Bruno Marchal wrote:
> 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".
The difference is reification, or Platonism, about numbers.
Which you claim not to
need.
> I hope you agree with the fact that in this sense everybody is
> *arithmetical* platonist,
That is obviously wrong. Formalists are not Platonists,
structuralists are not Platonists, Empiricists are not
Platonists.
>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.
Which of course is not any real existence at
all for the anti-Platonist, although he agees with
the truth of all the same mathematical propositions as the Platonist.
But you think the UD does things and behaves in certain
ways and generates certain appearances. So you think it
exists. So you are Platonising and reifying, although you claim
not to be.
> 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.
And many doubt "5 exists" in a "real" sense of existence -- many
doubt Platonism.
>My point is that comp, made
> precise enough, is empirically refutable.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
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Received on Sat Oct 07 2006 - 10:49:07 PDT