A hidden assumption

[jsfisher]

No, you contradict yourself by trying to force completeness on the incomplete.

You are not aware of it, because you are not aware of the researchable\non-researchable aspects of your consciousness.

Please point out contradictory statements I have made.

Before you say anything about ONNs you firsrt have to show that you understand ONNs.

Nonsense. You used natural numbers and arithmetic throughout your papers on ONNs. That is a fact. Whether I understand ONNs as you do or see them for the tripe that they really are is irrelevant.

You used natural numbers and arithmetic as a "hidden assumption". Your ONNs fail as fundamental.

 

[jsfisher]

And I shudder to think what tortured definition you are using for "locality".

You should shudder equally over "non-locality".

Keep in mind that in doron's world, non-X and X do not need to be complementary concepts in the normal sense of things. Understanding doron's usage of "locality" is unlikely to help in understanding "non-locality".

 

[doronshadmi]

Curiously enough, this does not appear to number among the Peano axioms.

And I shudder to think what tortured definition you are using for "locality".

The concept of Successor does not hold without Non-locality\Locality complementation.

 

[doronshadmi]

Please point out contradictory statements I have made.

X is both researchable AND complete.

Nonsense. You used natural numbers and arithmetic throughout your papers on ONNs. That is a fact. Whether I understand ONNs as you do or see them for the tripe that they really are is irrelevant.

You used natural numbers and arithmetic as a "hidden assumption". Your ONNs fail as fundamental.

No, I use arithmetic, but before that I define the basic term that enables it.

 

[doronshadmi]

Non-local: given any domain it is both belongs and does not belong to it.

Local: given any domain it belongs xor does not belong to it.

 

[jsfisher]

Please point out contradictory statements I have made.

X is both researchable AND complete.

I never said that. Try again. Please point out contradictory statements that I have made.

Nonsense. You used natural numbers and arithmetic throughout your papers on ONNs. That is a fact. Whether I understand ONNs as you do or see them for the tripe that they really are is irrelevant.

You used natural numbers and arithmetic as a "hidden assumption". Your ONNs fail as fundamental.

No, I use arithmetic, but before that I define the basic term that enables it.

Where did you do that? And what "basic term" enables all of arithmetic?

Be that as it may, though, that still leaves you with the consequence that your precious organic numbers are built on something else. Arithmetic, then, must be more basic than organic numbers, and therefore our organic numbers can be no more fundamental than arithmetic.

 

[doronshadmi]

I have an Idea of how we may communicate with each other.

My basic idea about mathematical science is this:

The simplest state is the best point of view for non-trivial formal premises and their results.

I ask my self: what is the simplest?

My answer is: Simplicity itself cannot be formally defined because any formal definition is more complex than simplicity itself.

My best analogy for this is: any sound (definition) is noisier (complex) than silence (simplicity) itself.

If listen (observed) from silence (simplicity) itself, we are enabling to hear (understand) any given sound (definition) no matter how noisy (complex) it is.

Furthermore, silence (simplicity) itself is the natural common (invariant) state of any possible sound (definition) and any relation among sounds (definitions).

The undefined cannot be researched, but it is the natural basis of the researchable.

I ask myself: what is non-researchable (naturally undefined)?

My answer: Total domainless, Total domain.

Total domainless is too weak in order to be defined because any definition is actually some categorical limitation.

Total domain is too strong in order to be defined because any definition is less categorical than total limitation.

So the researchable must be stronger than Total domainless and weaker than Total domain (in my previous posts I said that Total domainless is the strongest, and Total domain is the weakest, because I did not look at them from the point of view of formal definition (which is a researchable thing), but from the point of view of Total Symmetry and Total Asymmetry (total isolation, where no two things can be simultaneously associated with each other). But it does not matter, because the researchable is the result Strongest\Weakest complementation, which is weaker than the strongest and stronger then the weakest.

In other words, no researchable thing is total (complete).

Since formal language is a researchable framework, no defined premise or its deduced results are total (complete).

For example: Since cardinality is researchable, it cannot be also complete.

In other words, the Cantorean transfinite system cannot be both researchable and complete.

