A hidden assumption

[Apathia]

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.

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.

 

[PixyMisa]

Very simple. Symmetry itself it total unity. Asymmetry itself is total isolation.

No one of them is defined by the other.

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.

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.

That's because it is nonsense.

 

[ArmillarySphere]

Since apparently there's no definable difference between the researchable and non-researchable, it seems we can ignore the distinction altogether anyway...

 

[PixyMisa]

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.

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.

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.

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.

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.

No.

The superposition is the signature of the Symmetrical side (the unified side) of this researchable framework.

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.

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.

No.

As a result any researchable framework is permanently open and nothing is complete if it is researchable.

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.

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.

 

[PixyMisa]

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.

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).

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.

So you've redefined the meaning of the term "undefined", and by extension, "defined". Cute. Cute, but meaningless.

 

[jsfisher]

So you've redefined the meaning of the term "undefined", and by extension, "defined". Cute. Cute, but meaningless.

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.

 

[doronshadmi]

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).

 

[doronshadmi]

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

Not at all, no reseachable framework is complete (is both researchable AND complete) as explained in http://www.internationalskeptics.com/forums/showpost.php?p=3624115&postcount=647 .

 

[doronshadmi]

If it can't be defined then it is meaningless.

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"?

 

[PixyMisa]

PixMisa,

You are using "Meaningless" all along the way.

You finally noticed.

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

No.

So what do you mean by "Meaningless"?

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.

 

[PixyMisa]

Let us do it this way:

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

That's a good place to start.

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

Sure.

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

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).

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.

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).

That makes no sense.

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

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.

Nope.

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

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.

Total drivel. You can't distinguish your two thingies anyway.

An incomplete building-block cannot define a complete system.

You can't have a complete, consistent system.

The researchable is possible because it is incomplete (it is not Total).

Meaningless.

 

[doronshadmi]

Total drivel. You can't distinguish your two thingies anyway

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.

That has nothing to do with totality

Ok, so what is totality? (aftar all you wrote above "total drivel")

 

[PixyMisa]

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).

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")

Completeness.

 

[jsfisher]

A line is defined in terms of points.

I'm still waiting for you evidence supporting this claim. Got any?

 

[doronshadmi]

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.

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.

 

[doronshadmi]

I'm still waiting for you evidence supporting this claim. Got any?

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).

 

[sol invictus]

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).

You like David Hilbert, right? Why don't we see how he defines lines:

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.

 

[Apathia]

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.

 

[PixyMisa]

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.

Another pile of drivel.

You 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.

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.

Another analogy:

Apropos cabbages are more insolent than nativity bees.

By using this analogy, you're talking a load of old cobblers.

 

[doronshadmi]

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.

PixMisa will say that anything that is undefined is meaningless.

Do you agree with him?