Deeper than primes

[doronshadmi]

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”.

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.

 

[doronshadmi]

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.

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).

 

[doronshadmi]

Again what ““agreed reasoning” is the traditional reasoning“, be specific and cite a reference.

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 ...

 

[The Man]

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.

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.

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.

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.

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.

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.

 

[doronshadmi]

Remember Russell's paradox is about naïve set theory, based on the assumption that all classes are sets. .

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".

 

[doronshadmi]

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).

 

[Skeptical Greg]

​

 

[epix]

​

You look as if you saw God in His Divine Underwear. Well, you just did. After changing you nickname, you can consider a few options. But think twice about Roman Catholicism -- not the best choice available.

 

[The Man]

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.

So you have never considered the afore mentioned alternative?

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).

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.

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 ...

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

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.

Actually that is just a consequence of the assumption that all classes are sets.

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".

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?

 

[epix]

Remember Russell's paradox is about naïve set theory, based on the assumption that all classes are sets.

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 . . .

 

[epix]

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.

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.

 

[dlorde]

Did you follow each post since your previous visit, in order to support your conclusion?

No, I took a brief overview - and found it 'much the same'.

 

[doronshadmi]

So you have never considered the afore mentioned alternative?

It is not afore, it simply flat reasoning that can't get a non-flat reasoning.

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”?

No collection of the observed is the observer (please see http://www.internationalskeptics.com/forums/showpost.php?p=6338999&postcount=11566).

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

The magnitude of existence of the observer w.r.t the observed.

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

The observation of the observer (known also as a member of the observer) is not identical to the observer.

Actually that is just a consequence of the assumption that all classes are sets.

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 ...

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?

No, it simply shows that you are using the word "re-member" without understanding it.

 

[doronshadmi]

No, I took a brief overview - and found it 'much the same'.

So please take a non-brief look.

 

[doronshadmi]

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

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).

 

[The Man]

It is not afore, it simply flat reasoning that can't get a non-flat reasoning.

So you just don’t remember me mentioning and you quoting that alternative before?

No collection of the observed is the observer

It is when the “observer “ is the only one “observed”.

(please see http://www.internationalskeptics.com/forums/showpost.php?p=6338999&postcount=11566).

I’ve seen it already, and you’re still just fixated on the particular notation of the members of a set involving brackets.

The magnitude of existence of the observer w.r.t the observed.

Again, the question was “What is this “magnitude of existence“ you are referring to?” not where or to what you choose to ascribe it.

The observation of the observer (known also as a member of the observer) is not identical to the observer.

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.

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 …

Since you can not show any member that is not a member your claim “infinitely many ... sets, classes, etc... are incomplete” is all wrong.

No, it simply shows that you are using the word "re-member" without understanding it.

No it simply shows that you don’t, can’t or simply do not want to remember (or learn) anything.

 

[doronshadmi]

It is when the “observer “ is the only one “observed”.

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.

 

[doronshadmi]

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}}

 

[doronshadmi]

But the observer under observation is when the observation is of the observer,

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.

, 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

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).

 

[epix]

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).

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.