That is exactly what I wanted to say. You don't need to have a complete description of arithmetic. Our universe can be described by doing a number of computations from a finite set of rules. (To get to the current view of our universe you have to do about 10**60 computations for every point of space...)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.
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