Deeper than primes

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The Man said:
Evidently you have never considered the alternative that you are simply wrong about there being some “agreed” or “traditional reasoning” and how certain non-naive set theories actually deal with the possibility of “set X” being defined as a member of “set X”.
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Evidently your flat reasoning can’t consider the different level of existence of any given set (empty or not) such that the collector aspect of a given set exists independently of the collected objects, exactly because there is essential difference between “defined by” or “defined as” and “identical to” (which is a notion the no flat reasoning can get).

The rest of your post and the illusion of infinite "activity", clearly demonstrates your flat ability to deal with the independency of the collector aspect w.r.t the collected aspect of a given set, which is an invariant and inherent property of any infinite set, which also prevents from a given member of some set to be identical to that set.
 
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The Man said:
Since you now specifically assert “set A, is exactly infinite levels,” (as you alluded to before) then that infinite set of levels you ascribe to “A” is complete.
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The Man from flat-land missed again the notion that infinite levels are exactly incomplete, because of the essential difference between the collector aspect and the collected aspect (which is not a process, but it simply a proportion (which is different than 1:1) upon infinitely many levels between the magnitude of existence of the collector aspect and the collected aspect of a given set).
 
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The Man said:
Again what ““agreed reasoning” is the traditional reasoning“, be specific and cite a reference.
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The flat-land reasoning, where a set does not have different levels of existence.

EDIT:

The concept of Cardinality under flat-land clearly demonstrates the lack of levels, for example:

|{{{}}}|=1 and not 2, etc ...
 
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epix said:
Oopsy-toopsy.

From: epix
To: The Man

When I scrolled back to see once again Doron's transformations, I realized that they and the conclusion are more absurd than I anticipated. If there is a field of mathematics that may find the accomodation in "Philosophy & Religion" motel somewhat acceptable, then it is the set theory. But Doron's insistence on "Turbulent Transformational Paganism" with [.], []. , [_]_ and all those demigods non-local to Christianity flying around makes any modest link impossible.

There is a practical branch of the set theory that enables to shuffle items around for various purposes, such as a comparison of the string of elements. There is a kind of set called a "list" that is defined and implemented differently then the set itself. The list is the practical part, whereas the set is used more or less for logical manipulations. Some languages, such as Java, allow implementation of both forms: sets and lists.

Some calculators, such as TI-89 allow only a list manipulation as a part of the computational hierarchy. That means there had to be the "thou shall not . . ." and one of them is the "Circular definition":

Example 1.
Code: 
Define a = {a, b, c}
Error: Circular definition

The attempt to define a list with three elements, for example, results in an error message when the defining term is also a part of the expression to be defined. It follows that the story would be the same in the next example:

Example 2.
Code: 
Define y = 2x - 6y
Error: Circular definition

Some believe in "thou shall not," and some don't. So let's override the error to see what happens in the case of Example 2:

Define y = 2x - 6y => 2x - 62x - 6y... and the substitution of y goes to infinity -- if the calculator could concatenate the function with itself.

Here is the fun part:
Q: What is Circular definition?
A: Circular definition is a definition that is circular.

Quite "illuminating answer," but that's what circular definition is all about in a practical example.

It's dark and you leave point A for point B. You get disoriented and walk in circles around point A forever and ever ad infinitum -- if you happen to be a non-omniscient, immortal deity. So that's the "etymology" of the term Circular definition (See Doron's renditions of those trips nowhere.)

How he relates the Russell's paradox to the infinite regression is a mystery to me -- if he does it at all. Once you expand a set to include identical elements, the set is no longer a set but a list by definition and becomes "non-local" to the set theory that Russel's paradox is a part of.
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Remember Russell's paradox is about naïve set theory, based on the assumption that all classes are sets. His claims about the “infinite regression” really goes back to Doron’s preferred assertion that an infinite set is not complete and his preference for using some infinite activity like listing, visiting or adding brackets in some term rewriting, as his basis for it being incomplete. However, that the activity can not include all members that the set does only demonstrates that it is the activity that can not be completed while the set must be complete as the activity can only be completed when it has encompassed all the members of the set.



epix said:
But there is a funny extension, a set of arguments that actually takes the pure abstract, or the philosophy of the Russell paradox to the religion territory through a remarkable coincidence. It's a very strange stuff, coz it comes to light only when you try to explain to Doron his absurd mistakes that only a few are capable of making, and that's not that easy, coz it's like trying to find a grammar mistake in a text written in French when you barely speak that language.
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Yep and this is entirely his own religion, philosophy and personal language. The curious thing is that by his assertions of “direct perception” his religion, philosophy and personal language should be readily obvious and accepted by everyone (even to the point of communicating with a virus, as he asserted before). So if we “just don’t get it” or get it and simply don’t agree with it, then we must be restricting ourselves to some particular confined “reasoning” (“local-only”, “serial-only” or now the new “flat-land”) that he is more than happy to ascribe to us as opposed to simply considering that his notions as well as his understanding of current mathematics are simply wrong.
 
