Stathis Papaioannou wrote: > Brent Meeker writes: > > >>>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. > > > What more could we possibly ask of a theorem other than that it be true > relative to some > axioms? That a theorem should describe some aspect of the real world, or that > it should > be discovered by some mathematician, is contingent on the nature of the real > world, but that > it is true is not.
That it is a true description of the real world, or that it is a true theorem relative to the axioms. It is a mistake to conflate the two, which I suspect is done by people claiming mathematical theorems are true. 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 firstname.lastname@example.org To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---