A hidden assumption

I have revised my list.

Absurd things Doronshadmi believes:

  1. A set is equal to the union of its members.
  2. 2 is not part of { 2,3,4 } much like a severed finger is not part of your body.
  3. 2 may not be a member of { 2 }.
  4. A if B, A only if B, and A if and only if B are all equivalent
    constructs.
  5. Geometry is a very weak branch of Mathematics.
  6. There is no such thing as a number in standard Mathematics.
 
jsfisher said:
I have revised my list.

Absurd things Doronshadmi believes:

  1. A set is equal to the union of its members.
  2. 2 is not part of { 2,3,4 } much like a severed finger is not part of your body.
  3. 2 may not be a member of { 2 }.
  4. A if B, A only if B, and A if and only if B are all equivalent
    constructs.
  5. Geometry is a very weak branch of Mathematics.
  6. There is no such thing as a number in standard Mathematics.
Click to expand...

I invite you to read some of his pdfs and contributions to other forums.
You will find a number of other even more interesting denials and gaffs.
Here's an entertaining place to start:
http://www.physicsforums.com/showthread.php?t=30569
Note that he posts as "Lama" here.

Or just keep engaging him in this thread. Before long your list will contain some really outlandish things. It just gets clearer and clearer why professional mathematicians and math instructors don't give him the time of day.
 
jsfisher said:
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.

I am reasonably certain I would never say such a thing.

Good to know.

Yet another absurdity for the list!
Click to expand...
Know it is clear that you do not read my posts in order to understand them.

All you care is to play your "king of the hill" game.

You have Natural numbers, Rational numbers, Irrational numbers, ... etc., but not a general definition of it.


There is no general definition of the concept of number in traditional Math.
 
Apathia said:
I invite you to read some of his pdfs and contributions to other forums.
You will find a number of other even more interesting denials and gaffs.
Here's an entertaining place to start:
http://www.physicsforums.com/showthread.php?t=30569
Note that he posts as "Lama" here.

Or just keep engaging him in this thread. Before long your list will contain some really outlandish things. It just gets clearer and clearer why professional mathematicians and math instructors don't give him the time of day.
Click to expand...

Old material. Not relevant anymore.

Remember. we are talking about evolution of ideas.
 
doronshadmi said:
Know it is clear that you do not read my posts in order to understand them.

All you care is to play your "king of the hill" game.

You have Natural numbers, Rational numbers, Irrational numbers, ... etc., but not a general definition of it.
Click to expand...
You mean you don't know the general definition.

Natural numbers are subset of rational numbers.
Both rational and irrational numbers are subsets of real numbers.
Real numbers are a subset of complex numbers, where the imaginary part is zero.
And complex numbers are a subset of hypercomplex numbers, such as quaternions. Hypercomplex numbers can be viewed as being vectors of reals, so the generalisation is straightforward.

There is no general definition of the concept of number in traditional Math.
Click to expand...
Wrong.
 
Apathia said:
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.
Click to expand...
If you can't prove Godel's Incompleteness Theorem, that means that you've thrown out arithmetic as well.

Not much of an advance, I'd say.

Think again. You are undermining what you really want to achieve.
Click to expand...
He seems unconcerned about this flaw.
 
doronshadmi said:
Old material. Not relevant anymore.

Remember. we are talking about evolution of ideas.
Click to expand...

There doesn't appear to have been much substantive change in your views over the last four or five years. Your mangling of mathematical infinity remains unchanged.
We can only hope that your current material will soon be extinct.
 
doronshadmi said:
Know it is clear that you do not read my posts in order to understand them.

All you care is to play your "king of the hill" game.
Click to expand...

Call it what you will, but (a) you have been contradicting yourself, and (b) in your ONN descriptions, you do in fact assume the existing of both natural numbers and arithmetic.

Your so called organic natural numbers cannot stand on their own, and they are far, far removed from being any sort of basic building block.
 
Apathia said:
I invite you to read some of his pdfs and contributions to other forums.
You will find a number of other even more interesting denials and gaffs.
Here's an entertaining place to start:
http://www.physicsforums.com/showthread.php?t=30569
Note that he posts as "Lama" here.

Or just keep engaging him in this thread. Before long your list will contain some really outlandish things. It just gets clearer and clearer why professional mathematicians and math instructors don't give him the time of day.
Click to expand...

I think I have read all of his .PDF files. They get very repetitive after a while, but they do skip around in the most bizarre ways. I've also tracked down many of this posts in other fora.

Originally, I sincerely had this naive belief that somewhere at the base of his gibberish there was a glimmer of an idea (which got quickly buried in confusion). Alas, there was none.
 
PixyMisa said:
If you can't prove Godel's Incompleteness Theorem, that means that you've thrown out arithmetic as well.
Click to expand...

Not at all, Godel's Incompleteness explicitly supports my theory which is:

No resaechable thing is both consistent AND complete (total).

My theory provides the reason of this result, which is:

No reseachable thing is complete(total) AND resachable, because completeness (totality) is non-reseachable.
 
PixyMisa said:
You mean you don't know the general definition.

Natural numbers are subset of rational numbers.
Both rational and irrational numbers are subsets of real numbers.
Real numbers are a subset of complex numbers, where the imaginary part is zero.
And complex numbers are a subset of hypercomplex numbers, such as quaternions. Hypercomplex numbers can be viewed as being vectors of reals, so the generalisation is straightforward.
Click to expand...

A geranalization of X is an unchanged property of X under any manipolation.

For example: By my theory, a number is the simplest result (which is reseachable) of Symmetry\Asymmetry complementation.

Please show this unchanged property of the concept of Number by using standard Math.
 
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Apathia said:
We can only hope that your current material will soon be extinct.
Click to expand...
Why?

