Deeper than primes

[doronshadmi]

Doron again it does not matter what “A represents”

I simply gave an example of your inability to get Non-locality in terms of Membership.

A(represents "member") NXOR ~A(represents "not a member") is always FALSE (contradiction) for you, exactly because you are using a local-only view of the logical connective (mutuality) between A or ~A different (independent) states.

The general form is Non-locality(Logical connective)/Locality(Element) Linkage, which is mutual-independent no matter what Logical connectives or Elements are used (for example: in A=A, A≠A, A=~A, A≠~A expressions, = and ≠ are the mutual (non-local) aspect and A or ~A are the independent (local) aspect of the expressions, no matter if the result is always false or always true).

A non-limited view ( Non-locality(Logical connective)/Locality(Element) Linkage ) of A,~A in terms of NXOR/XOR logical connectives is:

Non-locality as expressed by NXOR:

A NXOR ~A
------------
F       F --> T (Non-locality) (True)
F       T --> F (Locality) (False)
T       F --> F (Locality) (False)
T       T --> T (Non-locality) (True)

Locality as expressed by XOR:

A XOR ~A
------------
F      F --> F (Non-locality) (False)
F      T --> T (Locality) (True)
T      F --> T (Locality) (True)
T      T --> F (Non-locality) (False)

A and “~A” are still mutually dependent.

Worng.

A or ~A is the difference (independent aspect) and any given logical connective is the connection (mutual aspect) of "A [Logical Connective] ~A" expression.

You are simply focused on the FT,TF input of that mutual-independent expression, and ignore the FF,TT input of that mutual-independent expression.

As a result you get this wrong conclusion:

... again A XOR NOT A is always TRUE (a tautology) while A NXOR NOT A is always FALSE (a contradiction).

Again.

A non-limited view ( Non-locality(Logical connective)/Locality(Element) Linkage ) of A,~A in term s of NXOR/XOR logical connectives is:

Non-locality as expressed by NXOR:

A NXOR ~A
------------
F       F --> T (Non-locality) (True)
F       T --> F (Locality) (False)
T       F --> F (Locality) (False)
T       T --> T (Non-locality) (True)

Locality as expressed by XOR:

A XOR ~A
------------
F      F --> F (Non-locality) (False)
F      T --> T (Locality) (True)
T      F --> T (Locality) (True)
T      T --> F (Non-locality) (False)

In A,A case we are using "A [Logical Connective] A" self-reference expression, which is a Logical connective between A to itself , where A is the local (independent) aspect and the logical connective is the non-local (mutual) aspect of this expression (for example: in A=A, or A≠A expressions, = and ≠ are the mutual (non-local) aspect and A is the independent (local) aspect of the expressions, no matter if the result is always false or always true).

Since you do not get the Non-local/Local linkage that stands at the basis of the "A [Logical Connective] A" self-reference expression, you do not get that this expression is simply limited to the FF,TT input and can't deal with FT,TF input.

Form this limited view, you are wrongly arrived to general conclusions about the nature of mutual-independency (that sands also at the basis of self-reference expressions), by writing this:

Similarly A XOR A is always FALSE (a contradiction) while A NXOR A is always TRUE (a tautology)

--------------------

The Man, your view of the discussed subject is closed under "A [Logical connective] A" or "A [Logical connective] ~A" expressions, without any under-standing of the Non-local/Local linkage that stands at the basis of both of them.

 

[doronshadmi]

…people just making up their own meanings for words and concepts…

If you don't use a religious view of "words and concepts ", then "words and concepts " are nothing but the current common agreement among people about given "words and concepts", as expressed in dictionaries, Wikipedia, referenced accepted articles etc…

If a novel view of "words and concepts " is expressed, then it will be tagged as "just making up" by persons that rejects novel ideas in principle, exactly as you do all along this thread The Man, which easily leads to the conclusion that you have a religious view of "words and concepts".