 

[jsfisher]

I have an Idea of how we may communicate with each other.

So, you accuse me of making contradictory statements, but when challenged for evidence, you instead change the subject.

Either support your accusation, or retract it.

My basic idea about mathematical science is this:

The simplest state is the best point of view for non-trivial formal premises and their results.

I ask my self: what is the simplest?

My answer is: Simplicity itself cannot be formally defined because any formal definition is more complex than simplicity itself.

Your conclusion (simplicity cannot be defined) does not follow from the premise (the definition would be more complex). Your logic is faulty. So, any further decision with this as a starting point is also flawed.

...faulty reasoning...

 

[nathan]

No researchable thing is complete (is total).

The completeness of a researchable thing is exactly its restriction.

Please clarify which of these two conflicting statements you are actually propounding.

 

[ArmillarySphere]

Apparently, in his post-modern mathematics, completeness is not a binary trait, but a sliding scale - some things are a little complete, other are a bit more...

I suppose by the same thinking, some functions are somewhat monotonous. Such as a sine.

 

[Apathia]

I have an Idea of how we may communicate with each other.

My basic idea about mathematical science is this:

The simplest state is the best point of view for non-trivial formal premises and their results.

I ask my self: what is the simplest?

My answer is: Simplicity itself cannot be formally defined because any formal definition is more complex than simplicity itself.

My best analogy for this is: any sound (definition) is noisier (complex) than silence (simplicity) itself.

If listen (observed) from silence (simplicity) itself, we are enabling to hear (understand) any given sound (definition) no matter how noisy (complex) it is.

Furthermore, silence (simplicity) itself is the natural common (invariant) state of any possible sound (definition) and any relation among sounds (definitions).

The undefined cannot be researched, but it is the natural basis of the researchable.

I ask myself: what is non-researchable (naturally undefined)?

My answer: Total domainless, Total domain.

Total domainless is too weak in order to be defined because any definition is actually some categorical limitation.

Total domain is too strong in order to be defined because any definition is less categorical than total limitation.

So the researchable must be stronger than Total domainless and weaker than Total domain (in my previous posts I said that Total domainless is the strongest, and Total domain is the weakest, because I did not look at them from the point of view of formal definition (which is a researchable thing), but from the point of view of Total Symmetry and Total Asymmetry (total isolation, where no two things can be simultaneously associated with each other). But it does not matter, because the researchable is the result Strongest\Weakest complementation, which is weaker than the strongest and stronger then the weakest.

In other words, no researchable thing is total (complete).

Since formal language is a researchable framework, no defined premise or its deduced results are total (complete).

For example: Since cardinality is researchable, it cannot be also complete.

In other words, the Cantorean transfinite system cannot be both researchable and complete.

Thanks for this effort Doron.

I have some questions.
Are you still claiming that from this perspective ".9999999...."
(that's a nonterminating sequence of nines after the decimal place)
Does not or should not be regarded as equal to 1?

Does it follow from this assertion that cardinality cannot be regarded as complete that Cantor's transfinite numbers have no justification?

How does this relate to Calculus?
Tensor Calculus and the mathematics of modern cosmology?

Mordern mathematics manipulates infinities (researchable or not).
If your system disallows this dymanmic, what does it offer as a real advancement in its place?

 

[doronshadmi]

The simplest state is the best point of view for non-trivial formal premises and their results.

Mordern mathematics manipulates infinities (researchable or not).

The non-researchable is invariant (cannot be manipulated).

But it is the best point of view for any manipulation, exactly as silence in the best point of view for any sound.

If you get this simple beauty, then you understand that my theory is more dynamic than what is called Modern Mathematics.

What is called dynamic does not hold exactly because 0.999...[base 10] is considered as a representation of value 1.

By my theory 0.999...[base 10] is a non-local value < local value 1, by 0.000...1[base 10] non-local value.

 

[doronshadmi]

Your conclusion (simplicity cannot be defined) does not follow from the premise (the definition would be more complex). Your logic is faulty. So, any further decision with this as a starting point is also flawed.

You have to look at it like this.

