Le 25-oct.-06, à 13:57, 1Z a écrit :
> Brent Meeker wrote: > >> It's even more than seeing where axioms and rules of inference lead. >> Given some axioms and rules of inference the only truths you can >> reach are those of the form "It is true that axioms => theorems". > > For formalists, all mathematical truths are of this form. And that is why the doctrine of formalism in mathematics (or just number theory) is dead since Godel has proved his incompleteness theorem. We definitely know today that number theoretical truth escapes all formal theories. Physicists can still dream today about a formal and complete theory of "everything-physical", but number scientist knows that the number realm is not completely formally unifiable. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
