1Z 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. > > Mathematical logic can't conjure up existential conclusions > without making existential assumptions. >
True. ;) > > 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. > > They do not disprove formalism, as I have explained. > True. Formalism is an existential assumption. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