Simplicity itself (total silence) cannot be defined (be sounded) exactly as any sound (definition) is more noisy (complex) than total silence (Simplicity itself).

This notion is also the basis of Logic itself, and there is no premise and conclusion here, but Total\Non-total complementation, which is researchable.

 

[doronshadmi]

No researchable thing is complete (is total).

The completeness of a researchable thing is exactly its restriction.

Please clarify which of these two conflicting statements you are actually propounding.

There is no conflict, since a researchable think is incomplete, otherwise it is not researchable.

Please read http://www.internationalskeptics.com/forums/showpost.php?p=3628609&postcount=707 for better understanding.

 

[doronshadmi]

Apparently, in his post-modern mathematics, completeness is not a binary trait, but a sliding scale - some things are a little complete, other are a bit more...

I suppose by the same thinking, some functions are somewhat monotonous. Such as a sine.

No, what you call sliding scale is incomplete (and researchable).

Completeness is total (no sliding scale holds) and non-researchabe.

 

[jsfisher]

You have to look at it like this.

Simplicity itself (total silence) cannot be defined (be sounded) exactly as any sound (definition) is more noisy (complex) than total silence (Simplicity itself).

It is more defective than your previous version, if that be possible.

Your conclusion (simplicity cannot be defined) does not follow from the premise (sound is more noisy than silence). Your logic is faulty. So, any further decision with this as a starting point is also flawed.

 

[doronshadmi]

It is more defective than your previous version, if that be possible.

Your conclusion (simplicity cannot be defined) does not follow from the premise (sound is more noisy than silence). Your logic is faulty. So, any further decision with this as a starting point is also flawed.

You did not get it.

Any definition cannot be Total in order to be defined.

Silence (simplicity) is (I did not write anything after the word "is" because no definition (sound) is simplicity (Silence) itself).

Sounds (definitions) has infinitely many states of noise (complexity) that no one of them is silence (simplicity).

Premise and conclusion are also definitions (complex things), so they are not simplicity itself (there is no duality of any kind at simplicity itself).


Some analogy:

Question: What is silence?

1. Answer: Definition: "No-sound at all"

2. No answer is given (which is the right answer, because any sound (definition) is not silence itself).

I use "sound" as a general description of any thought (vocally expressed or not).

No thought at all is the simplest state of your consciousness, which is the natural basis of every thought or any relation between thoughts.

It is non-local by nature and it is not limited by any particular thought (where any thought is local (limited) by nature).

The physical definition of Simplicity at its self state is known as "Vacuum", which is understood as the source of any energy\matter.

 

[Complexity]

Stark raving mad.

 

[jsfisher]

You did not get it.

I very much did get it. Your logic lacks...well...logic.

Any definition cannot be Total in order to be defined.

Gibberish.

Silence (simplicity) is (I did not write anything after the word "is" because no definition (sound) is simplicity (Silence) itself).

Using the word, "is", doesn't make it so. Silence and simplicity are not synonyms.

Sounds (definitions) has infinitely many states of noise (complexity) that no one of them is silence (simplicity).

Nor does your use of parentheses make something a fact.

Premise and conclusion are also definitions (complex things), so they are not simplicity itself (there is no duality of any kind at simplicity itself).

More gibberish.

Some analogy:

Why? You have provided ample evidence you are not very good with analogies.

Question: What is silence?

1. Answer: Definition: "No-sound at all"

2. No answer is given (which is the right answer, because any sound (definition) is not silence itself).

...and now you have provided more evidence.

I use "sound" as a general description of any thought (vocally expressed or not).

No thought at all is the simplest state of your consciousness, which is the natural basis of every thought or any relation between thoughts.

It is non-local by nature and it is not limited by any particular thought (where any thought is local (limited) by nature).

The physical definition of Simplicity at its self state is known as "Vacuum", which is understood as the source of any energy\matter.

Back to gibberish.


By the way, none of this provides any evidence I made contradictory statements. Got any, or was your accusation just a big fat lie?

 

[doronshadmi]

I very much did get it. Your logic lacks...well...logic.

Dear jsfisher,

There is no use to explain color to a blind man.

It was nice talking to you. I have learned a lot.

Have a nice life.