Deeper than primes

[doronshadmi]

Right, again. By the way, would it confuse you to point out that both A and ~A are expressions?

Call A "free variable" or "expression" , or call ~A "expression" , it still does not change anything exactly because the important thing is that A and ~A are different, exactly as you write, for example here:

T NXOR ~T and F NXOR ~F. Nothing else.

Again,

Let us use "free variable" and "expression".

I do not claim that A replacement = ~A expression's value (no matter if the replacement is logical propositions like T or F, or any other value).

I do claim that if the T,F logical propositions (which are used as inputs that checks the replacement of A and ~A expression's value) are the same logical propositions (input F F or input T T) and the result of the checking is T (the logical proposition T), then there is Non-locality (mutuality) among A free variable and ~A expression's value.

I do claim that if the T,F logical propositions (which are used as inputs that checks the replacement of A and ~A expression's value) are different logical propositions (input F T or input T F) and the result of the checking is T (the logical proposition T), then there is Locality (independency) among A free variable and ~A expression's value.

You can use "free variable" or "expression", yet it does not change anything.

Yet A/~A framework is mutuality/independency linkage.

 

[The Man]

No The Man, I clearly assert that a formula is the invariant aspcet and the data is the variant aspect of any formula\data linkage.

You simply can't grasp it.

So you are back to your pervious and demonstrably incorrect assertion that a formula does not change even when the type of data changes. Doron data isn’t just numbers, it is information. Part of that information is things like units and dimension or other types of information like scalar, vector or even tensor. Formulas relate that information (all of that information) and those formulas can and often must change as the data changes. Formulas even change one type of data into another. This “formula is the invariant aspect and the data is the variant aspect of any formula\data linkage” is just another one of your dichotomistic fantasies, another one of your different names for the same thing without any meaning.

 

[jsfisher]

...the important thing is that A and ~A are different, exactly as you write, for example here:

T NXOR ~T and F NXOR ~F. Nothing else.

Well, since you agree with that conclusion, why to you include other cases in your table for A NXOR ~A?

You agree that T NXOR ~T and F NXOR ~F are the only admissible possibilities, which reduce to T NXOR F and F NXOR T, yet you still include two other inaccessible possibilities of T NXOR T and F NXOR F.

Again,
...<repetitious wrongness snipped>...

 

[epix]

epix, just take into account that T and F are different, then ask yourself what enables the comparison between them.

Well, that's the beef of the matter. Doron, just follow the guiding light:

--------> "If an Electron Can Be in Two Places at Once, Why Can't You?"
http://discovermagazine.com/2005/jun/cover

The dual position of an electron, or a photon, provides the empirical background for the validity of A= ~A in a special case, as much as T and F can determine symbols that represent True and False. Suppose that T is substituted by '='. It means that F must be substituted by a symbol of comparison that doesn't hold two variables equal to each other -- symbols such as '>', '<', and so on.
But the comparison of T and F can select a "very likely" symbol for the negation option 'False'.

Proposition Alpha:
'T' is "collection of 2 straight lines"
'F' is "collection of 3 straight lines"

Proposition Beta:
'=' is "collection of 2 straight lines"
'≠' is "collection of 3 straight lines"

Now you can see that Alpha and Beta are "congruent" propositions. You can also see that the substitution for F is "determinable" due to F's dependency on the description of T. If you consider only the logical meaning of T = "equals to", the list of options for the F substitution becomes undesirably long.

You saw that your XOR truth table doesn't work in a real application of XOR. But electrons are real and can be in two different places at the same time. If you consider again the example where A can take on values from 4 to 7, and you chose A = 4, then ~A can take on only those values so that ~A ≠ 4. But there are two ways to express this limitation:

1. ~A ≠ 4
2. ~A > 4

I used the second option in that short source code, but the first option would do the job as well.

Doron, if ' ≠ ' and ' > ' are two different symbols, then how come they have an identical function in that XOR gate routing? Does this contradiction have something to do with the electrons being able to be in two different places at once? Work on it a bit . . .

The Discover magazine article asks the question why is it so that if electrons can be in two different places at once (A = ~A) why can't we, when our bodies include electrons.