The Man said:
Remember Russell's paradox is about naïve set theory, based on the assumption that all classes are sets. .
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Remember Russell's paradox is about naïve set theory, based on the assumption that a member of a given set is identical to that set.

EDIT:

It is a wrong assumption, because by following its flat reasoning, you actually can't re-member, so it is impossible to "Remember Russell's paradox".
 
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Let us understand Collection in terms of Observation.

Observation is not less than observer\observed linkage.

If the observed is identical to the observer, then there is no "room" for observations, or in other words, no concept is observed inducing the concept of empty observation.

So the concept of Set is possible only if the observed is not identical to the observer.

The notion of the observer is notated by the outer "{" "}" of any given set, whether the observed is nothing (emptiness) or something (non-emptiness).

The concept of "member" is possible exactly because there is a difference between the observer and the observed.

This difference is known only if the observer gets its existence independently of any observed concept, and by this direct perception of the observer, which is beyond any thought process, the observer is directly aware of the origin of any possible thought that can be expressed as some concept.

The current Mathematical activity uses the outer "{" "}" of any given set without the understanding that the outer "{" "}" represents the observer (the mathematician) as the source of any mathematical activity.

By understanding the difference between the observer and the observed, no member (which is an observed thing) is identical to the observer (represented by the outer "{" "}" of any given set).
 
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doronshadmi said:
Evidently your flat reasoning can’t consider the different level of existence of any given set (empty or not) such that the collector aspect of a given set exists independently of the collected objects, exactly because there is essential difference between “defined by” or “defined as” and “identical to” (which is a notion the no flat reasoning can get).

The rest of your post and the illusion of infinite "activity", clearly demonstrates your flat ability to deal with the independency of the collector aspect w.r.t the collected aspect of a given set, which is an invariant and inherent property of any infinite set, which also prevents from a given member of some set to be identical to that set.
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So you have never considered the afore mentioned alternative?


doronshadmi said:
The Man from flat-land missed again the notion that infinite levels are exactly incomplete, because of the essential difference between the collector aspect and the collected aspect (which is not a process, but it simply a proportion (which is different than 1:1) upon infinitely many levels between the magnitude of existence of the collector aspect and the collected aspect of a given set).
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Nope, I haven’t missed your fiat-land edicts and that they are “essential” only to you. So what is “exactly” missing from your “infinite levels” such that they are “exactly incomplete”?


Again what is this “magnitude of existence” you are referring to.


doronshadmi said:
The flat-land reasoning, where a set does not have different levels of existence.

EDIT:

The concept of Cardinality under flat-land clearly demonstrates the lack of levels, for example:

|{{{}}}|=1 and not 2, etc ...
Click to expand...

What “flat-land reasoning, where a set does not have different levels of existence.” is that? Again be specific and cite a reference.

Subsets and superset are fairly common aspects of most set theories I am aware of.


http://en.wikipedia.org/wiki/Superset


doronshadmi said:
Remember Russell's paradox is about naïve set theory, based on the assumption that a member of a given set is identical to that set.
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Actually that is just a consequence of the assumption that all classes are sets.

doronshadmi said:
EDIT:

It is a wrong assumption, because by following its flat reasoning, you actually can't re-member, so it is impossible to "Remember Russell's paradox".
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Is that why you keep going around in circles and evidently can’t remember what people have asserted or that what you would have liked them to assert was only asserted by you?
 
The Man said:
Remember Russell's paradox is about naïve set theory, based on the assumption that all classes are sets.
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That's one of the points that can serve as a launch pad for the peculiar voyage through Philosophy & Religion galaxy without relying on verbal description, which becomes inconsistent and useless in a tight conflict resolution situation.

The trivial connotation the naive set theory can suffer from is that the idea is simply naive. That's not the case though. The development of the set theory is an example of Man designing his own universe that is free of inconsistencies and capable evolving itself from the state of complete unawareness (all inorganic matter) to a partial awareness and desired full awareness of itself through highly organized matter called "brain." The evolution of the set theory is a conceptual model of an intelligent design trying to develop itself into a well-functioning logical system where the "naive part" is still in effect handling tasks that do not exceed it's capabilities, as much as all the logical sophistication the Nature has thrown into its own design cannot prevent the emergence of rather simple identity e = mc^2. The naive set theory is not obsolete; it just cannot handle all tasks needed to build the tiny model universe called Set Theory.