 

[doronshadmi]

This is heavy, just burying tensor calculus into a pile of triviality.

Let's try again.

A) 0000 = "a set of identical digits"
B) 1111 = "a set of identical digits not identical to (A)"

Tautology: "a needless repetition of an idea, statement, or word"
http://www.merriam-webster.com/dictionary/tautology

If the cardinality of (A) is 4 and the cardinality of (B) is 4 as well, then under that condition, (A) = (B). But if the 0's in (A) and the 1's in (B) repeat 4 times, and "TAUTOLOGY" <> "CONTRADICTION," then a contradiction emerges: due to the definition of tautology, both sets cannot have the same cardinal number. The error-free version is then

Contradiction is 0000 and Tautology is 1111111111111....

until someone says that there have been just enough 1's, and no further repetition is needed.

1111 ("TAUTOLOGY") or 0000 ("CONTRADICTION") are the minimal expression under the 16 logical connectives that are based 00,01,10,11 inputs.

For more detailes please see http://en.wikipedia.org/wiki/Logical_connective .

 

[The Man]

I simply gave an example of your inability to get Non-locality in terms of Membership.

Doron again it does not matter what “A represents” A and “~A” are still mutually dependent.

A(represents "member") NXOR ~A(represents "not a member") is always FALSE (contradiction) for you, exactly because you are using a local-only view of the logical connective (mutuality) between A or ~A different (independent) states.

Doron again it does not matter what “A represents” A and “~A” are still mutually dependent.

The general form is Non-locality(Logical connective)/Locality(Element) Linkage, which is mutual-independent no matter what Logical connectives or Elements are used (for example: in A=A, A≠A, A=~A, A≠~A expressions, = and ≠ are the mutual (non-local) aspect and A or ~A are the independent (local) aspect of the expressions, no matter if the result is always false or always true).

Doron, “~” (negation) is a logical connective that makes A and “~A” mutually dependent. You are ignoring your own “Non-locality(Logical connective)” to claim some imaginary “Locality(Element)” independence. So it is in fact you who is taking a “local only” view of your own notions. How can you expect anyone to take you or your notion of “Non-locality(Logical connective)” seriously when you deliberately ignore them yourself?

A non-limited view ( Non-locality(Logical connective)/Locality(Element) Linkage ) of A,~A in terms of NXOR/XOR logical connectives is:

Non-locality as expressed by NXOR:

A NXOR ~A
------------
F       F --> T (Non-locality) (True)
F       T --> F (Locality) (False)
T       F --> F (Locality) (False)
T       T --> T (Non-locality) (True)

Locality as expressed by XOR:

A XOR ~A
------------
F      F --> F (Non-locality) (False)
F      T --> T (Locality) (True)
T      F --> T (Locality) (True)
T      T --> F (Non-locality) (False)

Worng.

A or ~A is the difference (independent aspect) and any given logical connective is the connection (mutual aspect) of "A [Logical Connective] ~A" expression.

You are simply focused on the FT,TF input of that mutual-independent expression, and ignore the FF,TT input of that mutual-independent expression.

As a result you get this wrong conclusion:

Again Doron “~” (negation) is a logical connective, do not blame anyone else for your “wrong conclusion” based on your deliberate ignorance of your own “Non-locality(Logical connective)” assertion.

Again.

A non-limited view ( Non-locality(Logical connective)/Locality(Element) Linkage ) of A,~A in term s of NXOR/XOR logical connectives is:

Non-locality as expressed by NXOR:

A NXOR ~A
------------
F       F --> T (Non-locality) (True)
F       T --> F (Locality) (False)
T       F --> F (Locality) (False)
T       T --> T (Non-locality) (True)

Locality as expressed by XOR:

A XOR ~A
------------
F      F --> F (Non-locality) (False)
F      T --> T (Locality) (True)
T      F --> T (Locality) (True)
T      T --> F (Non-locality) (False)

In A,A case we are using "A [Logical Connective] A" self-reference expression, which is a Logical connective between A to itself , where A is the local (independent) aspect and the logical connective is the non-local (mutual) aspect of this expression (for example: in A=A, or A≠A expressions, = and ≠ are the mutual (non-local) aspect and A is the independent (local) aspect of the expressions, no matter if the result is always false or always true).