You don't have to be a heavy-duty PhD to answer the question. In such a case we could be . . . .
And that includes the Burger King option.

 

[doronshadmi]

A is a free variable.

According to Classical logic it can get only two values, which are True or False.

According to OM logic A gets any value or its negation.

So by OM logic A is not limited only to True or False values, for example, A value can be Included or Excluded.

If A = Included , then ~A = Excluded

If A = Excluded, then ~A = Included.

In both cases there are two different values, no matter what A value is.

By Classical logic we are using two variables, called A and B, such that B value is the same or different than A value, where again the values can be only True or False.

By using, for example, NXOR connective between A,B, and by limiting A or B values to True or False, A NXOR B is True if A=B, or A NXOR B is False if A≠B.

In that case NXOR truth table is:

By A=B case:
F NXOR F --> T
T NXOR T --> T
By A≠B case:
F NXOR T --> F
T NXOR F --> F

And we get:

A NXOR B
--------------
F NXOR F --> T
F NXOR T --> F
T NXOR F --> F
T NXOR T --> T


OM does not follow this tradition, which is local-only by nature, and it is local-only by nature because:

1) A=B is a single value, so the True result refers to a single value that cannot be simultaneity in more than a one state.

2) A≠B are two values , but the False result refers to the inability to be simultaneously in more than a one state.

In other words, Classical logic is tuned to deal with values that can't be simultaneously in more than a one state.

Instead, OM explicitly deals with conditions that enable to define the logic of Non-locality, which is the ability to be simultaneously in more than a one state.

In that case A=B is worthless because only a single value is defined.

So we left with A≠B and one of the cases of it is A ≠ ~A, where we deal with different values.

Now, by OM logic A value is not only T or F, but it is any given value or its negation, and by using this ability we can research the logical foundations of Membership, as follows:

A=Member

~A= the negation Member (in that case we can use a single word like Rebmem, exactly as F is ~T).

So we have this truth table of Membership if NXOR connective is used:

Member NXOR Rebmem.

Now we are using the True/False values as logical inputs that check Member NXOR Rebmem, and what we get is this truth table:

Member NXOR Rebmem
-------------------------------
F NXOR F --> T (Simultaneity of Member\Rebmem = Non-locality)
F NXOR T --> F (Non-simultaneity of Member\Rebmem = Locality)
T NXOR F --> F (Non-simultaneity of Member\Rebmem = Locality)
T NXOR T --> T (Simultaneity of Member\Rebmem = Non-locality)

Now let us check Member XOR Rebmem truth table:

Member XOR Rebmem
-------------------------------
F XOR F --> F (Simultaneity of Member\Rebmem = Non-locality)
F XOR T --> T (Non-simultaneity of Member\Rebmem = Locality)
T XOR F --> T (Non-simultaneity of Member\Rebmem = Locality)
T XOR T --> F (Simultaneity of Member\Rebmem = Non-locality)

 

[jsfisher]

A is a free variable.

According to Classical logic it can get only two values, which are True or False.

According to OM logic A gets any value or its negation.

"Any value" would include its negation. Why the redundancy?

"According to" Mathematics, a variable can take on any value within the domain under consideration. If the domain is that defined for logic, then the accessible values are true and false.

So by OM logic A is not limited only to True or False values, for example, A value can be Included or Excluded.

If A = Included , then ~A = Excluded

If A = Excluded, then ~A = Included.

As long as "excluded" exactly means "not included", sure. Real Mathematics allows the same.

In both cases there are two different values, no matter what A value is.

Only as long as "not" is unambiguously defined for the domain under consideration. For example, it is unclear what one might mean by "~{{2},banana}"

By Classical logic we are using two variables, called A and B, such that B value is the same or different than A value, where again the values can be only True or False.

You seem to be coming to grips with the concept of "independent variables."

By using, for example, NXOR connective between A,B, and by limiting A or B values to True or False, A NXOR B is True if A=B, or A NXOR B is False if A≠B.

