Deeper than primes

[doronshadmi]

Apparently you simply do not understand that circles are circular and by representing your “reasoning” with such circular “notations” you are affirming (perhaps if only subconsciously) the circularity of your own “reasoning”.

No The Man, T=T or F=F are self-reference comparisons, where the comparison is at least relation = and element T or F.

Your problem is that you do not get that Researchability is at least relation\element interaction, where relation is the non-local aspect and element is the local aspect of this interaction.

Wait, first you say “No” then assert that it is a tautology (without being able to spell tautology)? Again you simply inserting your latest catch phrases “ontological level” or “ontological view” in to your nonsensical gibberish assertions does not magically imbue them with any validity or meaning.

No, I assert that tautology is the result of self-reference relation\element interaction, where an element is compared with itself. You simply do not get it because your reasoning starts at the second level the results, and not at the first level of ontology, that enables the results.

If “X is the other option” then still “X is itself” as that other option. If “X” is T then “X” is not the other option or ~F. If “X” is F then “X” is not the other option or ~T. Again simply inserting “at the ontological level” into your nonsensical gibberish in no way detracts from the simple and trivial fact that you still have difficulty just understanding negation.

F≠F (X is-not itself) is simply the other option which is T=T where X (T in this case) is indeed itself.

T≠T (X is-not itself) is simply the other option which is F=F where X (F in this case) is indeed itself.

In both cases we are under self-reference comparison of relations = or ≠ with elements T or F, where F≠F or T≠T are called self-referance negation, such that F≠F is T=T and T≠T is F=F.

(T=T)≠(F=F) or (T≠T)≠(F≠F) are actually the same non self-reference comparison.

Once again I am talking to anyone who reads this thread ...

Talking without first understanding my arguments, is talking to yourself, because you are closed under notions that have nothing to do with my arguments.

 

[The Man]

No The Man, T=T or F=F are self-reference comparisons, where the comparison is at least relation = and element T or F.

You still made your equal signs and not equal signs into little circles indicating that perhaps only subconsciously you understood your reasoning to be circular. You can deny it as much as you want but your reasoning is circular and you represented it with, well, circles.

Your problem is that you do not get that Researchability is at least relation\element interaction, where relation is the non-local aspect and element is the local aspect of this interaction.

Your problem is that you just make stuff up and do not even bother to explore or understand the vast amount of actual research recourses that are available to you.

No, I assert that tautology is the result of self-reference relation\element interaction, where an element is compared with itself. You simply do not get it because your reasoning starts at the second level the results, and not at the first level of ontology, that enables the results.

Doron, you assert that everything is a result of your “relation\element interaction” it is just some amorphous blob that you pull out of you pocket to try and adsorb everything you can not be bothered to actually research or learn about.

F≠F (X is-not itself) is simply the other option which is T=T where X (T in this case) is indeed itself.

T≠T (X is-not itself) is simply the other option which is F=F where X (F in this case) is indeed itself.

Again simply a contradiction, regardless of the value of “X” (X ≠ X) is always FALSE.

In both cases we are under self-reference comparison of relations = or ≠ with elements T or F, where F≠F or T≠T are called self-referance negation, such that F≠F is T=T and T≠T is F=F.
.

(T=T)≠(F=F) or (T≠T)≠(F≠F) are actually the same non self-reference comparison.

You can call it whatever you like, while we will just call it nonsensical gibberish.

Remember this..

T≠T (or F≠F) is a false self-referential comparison. T=F is a false non self-referential comparison. Here it is:
[qimg]http://farm3.static.flickr.com/2731/4153069414_3abcabc22e_o.jpg[/qimg]

In both cases, comparison is fundamental.

No reference (self or otherwise) was made to your so called “self-referance negation”, that is the problem when you just try to make this C.R. A.P. up as you go. Not to mention that the negation of your “self-referential comparison” would be your “non self-referential comparison”.

Talking without first understanding my arguments, is talking to yourself, because you are closed under notions that have nothing to do with my arguments.

OK so now we can add that talking to someone by responding back a fourth on a discussion forum is another concept you simply do not understand. Doron, you do not understand you arguments, oh certainly you like to pretend that you do, but quite literally you have no idea what you are saying.

 

[jsfisher]

No The Man, T=T or F=F are self-reference comparisons

Nope. Not self references.

...where the comparison is at least relation = and element T or F.

Nope. The comparison is exactly equality, and the operands are exactly either T or F.