Doron A is not independent of itself nor is it independent of its negation. So now your claiming (“no matter if the result is always false or always true”) that the statement being a contradiction or tautology is as irrelevant to you as your own “Non-locality(Logical connective)” assertion. Again how can you expect anyone to take your notions and assertions seriously when you obviously don’t?

Since you do not get the Non-local/Local linkage that stands at the basis of the "A [Logical Connective] A" self-reference expression, you do not get that this expression is simply limited to the FF,TT input and can't deal with FT,TF input.

Since it is you Doron deliberately ignoring your own professed “Non-locality(Logical connective)” in negation you are limited by your own deliberate ignorance of your own assertions.

Form this limited view, you are wrongly arrived to general conclusions about the nature of mutual-independency (that sands also at the basis of self-reference expressions), by writing this:

Again Doron A is not independent of itself nor is it independent of its negation. Your “mutual-independency (that sands also at the basis of self-reference expressions)” is just your fantasy by not saying what you mean, some ‘totally connective total independence‘. Understandable as what you mean is simply self-contradictory nonsense, so you apparently try to obscure what you actually mean by misapplying words like mutual and independent. Just say what you mean Doron. If you mean a lack of dependence that is shared or reciprocal then mutual independence is an appropriate phrase. Heck you could even consider that they are connected to some degree by that shared independence (as I have pointed out to you before). However you insistence on your “total connective” “total isolation” extremes is just self-contradictory nonsense as even in “total isolation” they are connected by that “total isolation” (it is an aspect they would share as I have also pointed out to you before). Whereas dependence requires a dependent connection of some kind, independence does not infer or require a total lack of connection and in fact a mutual independence is a connection between that (shared or reciprocal) independence. Certainly in this regard these are not novel notions Doron, nor is your deliberate misuse of language in expressing them.

--------------------

The Man, your view of the discussed subject is closed under "A [Logical connective] A" or "A [Logical connective] ~A" expressions, without any under-standing of the Non-local/Local linkage that stands at the basis of both of them.

Once again Doron the closure is entirely yours by you deliberately ignoring the already well established meanings of the words you use as well as your own “Non-locality(Logical connective)” assertion, specifically when it comes to the logical connective of negation.

If you don't use a religious view of "words and concepts ", then "words and concepts " are nothing but the current common agreement among people about given "words and concepts", as expressed in dictionaries, Wikipedia, referenced accepted articles etc…

As I said before a dictionary gives common usage of words, so that "religious view of "words and concepts“" is again entirely yours.

If a novel view of "words and concepts " is expressed, then it will be tagged as "just making up" by persons that rejects novel ideas in principle, exactly as you do all along this thread The Man, which easily leads to the conclusion that you have a religious view of "words and concepts".

Doron you are easily lead to whatever conclusion you prefer, even when it is demonstrated, as above, to be false. Again if you can’t find (are just too lazy or deliberately deceitful to find) the correct words with their common usage to express what you mean, then define your own words (that is how new words are created and language changes). Your insistence on simply attempting to change existing well established words and concepts so they no longer represent the established meaning simply demonstrates your lack of interest in accurately expressing your own notions as your own notions.

 

[doronshadmi]

Doron, “~” (negation) is a logical connective that makes A and “~A” mutually dependent.

Wrong The Man, ~A is anything but A including the opposite of A in
"A [Logical connective] ~A" non self-reference expression.

There is AT LEAST Element aspect (notated, for example, by "A") and some Logical aspect (notated, for example, by "@") in any formal valid expression (notated, for example, as "@A").