It is an inherent feature of the brain that when it focuses on a certain task, it holds residuals of no particular importance, and so there is plenty to miss. This doesn't really matter when the task is accomplished. But . . . Imagine that you focus on getting from point A to point B. Your map and compass are among the closely watched objects. You get to the point B; you accomplished your task -- but you are missing your valet. So you go back from point B to point A (you already know the way) and your priorities changed. Now you pay attention to what's around your feet. There maybe a circumstance in the future that has to be dealt with and the journey from the old paradox discovered in the antiquity retaken. The priorities will change funny. There is a straightforward hint of would it could be . . .
:eye-poppi
 
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doronshadmi said:
In that case there is a thing which is identical to itself, and the twisted definition of "Things which equal the same thing" is just playing with words.
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That's true and for some reason Euclid failed to include this notion into his . . . well, axiomatic framework. His Common Notions have come under close scrutiny by generations of mathematicians who were trying to prove that some or all the Common Notions were actually provable theorems, but no one could succeed in that. And so basically the coherence of modern mathematics still relies on Euclid's Common Notions. It's like the Bill of Rights and the amendments to the Constitution.

C.N.0. Every thing is identical to itself. (Doron's extension of Common Notions.)

versus

C.N.1. Things which equal the same thing also equal one another.

C.N.0.
1. A = A
2. B = B
Therefore
3. A = A and B = B


C.N.1.
1. A = B
2. A = C
Therefore
3. B = C

Note the difference in both conclusions: C.N.1. is missing article A in its conclusion, whereas C.N.0. includes all articles of the premise. In other words, there is no conclusion in C.N.0; the conclusion is just a repetition of both premises.

Have you ever heard the term "circular reasoning." If you have, then there is a definition of that available in practical example: Click on "Deeper Than Primes" and follow poster doronshadmi. As the years pass by, his genius makes sure that the thread will go round the circles in a Joyful Twist of Self-Containment around the point M, where O is the circumference of the circle. M stands for Magnet. Magnet is an ancient god of Local Attraction and Non-Local Repulsion, the son of Axiom and Futility.

So you are back. Well, time has changed. They have those set theories and stuff. My name is Ekklund -- the mischievous demon Ekklund. You can call me Ekk.
 
The Man said:
So you have never considered the afore mentioned alternative?
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It is not afore, it simply flat reasoning that can't get a non-flat reasoning.

The Man said:
Nope, I haven’t missed your fiat-land edicts and that they are “essential” only to you. So what is “exactly” missing from your “infinite levels” such that they are “exactly incomplete”?
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No collection of the observed is the observer (please see http://www.internationalskeptics.com/forums/showpost.php?p=6338999&postcount=11566).

The Man said:
Again what is this “magnitude of existence” you are referring to.
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The magnitude of existence of the observer w.r.t the observed.

The Man said:
What “flat-land reasoning, where a set does not have different levels of existence.” is that? Again be specific and cite a reference.

Subsets and superset are fairly common aspects of most set theories I am aware of.


http://en.wikipedia.org/wiki/Superset
Click to expand...
The observation of the observer (known also as a member of the observer) is not identical to the observer.

The Man said:
Actually that is just a consequence of the assumption that all classes are sets.
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Since infinitely many ... sets, classes, etc... are incomplete w.r.t the observer, then the term "all" is always false in the case of infinitely many ...

The Man said:
Is that why you keep going around in circles and evidently can’t remember what people have asserted or that what you would have liked them to assert was only asserted by you?
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No, it simply shows that you are using the word "re-member" without understanding it.
 
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doronshadmi said:
It is not afore, it simply flat reasoning that can't get a non-flat reasoning.
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So you just don’t remember me mentioning and you quoting that alternative before?

doronshadmi said:
No collection of the observed is the observer
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It is when the “observer “ is the only one “observed”.

doronshadmi said:
(please see http://www.internationalskeptics.com/forums/showpost.php?p=6338999&postcount=11566).
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I’ve seen it already, and you’re still just fixated on the particular notation of the members of a set involving brackets.

doronshadmi said:
The magnitude of existence of the observer w.r.t the observed.
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Again, the question was “What is this “magnitude of existence“ you are referring to?” not where or to what you choose to ascribe it.

doronshadmi said:
The observation of the observer (known also as a member of the observer) is not identical to the observer.
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But the observer under observation is when the observation is of the observer, and when that observation is by that observer being observed the observations are identical to that of observer as the observed is identical to the observer, unless your observations are just of the wrong observer.

