Brent Meeker wrote:
> Tom Caylor wrote: > > 1Z wrote: > >> Tom Caylor wrote: > >> > >> > >>>> Again, the kind of formalism that says > >>>> everything can be brought under a single > >>>> formal scheme (the Hilbertian > >>>> programme) is different from the kind > >>>> that says mathematical truths are dependent on axioms, > >>>> and different truths will be arrived at under different > >>>> axioms. Of course the key point here > >>>> is "different truths". Tom is not entitled to assume that > >>>> all roads lead to Rome. > >>> If your definition of truth is limited to logical inference given a > >>> certain set of axioms and inference rules, then what are we trying to > >>> do on the Everything List? > >> That's *mathematical* truth. > > > > 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 > > 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. I suppose that is why he wants to base his case on the subset of arithmetic everyone agrees on. > 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 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 -~----------~----~----~----~------~----~------~--~---
