From: "Phil Roberts, Jr."
Newsgroups: sci.bio.evolution Subject: Re: Robot Evolution Date: Tue, 26 Dec 2006 00:18:54 -0500 (EST) Kent Paul Dolan wrote: > > Goedel was more than willing to admit that some > theorem unprovable in one system of arithmetic might > well be provable under a stronger set of axioms, but > he then showed that the stronger set of axioms would > form a system for which exactly the same sort of > unprovable sentence could again be written. Yes. Lucas addressed this issue, in response to Whitely and Bannaceraf as I recall: Banacerraf protests that "It is conceivable that another machine [or formal system] could do that as well." Of course. But that other machine was not the machine that the mechanist was claiming that I was. It is the machine that I am alleged to be that is relevant: and since I can do something that it cannot, I cannot be it. Of course It is still open for the mechanist to alter his claim and say, now, that I am that other machine which, like me, could do what the first machine could not. Only, if he says that, then I shall ask him "Which other machine?" and as soon as he has specified it, proceed to find something else which that machine cannot do and I can. I can take on all comers, provided only they come one by one in the sense of each being individually specified as being the one that it is: and therefore I can claim to have tilted at and laid low all logically possible machines. An idealized person, or mind, may not be able to do more than all logically possible machine can, between them, do: but for each logically possible machine there is something which he can can do and it cannot; and therefore he cannot be the same as any logically possible machine. (J. R. Lucas, 'The Monist', vol 52, pp 145-158) > > So, all you've proved is that the human mind _may_ > employ a stronger set of axioms, not that it is > somehow different in kind. Or maybe no axioms at all, at least not in any strict sense of the terms. Perhaps "all forms of reasoning are nothing but comparing", as Hume has maintained and, as such, actually ANAlogical (nonlogical): One should not think of analogy-making as a special variety of reasoning (as in the dull and uninspiring phrase "analogical reasoning and problems solving," a long-standing cliche in the cognitive science world), for that is to do analogy a terrible disservice. After all, reasoning and problem-solving have (at least I dearly hope!) been at long last recognized as lying far indeed from the core of human thought. If analogy were merely a special variety of something that in itself lies way out on the peripheries, then it would be but an itty bitty blip in the broad blue sky of cognition. To me, however, analogy is anything but a bitty blip -- rather, ITS THE VERY BLUE THAT FILLS THE WHOLE SKY OF COGNITION -- ANALOGY IS EVERYTHING... (Douglas Hofstadter) [emphasis mind]. PR www.rationology.net