Once again Doron the closure is entirely yours by you deliberately ignoring the already well established meanings of the words you use as well as your own “Non-locality(Logical connective)” assertion, specifically when it comes to the logical connective of negation.

Worng.

The traditional view of NOT as unary is fundamentally wrong because the Truth table of ~ can't avoid A in order to be expressed, as follows:

A ~A
T  F
F  T

("@A" can't be avoided if we are dealing with valid formal expressions).

Doron A is not independent of itself

I don't claim such a thing.

... nor is it independent of its negation.

You are wrong because any logical aspect (which is non-local) is not the Element aspect (which is local)
in any given logical aspect/Element aspect expression.

For example: In "NOT XOR" expression, "NOT" is the logical aspect and "XOR" is the element aspect of the given logical aspect/Element aspect expression.

The same thing holds also in "NOT NOT" expression.

Again ,there is AT LEAST Element aspect (notated, for example, by "A") and some Logical aspect (notated, for example, by "@") in any formal valid expression (notated, for example, as "@A").

independence does not infer or require a total lack of connection and in fact a mutual independence is a connection between that (shared or reciprocal) independence.

Too much words, it simply the intermediate result of mutual-independency linkage, which is weaker than total mutuality (Non-locality-only, or total connectivity) and stronger than total independency (Locality-only, or total isolation).

The novel view is the Non-local aspect of mutual-independency state, which is wrongly taken by your local-only reasoning as a contradiction.

 

[jsfisher]

The traditional view of NOT as unary is fundamentally wrong

It is not a view. It is a definition. You know, that thing you have yet produce for anything you invent. Definitions are not subject to the Whim o' Doron.

...because the Truth table of ~A can't avoid A in order to be expressed

Since negation is defined in terms of its lone operand, why would you fantasize otherwise? By definition, ~A is related to A.

If they were unrelated, then negation would be a worthless operation. Is that all you can invent, Doron, worthless operations? Please provide evidence to the contrary.

 

[doronshadmi]

Since negation is defined in terms of its lone operand, …

It is a wrong view of that subject since ~ alone is meaningless exactly as A alone is meaningless.

Again,

The traditional view of NOT as unary is fundamentally wrong because the Truth table of ~ can't avoid A in order to be expressed, as follows:

A ~A
T  F
F  T

If they were unrelated, then negation would be a worthless operation.

They are related by the intermediate mutual-independency state, which is the result of Non-locality/Locality Linkage.

Your wrong "unrelated" view is derived from your Local-only view of the considered subject.

As long as The Man and you get Non-locality as a contradiction (because of your Local-only view of it) you will not get OM.

Also ~A is anything but A including the opposite of A.

 

[jsfisher]

It is a wrong view of that subject

Don't be silly. A definition is not a point of view. It is, well, a definition. Definitions have no need to win popularity contests, and they certainly don't need your approval, Doron.

Negation in logic has a definition. You unhappiness with that fact is of no consequence.

since ~ alone is meaningless exactly as A alone is meaningless.

Neither is meaningless. The tilde, standing as a negation operator, has a well-defined meaning. The A, standing as a boolean variable, has a well-defined meaning.

Again....

Repetition does not make your fantasies any less fantastic, Doron. Claiming something is incorrect because you are unhappy with its definition is bogus no matter how many times you restate your claim.

 

[doronshadmi]

Doron you are easily lead to whatever conclusion you prefer, even when it is demonstrated, as above, to be false. Again if you can’t find (are just too lazy or deliberately deceitful to find) the correct words with their common usage to express what you mean, then define your own words (that is how new words are created and language changes). Your insistence on simply attempting to change existing well established words and concepts so they no longer represent the established meaning simply demonstrates your lack of interest in accurately expressing your own notions as your own notions.

The Man, a language is developed not only by the amount of new words, but also by deeper understanding of already given words.

jsfisher and you have clear approach of a religious-like dogma about their expertise, which actually prevents any meaningful communication with persons that do not follow with their agreed dogma.

