Boolean Logic cannot deal with infinitely many objects

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The discussion centers on the limitations of Boolean logic and Cantor's diagonalization method when applied to infinite sets. The author argues that Cantor's method cannot account for all combinations in an infinite list, leading to the conclusion that 2^aleph0 equals aleph0, which contradicts established mathematical principles. They present examples of finite combinations and assert that the diagonalization results do not yield new combinations, implying that Boolean logic fails with infinitely many objects. The conversation includes critiques of the author's reasoning and calls for a better understanding of mathematical concepts, particularly Cantor's argument. Ultimately, the thread highlights the complexities and misunderstandings surrounding infinite sets and their treatment in mathematics.
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  • #213
Well it look that Z

is one of the 10.

Thank you Organic.

What do you think?

[zz)]
 
  • #214
Once upon a time a little fish asked his mother: "Mammy, one of my friends told me the that there exist somthing, which its name is 'water', so Mammy where can we find this water?"

Without another point of view on something, it is hard to understand it.

Please read this: http://www.math.rutgers.edu/~zeilberg/PG/Introduction.html

by Prof. Doron Zeilberger.
 
  • #215
I will be honest with you Organic,
I know already Doron and i like his work very much!

I told him that i do not agree
with his direction for the new mathematics.

Computer are only the justification
to create a new mathematics.

What we have to do is the opposite direction
that Doron sagest us here.


Just Look on this point.

.



Moshek
 
  • #216
What is the opposite direction of Prof. Zeilberger?
 
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  • #217
Dear Organic,

I will try answer you,
and you are one of the 10
Altow you don’t know at all !
Euclidian mathematics.

But before I do that
please tell me if you don’t mind,
have you been already
in the forest of the monkeys?

Yours
Moshek
 
  • #218
What is the forest of the monkeys?

Is it a mathematical slang?
 
  • #219
If you come to that so high point in mathematics,
(and you also look like a monkey)
I can't believe that you don’t know "The answer".
 
  • #220
From an organic point of view, we never left the forest of the monkeys, because all complexed organism on this planet are DNA products 3 to 4 billion years old.
 
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  • #221
Organic,

This is not so good answer, ( like pupil to his teacher...)
I will come back in few day's to your 2 questions.

Maybe you will have until than "The answer"

untill thay you will enjoy to look on:

http://www008.upp.so-net.ne.jp/gps1999



Your's
Moshek
 
  • #222
In my opinion, there is no "The Answer".
 
  • #223
ok

:wink:
 
  • #224
Organic:

here you can find what is the forest of the monkey


The Book: Mount Analogue ( 1959)


René Daumal’s is a twentieth century classic, combining the author’s poetic gifts and philosophical accomplishments in a manner that is both entertaining to read and profound to contemplate. Among other things, this is a marvelous tale in which the narrator/author, one of an intrepid company of eight, sets sail in the yacht Impossible to search for Mount Analogue, the solid, geographically located, albeit hidden, peak that reaches inexorably towards heaven—as Mount Olympus reached to the home of the Greek gods, or Mount Sinai to the presence of Yahweh. Daumal, often described as one of the most gifted literary figures in twentieth-century France, died before the novel was completed, providing an uncanny one-way quality to the journey.


About the Author
René Daumal (1908-44), a follower of the teachings of G.I. Gurdjieff, also studied Sanskrit, philosophy, science, mathematics, and medicine. He was an editor of the French poetry and surrealist review Le Grand Jeu, and the novel Mount Analogue was first published posthumously, in 1952
 
  • #225
Organic

The forest of the monkeys is the base of the Mount Analogue.
I am sory that i take in advance that you know about this place.

Moshek
 
  • #226
Then, I repeat:

From an organic point of view, we never left the forest of the monkeys, because all complex organism on this planet are DNA products 3 to 4 billion years old.

The DNA is the base of this mountain, and the fulfillment of the uniqueness of each complex system (based on DNA) is its private peek.

Shortly speaking, DNA principle is general (or maybe global) but its fulfillment is unique (or maybe local).

Global and Local are complementary concepts of Mount Analogue.


Yours,

Organic
 
  • #227
what if global=local somehow? what i mean is that what if the "opposite" ways of looking at mount analogue are complementary but both inadequate so that a transcendence of the opposites is needed in order to really start up that mountain. rather than see things dualistically as global and local, perhaps there is a way to look at it ONE way that is the RIGHT way. but will doing that be the equivalnt of reaching the base of the mountain, or reaching its peak? i think its base. the peak is not something i can imagine yet.
 
  • #228
Hi phoenixthoth,


What you call ONE is the BALANCE that exists between opposite concepts, giving them the chance to complement each other instead of destroying each other, when they are meeting.

So, the minimal condition for any thinkable system must be at list 0=x-x where the left size (notated as 0) is the balance and the right side is the opposite's communication environment (notated as x-x).

