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.domain.name.hidden
To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list
-~----------~----~----~----~------~----~------~--~---
Received on Sat Oct 07 2006 - 08:50:30 PDT