1Z wrote: > Bruno Marchal wrote: > > 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/ > > > Again, the kind of formalism that says > everything can be brought under a single > formal scheme (the Hilbertian > programme) is different from the kind > that says mathematical truths are dependent on axioms, > and different truths will be arrived at under different > axioms. Of course the key point here > is "different truths". Tom is not entitled to assume that > all roads lead to Rome.
If your definition of truth is limited to logical inference given a certain set of axioms and inference rules, then what are we trying to do on the Everything List? --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
