Le 07-oct.-06, à 11:37, 1Z a écrit :

> > > Bruno Marchal wrote: > >> I did not have problem with the expression "platonic object" but be >> careful because it makes some people believe (cf Peter Jones) that we >> are reifying numbers and mathematical objects. > > That is exactly what mathematical Platonism has always meant [*] > > But "reifying" doesn't mean treating as material. Platonic objects are > supposed > to immaterial, somehow. Well, you beleive the UD exists, > and you believe matter doesn't so you belive in > immaterial entitities, so you are a Platonist. <snip> So we agree on this since the beginning!!! I was just referring to a nuance you did introduce between believing that the number 5 exist (say), and believing in the independent truth of the proposition "It exist a number which is equal to 5". I hope you agree with the fact that in this sense everybody is *arithmetical* platonist, with the exception of the ultra-intuitionist (who does not believe in number which are too much big (yet finite). I am certainly an arithmetical realist (platonist), but I would not assert that I am a set-theoretical platonist. (Note that I would not necessarily deny it, I'm just currently agnostic on big sets). Note that by using godel's arithmetization device, it can be shown that the UD exists in exactly the same sense than saying that 5 exists. And I am not willing to defend the idea that "5 exists", just that comp ("yes doctor" + Church Thesis + "5 exists" (say)) entails that physics is a branch of number theory (including recursion theory like in Yuri Manin's book), and constructively so. My personal opinion if comp is true or false is ... personal. Ok I let you know that I have no doubt that "5 exists", few doubt that CT is true, some doubt that "yes doctor" is true. My point is that comp, made precise enough, is empirically refutable. 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 -~----------~----~----~----~------~----~------~--~---