Le 27-oct.-06, à 00:40, 1Z a écrit :
>>> Tom Caylor: >>> Mathematical logic is richer than that. This is what Bruno is >>> saying, >>> that the math path points toward Rome. And it is no more scary (a la >>> possible spirits lurking under/in every rock) than the matter path. >>> Limiting math as you are doing, and as Brent Meeker does in his >>> response to my (X and not-X) note, is ignoring such evidence as the >>> proofs of Godel and Tarski's Indefinability Theorem. >>> >>> Tom >> >> Brent Meeker: But as I understand it, Bruno wants to identify >> "mathematical existence" with true existence statements about >> mathematical objects. >> Some of these are unprovable. They can be consistently added to the >> axioms. But also their negation can be consistently added to the >> axioms. But not both. So there are disjoint realms of consistent >> mathematics - some are Rome, some are Athens, some are Tuva, most are >> Harry Potter's home town. > > 1Z (Peter Jones): I suppose that is why he wants to base his case on > the > subset of arithmetic everyone agrees on. Exactly. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
