Le mardi 10 octobre 2006 22:41, [EMAIL PROTECTED] a écrit :
> Bruno:
> you wrote:
> "...I do believe that 5 is equal to 1+1+1+1+1, ..."
> Why not 1+1+1+1+1+1+1?  you had a notion somewhere in your mathemaitcally
> instructed mind that you have to stop at exactly the 5th addition, because
> there is a quantity (???) in the number '5' that made you stop there. Now
> "quantity" is also expressed by numbers, lots of them in applying 'rules',
> so don't we see here a circularity?

The successor axiom and the definition of addition make you stop there.
If you choose other axioms and/or operations definitions and/or another 
language to express it, it has of course another meaning ;)

> It looks as if the 'numbers' represent quantities?  how about algebra?
> What "key" made you stop at the fifth '1'?
> (I wrote in a similar sense a post to Colin, an hour ago).
> You ended your reply with:
> >>"My" Platonism is the explicit or implicit standard platonism of most
> working mathematicians.<<
> Q: is there a way to reach an agreement between  the "working
> mathematicians" and the rest of the world (common sense people)?
> John
> ----- Original Message -----
> From: "Bruno Marchal" <[EMAIL PROTECTED]>
> To: <everything-list@googlegroups.com>
> Sent: Tuesday, October 10, 2006 8:06 AM
> Subject: Re: The difference between a 'chair' concept and a 'mathematical
> concept' ;)
> 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.
> Bruno
> http://iridia.ulb.ac.be/~marchal/
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