A hidden assumption

doronshadmi said:
No, it is not an holistic mathematical paradigm.

It is a whole\parts paradigm where both the whole and the parts are a vital complementation.
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OK then, that. It's what I meant. But I don't see your system expressing that.

The complementation that your are trying to get at isn't just a mutual independence but a mutual interdependence.
In any case Complements don't negate each other, but allow their full expression.

But in the case of the Finite/Infinite Complement, your system takes scissors to the Infinte side.

This is how you try to eliminate the paradoxes. But a mature mathematic is actually rooted in paradox or all your talk about Complmentation is a sham.
 
doronshadmi said:
Very simple. Symmetry itself it total unity. Asymmetry itself is total isolation.

No one of them is defined by the other.
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They're not defined at all. "Symmetry itself it total unity" is not a definition, it's drivel.

If they are related with each other (they complement each other) then the result is Mutual Independency, where the Mutual aspect of this complementation is the result of total unity and the Independency aspect of this complementation is the result of total isolation.
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More drivel.

Total Unity is non-researchable at its self state.

Total Isolation is non-researchable at its self state.

When complement each other, the result is nor total unity neither total isolation, and this result is researchable.

You try to understand the non-researchable in terms of the researchable, and you get nonsense all along the way.
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That's because it is nonsense.
 
Since apparently there's no definable difference between the researchable and non-researchable, it seems we can ignore the distinction altogether anyway...
 
doronshadmi said:
No, it is no more than your current inability to distinguish between the analogy and the abstract notion that stands in the basis of it.
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Not my fault that you make bad analogies.

It is a simple fact that both X and the negation of X must simultaneously be related with each other in order to get a researchable framework.
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What is that supposed to mean? The negation of X is the negation of X. X and its negation have to be related because, well, the negation of X is the negation of X.

Please read this very carefully:

I showed how 2-valued logic cannot be found (T or F are totally isolated) without the fundamental state of unity that enables them to be interact with each other without immediately eliminating each other.
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So: Two-valued logic has two values. Another astounding breakthrough!

They are not eliminating each other because Symmetry at its self state is both the eliminated state (total unity) and the coordinator (the common basis) that enables to save their self identities without contradicting each other.
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They are not "eliminating each other" because that concept has no meaning.

It is done by a superposition of identities that avoids the immediate elimination of T and F when interact with each other.
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No.

The superposition is the signature of the Symmetrical side (the unified side) of this researchable framework.
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No.

The collection of distinct things (and in this case, T\F collection) is the signature of the Asymmetrical side (the isolated side) of this researchable framework.
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No.

Furthermore, our own cognition is the result of Symmetry\Asymmetry sides, which complement each other into a one consistent framework that can be changed by paradigm-shifts, because no reachable framework can fully express to complements of Symmetry at its self state.
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No.

As a result any researchable framework is permanently open and nothing is complete if it is researchable.
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No.

At the moment that this simple notion is understood, we immediately understand that the whole idea of actual infinity as a researchable framework does not hold.
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No. There is a whole class of mathematics that deals with transfinite numbers. In fact, in a very significant sense, you've just thrown out all of calculus. Much as high-school students around the world would rejoice at this, your statement is simply not true.
 
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doronshadmi said:
The reseachable is not defined by the non-researchable. The non-researchable is simply the simplest point of view that enables us to understand infinitely many never ending finer levels of the researchable (that can be abstract or not, it does not matter).

The non-researchable cannot be defined.
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If it can't be defined then it is meaningless. So you've found yet another way to fail.

The reseachable is the result of the complementation between total symmetry (which is undafined and non-reseachable) and total isolation (which is undafined and non-reseachable).
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You provided a definition for "symmetry" before. Now you tell us it can't be defined. Whatever, dude.

By "undefined" I mean that any definition is more complex than Symmetry or Asymmetry at their self states.
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So you've redefined the meaning of the term "undefined", and by extension, "defined". Cute. Cute, but meaningless.
 
