Stathis Papaioannou wrote: > 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
But the fact that a theorem is true relative to some axioms doesn't make it true or existent. Some mathematicians I know regard it as a game. Is true that a bishop can only move diagonally? It is relative to chess. Does chess exist? It does in our heads. But without us it wouldn't. Brent Meeker --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
