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Re: set

by John Mikes :: Rate this Message:

It seems I am not careful enough to apply my vocabulary to you

and I feel some circularity in your thinking about 'learned' and 'axiomatic' notions. Let me try again, now in italics.

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On Sun, Jul 5, 2009 at 3:26 AM, Bruno Marchal <marchal@...> wrote:

"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."

'Natural' I used as 'without further consideration, as whatever comes to mind'. We all learned a lot 'in school' that cuts short solutions without going into (scientific?) nitty-gritties. We now try to dig into those and re-evaluate the short-cuts or formal <abbreviations> as to their full content, we just 'believed'.

We also believed 'in school' that God created the world as it is, yet in later studies we scrutinize the details and try to look into more than just the final phrases 'learned' in school.

Once you identified 3 and 4 I need more knowledge to get to the abbreviation of 34. You can say: 34 is a set with the value of '34', but then you involved characteristics of the set -

as "known" stuff, - which is just what I am scrutinizing.

"Find it natural" stands for lack of scrutinizing.

------

I think you referred to my sentence:

> Nothing is excluded
> from the a/effects (relations) of the rest of the world.<

when you remarked:

BM: "...This sentence seems to me far more subtle than anything I am trying to explain."

It reflects my 'totality' based worldview: an interrelated world, ALL elements in relation with ALL elements - securing the image of 'order' upon which we can base a science. No part can be excluded or isolated, (not even elements within a set) it would 'create' havock in theories we try to learn/formulate.
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BM: "...Be careful with the term "uncountable" which will have a precise technical meaning.

I call 'uncountable' what we cannot count (in toto) - the effects exercised on items within a set (as well as on anything in the world) by "the rest of the world" to which we have only a limited access - eo ipso we CANNOT count the unknown part. Infinite IMO is uncountable, because you can always add 'another' to it (common sense argument). I try to evade the word 'infinite' because of too many 'technical' connotations attached to it, use rather unlimited, which may refer to a finite item of which we don't know (yet?) the total.

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BM: "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".

I appreciate the 'axiomatize' what I understand as retrospect formulations to make our theories workable. Not vice versa.

I feel the paragraph as 'reverse thinking': our intuition is the working of our human mindset, I would not apply it as proof for getting the basics right, of which our mindset is a product.

Similarly the 'universal machine' is a product of the human mind so it cannot be invoked as evidencing the total which includes the human mind. (Circularity).

BM: "...What is the "occamisation of a set"?

The application of Occam's razor to cut off all that makes "it" harder to understand and concentrate on the easy part. It includes the (limited?) understanding of a problem by the person doing such 'occamization' - whatever he finds just complicating the issues he emphasizes. Such issues, however, may reach into the roots of our poor (mis?)understanding. I find 'Occam' the ultimate reductionism.

(I wonder if Russell will excommunicate me for that?)

John

Original message:
On 04 Jul 2009, at 22:42, John Mikes wrote:

> 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 Gödel, ...

> 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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