“(known also as a member of the observer)”?

Don’t you mean ‘a member of the observed‘?

No wonder you’re looking at the wrong observer.

doronshadmi said:
Since infinitely many ... sets, classes, etc... are incomplete w.r.t the observer, then the term "all" is always false in the case of infinitely many …
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Since you can not show any member that is not a member your claim “infinitely many ... sets, classes, etc... are incomplete” is all wrong.

doronshadmi said:
No, it simply shows that you are using the word "re-member" without understanding it.
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No it simply shows that you don’t, can’t or simply do not want to remember (or learn) anything.
 
The Man said:
It is when the “observer “ is the only one “observed”.
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And yet the observed is not identical to the observer, otherwise there is no observation.

For example:

The observer is represented by the outer "{" "}", where the observed is represented by the internal "{""}", of observation "{{}}".

In "A = A" expression, "=" represents the observer and "A" represents the observed.

This difference is known only if the observer gets its existence independently of any observed concept exactly as the empty set exists independently of its contents (it is not identical to emptiness).

{} means that the observer exists independently of the observed (existence without thoughts).

{{}} means that the observer observes the concept of the empty set (a thought about {}, which is not identical to the observer (the outer "{""}")).

{{{}}} means the the observer observes the concept of non-empty set (a thought about {{}}, which is not identical to the observer (the outer "{""}")).

There is also a level that is beyond the observer, such that it is un-marked even as {}.

By using an analogy I call this level "The trunk", where the outer "{""}" is its Non-local aspect and the inner "{""}" is its Local aspect.

Non-locality and Locality are derive from the trunk but they are not derive from each other.

Because of this independency, thoughts are shareable among observers, and the mathematical science is a formal framework, which shares thoughts among observers, such that both the observer and the observed are independent and significant factors of that science, where the un-marked (un-manifested, if you will) is their origin.
 
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The set of all sets that are written by eleven words = {{The set of all sets that are written by eleven words}, {The set of all sets that are written by one word}, {The set of all sets that are written by two words}, …}.


{{The set of all sets that are written by eleven words}, {The set of all sets that are written by one word}, {The set of all sets that are written by two words}, …} ≠ {{The set of all sets that are written by eleven words}}
 
The Man said:
But the observer under observation is when the observation is of the observer,
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Observation is a result of the linkages among the observer and the observed.

If the observer and the observed are identical, then there is no observation, and the expression "under observation" is false.

The Man said:
, and when that observation is by that observer being observed the observations are identical to that of observer as the observed is identical to the observer
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Again, if there is no difference between the observer and the observed, then there is no observation.

In other words, Observation is at least {{}}, where the observer is the outer "{""}" and the observed is the inner "{""}", where the observer and the observed are derive from the un-manifested, and they do not derive from each other.

Because of this independency, the observer exists independently of the observed (existence without thoughts, that is notated as {}, exactly as the empty set exists independently of its contents (it is not identical to emptiness)), and if the observer is observed, then the observed is not the observer (we have an observer that observes itself as an observer without thoughts, which is a thought, and this case is notated as {{}}, which is different than {}, which is the observer without thoughts).
 
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doronshadmi said:
No, it simply A=A, which is an axiom, and an axiom does not need any conclusion.

This axiom has two aspects, the local aspect is represented by "A" and the non-local aspect is represented by "=" (please read http://www.scribd.com/doc/16542245/OMPT page 16).
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A theorem proposition must reach a conclusion, so must an axiom, and a conclusion relies on the existence of premises. Axioms are the elements of a math construct and, unlike the theorems, cannot be proven, but they should be logically concluded, not just observed. You get to an axiom only through a theorem, and only when you fail to prove this theorem, you may consider the theorem an axiom. Since theorems always include premises and a conclusion, the axiom inherits this property. You just don't go around setting arbitrary relationships of axiomatic character such as A = A. That's why OM can't be applied within the realm of sanity, especially not when you call "=" a "non-local aspect" and at the same time an "observer" with hundreds of decibels of a sheer redundancy.

Euclid had to run into the "A=A" one way or the other through apparent congruencies, but didn't handle it well enough, coz Common Notions are entirely verbalized:

C.N.4. Things which coincide with one another equal one another.

