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.


> 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?

Bruno


http://iridia.ulb.ac.be/~marchal/


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