Your problem is that you do not get that Researchability is at least relation\element interaction, where relation is the non-local aspect and element is the local aspect of this interaction.

Nope. This is just something you made up.

No, I assert that tautology is the result of self-reference relation\element interaction, where an element is compared with itself.

Nope. Your assertion is without merit.

You simply do not get it because your reasoning starts at the second level the results, and not at the first level of ontology, that enables the results.

Nope. You inability to develop and articulate a framework that is without contradiction is your failing and your failing alone. It is your notions that are baseless, and that is what others see.

F≠F (X is-not itself)

Nope.

...is simply the other option which is T=T where X (T in this case) is indeed itself.

Other option? T=T has no options. Stop inventing meaningless tripe.

T≠T (X is-not itself) is simply the other option which is F=F where X (F in this case) is indeed itself.

Ditto.

In both cases we are under self-reference

None of them are self references.

...comparison of relations = or ≠

None of them are comparisons of relations.

...with elements T or F

Elements? Comparisons don't have elements.

...where F≠F or T≠T are called self-referance negation

Nobody with any knowledge of Mathematics call them that.

...such that F≠F is T=T and T≠T is F=F.

Still wrong.

(T=T)≠(F=F) or (T≠T)≠(F≠F) are actually the same non self-reference comparison.

No it isn't, but it is wrong, too.

Talking without first understanding my arguments, is talking to yourself, because you are closed under notions that have nothing to do with my arguments.

We do understand your arguments. They are contradictory, inconsistent rubbish, but we understand them completely.

 

[Little 10 Toes]

In this case you are talking to yourself because you do not get things from the ontological level.

No he isn't. I pretty much understand most of where he's coming from.

You do not understandthis drawing because you do not use an ontological view of it.

Is it a deformed Ithorian?

 

[doronshadmi]

Let me help you The Man.

(T=T)=(T=T) is what you call tautology, and it is based on the ontological level of T's self-reference.

For clearer understanding T and (T=T) are representations of T's self-reference .

So, T = T is the tautology that is based on T (which is T's self-reference) .

At the ontological level ~T is (T≠T) is (F=F) is F.

T=T is a true statmant.

T≠T is a false statmant.

Contradiction is the claim that T is (T AND F).

In both levels Comparison is the core of Logic.

By understanding the Two levels of Comparison, you can distinguish between those levels during reasoning, and you do not wrongly mix them, where the result of this mixing is gibberish that can be seen all along your last posts on this subject.

In other words:

or

(T=T) ≠ T

So as you see = and ≠ of the "ontological level" are different than = and ≠ of the "used level".

Let us improve the notations in order to clearly distinguish between the ontological level and the used level:

The ontological level (T=T) = T ≠ the used level (T = T).

The ontological level (T≠T) = F ≠ the used level (T ≠ T).

Again, In both levels Comparison is the core of Logic, where Comparison is at least Relation (Non-locality) \ Element (Locality) Interaction (REI).

Without REI Non-locality is total connectivitiy and too strong for research, and Locality is total isolation and too weak for research.

 

[doronshadmi]

No he isn't. I pretty much understand most of where he's coming from.

Where is coming from is a second level reasoning, which does not help him to get the ontological level of it.

So your "pretty much understand" The Man does not halp you to get the ontology level of Logic.

 

[doronshadmi]

Edit:

Here are the notations of the ontological level of two-valued logic:

T=T is T is T’s self-reference comparison.

F=F is F is F’s self-reference comparison.

~T is T≠T is F=F is F is F’s self-reference comparison.

~F is F≠F is T=T is T is T’s self-reference comparison.

T=T ≠ F=F is T≠F is non self-reference comparison.

T=T = F=F is T=F is an invalid ontological expression, because two elements cannot be in self-reference comparison.

 

[zooterkin]

In other words:

Redefining the word, "word", now?

 

[zooterkin]

Here are the notations of the ontological level of two-valued logic:

T=T is T is T’s self-reference comparison.

F=F is F is F’s self-reference comparison.

~T is F=F is F’s self-reference comparison.

~F is T=T T’s self-reference comparison.

T≠F is non self-reference comparison.

T=F is invalid ontological expression, because two elements cannot be in self-reference comparison.

If it wasn't for ample prior evidence to the contrary, I'd say you were overthinking this...

 

[doronshadmi]

If it wasn't for ample prior evidence to the contrary, I'd say you were overthinking this...

What do you mean by "ample prior evidence to the contrary"?

