Yes, Bruno, it helps - however: I did not want to put you into any apology! The list is a free communication among free spirits and controversy is part of it. What I 'read' in your reply still "sticks" within 'math' and my principal point is: the image represented is STILL what a human mind MAY think, irrespective of 'machines' above it - as well humanly thought out. Of course smart mathematicians came up with ideas similar to what I thought and produced 'remedies' to cover the uncovered. Math extends as we go.

*"...But, once we assume comp, N is "ontologically" enough, all other sort of numbers do necessarily appear as unavoidable epistemological constructions,..."* I am not for the *'ontological'* because that is based on whatever we KNOW and I prefer the '*epistemological' (*"in spe" acquirable) totality. Extending *yesterday's* ontology into *tomorrow's* by epistemic enrichment . We cannot override the capabilities of our 'mind', restricted by the brain- tissue - function and bordered by our 'existence'. And - I condone it happily: the best we can do is math-ways (not mathematics) with all freedom within. WITHIN is the word. I represent in my thinking the humbleness of being restricted. I call it my scientific agnosticism - *allowing* "things" beyond our limitations. This is why I don't use "truth" or even "everything". And I use common sense. (Mine - that is <G>) So far you always pronounced the (infinite?) series of NATURAL numbers and I jumped on a number-wise defined item that was outside of them. Sorry, when it comes to speculation, I am jumpy. I did not know about those non-natural naturals. Have a good day John On Fri, Sep 18, 2009 at 3:23 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > > On 17 Sep 2009, at 18:17, John Mikes wrote: > > > Dear Bruno, > > > > it is not very convincing when you dissect my sentences and > > interject assuring remarks on statements to come later in the > > sentence, negating such remarks in advance, on a different basis. > > > > I argued that - upon what you (and the rest of the multimillion > > mathematicians past and present) live with - the applied > > nomenclature is incomplete. It is not a counter-argument that "it is > > used by many" or "for so many purposes". Of course it is in use, > > that was my point. > > I am not basing my position on opinions from "within" the argued > > position. > > (May the "-2 level" point to a 'total senselessness' of my opinion? > > I did not understand it, nor did I the (N + *) structure, which > > therefore I find irrelevant in the question what "I" raised. (I, not > > Rieman, Cantor, etc.). > > > > There is the idea of including 'quantities' in our worldview (excuse > > my naive reference, but you illustrated earlier "2" as "II" and "3" > > as "III" etc. and THIS in my mind means sort of a quantity) and such > > 'system' would be qualitatively > > infinite if we try to include quantities from all directions (math > > is the level of handling such quantities that 'came up' in the past > > - gradually - and we may expect more to come, new discoveries, > > extending the qualitative inventory) > > although in your words 'everything' can be expressed by (many many?) > > of your natural numbers (except square root 2?) - what is exactly > > my point. > > > > I did not want to open a scientific argument - I am no match for > > you, or any other 'mathematically educated' person. I scribbled a > > 'qualitative' idea of thinking in 'wider' terms than the defined > > 'natural numbers' in a worldview of a (qualitative) "totality" - > > what I pursue, but do not understand in my sci.fic agnosticism. > > > > I am sorry if I bored you with my remark. > > I apologize if I gave that impression, but I try sometimes to be not > too much long in the mails, and being short can have given that > impression. Sorry. My point was just that there is a sense where > natural numbers are not enough in math, and that is why mathematicians > have extended the set N. N, then Z, then Q, then R, then the complex > numbers, then the quaternions, octonions, etc. > But, once we assume comp, N is "ontologically" enough, all other sort > of numbers do necessarily appear as unavoidable epistemological > constructions, if only to understand the (additive-multiplicative) > behavior of the natural numbers, a bit like Riemann use complex > numbers to provide information on the prime (natural) numbers. > > Without digging a bit more on the technical issue, I can hardly say > more than my usual: there is only natural number, together with the > additive and multiplicative law. This, assuming comp, already defines > a "matrix" of number's dreams, and those cannot avoid the internal > phenomenological appearance of richer structures, like the "other" > numbers, and indeed like the whole physical appearances. > > Does this help you a little bit? > > Best, > > Bruno > > > > http://iridia.ulb.ac.be/~marchal/ > > > > > > > --~--~---------~--~----~------------~-------~--~----~ 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 everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---