This dogmatic behavior is anti-evolutionist by nature because it does not allow changes (mutations) in already agreed terms, and as a result things must be put side by side under disjoint context-dependent frameworks.

A general view of this demand gives fragmented isolated closed areas of knowledge that speck with each other only by “happy accidents”, and as a result no deep understanding is developed among this fragments.

Organic Mathematics fundamentally changes this approach by asserting that there is a common “trunk” to these fragments, and only then they can really be considered as “branches” of a one organic body of knowledge.

Organic Mathematics is a non context-dependent framework, and this is probably the main reason of your misunderstanding of it.

 

[jsfisher]

Organic Mathematics fundamentally changes this approach by asserting that there is a common “trunk” to these fragments, and only then they can really considered as “branches” of a one organic body of knowledge.

Nonsense. Organic Mathematics produces nothing. Instead, it makes everything it touches meaningless.

You have just provided one of many simple examples of this with your ridiculous claims for the negation operator. In your Organic Mathematics fantasy world, the negation operator is totally worthless. Organic Mathematics is totally worthless. And yet you, Doron, cling to it blindly as religious dogma without ever producing any kind of real result.

Isn't that what faith is?

 

[doronshadmi]

Neither is meaningless. The tilde, standing as a negation operator, has a well-defined meaning. The A, standing as a boolean variable, has a well-defined meaning.

Only if ~ ; A are linked into a one expression.

In that case Non-locality (~}/Locality (A) Linkage is used as mutual-independent framework.

Don't be silly. A definition is not a point of view.

Don't be silly. A definition is exactly the result of the depth of your view of the considered subject.

Instead, it makes everything it touches meaningless.

Only if it touches a dogmatic mind.

real result

Please define "real result".

 

[jsfisher]

Only if ~ ; A are linked into a one expression.

Nonsense. They each have meaning separate from each other. Have you no concept whatsoever as to what a definition is?

In that case Non-locality (~}/Locality (A) Linkage is used as mutual-independent framework.

That appears to answer my question. No, you have no concept what a definition is, at least not for the negation operator nor a variable.

Don't be silly. A definition is exactly the result of the depth of your view of the considered subject.

Your dictionary is still broken, Doron.

Please define "real result".

What, again? It has been done before, several times. You failed to respond then with a real result, several times. Why should we expect something different this time?

 

[doronshadmi]

Nonsense. They each have meaning separate from each other. Have you no concept whatsoever as to what a definition is?

Nonsense. They have meaning only if thay are mutually-independent of each other. You hane no idea of how a definition is possiple, in the first place.

It has been done before, several times.

Not even once.

 

[jsfisher]

Not even once.

Denial is in the next country over.

 

[doronshadmi]

Denial is in the next country over.

You indeed denial the qualitative foundation of the mathematical science.

Nonsense. They each have meaning separate from each other.

Worng, for example:

A= “It is raining”

B="All we nned is love"

In both cases "A" or "B" have meaning only if "=" ("=" = "iff", in this case) is also used.

Try to use:

A

B

=

and see by yourself that you don't get any meaningful expression.

 

[The Man]

Wrong The Man, ~A is anything but A including the opposite of A in
"A [Logical connective] ~A" non self-reference expression.

No Doron we have been over this before “anything but” would be an informal or natural language definition of “not”. “NOT” (a different representation than "not") also represented as “~” has a formal definition in logic as negation. Again in a two value system “anything but” one value can only be the negation of that value, so the informal common language definition of “not” (“anything but”) overlaps with the formal logical definition of “NOT” (negation) only in the case of a two value system.

There is AT LEAST Element aspect (notated, for example, by "A") and some Logical aspect (notated, for example, by "@") in any formal valid expression (notated, for example, as "@A").

Which is “~A” as the negation of A.

Worng.

Indeed you are as wrong in ignoring the logical connective of negation as you are in your spelling of “wrong”.