Your way of describing A=A is virtually identical to C.N.4 (Recall the "extension" C.N.0) Since C.N.0 = C.N.4, and C.N.0 suffers from circular reasoning, then C.N.4. has the same problem and the world of mathematics is in danger to be doronized and rendered ineffective, except for minor monetary transactions, coz Euclid's Common Notion's are pretty much in effect.
 
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doronshadmi said:
In "A = A" expression, "=" represents the observer and "A" represents the observed.
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I still remember those times when '=' used to be "equals to" and we knew that both A's were identical to each other. Today, '=' is an "observer" that observes both A's. '1 + 1 observes' anything that comes after, like 3, 20, 1914, 1939, 2012 and so on.
 
doronshadmi said:
(please read http://www.scribd.com/doc/16542245/OMPT page 16).
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Reading without understanding lacks purpose, and the purpose of the text suggested to read had to be implied. Your text issues several warning signs not to spend to much time reading, but otherwise it appears to be far more coherent than the hybrids that accumulate in your posts.

The increase in the engine power demands changes in the transmission design, as much as the processor power demands changes in the bus design. And so you have published your idea that relates to that. Why do you stress some "new thinking" is a mystery. Just leave this to the folks who will read your organic ways to bridge gaps and find it worth to implement. That's about it.

For the "other guy":

The solution is "doRon" -- smack in the middle. The bridging is symbolized in the text by the underscore; elements are symbolized by dots. That means the basic connection is ._. (dot, line, dot.) That creates the congruent complement: {doRon}=={moRse}, coz ._. is assigned to letter R in the Morse code. That should fix the gap between the L and Z arrays, right?
 
Let us use the empty set in order to define the concept "magnitude of existence".

Definition A: That has no successor has "the maximal magnitude of existence".

Definition B: That has no predecessor has "the minimal magnitude of existence".

The current scientific method, which developed since the 17th century, states that the researcher must be omitted form the research environment, in order to avoid results that are influenced by subjective tendencies of the researcher. It must be stressed that Aristotle determined 4 causes that sands at the basis of any existing thing, which are:

1) The material cause (from what material a given thing is made?).

2) The efficient cause (what are the natural forces that change a given thing?)

3) The formal cause (what is the "blueprint" in once mind that has an influence on a given thing?)

4) The final cause (what is the final goal in once mind, that has an influence on a given thing?)

The current scientific method uses only causes (1) and (2), in order to avoid any researcher's subjective influence on the result.

A question: Is it possible to return the researcher to the research environment and also avoid his\her subjective influence of the results?

My answer: I think that it is can be done if the "researcher" returns to the research environment as a general concept.

Let us use definitions A and B in order to demonstrate this notion.

{} describes the "researcher" in terms of definition A where what is between {} is the "researched" in terms of definition B (known also as "emptiness").

The outer "{""}" of {{}} describes the "researcher" in terms of definition A, where the inner "{""}" of {{}} describes the "researched" in terms of the model of the "researcher" that his\her "researched" subject is "emptiness".

At {{}} case "the magnitude of existence" of the "researched" is greater than "emptiness" (it has a predecessor) and smaller than the "researcher" (it has a successor).

Whether a non-empty collection is finite or infinite, it has both predecessor ("emptiness") AND successor ("researcher").

Anything that has both predecessor ("emptiness") AND successor ("researcher"), can't be reduced to "emptiness" AND can't be extended to "researcher". Because of this reason any given infinite collection can't have an exact Magnitude that is described by Cardinality.

If we symbolize these notions then: 0 < x < ∞, where ∞ represents the "the maximal magnitude of existence"("researcher") , 0 represents "the minimal magnitude of existence" ("emptiness"), and x represents "the magnitude of existence" that is > "emptiness" AND < "researcher" (any non-empty collection, whether it is finite or infinite).

By carefully research "the magnitude of existence" of an infinite collection, it is concluded that the universal quantifier "for all" has no meaning, because the accurate "magnitude of existence" of any given infinite collection can't be satisfied ( x < ∞). On the contrary, the universal quantifier "for all" has a meaning in the case of finite collections, because given any member of a finite collection it is defined as its final element, which in turn provides the accurate "magnitude of existence" that is described by an accurate Cardinality (A finite collection does not converge and does not diverge, which is a property that enables to determine its accurate cardinality).

In other words, if x is the cardinality of an infinite collection then x < ∞ prevents it accurate value.

Since the cardinality of any given infinite collection is inaccurate, then the 1-1 correspondence technique can't be used to determine any meaningful thing about the cardinality of such collections.