PixyMisa said:
So you've redefined the meaning of the term "undefined", and by extension, "defined". Cute. Cute, but meaningless.
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You obviously missed out on the define\undefined complementation. The complementation creates the redefined XOR researchable realm coupled to an incomplete superposition of valence sufficiency.

Once everyone completes their worksheets, we'll have recess then nap time.
 
Let us do it this way:

The researchable holds only if the conclusion and the premise are not the same.

In other words, there must be at least two states that can be associated with each.

At Total Symmetry self state no two things can be found. In other words, the premise and conclusion are the same.

For example: given any domain, Total Symmetry cannot be researched because no domain exists at Total Symmetry self state (Total Symmetry is The Domainless itself).

At total Asymmetry self state no two things can be found. In other words, the premise and conclusion are the same.

For example: given any domain, Total Asymmetry cannot be researched because the domain is Asymmetry itself (Total Asymmetry is The Domain itself).

The researchable holds as a result of Domainless\Domain complementation.

The complement result is weaker than The Domainless at its self state and stronger than The Domain at its self state.

There is no doubt that a Set is a researchable thing.

In that case a set is weaker than The Domainless at its sealf state and stronger than The Domain at its self state. In other words, a set is not a total thing and therefore incomplete.

An incomplete building-block cannot define a complete system.

The researchable is possible because it is incomplete (it is not Total).
 
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PixMisa said:
If it can't be defined then it is meaningless.
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PixMisa,

You are using "Meaningless" all along the way.

A Formal framework has a meaning as long as it is a meaningless game.

So what do you mean by "Meaningless"?
 
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doronshadmi said:
PixMisa,

You are using "Meaningless" all along the way.
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You finally noticed.

A Formal framework has a meaning as long as it is a meaningless game.
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No.

So what do you mean by "Meaningless"?
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If you use a term without defining it, it renders the expression containing that term meaningless.

If you say that the term cannot be defined, the term is by definition meaningless.

If you write a sentence that cannot be parsed grammatically, that is also meaningless.

You have persisted in all three of these actions throughout this thread.
 
doronshadmi said:
Let us do it this way:

The researchable holds only if the conclusion and the premise are not the same.
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That's a good place to start.

In other words, there must be at least two states that can be associated with each.
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Sure.

At Total Symmetry self state no two things can be found. In other words, the premise and conclusion are the same.
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That has nothing to do with totality, symmetry, self, or state, so I consider your choice of nomenclature to be poor.

For example: given any domain, Total Symmetry cannot be researched because no domain exists at Total Symmetry self state (Total Symmetry is The Domainless itself).
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Sorry, that makes no sense.

At total Asymmetry self state no two things can be found. In other words, the premise and conclusion are the same.
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Symmetry=Asymmetry. Okay...

For example: given any domain, Total Asymmetry cannot be researched because the domain is Asymmetry itself (Total Asymmetry is The Domain itself).
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That makes no sense.

The researchable holds as a result of Domainless\Domain complementation.
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But you just said that they're the same.

The complement result is weaker than The Domainless at its self state and stronger than The Domain at its self state.
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Nope.

There is no doubt that a Set is a researchable thing.
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If you say so.

In that case a set is weaker than The Domainless at its sealf state and stronger than The Domain at its self state. In other words, a set is not a total thing and therefore incomplete.
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Total drivel. You can't distinguish your two thingies anyway.

An incomplete building-block cannot define a complete system.
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You can't have a complete, consistent system.

The researchable is possible because it is incomplete (it is not Total).
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Meaningless.
 
PixyMisa said:
Total drivel. You can't distinguish your two thingies anyway
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Yes, I can.

Total Symmetry is The Domainless.

Total Asymmetry is The Domain.

The reseachable is weaker than Total Symmetry and stronger than Total Asymmetry.

Furthermore.

The Domainless cannot be but the relater of Domainless\Domain complementation.

The Domain cannot be but the related of Domainless\Domain complementation.

As a result no relater is related and vice versa.

