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/


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