Furthermore, the Contor's diagonal upon decimal representation of irrational numbers, actually proves that it is impossible to determine the accurate value of x if x is related to an infinite collection.

Moreover, the ability to define a 1-1 correspondence between the natural numbers and a proper subset of them is a direct result of the impossibility to define the accurate cardinality of an infinite collection.

I wish to add that Russell's paradox does not hold that has cardinality ∞ can't be identical to any of its members, because any given member has at most x "magnitude of existence" and x < ∞ .
 
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doronshadmi said:
And yet the observed is not identical to the observer, otherwise there is no observation.
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Simply nonsense

doronshadmi said:
For example:

The observer is represented by the outer "{" "}", where the observed is represented by the internal "{""}", of observation "{{}}".
Click to expand...

You are still just fixated on a particular representation of the members of a set which involves brackets.

doronshadmi said:
In "A = A" expression, "=" represents the observer and "A" represents the observed.
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Just your ‘relation/element’ dichotomy renamed.

doronshadmi said:
This difference is known only if the observer gets its existence independently of any observed concept exactly as the empty set exists independently of its contents (it is not identical to emptiness).
Click to expand...

Once again the empty set does not exist “independently of its contents” it is specifically defined as, and thus dependent on, having no members.


doronshadmi said:
{} means that the observer exists independently of the observed (existence without thoughts).
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No it doesn’t, it just represents the empty set.

doronshadmi said:
{{}} means that the observer observes the concept of the empty set (a thought about {}, which is not identical to the observer (the outer "{""}")).
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Actually it just represents a set whose only member is the empty set.


doronshadmi said:
{{{}}} means the the observer observes the concept of non-empty set (a thought about {{}}, which is not identical to the observer (the outer "{""}")).
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It just represents a set whose only member is set whose only member is the empty set

doronshadmi said:
There is also a level that is beyond the observer, such that it is un-marked even as {}.

By using an analogy I call this level "The trunk", where the outer "{""}" is its Non-local aspect and the inner "{""}" is its Local aspect.

Non-locality and Locality are derive from the trunk but they are not derive from each other.

Because of this independency, thoughts are shareable among observers, and the mathematical science is a formal framework, which shares thoughts among observers, such that both the observer and the observed are independent and significant factors of that science, where the un-marked (un-manifested, if you will) is their origin.
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Again, simply nonsense.
 
doronshadmi said:
Observation is a result of the linkages among the observer and the observed.
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So? The observer is already ‘linked’ to itself even when not ‘observing’ itself.


doronshadmi said:
If the observer and the observed are identical, then there is no observation, and the expression "under observation" is false.
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Simply nonsense.

doronshadmi said:
Again, if there is no difference between the observer and the observed, then there is no observation.
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Again simply nonsense.

doronshadmi said:
In other words, Observation is at least {{}}, where the observer is the outer "{""}" and the observed is the inner "{""}", where the observer and the observed are derive from the un-manifested, and they do not derive from each other.
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You are deliberately conflating a representation of a set whose only member is the empty set with some “un-manifested” dichotomistic nonsense that most likely can to you during some TM.

doronshadmi said:
Because of this independency, the observer exists independently of the observed (existence without thoughts, that is notated as {}, exactly as the empty set exists independently of its contents (it is not identical to emptiness)), and if the observer is observed, then the observed is not the observer (we have an observer that observes itself as an observer without thoughts, which is a thought, and this case is notated as {{}}, which is different than {}, which is the observer without thoughts).
Click to expand...

Doron this was nonsense before, it is still nonsense now and it will continue to be nonsense no matter how many times you repeat it. Has the thought never occurred to you that your “direct perception” and whatever thoughts that might have come to you during some TM were just nonsense?
 
The Man said:
So? The observer is already ‘linked’ to itself even when not ‘observing’ itself.
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Some problems to distinguish between Observer and Observation, The Man?

The Man said:
Once again the empty set does not exist “independently of its contents” it is specifically defined as, and thus dependent on, having no members.
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Once again you can't distinguish between "defined by or as" and "identical to". After all flat-land is all you get, nothing has been changed all along this thread.


Here is more stuff that can't be comprehended from flat-land: http://www.internationalskeptics.com/forums/showpost.php?p=6347415&postcount=11584 .
 
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doronshadmi said:
Let us use the empty set in order to define the concept "magnitude of existence".

Definition A: That has no successor has "the maximal magnitude of existence".

