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" <[EMAIL PROTECTED]> To: <[email protected]> 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/ -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.407 / Virus Database: 268.13.1/466 - Release Date: 10/07/06 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