The traditional view of NOT as unary is fundamentally wrong because the Truth table of ~ can't avoid A in order to be expressed, as follows:

A ~A
T  F
F  T

Who said anything about ‘avoiding A’?

("@A" can't be avoided if we are dealing with valid formal expressions).

That is why it is “~A”, stop simply ignoring the logical connective of negation.

I don't claim such a thing.

Really

(for example: in A=A, or A≠A expressions, = and ≠ are the mutual (non-local) aspect and A is the independent (local) aspect of the expressions, no matter if the result is always false or always true).

As your examples only reference A to itself what were you claiming A as “the independent (local) aspect” of those examples was independent of?

You are wrong because any logical aspect (which is non-local) is not the Element aspect (which is local)
in any given logical aspect/Element aspect expression.

Doron no one cares about your nonsense dichotomy ascriptions, but you. Since negation is a logical connective and not your ‘local element’ in the expression “~A”, evidently you do not even care about your own nonsense dichotomy ascriptions.

For example: In "NOT XOR" expression, "NOT" is the logical aspect and "XOR" is the element aspect of the given logical aspect/Element aspect expression.

The same thing holds also in "NOT NOT" expression.

Again Doron no one cares about your nonsense dichotomy ascriptions, but you. Since “~A” (NOT A) meets your ascription above and you still ignore the logical connective of negation, evidently you do not even care about your own nonsense dichotomy ascriptions.

Again ,there is AT LEAST Element aspect (notated, for example, by "A") and some Logical aspect (notated, for example, by "@") in any formal valid expression (notated, for example, as "@A").

Again that is why it is “~A”, stop simply ignoring the logical connective of negation.

Too much words, it simply the intermediate result of mutual-independency linkage, which is weaker than total mutuality (Non-locality-only, or total connectivity) and stronger than total independency (Locality-only, or total isolation).

“Too much words”? So you are just lazy? Besides that you used 5 more words (excluding the “Too much words”) to say absolutely nothing of any meaning to anyone but you.

The novel view is the Non-local aspect of mutual-independency state, which is wrongly taken by your local-only reasoning as a contradiction.

Doron a shared or reciprocal lack of dependence is not a contradiction. It is simply your insistence on your nonsense extremes (as your “total independence” has been shown to be years ago) that are contradictory. Again it is just you that is “wrongly taken” by your own imaginary extremes.

 

[doronshadmi]

Again Doron no one cares about your nonsense dichotomy ascriptions,

The Man, mutual-independency is not mutual-only or independent-only, so the nonsense dichotomy is entirely the result of your local-only reasoning.

The rest of your post is collapsed under this nonsense.

“NOT” (a different representation than "not") also represented as “~” has a formal definition in logic as negation.

Nonesense.

"~" has no meaning unless it is used with "A" as formal meaningful expression.

Also "A" has no meaning unless it is used with some logical connective, for example: "A=A".


More example:

A= “It is raining”

B="All we nned is love"

In both cases "A" or "B" have meaning only if "=" ("=" = "iff", in this case) is also used.

Try to use:

A

B

=

and see by yourself that you don't get any meaningful expression (and so is the case with "~" alone).

"~" can be considered as a connective, only if it refers to some element (where this element can be also "~" in "~~" expression).

your nonsense extremes (as your “total independence” has been shown to be years ago) that are contradictory.

By using a local-only reasoning A NXOR ~A is a contradiction.

You can't define contradiction of total state , because it is totally independent.

A meaningful formal framework is AT LEAST mutual-independency, which is something that you simply don't get.

 

[The Man]

The Man, a language is developed not only by the amount of new words, but also by deeper understanding of already given words.

Doron that would require you actually understanding the words first to get your “deeper understanding” and you demonstrably do not understand the words you use. Simply trying to force your own meaning on well established words and concepts is not a “deeper understanding” it is simply being lazy or deliberately deceptive. You constantly use the expression “in other words” just before you try to give a more descriptive explanation of what you mean. So you know there are “other words” and you know how to find them. Thus simply trying to abscond with already established concepts or words instead of simply using your “other words” from the start again indicates you are either simply lazy or deliberately deceptive.

jsfisher and you have clear approach of a religious-like dogma about their expertise, which actually prevents any meaningful communication with persons that do not follow with their agreed dogma.

