Bruno asked:* "are you OK with this?"* - NO, I am not OK: as I follow, 0 is NOT a number, it does not change a number. But how do you *" A D D "* a number to another one if it is not identified as a quantity? Can you add an electric train to the taste of a lolly-pop? You speak about 'axioms' (- in my words they are inventions to prove a theory's applicability.) So no *reversing* please: proving the theory by axioms.

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May I repeat the main question: is YOUR number a quantity? so you can add (two = *II *to three = *III* and get five = *IIIII*) ?? If THAT is your axiom then numbers are quantity specifiers. We may AGREE on that, but then numbers are indeed the products of human thinking applied as humans think. *Q E D * * * *Bruno: "...**That's very good, but we can also develop general statement. We would not have discover the universal number (the computers) without agreeing on those principles."* * * That's a practicality and very fortunate. Does not enlighten the problem of what 'numbers' may be, if not quantifiers. JOhn On Thu, May 2, 2013 at 4:54 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > On 01 May 2013, at 22:09, John Mikes wrote: > > Bruno asked why I have problems how to figure out *'numbers'*. * * > > In his texts (as I remember and I have no quotes at hand) the "world" can > be construed from a large enough amount of numbers in simple arithmetical > ways (addition-subtraction). Also: numbers do not mean quantities. > If his older post with pegs (II=two, IIII=four etc.) is OK, the 'words' > two and four DO mean quantities. If not, as 'numbers' they are meaningless > combinations of letters (sounds?) we could call the series any way, as well > as e.g.: > tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any other > language (eins,zwei,drei, - egy, kettő, három) as they developed in diverse > domains/lifestyles. The 'numbers' would be like "Ding an Sich" (German) > however used as qualifiers for quantities if so applied (see Bruno's 'pegs' > above). > > > The terms we are using are not important. All we need is some agreement on > some theory. > Most things we need for the natural numbers can be derived from the > following axioms (written in english): > > any number added to zero gives the number we started with (= x + 0 = x) > 0 is not the successor of any natural number > if two numbers are different, then they have different successors > a number x added to a successor of a number y gives a successor of the sum > of x and y. > > Are you OK with this? > > In science we know that we cannot define what we are talking about, but we > can agree on some principles about them. > Bruno: *"...We would not have discover(ed) the universal number (the computers) without agreeing on those principles." * * * To have discovered the 'universal number'(?) (i.e. computers) is fine but that does not imply understanding on numbers: like "numbers are such as to be applicable for..." etc. My agnosticism needs more than that. Sorry. > > > > > More reasonably sounds the idea of my wife, Maria, who assigns the > primitive development of quantities originally to proportions: "larger > (amount)" - "smaller (amount)" evolving in some thousand centuries into the > process of 'counting' the included units. > > > That's very good, but we can also develop general statement. We would not > have discover the universal number (the computers) without agreeing on > those principles. > > > > I published on this list my thought for developing the Roman numbering > signs. I started with 2 - a PAIR of hands etc. (not with one, which means > only the existence) and branching into 5 (as fingers, as in pentaton music) > already as 'many'. > > > OK. > > > > I still have no idea what description could fit *'number'* in Bruno's > usage (I did not study number - theory - to keep my common sense > (agnostic?) thinking free). > > > See above. > > Bruno > > John > > > > John Mikes > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.