Re: set

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On 04 Jul 2009, at 22:42, John Mikes wrote:```
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> Dear Bruno, thanks for the prompt reply, I wait for your further
> explanations.
> You inserted a remark after quoting from my post:
> *
> > If you advance in our epistemic cognitive inventory to a bit better
> > level (say: to where we are now?) you will add (consider) relations
> > (unlimited) to the names of 'things' and the increased notion will
> > exactly match the 'total' (what A was missing from the 'sum'). It
> > will also introduce some uncertainty into the concept (values?) of a
> > set.
>
> I am not sure that I understand.
> *
> Let me try to elaborate on that: What I had in mind was my
> 'interrelated totality' view.
> As you find it natural that 3 (!!!) and 4 (!!!!) make 34 - if
> written without a space in between - representing a quite different
> meaning - (not 7 as would be plainly decipherable: 3+4),

I am not sure What you mean by finding "natural". I have just learn in
school to abbreviate IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII by 3*10 +4,
itself abbreviated by 34.

>  so all elements of a set carry relations to uncountable items in
> the unlimited totality (even if you try to restrict the
> applicability into the identified  {  }  set. Nothing is excluded
> from the a/effects (relations)  of the rest of the world.

This sentence seems to me far more subtele than anything I am trying
to explain. Be careful with the term "uncountable" which will have a
precise technical meaning.

> No singularity or nivana IN OUR WORLD
>
> Your 2+2=4 includes a library of conditions, axioms, relations,
> clarifiers, just as e.g. the equation 4-2=2 includes the notion "NOT
> in ancient Rome" (where it would have been '3')

We will axiomatized some mathematical notions, but only when we are
sure that we get the intuition right. The reason will NOT be a search
of explicit rigor, but will be related in helping universal machine to
get the "understanding".

Concerning the natural numbers, the more we will be familiar with
them, the more we will be aware we don't really know what they capable
of, and why they are fundamentally mysterious. But there is no need to
add more mystery than the very subtle one which will grow up. This is
not obvious, and has begun with the work of Dedekind, and GĂ¶del, ...

> So I referred to the tacitly included 'relations' (I use this word
> for all kinds of knowables in connection with potential effects of
> other items) implied in your technical stenography.
> Since the relationally interesting items are unlimited, there is no
> way WE (in our present, limited mind) could exclude uncertainty FOR
> 'ANY' THING. Sets included. Occamisation of a set does not make it
> rigorous, just neglects additional uncertainty.

I still have no clues why and how you relate "infinity" with
uncertainty. What is the "occamisation of a set"?

>
> Have a good weekend

I wish you the same,

Bruno

http://iridia.ulb.ac.be/~marchal/

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