Le 29-août-06, à 20:45, 1Z a écrit :

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> The version of AR that is supported by comp > only makes a commitment about mind-independent *truth*. The idea > that the mind-independent truth of mathematical propositions > entails the mind-independent *existence* of mathematical objects is > a very contentious and substantive claim. You have not yet answered my question: what difference are you making between "there exist a prime number in platonia" and "the truth of the proposition asserting the *existence* of a prime number is independent of me, you, and all contingencies" ? > Where is it shown the UD exists ? If you agree that the number 0, 1, 2, 3, 4, ... exist (or again, if you prefer, that the truth of the propositions: Ex(x = 0), Ex(x = s(0)), Ex(x = s(s(0))), ... is independent of me), then it can proved that the UD exists. It can be proved also that Peano Arithmetic (PA) can both define the UD and prove that it exists. > >> Tell me also this, if you don't mind: are you able to doubt about the >> existence of "primary matter"? I know it is your main fundamental >> postulate. Could you imagine that you could be wrong? > > It is possible that I am wrong. It is possible that I am right. > But you are -- or were -- telling me matter is impossible. Only when I use Occam. Without Occam I say only that the notion of primary matter is necessarily useless i.e. without explanatory purposes (even concerning just the belief in the physical proposition only) . This is a non trivial consequence of the comp hyp. (cf UDA). > But the negative integers exist (or "exist"), so it has > an existing predecessor. Yes. But the axiom Q1 "Ax ~(0 = s(x)" is not made wrong just because you define the negative integer in Robinson Arithmetic. The "x" are still for "natural number". The integer are new objects defined from the natural number. All right? To take another example, you can define in RA all partial recursive functions, but obviously they does not obey to the Q axioms, they are just constructs, definable in RA. 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 -~----------~----~----~----~------~----~------~--~---