Brent Meeker writes (quoting Peter Jones and SP): > >>Arithemtical Platonism is the belief that mathematical > >>structures *exist* independently of you, > >>not just that they are true independently of you. > > > > > > What's the difference? > > > > Stathis Papaioannou > > You could regard the theorems of arithmetic as just being relative to Peano's > axioms: "1+1=2 assuming Peano" Somewhat as Bruno presents his theorems as > relative to the "axiom" of COMP. > > Brent Meeker
Even if you say that, there is still a sense in which arithmetic is independent of the real world. The same can be said of Euclidian geometry: it follows from Euclid's axioms *despite* the fact that real space is not Euclidian. The fact that real space is not Euclidian means that Euclidian geometry does not describe the real world, not that it is false or non-existent. Stathis Papaioannou _________________________________________________________________ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