(Some corrections done in http://www.internationalskeptics.com/forums/showpost.php?p=5382237&postcount=7269)

EDIT: I improved the representations of my notions in order to avoid confusion with the current agreed notations.

 

[doronshadmi]

Redefining the word, "word", now?

No, simply using the phrase "in other words", where words are also marked by notations, so?

 

[doronshadmi]

http://www.internationalskeptics.com/forums/showpost.php?p=5382237&postcount=7269 can ontologically be generalized as follows (X and Y are not necessarily True and False):


a) Self-comparison is only a relation between X to itself.

b) By (a) the relation must be "=" and X is exactly one value, so Self-comparison must be exactly X=X that can be reduced to X notation.

c) By (b) X≠X is an invalid ontological expression.

d) Others-comparison is at least between X=X and Y=Y, such that X=X ≠ Y=Y.

e) By (d) X=X = Y=Y is an invalid ontological expression.

f) By (a) to (e) the ontological level of two-valued logic is X=X ≠ Y=Y that can be reduced to X≠Y notation.

X≠Y is represented also as:

When using the ontological level , we get the second logical level as follows:

If X is true and Y is false, then:

X=X or X≠Y are true statmants.

X≠X or X=Y are a false statmants.

Contradiction is the claim that X is (X AND Y).

In both levels Comparison that is based on Relation (Non-locality) \ Element (Locality) Interaction enables Logic.



(In general X and Y are not necessarily T and F and in that case X and Y are any different values)

 

[The Man]

Let me help you The Man.

Let us help you Doron.

(T=T)=(T=T) is what you call tautology, and it is based on the ontological level of T's self-reference.

What we call a tautology is a statement that is always TRUE regardless of the TRUE of FALSE values contained in the statement. In its simplest form (X = X) is a tautology since it is TRUE whether X is TRUE or FALSE. Your “ontological level of T's self-reference” is just your own nonsense based on your own circular reasoning.

For clearer understanding T and (T=T) are representations of T's self-reference .

For a clearer understanding do some freak’n research.

So, T = T is the tautology that is based on T (which is T's self-reference) .

It is not based on your circular reasoning and incorrect ascription of “self-reference” it is based on the simple fact that (X = X) is always TRUE regardless of the value of X.

At the ontological level ~T is (T≠T) is (F=F) is F.

Well that makes your “ontological level” self-contradictory as (F=F) is a TRUE statement and as much a tautology as (T=T) or (X=X).

T=T is a true statmant.

(F=F), (X=X) and (Z=Z) are also TRUE statements as well as tautologies.

T≠T is a false statmant.

(F≠F), (X≠X) and (Z≠Z) are also FALSE statements as well as contradictions.

Once again you simply employing your favorite pastime of underlining everything does not suddenly or magically imbue your claims with any validity or meaning.

Contradiction is the claim that T is (T AND F).

No, contradiction is specifically the negation of a tautology meaning it is a statement that is always FALSE regardless of the values in that statement. (X≠X) is always FALSE just as (X AND ~X) is, no matter if X is TRUE or FALSE.

Your inability or simple unwillingness to understand these simple and basic concepts has resulted in you making such ridiculous and contradictory claims as “Belongs AND does not Belong”.

In both levels Comparison is the core of Logic.

By understanding the Two levels of Comparison, you can distinguish between those levels during reasoning, and you do not wrongly mix them, where the result of this mixing is gibberish that can be seen all along your last posts on this subject.

Doron it is the creation of your fantasy “levels” (along with your lack of any comprehensive research) that results in you spouting your “gibberish”, which can be seen all along this thread in your posts.

In other words:

[qimg]http://farm3.static.flickr.com/2507/4161716293_84939d3c0e_o.jpg[/qimg]

or

(T=T) ≠ T

So as you see = and ≠ of the "ontological level" are different than = and ≠ of the "used level".

Which simply makes your "ontological level" contradictory and inconsistent with such comparative assertions like = or ≠. It would seem that you simply do not understand that in using = or ≠ at your "ontological level" you are still, well, using them. Attempting to separate such use by claiming it is not “of the "used level"” is just your typical nonsensical “gibberish” resulting from you just imagining these self-contradictory and self-inconsistent “levels”.

Let us improve the notations in order to clearly distinguish between the ontological level and the used level:

The ontological level (T=T) = T ≠ the used level (T = T).

The ontological level (T≠T) = F ≠ the used level (T ≠ T).

