Bruno Marchal wrote:
> 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.
If your Platonism is about truth, bot existence, you cannot show
that matter is redundant, because if your UD doesn't exist
in Platonia, it doesn't exist in the material world either, so it
doesn't exist at all, and therefore cannot replace anything that does
exist.
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Received on Tue Oct 10 2006 - 10:10:37 PDT