I said to Brent,
Le 31-août-07, à 11:00, Bruno Marchal a écrit : > So, no, I don't see why you think my objection is a non-sequitur. It > seems to me you are confusing arithmetic and Arithmetic, or a theory > with his intended model. Brent, rereading your post I think there is perhaps more than one confusion. I cannot really be sure, because your wording "arithmetic" is ambiguous. Let me sum up by singling out three things which we should not be confused: 1) A theory about numbers/machines, like PA, ZF or any lobian machine. (= finite object, or mechanically enumerable objet) 2) Arithmetical truth (including truth about machine). (infinite and complex non mechanically enumerable object) 3) A meta-theory of PA (that is a theory about PA) (again a mechanically enumerable object) Only a meta-theory *about* PA, can distinguish PA and arithmetical truth. But then Godel showed that sometimes a meta-theory can be translated in or by the theory/machine. Rich theories/machine have indeed self-referential abilities, making it possible for them to guess their limitations. By doing so, such machines infer the existence of something transcendenting (if I can say) themselves. OK? 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 [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 -~----------~----~----~----~------~----~------~--~---