Doron you simply claiming you are not using such comparative assertions while you are using them again only demonstrates you are simply just deluding yourself. Your only claim is actually that you are using them differently and thus inconsistently.

Again, In both levels Comparison is the core of Logic, where Comparison is at least Relation (Non-locality) \ Element (Locality) Interaction (REI).

Without REI Non-locality is total connectivitiy and too strong for research, and Locality is total isolation and too weak for research.

Doron consistency is a “core of Logic” and you are simply claiming your “levels” of “Comparison” are just inconsistent.

I must say Doron, using = and ≠ to show or claim that you are not using = and ≠ is certainly a new level of self-inconsistency and self-contradiction, even just for you.

 

[MosheKlein]

Opinion 104: The Shocking State of Contemporary "Mathematics", and the Meta-Shocking Fact that Very Few People Are Shocked
By Doron Zeilberger

Written: Oct. 28, 2009

I just came back from attending the 1052nd AMS (sectional) meeting at Penn State, last weekend, and realized that the Kingdom of Mathematics is dead. Instead we have a disjoint union of narrow specialties, and people who know everything about nothing, and nothing about anything (except their very narrow acre). Not only do they know nothing besides their narrow expertise, they don't care!

http://www.math.rutgers.edu/~zeilberg/OPINIONS.html

 

[doronshadmi]

Let us help you Doron.



What we call a tautology is a statement that is always TRUE regardless of the TRUE of FALSE values contained in the statement. In its simplest form (X = X) is a tautology since it is TRUE whether X is TRUE or FALSE. Your “ontological level of T's self-reference” is just your own nonsense based on your own circular reasoning.




For a clearer understanding do some freak’n research.



It is not based on your circular reasoning and incorrect ascription of “self-reference” it is based on the simple fact that (X = X) is always TRUE regardless of the value of X.




Well that makes your “ontological level” self-contradictory as (F=F) is a TRUE statement and as much a tautology as (T=T) or (X=X).



(F=F), (X=X) and (Z=Z) are also TRUE statements as well as tautologies.



(F≠F), (X≠X) and (Z≠Z) are also FALSE statements as well as contradictions.

Once again you simply employing your favorite pastime of underlining everything does not suddenly or magically imbue your claims with any validity or meaning.



No, contradiction is specifically the negation of a tautology meaning it is a statement that is always FALSE regardless of the values in that statement. (X≠X) is always FALSE just as (X AND ~X) is, no matter if X is TRUE or FALSE.

Your inability or simple unwillingness to understand these simple and basic concepts has resulted in you making such ridiculous and contradictory claims as “Belongs AND does not Belong”.



Doron it is the creation of your fantasy “levels” (along with your lack of any comprehensive research) that results in you spouting your “gibberish”, which can be seen all along this thread in your posts.




Which simply makes your "ontological level" contradictory and inconsistent with such comparative assertions like = or ≠. It would seem that you simply do not understand that in using = or ≠ at your "ontological level" you are still, well, using them. Attempting to separate such use by claiming it is not “of the "used level"” is just your typical nonsensical “gibberish” resulting from you just imagining these self-contradictory and self-inconsistent “levels”.



Doron you simply claiming you are not using such comparative assertions while you are using them again only demonstrates you are simply just deluding yourself. Your only claim is actually that you are using them differently and thus inconsistently.



Doron consistency is a “core of Logic” and you are simply claiming your “levels” of “Comparison” are just inconsistent.

I must say Doron, using = and ≠ to show or claim that you are not using = and ≠ is certainly a new level of self-inconsistency and self-contradiction, even just for you.

"Thank you" for ignoring http://www.internationalskeptics.com/forums/showpost.php?p=5382436&postcount=7274.

Since you are able to get things only by T,F terms, you miss the ontological core that enables them in the first place.

So let us try another way to understand the ontological core of Logic.

By ontology we ask "what enables a thing before it is used for some purpose?”

For example, we can ask:”What enables Negation?”

The ontological answer to this question is as follows:

Negation is based on the ability to compare different things, such that ~X is anything but X.

It means that there must be some other thing, which is ~X that is comparable with X, otherwise ~ is on X and the result is nothing at all.

In that case we ask: “What enables X as a researchable thing?”

The ontological answer is:”X’s sameness-comparison”.

X’s sameness-comparison is a unary connective of a thing to itself, notated as =X, where "=" is the unary connective and X is the element.