In that case NXOR truth table is:

By A=B case:
F NXOR F --> T
T NXOR T --> T
By A≠B case:
F NXOR T --> F
T NXOR F --> F

And we get:

A NXOR B
--------------
F NXOR F --> T
F NXOR T --> F
T NXOR F --> F
T NXOR T --> T

Although that is a non-standard presentation of truth tables, you've captured the essence.

OM does not follow this tradition, which is local-only by nature, and it is local-only by nature because:

1) A=B is a single value, so the True result refers to a single value that cannot be simultaneity in more than a one state.

Yes, equality is a logic-valued binary operator. It produces a single true/false result for any pair of operands.

2) A≠B are two values , but the False result refers to the inability to be simultaneously in more than a one state.

Ok, your inequality operator doesn't match the inequality operator in Mathematics. I can express the definition for A ≠ B as follows:

(A ≠ B) = ~(A = B)​

How do you define your inequality operator?

In other words, Classical logic is tuned to deal with values that can't be simultaneously in more than a one state.

That is how Classical Logic is defined. It was intentional it behave that way. Mathematics, itself, has no such limitation or requirement.

Instead, OM explicitly deals with conditions that enable to define the logic of Non-locality, which is the ability to be simultaneously in more than a one state.

Define? You have yet to define anything. Are you going to surprise us now?

In that case A=B is worthless because only a single value is defined.

How is that worthless? Seems rather useful to me. The result of the equality operator is either true or false, a single value, and that result is based on the operator's two operands.

This is an entirely reasonable arrangement for a binary operator.

So we left with A≠B and one of the cases of it is A ≠ ~A, where we deal with different values.

Where are you going with this? A ≠ A is also a "case", it just happens to be one for which the result is universally false. At least that is how it works in real Mathematics. Since you have yet to define your inequality operator for Doronetics, there is no telling how it behaves, I suppose.

Now, by OM logic A value is not only T or F, but it is any given value or its negation

Again, "any given value" already includes its negation as a possibility.

...and by using this ability we can research the logical foundations of Membership, as follows:

A=Member

Meaning what, exactly? Are there some implied parameters, here, and what you are saying is "something₁ is a member of something₂"? Is "Member" a true/false valued proposition? Or did you have something else in mind?

~A= the negation Member (in that case we can use a single word like Rebmem, exactly as F is ~T).

So, whatever you meant by "Member", this "Rebmem" is everything except that. Yes? And if "Member" is a true/false valued proposition, then "Rebmem" must also be a true/false valued proposition, yes?

So we have this truth table of Membership if NXOR connective is used:

Member NXOR Rebmem.

Now we are using the True/False values as logical inputs that check Member NXOR Rebmem, and what we get is this truth table:

Member NXOR Rebmem
-------------------------------
F NXOR F --> T (Simultaneity of Member\Rebmem = Non-locality)
F NXOR T --> F (Non-simultaneity of Member\Rebmem = Locality)
T NXOR F --> F (Non-simultaneity of Member\Rebmem = Locality)
T NXOR T --> T (Simultaneity of Member\Rebmem = Non-locality)

Now let us check Member XOR Rebmem truth table:

Member XOR Rebmem
-------------------------------
F XOR F --> F (Simultaneity of Member\Rebmem = Non-locality)
F XOR T --> T (Non-simultaneity of Member\Rebmem = Locality)
T XOR F --> T (Non-simultaneity of Member\Rebmem = Locality)
T XOR T --> F (Simultaneity of Member\Rebmem = Non-locality)

All this accomplished is that you have shown "Rebmem" isn't the negation of "Member."

Relabeling things from A/~A to Member/Rebmem doesn't change the meaning.

 

[Little 10 Toes]

Since this thread is going faster than I can handle right now, I'll bow out for the moment. But doronshadmi has admitted that A and ~A are different.

 

[jsfisher]

Since this thread is going faster than I can handle right now, I'll bow out for the moment. But doronshadmi has admitted that A and ~A are different.

...and then he contradicts his admission.

 

[The Man]

...and then he contradicts his admission.

