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?
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" <marchal.domain.name.hidden>
To: <everything-list.domain.name.hidden>
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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Received on Tue Oct 10 2006 - 16:51:25 PDT