Y’s sameness-comparison is a unary connective of a thing to itself, notated as =Y, where "=" is the unary connective and Y is the element.

Negation is difference-comparison, and therefore it is binary connective of X with Y.

Without Negation as binary connective of X with Y, X or Y are isolated of each other, and each one of them is closed under “=” unary connective of sameness-comparison.

Pay attention that that at the ontological core of Logic True or False concepts are not found, simply because True and False are some particular cases of Sameness\Difference Comparison, where Sameness\Difference Comparison is their ontological core.

Here is a representation of the ontological core of Logic:

that can be notated also as =X ≠ =Y, where "=" is unary connective of sameness-comparison and "≠" is binary connective of difference-comparison.

Again, True and False are not found at the ontological core of Logic.

The buliding-blocks of the ontological core of Logic are Relations = or ≠ connectives, and X or Y, such that = is non-local w.r.t X or Y and ≠ is non-local w.r.t =X or =Y.

In other words, the ontological core of Logic is based on Non-locality\Locality Linkage.

No, contradiction is specifically the negation of a tautology meaning it is a statement that is always FALSE regardless of the values in that statement. (X≠X) is always FALSE just as (X AND ~X) is, no matter if X is TRUE or FALSE.

Your inability or simple unwillingness to understand these simple and basic concepts has resulted in you making such ridiculous and contradictory claims as “Belongs AND does not Belong”.

1) At the ontological core of Logic TRUE or FALSE are not found.

2) “Belongs AND does not Belong” is exactly the non-locality of "=" w.r.t X or Y, or the non-locality of "≠" w.r.t =X or =Y.

 

[Gaspode]

Some posts moved to AAH.

Remember rule 12 - attack the argument, not the arguer.

Replying to this modbox in thread will be off topic  Posted By: Gaspode

 

[The Man]

"Thank you" for ignoring http://www.internationalskeptics.com/forums/showpost.php?p=5382436&postcount=7274.

I did not ignore it, but if you are insisting on some remark then “nonsensical gibberish” would about sum it up.

Since you are able to get things only by T,F terms, you miss the ontological core that enables them in the first place.

So let us try another way to understand the ontological core of Logic.

By ontology we ask "what enables a thing before it is used for some purpose?”

For example, we can ask:”What enables Negation?”

The ontological answer to this question is as follows:

Negation is based on the ability to compare different things, such that ~X is anything but X.

That is not negation, you are still confusing negation with not equal to. 5 “is anything but” 3 however the negation of 3 is -3.

It means that there must be some other thing, which is ~X that is comparable with X, otherwise ~ is on X and the result is nothing at all.

Again that “other thing” is specifically defined as the negation of X. Again you can do all the “comparisons” you want or require, but it will not change the mutual dependence by negation of X with ~X and your “comparisons” are superfluous in that regard.

In that case we ask: “What enables X as a researchable thing?”

The ontological answer is:”X’s sameness-comparison”.

X’s sameness-comparison is a unary connective of a thing to itself, notated as =X, where "=" is the unary connective and X is the element.

Y’s sameness-comparison is a unary connective of a thing to itself, notated as =Y, where "=" is the unary connective and Y is the element.

Comparing something to itself is meaningless, it is a tautology and tells one nothing. Your “ontological answer is:”X’s sameness-comparison”” is a dead end a circular cul-de-sac as you even represent with your circular equal signs.

Negation is difference-comparison, and therefore it is binary connective of X with Y.

Without Negation as binary connective of X with Y, X or Y are isolated of each other, and each one of them is closed under “=” unary connective of sameness-comparison.

Negation is not a “comparison” your are simply still confusing negation with not equal to which is a comparative assertion stating some difference. Negation is not a “connective of X with Y” it is a connective of X with ~X.

Pay attention that that at the ontological core of Logic True or False concepts are not found, simply because True and False are some particular cases of Sameness\Difference Comparison, where Sameness\Difference Comparison is their ontological core.

Pay attention, in logic True or False are not concepts they are values. If you are claiming that your “ontological core of Logic” has no value then I’m certainly inclined to agree.

Here is a representation of the ontological core of Logic:

[qimg]http://farm3.static.flickr.com/2532/4162373367_f46d7871bd_o.jpg[/qimg]

Just your silly glasses again still signifying the circular reasoning of your “ontological core of Logic”

that can be notated also as =X ≠ =Y, where "=" is unary connective of sameness-comparison and "≠" is binary connective of difference-comparison.

