Re: set
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 II 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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Re: set
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.
-
On Sun, Jul 5, 2009 at 3:26 AM, Bruno Marchal marc...@ulb.ac.be wrote:
I am not sure What you mean by finding natural. I have just learn in
school to abbreviate II 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.*
-
**
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. *
**-
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 II 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
Re: set
On 05 Jul 2009, at 14:37, John Mikes wrote: 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. In some school the motto is that God is a human product. It is crazy what you can make children believe! 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. It is your right to scrutinize, even for billions years. But you can miss some trains. -- 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. I build on what 99% of people know or remember of arithmetic. It is not really the time to re-evaluate them, it is on the contrary the time to remember them, and use them. There is no magic, it asks for works. But here just ask question when you don't understand a solution to an exercise, for example. Mathematical intuitions about some object comes from playing with those objects. It needs a minimum amount of exercise and practice, for not being fool by the superficial choice of the words. - BM: ...Be careful with the term uncountable which will have a precise technical meaning. I call 'uncountable' what we cannot count (in toto) Good try. But what do you mean by we ? I asked you that question before. We the humans? We the mammals? We the animals? We the live being? We the universal numbers? We use the universal numbers with oracle, ... And then there is the problem to define count, which is a very interesting unsolved problem. But there are progress: we can explain why universal machine have difficulties when they try to define concept like 0, 1, 2, 3 - 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. We, and by we I mean the readers of the posts of this thread, will be invited, I'm afraid there is no escape, of a bit Cantor theory of the Infinites, note the s. Cantor discovered the Diagonalization technic, which works in set theory, mathematical logic and computer science. - 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. Yes, yes, yes. Important to always keep this in mind. Theories/ machines/numbers are tools, they just push light on something, but they can introduce shapes and shadows themselves. Be careful now of not confusing a theory and the betted things the theory is supposed to talk about. In the case of numbers and machine they can be both the studying thing and the studied things, and this makes some hard to predict surprises if I can say. * 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). I think that the idea that ''universal machine' is a product of the human mind is a product of your mind. And as such I respect that idea as an opinion. My opinion is that the universal numbers are indeed the product of universal numbers, and they have only partial controls on the relations. But there can be notable historical events like when amoeba invented the cable to develop into what we call brain, which are universal machine/number ... But this happened before, and after ... A more human-biased account could be that the universal machine
Re: Non unique Universe
hi, I am not very much into string theory but i liked the paper, it was pretty much self-contained for me, a computer-scientist, . On the other side, It seems that the main conclusions are extracted from the Löwenheim–Skolem theorem and not from Godel Incompleteness theorem. So the abstract is a little sleight of hand and, possibly, misleading. Regards, José. http://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem On Thu, Jul 2, 2009 at 6:30 AM, ronaldheldronaldh...@gmail.com wrote: http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0216v1.pdf comments? --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