This simple notion can easily addressed as 2-valued logic, where the relater is the Symmetrical side of 2-valued logic (TT or FF) and the related is the asymmetrical side of 2-valued logic (TF or FT).

Symmetry\Asymmetry complementation is the universal principle of any given Logic.

PixyMisa said:
That has nothing to do with totality
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Ok, so what is totality? (aftar all you wrote above "total drivel")
 
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doronshadmi said:
Yes, I can.

Total Symmetry is The Domainless.

Total Asymmetry is The Domain.

The reseachable is weaker than Total Symmetry and stronger than Total Asymmetry.

Furthermore.

The Domainless cannot be but the relater of Domainless\Domain complementation.

The Domain cannot be but the related of Domainless\Domain complementation.

As a result no relater is related and vice versa.

This simple notion can easily addressed as 2-valued logic, where the relater is the Symmetrical side of 2-valued logic (TT or FF) and the related is the asymmetrical side of 2-valued logic (TF or FT).
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Yeah, whatever. But how do you actually tell them apart? You say they can magically do all these things, but you also say that they have identical properties. That doesn't work too well.

Ok, so what is totality? (aftar all you wrote above "total drivel")
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Completeness.
 
PixyMisa said:
Yeah, whatever. But how do you actually tell them apart? You say they can magically do all these things, but you also say that they have identical properties. That doesn't work too well.
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No.

There is no magic here.

Total Domainless and Total Domain are not reseachable at their self states.

If complement each other, then the result is weaker than Total Domainless and stronger than Total domain.

In other words no totality is found at complementation state, or in other words the complementation is not complete (it is not total) and therefore it is reseachable.

Only researchable things can be defined.

Some analogy:

Any sound is more complex than the simplicity of total silence.

By using this analogy, any definition is more complex than totality itself.
 
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jsfisher said:
I'm still waiting for you evidence supporting this claim. Got any?
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Still waiting for your evidence that a line is not defined as a collection by Standard Math (and you have to do it without using a function, because a function is non-local, otherwise no two things can be related with each other without its non-locality).
 
doronshadmi said:
Still waiting for your evidence that a line is not defined as a collection by Standard Math (and you have to do it without using a function, because a function is non-local, otherwise no two things can be related with each other without its non-locality).
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You like David Hilbert, right? Why don't we see how he defines lines:

books


There you go - they are not defined in terms of collections of points. In fact they are not defined at all (there) - they are axiomatic.
 
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As clever and as devastating as Zeno of Elea.
The Arabian Algebraists, Descartes, Newton, Einstein, Cantor, Godel, Bohr, et al, hang their heads in shame!
At one sweep Western science crumbles!

A tragedy in one act.
 
doronshadmi said:
No.

There is no magic here.

Total Domainless and Total Domain are not reseachable at their self states.

If complement each other, then the result is weaker than Total Domainless and stronger than Total domain.

In other words no totality is found at complementation state, or in other words the complementation is not complete (it is not total) and therefore it is reseachable.

Only researchable things can be defined.
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Another pile of drivel.

You said:
doronshadmi said:
At Total Symmetry self state no two things can be found. In other words, the premise and conclusion are the same.

At total Asymmetry self state no two things can be found. In other words, the premise and conclusion are the same.
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Those definitions are identical. How do you get from there to, well, anywhere?

Some analogy:

Any sound is more complex than the simplicity of total silence.

By using this analogy, any definition is more complex than totality itself.
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Another analogy:

Apropos cabbages are more insolent than nativity bees.

By using this analogy, you're talking a load of old cobblers.
 
sol invictus said:
You like David Hilbert, right? Why don't we see how he defines lines:

[qimg]http://books.google.com/books?id=Ji04AAAAMAAJ&pg=PA3&img=1&zoom=3&hl=en&sig=O-SwMHW296hU5znCUwP-LktN8A0&ci=112,487,689,830&edge=1[/qimg]

There you go - they are not defined in terms of collections of points. In fact they are not defined at all (there) - they are axiomatic.
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PixMisa will say that anything that is undefined is meaningless.

