Bruno Marchal wrote: > Le 27-oct.-06, à 16:51, 1Z a écrit : > > > > > > > Bruno Marchal wrote: > > > >> Le 26-oct.-06, à 18:02, 1Z a écrit : > >> > >>> Measure is a lot more difficult in MMW. It has to be > >>> deprived by apriori necessity. Do you have > >>> a solution? > >> > >> A good candidate for apriori necessity (and possibility) is > >> provability > >> (and conssitency) by a lobian machine. > >> > >> > >> http://iridia.ulb.ac.be/~marchal/ > > > > Are Lobian machines apriori necessary themselves ?. > > > > > Lobian machines are apriori themselves in the same sense than numbers > and their effective relations are a priori themselves.
That's in the sense of abstract truth, not in the sense of real existence, then. (Remember: anti-Platonists agree that "2+2=4" is a necessary apriori truth, they just disagree that "2" exists). > So a strict > answer is NO. Since Dedekind-Godel we know that we cannot prove the mathematical > existence of numbers from pure logic. That is why such things as Peano > Arithmetic exists. Questions about real, ontological existence, beyond mathematical existence, are separate. Anti-Platonists can and do accept Godel. > But the answer is "YES" once we postulated the existence of numbers, > like Peano Arithmetic does. > > Note that all self-referentially correct classical machine are lobian. > > 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 -~----------~----~----~----~------~----~------~--~---