Again, True and False are not found at the ontological core of Logic.

The buliding-blocks of the ontological core of Logic are Relations = or ≠ connectives, and X or Y, such that = is non-local w.r.t X or Y and ≠ is non-local w.r.t =X or =Y.

In other words, the ontological core of Logic is based on Non-locality\Locality Linkage.


1) At the ontological core of Logic TRUE or FALSE are not found.

2) “Belongs AND does not Belong” is exactly the non-locality of "=" w.r.t X or Y, or the non-locality of "≠" w.r.t =X or =Y.

Again Doron just your usual nonsensical gibberish and abominable understanding of basic operations like negation.

 

[jsfisher]

Moshe! Welcome back!

How's your search for a real world application of Organic Mathematics going?

As for this post of yours:

Opinion 104: The Shocking State of Contemporary "Mathematics", and the Meta-Shocking Fact that Very Few People Are Shocked
By Doron Zeilberger

Written: Oct. 28, 2009

I just came back from attending the 1052nd AMS (sectional) meeting at Penn State, last weekend, and realized that the Kingdom of Mathematics is dead. Instead we have a disjoint union of narrow specialties, and people who know everything about nothing, and nothing about anything (except their very narrow acre). Not only do they know nothing besides their narrow expertise, they don't care!

http://www.math.rutgers.edu/~zeilberg/OPINIONS.html

...generally it is considered proper to clearly delineate someone's words in some distinctive way. For example, I have reproduced your post within a "quote box". You should have done something like that in your post to clearly indicate you were reciting an excerpt from Opinion 104.

Ok, that aside, is there some aspect of the opinion piece you'd like to discuss? You didn't say anything of your own about the piece. Do you agree with it in its entirety? ...in part? Do you disagree with any of it? What parts do you find relevant to this thread?

 

[jsfisher]

Negation is based on the ability to compare different things, such that ~X is anything but X.

This is just so wrong.

Negation is not based on any ability. Nor is it based on comparison.

You also conflate things. Did you mean to restrict "negation" to just the realm of logic? That is certainly not implicit in your gibberish; in fact the opposite is implied.

You claim the bogus notion, "~X is anything but X." That's not negation; it's complementation, but it is wrong either way.


I realize it is very hard for you, doron, but please try to stay focused on one topic for a while. Please try to stay consistent with your terminology and notation, too. Too much to ask?


Oh, and this is important: What difference does it make whether negation is "based on an ability to compare" or not? What is the demonstrable consequence of your misguided notion?

 

[doronshadmi]

That is not negation, you are still confusing negation with not equal to. 5 “is anything but” 3 however the negation of 3 is -3.

Again we see that you limit negation only to two values.

5 “is anything but” 3 is a wrong example of my argument, under this limitation.

The right one is this: under two-valued system -3 “is anything but” 3 , and since we have exactly two values then “anything but” 3, is exactly -3, where in both cased 3 is itself (notated as =(3)) and -3 is itself (notated as =(-3)).

Also in this case =(3) ≠ =(-3), where ≠ is non-local w.r.t =(3) or =(-3) and = is non-local w.r.t (3) or (-3).

Again we see that you do not get the ontological core of Negation, because your notion is limited only to the particular case of using two-valued system of this concept.

You are like a user that knows how to use X in some particular way, but has no understanding of what enables X in the first place.

As a result you are closed under the illusion the that your particular use of X, is X.

...but it will not change the mutual dependence by negation of X with ~X

It will not change the fact that =(X) ≠ =(~X) under the limitations of two-valued system, where ≠ is non-local w.r.t =(X) or =(~X).

Also without this limitation it will not change the fact that =X ≠ =Y, where ≠ is non-local w.r.t =X or =Y.

Comparing something to itself is meaningless, it is a tautology and tells one nothing.

Comparing something to itself is the minimal term of Researchability, where X is compared to itself by =, where = is non-local w.r.t X.

Your narrow view of this subject is indeed resulted as “meaningless” under your limited notion.

Pay attention, in logic True or False are not concepts they are values.

You are talking about the level of using the particular case of Two-valued logic.

I am talking about the ontological core of any logic, where True or False are the concepts of the particular case of Two-valued system.

Again Doron just your usual nonsensical gibberish and abominable understanding of basic operations like negation.

Your notion, which is limited to the use of the particular case of two-valued system, prevents from you to understand the ontological core of Negation, which goes beyond using two-valued system.