Le 09-oct.-06, à 23:56, Colin Geoffrey Hales a écrit :

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> ...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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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