Well that is because he is simultaneously in two states, agreeing with himself AND disagreeing with himself. Non-locally this is not a problem, which is why he has a problem when we disagree with him. As this is construed as being simply local, in order to be non-local, however, we must (as he does) disagree with him AND agree with him simultaneously. A rather pointless exercise as there can be no resulting evaluation.

Let’s just take negation.

Proposition “A” is simultaneously TRUE AND FALSE

Thus the negation of “A” is simultaneously FALSE AND TRUE.

One could perhaps distinguish the two by ordering (though Doron apparently doesn’t like ordering in his OM) as proposition “A” is simultaneously TRUE AND FALSE while the negation of “A” is simultaneously FALSE AND TRUE.

However there is no reason “A” should be TRUE AND FALSE as opposed to FALSE AND TRUE. So the principle function of negation loses all relevance (probably why Doron tries to attribute logical negation to the common inference of “anything but”). However as I have stated before in a two value system, or binary logic, the two meanings overlap so “anything but TRUE” is still only “FALSE”. Doron apparently wants to make it a three value system of TRUE, FALSE and (perhaps) MAYBE. Unfortunately the MAYBE just becomes a third “state” which Doron apparently does not like either. As he tends to balk at such inferences, specifically by stating his “superposition” does not use the principle of superposition. Again this is simply not a problem for him as he can disagree with himself and agree with himself simultaneously. As I have said many times before, I have no problem with that, if that was simply the way that he presented his notions. However it is the continuing misrepresentation and misuse of well established and demonstrably useful concepts as just some particular aspect of him just disagreeing AND agreeing with himself simultaneously that keeps me here disagreeing with him and his agreement to disagree with himself and those well established and demonstrably useful concepts .

 

[jsfisher]

Well that is because he is simultaneously in two states, agreeing with himself AND disagreeing with himself. Non-locally this is not a problem, which is why he has a problem when we disagree with him. As this is construed as being simply local, in order to be non-local, however, we must (as he does) disagree with him AND agree with him simultaneously. A rather pointless exercise as there can be no resulting evaluation.

Well put.

Let’s just take negation.

Proposition “A” is simultaneously TRUE AND FALSE

Thus the negation of “A” is simultaneously FALSE AND TRUE.

No. See, that's just wrong. ~A is anything but A, including A. Sure, it can be False AND True, but it doesn't have to be. You get to choose. It can be True, it can be False, and it can be True and False (which is completely different from False and True).

I don't know how you made such a mistake.

Moreover, you can now add something meaningless like A = banana and ~A = Rebban, then apply half-adder logic, HAL:

banana HAL Rebban
   F         F    -->    F               (Need handout)
   F         T    -->    T               (Mine, all mine)
   T         F    -->    T               (Mine, all mine)
   T         T    -->    T, carry the T  (One for me, and one to share)

You just don't get HAL logic!!

 

[epix]

I'm not familiar with all the dark alleys that doronetics walks through, so I would find the shortest way leading to the nearest liquor store. (You've mentioned the classic period, so there is no GPS to show the beeline.) But there are some similarities, which I've found interesting.

Now I sort of understand your insistence on having proposition variables A and ~A, in your truth table, which is the place where your definition of "local" and "non-local" takes place. That sort of understanding travels via

A is to LOCAL as ~A is to ~LOCAL

Here is another, related similarity. This one is not that apparent without invoking the classic period of quantum mechanics that put the words "local" and "non-local" in to the dictionary of physics.

Since "similarity" doesn't equal "identity," there is no need for definitions; just let's say that locality and non-locality consist of two major ingredients: distance and influence. Both ingredients refer to subatomic particles. When the distance between particle A and B is "short," both particles are said to live in local space and when the distance between A and B is "long," the particles are non-local. But this terminology is modified by the second ingredient, that is by the influence, coz A can have external influence on B.

Now let's lay all possible combinations down on the table with '_' (understrike) symbolizing the influence.