Do you agree with him?
 
Apathia said:
As clever and as devastating as Zeno of Elea.
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No researchable thing is complete (is total).

We are very lucky that this is the case, because there is no limit to any development at the non-arbitrary game of evolution.
 
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doronshadmi said:
Still waiting for your evidence that a line is not defined as a collection by Standard Math (and you have to do it without using a function, because a function is non-local, otherwise no two things can be related with each other without its non-locality).
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I didn't make the claim. You did, so the obligation falls to you to support your statement.

But you can't, can you? So it is with just about all of your claims. You cannot support them. Instead, you wave your hands and stamp your feet, then accuse us of being the problem.

You think and act like a 5 year-old, and chastise us for not doing the same. Did you know that 5 year-olds cannot grasp the concept of number? Sure, they can cope with 3 oranges or 3 pencils, but not with just 3. That's too abstract. Then again, that's where evolution (which you cherish but understand not) has brought us: Cognitive abilities develop in children as they mature; there is no "inherited knowledge", quite the opposite, in fact.

Many 5 year-olds have imaginary friends, too. doronshadmi, do you have imaginary friends?
 
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doronshadmi said:
PixMisa will say that anything that is undefined is meaningless.

Do you agree with him?
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I'd prefer to let her/him speak for her/himself (English really has a major deficiency).

Language enables communication, and in order to communicate, one must share a common vocabulary. You insist on using standard terms in non-standard ways, and at the same time you refuse to give definitions of your usage.

If you talk to someone using language they cannot understand, you're the fool.
 
doronshadmi said:
PixMisa will say that anything that is undefined is meaningless.

Do you agree with him?
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You missed the whole point. Hilbert was saying (correctly) that what points, lines, and planes are is inferred from the axioms. Geometry, after all, is an axiomatic system (and not subject to Gödel's incompleteness theorems, by the way).

Euclid did offer definitions for points and lines, but in and of themselves they are not all that helpful. It is from the axioms of geometry that the definitions take on substance.
 
doronshadmi said:
No researchable thing is complete (is total).

We are very lucky that this is the case, because there is no limit to any development at the non-arbitrary game of evolution.
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And we are lucky that mathematics is able to transcend the restrictions you slap on it.
 
jsfisher said:
Did you know that 5 year-olds cannot grasp the concept of number?
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By standard mathematics you have Natural Numbers, Rational Numbers, Irrational numbers, etc... , but there is no general definition to Number.

Children may not understand the sophisticated manipulations that adults can do with numbers, but they have a simple (and simple is not trivial) point of view of the concepts that can lead to the general definition of Number, as I did in my theory.

A number is the simplest building-block of the researchable.

Your sophisticated manipulations of that building-block, do not allow you to get this beautiful and straightforward simplicity, because your ability to get simple notions was lost over the years of your mathematical sophisticated training.

So is the case of a line or a point, they are undefined terms, and understood according different context dependent axiomatic systems that there is no common basis between them accept that they are using the words "Line" and/or "Point".

In other words, there is no generalization of these concepts according to the context dependent paradigm.

Since most of the axiomatic systems are using sets, then the concept of Line is not an
atom, but it is a thing that is defined by other building-blocks (you can call them points or not, but it does not change the fact that a line is not an atom by standard Math.)


Professional mathematicians do not afraid to use Lines and points as related object (only people that have troubles with their abstract abilities avoid it).

