Le 09-oct.-06, à 23:56, Colin Geoffrey Hales a écrit :
> ...But it's not. Lets talk about the object with this property of five > in > platonia as <5>. Here in reality what we are doing is creating a label > I > and interpreting the label as a pointer to storage where the value in > the > storage (call it [I]) is not an integer, but a symbolic > representation of > property of five_ness as mapped from platonia to reality. What we are > doing is (very very metaphorically) shining a light (of an infinity of > possible numbers) on the object <5> in platonia and letting the > reflected > light inhabit [I]. We behave as if <5> was in there, but it's not. I think you are reifying number, or, put in another way, you put much more in "platonia" than I am using in both the UDA and the AUDA (the arithmetical UDA alias the interview of the lobian machine). Some people makes confusion here. All I say is that a reasoner is platonist if he believes, about *arithmetical* propositions, in the principle of excluded middle. Equivalently he believes that if you execute a program P, then either the program stop or the program does not stop. I don't believe at all that the number 5 is somewhere "there" in any sense you would give to "where" or "there". I do believe that 5 is equal to 1+1+1+1+1, and that for any natural number N either N is a multiple of 5 or it is not. So platonism is just in opposition to ultra-intuitionnism. We know since Godel that about numbers and arithmetic, intuitionnism is just a terminological variant of platonism (where a platonist says (A or ~A), an intuitionnist will say ~~(A or ~A), etc. "My" Platonism is the explicit or implicit standard platonism of most working mathematicians. 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 -~----------~----~----~----~------~----~------~--~---