Because you wish to force the totality of the non-researchable on the researchable, as some restriction that prevents any Evolution of it?

Well save your power for real creativity because totality is complete without any help from you and any definition is more complex than completeness at its self state.

Definitions work only when we deal with the researchable.
 
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jsfisher said:
(a) you have been contradicting yourself
Click to expand...
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.
jsfisher said:
Your so called organic natural numbers cannot stand on their own,
Click to expand...
Before you say anything about ONNs you firsrt have to show that you understand ONNs.
 
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doronshadmi said:
Not at all, Godel's Incompleteness explicitly supports my theory which is:

No resaechable thing is both consistent AND complete (total).
Click to expand...
No.

Gödel's (first) incompleteness theorem states this:

To every
Inline1.gif
-consistent recursive class
Inline2.gif
of formulas, there correspond recursive class-signs
Inline3.gif
such that neither (
Inline4.gif
Gen
Inline5.gif
) nor Neg(
Inline6.gif
Gen
Inline7.gif
) belongs to Flg(
Inline8.gif
), where
Inline9.gif
is the free variable of
Inline10.gif
Click to expand...

See the difference?

My theory provides the reason of this result, which is:

No reseachable thing is complete(total) AND resachable, because completeness (totality) is non-reseachable.
Click to expand...
Total nonsense.

Gödel proved his theorem. You can't "provide the reason of this result". It's proved within the very formal system to which it applies. (Actually, it's proved once for an entire class of formal systems, including arithmetic.)
 
PixyMisa said:
No.

Gödel's (first) incompleteness theorem states this:



See the difference?


Total nonsense.

Gödel proved his theorem. You can't "provide the reason of this result". It's proved within the very formal system to which it applies. (Actually, it's proved once for an entire class of formal systems, including arithmetic.)
Click to expand...
He did it because he used non-locality as a hidden assumption.

Without non-locality no two things can be considered as class (or more generally, the Multitude does not hold).

You cannot grasp this simplicity because your mind is lost by sophisticated games.
 
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doronshadmi said:
He did it because he used non-locality as a hidden assumption.

Without non-locality no two things can be considered as class (or more generally, the Multitude does not hold).

You cannot grasp this simplicity because your mind is lost by sophisticated games.
Click to expand...
Gödel's incompleteness theorem holds true for arithmetic, Doron. It's provably true for arithmetic using arithmetic.

You know, that 1+1=2 stuff? Provably incomplete, using nothing more than that 1+1=2 stuff.
 
PixyMisa said:
Gödel's incompleteness theorem holds true for arithmetic, Doron. It's provably true for arithmetic using arithmetic.

You know, that 1+1=2 stuff? Provably incomplete, using nothing more than that 1+1=2 stuff.
Click to expand...

Yes, I Know. But arithmetic does not hold without Non-locality\Locality complementation.

The same hidden-assumption can be found in Hilbert's Axioms of Geometry. ( http://www.internationalskeptics.com/forums/showpost.php?p=3625059&postcount=667 ).

He uses a line and a point without understanding them as non-local atom (line) and local atom (point) that are not defined by each other, but can be used in order to get a researchable framework, if they complement each other.

So as you see, from this general point of view of the researchable, we are enable to understand that incompleteness is a fundamental property of the researchable, whether it is called Geometry or Arithmetic.

Simple, isn't it? (and it also can be shown at the basis of Logic).
 
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doronshadmi - Where do you see this thread going?

You've failed to persuade a single person that there is anything of value in your work.

We can continue the tedious cycles of "Yes, it is!", "No, it isn't." until the cows come home.

I'll be shocked if anyone changes their mind.

If you're tryiing to get your work out to where the world can see it, you've accomplished that.

Too bad that, in the light of day, it doesn't hold up.

I suggest that you take the approach of "we'll just have to disagree", pick up your marbles, and go home.
 
doronshadmi said:
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.
Click to expand...

Please point out contradictory statements I have made.

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

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.
 
PixyMisa said:
And I shudder to think what tortured definition you are using for "locality".
Click to expand...

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".
 
PixyMisa said:
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".
Click to expand...
The concept of Successor does not hold without Non-locality\Locality complementation.
 
jsfisher said:
Please point out contradictory statements I have made.
Click to expand...
X is both researchable AND complete.


jsfisher said:
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.
Click to expand...
No, I use arithmetic, but before that I define the basic term that enables it.
 
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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.
 
doronshadmi said:
jsfisher said:
Please point out contradictory statements I have made.
Click to expand...
X is both researchable AND complete.
Click to expand...

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


jsfisher said:
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.
Click to expand...
No, I use arithmetic, but before that I define the basic term that enables it.
Click to expand...

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.
 
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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.
 
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doronshadmi said:
I have an Idea of how we may communicate with each other.
Click to expand...


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.
Click to expand...

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...
Click to expand...
 
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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.
 
doronshadmi said:
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.
Click to expand...

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

Apathia said:
Mordern mathematics manipulates infinities (researchable or not).
Click to expand...
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.
 
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jsfisher said:
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.
Click to expand...
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.
 
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ArmillarySphere said:
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.
Click to expand...
No, what you call sliding scale is incomplete (and researchable).

Completeness is total (no sliding scale holds) and non-researchabe.
 
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doronshadmi said:
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).
Click to expand...


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.
 
jsfisher said:
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.
Click to expand...
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.
 
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doronshadmi said:
You did not get it.
Click to expand...

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

Any definition cannot be Total in order to be defined.
Click to expand...

Gibberish.

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

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).
Click to expand...

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).
Click to expand...

More gibberish.

Some analogy:
Click to expand...

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).
Click to expand...

...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.
Click to expand...

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?
 
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