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.

## Advertising

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. John M On Thu, Sep 17, 2009 at 10:01 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > Hi John, > > On 17 Sep 2009, at 15:14, John Mikes wrote: > > > > You went out of your way and did not save efforts to prove how inadequate > and wrong (y)our number system is. (ha ha). > > > Wrong ? > > > > > Statement: *if square-rooting is right* (allegedly, and admittedly) > > > > Well, it is certainly right if we want that to measure by a number length > of the diagonal of the square unity. > > > > > *then THERE IS such a 'quantity'* (call it number and by this definition > it must be natural) > > > > It cannot be natural number. It has to be strictly bigger than 1, and > strictly bigger than 2. But there was some hope that it could be the ratio > of two natural number, so that it can live in arithmetic with addition and > multiplication. > > > > > *we consider as the square root of '2'*. > You gave the plastic elemenary rule, how to get to it. Thankyou. Accepted. > > I believe the '1' and the sophistication of Pythagoras. *(provided that * > *< 1^2 = 1 > which is also 'funny') a n d :* > If it is not part of your series *of* - what you call: - *natural numbers*, > then *YOUR* series is wrong. > > > > You could as well told something like "My cave is at the level -2 (minus > two) of the building ... > > > > We need another system (if we really need it). > > > That is why N (the set of natiral numbers, alias positive integers) has > been extended into Z, all the integers, itself included in Q (he ratio). The > my point was that Q was still not enough to define the length of the > diagonal, we need the real numbers, which are more difficult to define in > the structure (N, +, *). > > From a logical point of view, N, Z, and Q are roughly equivalent. The real > numbers are not, most are not definable in the structure N. yet, and we will > see this (probably), most real numbers that we encounter in math and physics > can still be defined in the structure (N,+,*). It is an open problem in math > and physics if there is anything we cannot define in (N,+,*), and indeed it > is an indirect consequence of COMP that we can. This probably why formal set > theory is studied only by logicians. > > Of course Riemann and number theorists, and knot theorists, are used to > escape from the (N, +, *) structure all the time, and that is why we use > analysis (based on the real numbers). But we have not yet find a theorem > which *needs* to escape the structure (N, +, *), except those found by > logicians to just provide examples. In the mechanical theory of mind, we > have to escape the structure (N, +, *). Indeed the first person notion needs > even more than Cantor paradise, from its point of view, and that is why and > how the epistemology of comp is necessarily far bigger than its ontology. I > may come back on this, but it asks for more model theory and logic to > address the question technically. > > 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 -~----------~----~----~----~------~----~------~--~---