Bruno Marchal wrote: > > Le 12-juil.-07, à 18:43, Brent Meeker a écrit : > >> Bruno Marchal wrote: >>> >>> Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit : >> ... >>> Our universe is the result of some set of rules. The interesting >>> thing is to discover the specific rules that span our universe. >>> >>> >>> >>> >>> Assuming comp, I don't find plausible that "our universe" can be the >>> result of some set of rules. Even without comp the "arithmetical >>> universe" or arithmetical truth (the "ONE" attached to the little >>> Peano >>> Arithmetic Lobian machine) cannot be described by finite set of rules. >> But it can be "the result of" a finite set of rules. Arithmetic >> results from Peano's axioms, but a complete description of arithmetic >> is impossible. > > > I don't understand. > > Let us define ARITHMETIC (big case) by the set of true (first order > logical) arithmetical sentences. (like "prime number exist", > Let us define arithmetic (lower case) by the set of provable (first > order logical) arithmetical sentences, where "provable" means provable > by some sound lobian machine. > By incompleteness, whatever sound machine you consisder the > corresponding "arithmetic" is always a proper subset of ARITHMETIC. > > So arithmetical truth (alias ARITHMETIC) cannot be described by any > finite set of rules. Finite sets or rules can never generate the whole > of arithmetical truth. > > OK? > > Bruno
Yes, I understand. But ARITHMETIC is generated by or results from Peano's axioms - right? 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?hl=en -~----------~----~----~----~------~----~------~--~---