Definition B: That has no successor has "the minimal magnitude of existence".
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Both of these purported ‘Definitions’ specifically invoke your “concept "magnitude of existence", they do not define it. Also they give the same conditional reference “has no successor” to both your “maximal magnitude of existence” and “minimal magnitude of existence”.


doronshadmi said:
The current scientific method, which developed since the 17th century, states that the researcher must be omitted form the research environment, in order to avoid results that are influenced by subjective tendencies of the researcher. It must be stressed that Aristotle determined 4 causes that sands at the basis of any existing thing, which are:

1) The material cause (from what material a given thing is made?).

2) The efficient cause (what are the natural forces that change a given thing?)

3) The formal cause (what is the "blueprint" in once mind that has an influence on a given thing?)

4) The final cause (what is the final goal in once mind, that has an influence on a given thing?)

The current scientific method uses only causes (1) and (2), in order to avoid any researcher's subjective influence on the result.
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No Doron, we also use double blind protocols, control samples, peer review and independent repeatability to address the subjective aspects of some particular researcher.

doronshadmi said:
A question: Is it possible to return the researcher the research environment and also avoid his\her subjective influence of the results?
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Doron the researcher has never left the research environment, only the bias they might bring with them has been force out (under proper protocols).

doronshadmi said:
My answer: I think that it is can be done if the "researcher" returns to the research environment as a general concept.

Let us use definitions A and B in order to demonstrate this notion.

{} describes the "researcher" in terms of definition A where what between {} is the "researched" in terms of definition B (known also as "emptiness").

The outer "{""}" of {{}} describes the "researcher" in terms of definition A, where the inner "{""}" of {{}} describes the "researched" in terms of the model of the "researcher" that his\her "researched" subject is "emptiness".

At {{}} case "the magnitude of existence" of the "researched" is greater than "emptiness" (it has predecessor) and smaller than the "researcher" (it has a successor).

Please pay attention where a non-empty collection is finite or infinite, it has both predecessor ("emptiness") AND successor ("researcher").
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Now your just conflating a particular notation of a set with a "researcher" and the "researched"

doronshadmi said:
Anything that has both predecessor ("emptiness") AND successor ("researcher"), can't be reduced to "emptiness" AND can't be extended to "researcher". Because of this reason any given infinite collection can't have an exact Magnitude that is described by Cardinality.
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Again simply nonsense.

doronshadmi said:
If we symbolize these notions then: 0 < x < ∞, where ∞ represents the "the maximal magnitude of existence"("researcher") , 0 represents "the minimal magnitude of existence" ("emptiness"), and x represents "the magnitude of existence" that is > "emptiness" AND < "researcher" (any non-empty collection, whether it is finite or infinite).
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This still does not define what you mean by this “magnitude of existence” you refer to or how you determine its “magnitude” or “existence”


doronshadmi said:
By carefully research "the magnitude of existence" of an infinite collection, it is concluded that the universal quantifier "for all", has no meaning because the accurate "magnitude of existence" of any given infinite collection can't be satisfied ( x < ∞). On the contrary, the universal quantifier "for all" has meaning in the case of finite collections, because given any member of a finite collection it is defined as its final element, which in turn provides the accurate "magnitude of existence" that is described by an accurate Cardinality.
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Doron just making up crap does not constitute “carefully research "the magnitude of existence"”. Again what is this “magnitude of existence” you refer to? Your above assertions seem to indicate that it is just the cardinality of a set.

Doron if your "magnitude of existence" “can't be satisfied” as you claim, then that is just your problem.

doronshadmi said:
In other words, if x is the cardinality of an infinite collection then x < ∞ prevents it accurate value.
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In other words you can’t show that an infinite set is incomplete as you have claimed before?


doronshadmi said:
Since the cardinality of any given infinite collection is inaccurate, then the 1-1 correspondence technique can't be used to determine any meaningful thing about the cardinality of such collections.
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“inaccurate”? By how much?

doronshadmi said:
Furthermore, the Contor's diagonal upon decimal representation of irrational numbers, actually proves that it is impossible to determine the accurate value of x if x is related to an infinite collection.
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You’re not familiar with meaning of the word “accurate” are you?

doronshadmi said:
Moreover, the ability to define a 1-1 correspondence between the natural numbers and a proper subset of them is a direct result of the impossibility to define the accurate cardinality of an infinite collection.
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No Doron it just shows that they are accurately (to a 1-1 correspondence) the same size.


doronshadmi said:
I wish to add that Russell's paradox does not hold that has cardinality ∞ can't be identical to any of its members, because any given member has at most x "magnitude of existence" and x < ∞
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Really, so what is the maximum cardinality “any of its members” can have?