For example:

1. Why set theory?

Why do we do set theory in the first place? The most immediately familiar objects of mathematics which might seem to be sets are geometric figures: but the view that these are best understood as sets of points is a modern view. Classical Greeks, while certainly aware of the formal possibility of viewing geometric figures as sets of points, rejected this view because of their insistence on rejecting the actual infinite. Even an early modern thinker like Spinoza could comment that it is obvious that a line is not a collection of points (whereas for us it may hard to see what else it could be) (Ethics, I.15, scholium IV, 96).

http://www.seop.leeds.ac.uk/entries/settheory-alternative/

Prof. Randall Holmes (http://math.boisestate.edu/~holmes/ )


Hilbert: I.1: Two distinct points A and B always completely determine a straight line a. ...
( http://en.wikipedia.org/wiki/Hilbert's_axioms )

Well, Hilbert is wrong, because a non-local element like a line cannot be completely determined by local elements like points.

I explicitly show it by using Symmetry as the basis of non-locality and Asymmetry as the basis of locality.

Furthermore, I explicitly show that Symmetry/ Asymmetry is the basis of Logic itself.

It is rigorously written in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .
 
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doronshadmi said:
On the contrary.

The completeness of a researchable thing is exactly its restriction.
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You are missing the irony that your "Incompleteness" is denying Mathematics the ability to work with Infinity as a real concept. You lose the dynamic that is at the base of Calculus, Transfinite Numbers, Godel's Incompleteness Theorm, and the math modern physics depends upon.

Think again. You are undermining what you really want to achieve.
 
doronshadmi said:
A number is the simplest building-block of the researchable.
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So, we can just ignore geometry (in its several forms), topology, set theory, logic and several other branches of Mathematics for their lack of numbers.

Curious, isn't it though, that this alleged most fundamental building block, the number, is not that basis of your pet theory.

Your sophisticated manipulations of that building-block, do not allow you to get this beautiful and straightforward simplicity, because your ability to get simple notions was lost over the years of your mathematical sophisticated training.
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I don't believe in Santa Claus and the Tooth Fairy any more either.

So is the case of a line or a point, they are undefined terms, and understood according different context dependent axiomatic systems that there is no common basis between them accept that they are using the words "Line" and/or "Point".
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Ah! So you have changed your position on the definition of line?

Since most of the axiomatic systems are using sets, then the concept of Line is not an
atom, but it is a thing that is defined by other building-blocks (you can call them points or not, but it does not change the fact that a line is not an atom by standard Math.)
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You've gone full circle in a single post. How every efficient of you. You are back to your flawed belief about the definition of a line. Got any evidence to support that?

...
Hilbert: I.1: Two distinct points A and B always completely determine a straight line a. ...
( http://en.wikipedia.org/wiki/Hilbert's_axioms )

Well, Hilbert is wrong, because a non-local element like a line cannot be completely determined by local elements like points.
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Poor Hilbert. Undone by a 5 year-old.

I explicitly show it by using Symmetry as the basis of non-locality and Asymmetry as the basis of locality.
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No, all you have done is constructed your own person vocabulary and used it to construct gibberish.

Furthermore, I explicitly show that Symmetry/ Asymmetry is the basis of Logic itself.
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Ditto.

It is rigorously written in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .
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Ditto.
 
jsfisher said:
So, we can just ignore geometry (in its several forms)
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On the contrary.

You have to re-examine the foundations of the mathematical science in order to define something that is even simpler than Symmetry\Asymmetry complementation.

There is no doubt that the mathematical science of the past 2500 years is based on undefined fundamental concepts like Line, Point, Number, Non-Finite etc.

The context dependent paradigm is the result these undefined fundamental concepts.

At the moment that these fundamental concepts are defined, then and only then the mathematical science is changed by a paradigm shift and becomes the organic framework that each part of it feeds and be fed by the rest of the parts as a one comprehensive method, which is developed according to the laws of evolution.

This paradigm-shift cannot be done if the difference between the researchable and the non-researchable is not understood, and this understanding cannot be achieved unless the mind is not aware of itself as an inseparable factor of this understanding.


When the consciousness is awaken to its own abilities the Phoenix effect is inevitable because of the consciousness' inventible power.
 
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doronshadmi said:
On the contrary....
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You don't even understand your own posts, do you.

You said, "a number is the simplest building-block of the researchable." I commented on that because (1) the number is not the basis for all symmetry\asymmetry complementation gibberish you spew, and (2) so many things in Mathematics have no basis in numbers.

