "irrationality" (lack of objectivity) that is part and parcel of fixating on a supremely valued end irrespective of the context. [endquote from my paper] Rationology 101 How the Author of Genesis Got It Right (and the Golden Rule Got It Wrong http://www.rationology.net PR