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On Jul 7, 12:59 pm, Bruno Marchal <[EMAIL PROTECTED]> wrote: > Le 06-juil.-07, à 14:53, LauLuna a écrit : > > > But again, for any set of such 'physiological' axioms there is a > > corresponding equivalent set of 'conceptual' axioms. There is all the > > same a logical impossibility for us to know the second set is sound. > > No consistent (and strong enough) system S can prove the soundness of > > any system S' equivalent to S: otherwise S' would prove its own > > soundness and would be inconsistent. And this is just what is odd. > > It is odd indeed. But it is. No, it is not necessary so; the alternative is that such algorithm does not exist. I will endorse the existence of that algorithm only when I find reason enough to do it. I haven't yet, and the oddities its existence implies count, obviously, against its existence. > > I'd say this is rather Lucas's argument. Penrose's is like this: > > > 1. Mathematicians are not using a knowably sound algorithm to do math. > > 2. If they were using any algorithm whatsoever, they would be using a > > knowably sound one. > > 3. Ergo, they are not using any algorithm at all. > > Do you agree that from what you say above, "2." is already invalidate? Not at all. I still find it far likelier that if there is a sound algorithm ALG and an equivalent formal system S whose soundness we can know, then there is no logical impossibility for our knowing the soundness of ALG. What I find inconclusive in Penrose's argument is that he refers not just to actual numan intellectual behavior but to some idealized (forever sound and consistent) human intelligence. I think the existence of a such an ability has to be argued. If someone asked me: 'do you agree that Penrose's argument does not prove there are certain human behaviors which computers can't reproduce?', I'd answered: 'yes, I agree it doesn't'. But if someone asked me: 'do you agree that Penrose's argument does not prove human intelligence cannot be simulated by computers?' I'd reply: 'as far as that abstract intelligence you speak of exists at all as a real faculty, I'd say it is far more probable that computers cannot reproduce it'. I.e. some versions of computationalism assume, exactly like Penrose, the existence of that abstract human intelligence; I would say those formulations of computationalism are nearly refuted by Penrose. I hope I've made my point clear. Best --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---