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
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