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 <marchal.domain.name.hidden> 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/
>
>
>
>
> >
>
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Received on Fri Sep 18 2009 - 08:33:01 PDT