Bruno Marchal wrote: > Le 21-août-06, à 18:55, David Nyman a écrit : > > > > >> I don't think Bruno and Stathis are arguing that numbers are > >> neceesarily > >> the only things that exist (although a standard Platonist might argue > >> that > >> that they are the only things that exist necessarily..) > > > > But aren't they claiming that numbers are the only things necessary > > (together with the operations required for CT+YD, whatever they might > > be) to account for *our* existence? If not, what else is required? > > > > Since the failure of logicism, by Godel's theorem, we can argue that > numbers does not necessarily exist. Numbers does not come from logic > alone. If you want them,
to exist > you have to do a ontological commitment. ..and if you want to play with them as a formal system, you don't. > To > believe, like all mathematicians, in the structure (N,+,*,0,1) is > enough for that (actually to believe in (N,+,*,0,1) is too much, but I > don't want to enter in the technical details before it is really > necessary). > > 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 -~----------~----~----~----~------~----~------~--~---
