Hi, 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/ > > > > > > -- > 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---