Now, you contradict yourself (again).
 
Apathia said:
You are missing the irony that your "Incompleteness" is denying Mathematics the ability to work with Infinity as a real concept.
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Not at all.

The real concept of infinity (what is called actual infinity) is total simplicity.

This simplicity is the common ground of anything that is not total simplicity.

As a result infinitely many things are able to be developed as organs of a one comprehensive realm, that no part of it is totally complete and therefore change and can be changed forever according to the non-arbitrary laws of Evolution.

The realm of the researchable is the realm where the total and the unchanged expresses itself by infinitely many creative and unexpected ways that must be incomplete in order to be expressed.
 
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jsfisher said:
You don't even understand your own posts, do you.

You said, "a number is the simplest building-block of the researchable." I commented on that because (1) the number is not the basis for all symmetry\asymmetry complementation gibberish you spew, and (2) so many things in Mathematics have no basis in numbers.

Now, you contradict yourself (again).
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My definition of Number is not what you (by using the current paradigm) call a number.

This building-block is called the Organic Natural Number, and it is the the simplest building-block of Symmetry\Asymmetry complementation (the reseachable).

You still try to understand a paradigm-shift in terms of the old paradigm, and you fail.
 
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doronshadmi said:
My definition of Number is not what you (by using the current paradigm) call a number.
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This surprises no one. We've come to expect that what you mean has nothing to do with what you actually say. Having your own private vocabulary is a major part of all that.

This building-block is called the Organic Natural Number, and it is the the simplest building-block of Symmetry\Asymmetry complementation (the reseachable).
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You are still trying to avoid the obvious. So, instead you contradict yourself. Your framework doesn't use the number as a fundamental building-block; it is a result (that follows after pages of gibberish). Moreover, the number (be it organic or inorganic) is not the basis of many, many branches of Mathematics.

You still try to understand a paradigm-shift in terms of the old paradigm, and you fail.
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Yeah, all that insistence we have for words having meaning and standard terminology...that's just so third grade!
 
jsfisher said:
Your framework doesn't use the number as a fundamental building-block; it is a result
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Ok. English problems.

Let's do it like this:

You have a reseachable realm.

The simplest thing that is also reseachable (and I call it the building-block of the researchable, which is not the non-reseachable) is defined by the Organic Naturel Number.

You may say that I said that the researchable cannot be researched by the researchable.

Well ONN is not used to reserach the researchable, but it is the researchable at it most basic form.
jsfisher said:
the number (be it organic or inorganic) is not the basis of many, many branches of Mathematics.
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There is no such general thing as number in standard Math, so please save your words.
 
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doronshadmi said:
You have a reseachable realm.

The simplest thing that is also reseachable (and I call it the building-block of the researchable, which is not the non-reseachable) is defined by the Organic Naturel Number.
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Yes, that is just about what you said before. You are still contradicting yourself. By the way, you presuppose the existence of both (standard) numbers and arithmetic in your ONN treatise. That makes your organic numbers more like compost than anything more substantive.

You may say that I said that the researchable cannot be researched by the researchable.
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I am reasonably certain I would never say such a thing.

Well ONN is not used to reserach the researchable, but it is the researchable at it most basic form.
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Good to know.

There is no such general thing as number in standard Math, so please save your words.
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Yet another absurdity for the list!
 
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doronshadmi said:
Not at all.

The real concept of infinity (what is called actual infinity) is total simplicity.

This simplicity is the common ground of anything that is not total simplicity.

As a result infinitely many things are able to be developed as organs of a one comprehensive realm, that no part of it is totally complete and therefore change and can be changed forever according to the non-arbitrary laws of Evolution.

The realm of the researchable is the realm where the total and the unchanged expresses itself by infinitely many creative and unexpected ways that must be incomplete in order to be expressed.
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I think I get what you are aiming at here, but your arrow is unable to reach its mark.
 
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