Please pay attention that from this model, (the 0 result of x-x=mutual destruction) XOR (the 0 result of x-x=mutual communication).


Maybe the Meta system is:
Code: 
       (the 0 result of x-x = mutual destruction)
? = XOR
       (the 0 result of x-x = mutual communication)
where the answer to ? is given by self-aware systems.



Yours,

Organic
 
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  • #229
seems like destruction balances communication in this theory. what if those are the same thing in that sometimes communication is or results in destruction? what i mean by that is the following example:
an intense frequency penetrates a solid object and it shatters.

maybe it's best to not name certain things:
0=x-x is ?

this idea is expressed in group theory that everything (in a group) has an opposite that cancels it.

it also mentions the idea of IDENTITY: 0=0 yet, in a way, 0!=0 because x-x has more information in it than just 0 yet x-x=0 which results in information loss aka destruction through communication.
 
  • #230
Dear Organic and Phoenix:

For being in the forest of the monkey
first you must understand
that we are only the monkey of Euclid.

Yes, "global=local" is a key point to start the travel.
in the sense of it duality on mathematics as a whole.
But if we will work very hard together as a tim
we may start the travel to mount Analogue not before 2006.

The pick is the non-Euclidean mathematics
that non of us can see it today,
because it is not exist yet
it is Only a potential now.

Interesting work:

http://modular.fas.harvard.edu/sga/from_grothendieck.pdf

Moshek
 
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  • #231
why do you say 2006?

the two concepts for which global=local are Ø and any singleton which is representable as a point. some people conjecture that somehow consciousness has a dual nature: point-like and (with an infinite distribution)-like. perhaps this relates to self aware structures? perhaps global analysis on on part of the dualaity is local analysis on the other part.
 
  • #233
Hi,

If the Meta system is:
Code: 
       (the 0 result of x-x = mutual destruction)
? = XOR
       (the 0 result of x-x = mutual communication)
where the answer to ? is given by self-aware systems, then maybe this is the deep meaning of any open system, which means:

result = ? (where ? is a legal answer)

From the above we maybe can give a moral interpretation to Math results, given by self-aware systems.
 
  • #234
that kind of sounds like reinventing the wheel in terms of godel's incompleteness theorems and undecidability: things where you can prove ? is the answer, roughly speaking. i don't know, perhaps the existence of self-aware structures will be ? within the other known structures so one can express their free will in order to believe they exist or don't.
 
  • #235
Well phoenix,

In 1823 Bolyai and Lobachevsky's
without knowing one about the other
invent the Non-Euclidean geometry.
But most of it was already known to Gauss.

In 2006 It may be declare by the IMC in Madrid
who is the new Gauss that can lead us to the
Mount of Analogue , A Non-Euclidean mathematics.
 
  • #236
I think you miss the point.

1) phoenixthoth is self-aware system.

2) phoenixthoth has the ability to decide if he a destroyer XOR communicator.

3) phoenixthoth decisions has an influence on itself and its environment.

4) phoenixthoth responsibility as a participator is extremely important.
 
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  • #237
Originally posted by Organic
I think you miss the point.

1) phoenixthoth is self-aware system.

2) phoenixthoth has the ability to decide if he a destructor XOR communicator.

3) phoenixthoth decisions has an influence on itself and its environment.

4) phoenixthoth responsibility as a participator is extremely important.

1) embedded in a larger SAS

2) i don't think it's xor. let me try to explain. a communicator can be a destroyer at the same time yet destruction is the intention of the one communicated TO not the one doing the communicating. like a high intensity sound wave shattering a glass. it is the glass' intention to be a destroyer from a certain point of view, all the sound wave wants to do is communicate but the power is overwhelming unintentionally. now i think this is expressed in the information loss, also known as destruction, in the equation x-x=0 or 0=0. those seem to be different equations because x-x has more information that has been destroyed AND communicated from x to x in a self-awareness sense.

3) yes and vice versa.

4)yes, as is the responsibility of all SAS's.
 
  • #239
phoenixthoth,


About a moral interpretation to Math results.

If the Meta system is:
Code: 
       (the 0 result of x-x = mutual destruction)
? = XOR
       (the 0 result of x-x = mutual communication)
where the answer to ? is given by self-aware systems, then maybe this is the deep meaning of 'Right and Worng'.

It is good to be a (sum=commounicator), it is bad to be a (sum=destroyer).

Therefore, (0=mutual destruction) XOR (0=mutual communication).
 
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  • #240
yes i think that does give a deeper meaning of right and wrong but keep in mind it also depends very much on your perspective. from one perspective, x-x is mutual destroy and from another x-x is mutual communicate. since infinity-infinity is not "always" zero, perhaps that object does not "always" destroy itself, if that makes any sense.
 

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