No Doron you deliberately using words that you even assert do not represent the concept intended as opposed to your “other words” (whether you find them in some reference or come up with your own words) “prevents any meaningful communication”. The fact that you are using existing words with your own personal meaning amounts to your own personal language anyway. So your better off coming up with your own words, again unless your are just lazy or deliberately trying to decive.

This dogmatic behavior is anti-evolutionist by nature because it does not allow changes (mutations) in already agreed terms, and as a result things must be put side by side under disjoint context-dependent frameworks.

Doron your ‘mutant’ terms are yours alone so it is just your own personal language, but you simply want to pretend and insist it is common or “natural” language (by changing existing words And concepts so the no longer represent the meanings of those words and concepts). That is the only “dogmatic behavior” here. It seems you would just like to skip the whole process of demonstrating the relevance and utility of your notions and interpretations and simply rewrite the common usages of words and concepts to conform to your own interpretations. That is dogma at its most dogmatic, Doron

A general view of this demand gives fragmented isolated closed areas of knowledge that speck with each other only by “happy accidents”, and as a result no deep understanding is developed among this fragments.

A general view on your insistence on your own personal language without creating and defining your own words for that language result in your inability to relate you notions in any meaningful fashion.

Organic Mathematics fundamentally changes this approach by asserting that there is a common “trunk” to these fragments, and only then they can really be considered as “branches” of a one organic body of knowledge.

Organic Mathematics is a non context-dependent framework, and this is probably the main reason of your misunderstanding of it.

No Doron it is specifically your ‘mutant’ words and personal language. Again you know there are “other words” and you can find them when you actually try, so start using “other words” or come up with your own. Again simple using words and concepts where you assert you do not use the meanings of those words or concepts, simply indicates that you have absolutely no interest in accurately expressing your own notions as your own notions.

 

[The Man]

The Man, mutual-independency is not mutual-only or independent-only, so the nonsense dichotomy is entirely the result of your local-only reasoning.

Again Doron that is simply your own personal dichotomy, for everyone else it is simply a shared lack of dependence. So “the nonsense dichotomy is entirely the result of your local-only reasoning”.

The rest of your post is collapsed under this nonsense.


Nonesense.

"~" has no meaning unless it is used with "A" as formal meaningful expression.

Also "A" has no meaning unless it is used with some logical connective, for example: "A=A".


More example:

A= “It is raining”

B="All we nned is love"

In both cases "A" or "B" have meaning only if "=" ("=" = "iff", in this case) is also used.

Try to use:

A

B

=

and see by yourself that you don't get any meaningful expression (and so is the case with "~" alone).

"~" can be considered as a connective, only if it refers to some element (where this element can be also "~" in "~~" expression).

Again Doron "~" has a well defined meaning called negation.

 

[doronshadmi]

Again Doron that is simply your own personal dichotomy, for everyone else it is simply a shared lack of dependence. So “the nonsense dichotomy is entirely the result of your local-only reasoning”.

"a shared" means "connectivity".

"lack of dependence" means "isolation".

So your phrase has a meaning exactly because you used "connectivity"/"isolation" linkage that is equivalent to Mutual-Independency, which is not a local-only framework, as your framework is, for example:

... "~" has a well defined meaning called negation.

Only if it refers to some element, or in other words Mutual-Independency framework is used.

your nonsense extremes (as your “total independence” has been shown to be years ago) that are contradictory.

By using a local-only reasoning A NXOR ~A is a contradiction.

You can't define contradiction in the case of total state because it is totally independent.

A meaningful formal framework is AT LEAST mutual-independency, which is something that you simply don't get.