If you can cite a maximum, why that particular maximum?
 
doronshadmi said:
Some problems to distinguish between Observer and Observation, The Man?
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Nope, evidently you just have some problems distinguishing between the observed and an observation, Doron.

doronshadmi said:
Once again you can't distinguish between "defined by or as" and "identical to". After all flat-land is all you get, nothing has been changed all along this thread.
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Once again that is still just your nonsensical claim and not matter how many times you try to ascribe it to someone else it still remains entirely yours as does your fiat-land.

doronshadmi said:
Here is more stuff that can't be comprehended from flat-land: http://www.internationalskeptics.com/forums/showpost.php?p=6347415&postcount=11584 .
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That post, as usual Doron, simply shows the problems in comprehension to be just yours.
 
doronshadmi said:
If the observer and the observed are identical, then there is no observation, and the expression "under observation" is false.
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A contradiction can be observed only in structures possessing a certain amount of coherency. Sometimes we get lucky:

a) We have an observer A and the relationship symbol '='

b) Observer and the observed are identical: A = A.

Apocalypse1: You call '=' an "observer" and a "non-local aspect." Since 'A' and "=" are different, they both cannot be observers.

Apocalypse2: If the observer and the observed are identical, then there must be '=' between them to define the relationship: A = A. Since '=' is also an observer by Organic Mathematics, then the observer is present smack in the middle of the A=A expression, and that means both A's are under observation, which contradicts your statement that there is no observation when A = A.
 
epix said:
A = A. Since '=' is also an observer by Organic Mathematics, then the observer is present smack in the middle of the A=A expression, and that means both A's are under observation, which contradicts your statement that there is no observation when A = A.
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You have missed my claim.

My claim is that "=" and "A" are not the same thing ("=" represents the observer and "A" represents the observed) and because of this difference observation is possible.
 
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The Man said:
Also they give the same conditional reference “has no successor” to both your “maximal magnitude of existence” and “minimal magnitude of existence”.
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It was corrected during your reply.

But the "important" thing here that you read reply like a copy machine, without realize that it is a typo, and take this trivial typo, which anyone (but you) can immediately understand as a typo mistake, and use it as one of your arguments against OM.

The Man said:
No Doron, we also use double blind protocols, control samples, peer review and independent repeatability to address the subjective aspects of some particular researcher.
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You mean to separate the subjective aspect of some particular researcher, from his/her scientific work (in this case the opinions, beliefs, and other subjective aspects of the researcher are clearly separated from his/her scientific research, or in other words, you reinforce my claim about the subjective-only approach of the modern science about the concept of the "researcher")

OM changes this subjective-only approach about the concept of the "researcher", by use it as a non-personal (general) concept, and the outer "{""}" of the concept of set, is one of the sufficient ways to express the non-personal (general) concept of the "researcher", which can't be grasped in flat-land, where the "researcher" is still a subjective-only concept.
The Man said:
Now your just conflating a particular notation of a set with a "researcher" and the "researched"
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No, I use "A" or "{""}" to express the notion of sets, and in both cases "that has no successor" (the non-personal aspect of the "researcher") is involved, which is something that can't be comprehended from flat-land.
 
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The Man said:
Nope, evidently you just have some problems distinguishing between the observed and an observation, Doron.
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Evidently you have no clue what really observation is, The Man.

The reason: It can't be known from flat-land.
 
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The Man said:
Doron if your "magnitude of existence" “can't be satisfied” as you claim, then that is just your problem.
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"Can't be satisfied" is a normal property of any framework, which is strong enough to deal with Arithmetic, so please give me a break (go learn Godel's incompleteness theorems).
 
The Man said:
doronshadmi said:
In other words, if x is the cardinality of an infinite collection then x < ∞ prevents it(s) accurate value.
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In other words you can’t show that an infinite set is incomplete as you have claimed before?
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No, in other words you do not understand that an inaccurate Cardinality means that the given collection is incomplete (its exact magnitude can't be satisfied).
 
The Man said:
“inaccurate”? By how much?
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Do you want the inaccurate or accurate value?

The Man, since you play this kind of game about infinite collections, then please tell us what is exactly the result of aleph1 - aleph0 ?
 
doronshadmi said:
Do you want the inaccurate or accurate value?

The Man, since you play this kind of game about infinite collections, then please tell us what is exactly the result of aleph1 - aleph0 ?
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Ok, so doesn't understand the term, inaccurate, either.
 
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