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/ --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