1. A__B /local and influence
2. A....B /local and no influence
3. A____________B /non-local and influence
4. A....................B /non-local and no influence

The obvious question is which option(s) is or are true. But due to the logic of opposites

QUESTION is to OBVIOUS as ANSWER is to NOT OBVIOUS

the answer remained obscured even to Herr Professor:

The following idea characterises the relative independence of objects far apart in space A and B: external influence on A has no direct influence on B; this is known as the Principle of Local Action, which is used consistently only in field theory. If this axiom were to be completely abolished, the idea of the existence of quasienclosed systems, and thereby the postulation of laws which can be checked empirically in the accepted sense, would become impossible.

So lets take a bold step in abolishing the axiom, that is A has no direct influence on B.
How we are going to do that?
Well, if A has no direct influence on B, then B is independent of A. In order to change that, set B = ~A. Since A and ~A are "dependent" particles, all you have to do is to specify what is local and what is non-local and examine the four options for True and False by running it through XOR and NXOR gate, as shown bellow.

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)

But there is a problem that I already pointed out and demonstrated: there is no real XOR and NXOR gate that would "empirically" evaluate Doron's truth tables. But this fact contradicts the last sentence of Albert Einstein's conjecture:

If this axiom were to be completely abolished, the idea of the existence of quasienclosed systems, and thereby the postulation of laws which can be checked empirically in the accepted sense, would become impossible.

Who got the smarts here?
Albert Einstein - no doubt about it. And that means there is a system that can accept Doron's XOR/NXOR theoretical tables on the empirical level, and the system is right here -------------->

If Doron's tables happen to be correct, then the truth will not be available only to the highly educated personnel that operates the LHC; the truth will be known to EVERYONE.


You know, Doron, I thought you were going to intervene here:

The dual position of an electron, or a photon, provides the empirical background for the validity of A= ~A . . .

That's nonsense, coz the physical property of an electron have no bearing on a logical property of A<> ~A, coz the term is an abstract logical axiom, as much as mathematical infinity is a purely abstract concept.

 

[The Man]

Well put.



No. See, that's just wrong. ~A is anything but A, including A. Sure, it can be False AND True, but it doesn't have to be. You get to choose. It can be True, it can be False, and it can be True and False (which is completely different from False and True).

I don't know how you made such a mistake.

Moreover, you can now add something meaningless like A = banana and ~A = Rebban, then apply half-adder logic, HAL:

banana HAL Rebban
   F         F    -->    F               (Need handout)
   F         T    -->    T               (Mine, all mine)
   T         F    -->    T               (Mine, all mine)
   T         T    -->    T, carry the T  (One for me, and one to share)

You just don't get HAL logic!!

Oh no!!! jsfisher going all non-local on us with his banana!!

It is spreading (non-locally that is)!!

Thank you for that, I know everything hasn't been quite right with me, but I can assure you now, very confidently, that it's going to be all right again. I feel much better now. I really do.

 

[jsfisher]

One more thing of note: My HAL logic trumps NXOR reasoning any day of the week. In terms of bridging Mathematics and ethnics, the best Doronetics with its NXOR reasoning can do is emulate absentee fathers with its non-local parentis. HAL logic, on the other hand, has built into it the fundamentals of charity (F HAL F) and sharing (T HAL T).

Isn't that a better result?


I'll all a-tingle.

 

[jsfisher]

By the way, in my zeal to post the basics of HAL, I inadvertently used the AND/OR variant. In the more common version, which also serves as the foundation for the advanced FAL, the result for T HAL T is F, carry the T (caring is sharing).

While the variant has its own richness, particularly in the Ethics/Mathematics interaction realm, the regular HAL and its follow-on FAL present of breadth of research discovery space unsurpassed by any common technique of comparable complexity. I will, therefore, stay with the traditional HAL treatment.

 

[doronshadmi]

Only as long as "not" is unambiguously defined for the domain under consideration. For example, it is unclear what one might mean by "~{{2},banana}"

Since ~ is "Anything but A" and A="{{2},banana}", then ~A is not necessarily the opposite of A, ~A is fist pf all different than A, and this is the important thing here.

How is that worthless? Seems rather useful to me. The result of the equality operator is either true or false, a single value, and that result is based on the operator's two operands.

This is an entirely reasonable arrangement for a binary operator.

By A=A = A=B I mean that we have one and only one value (differentially is impossible). A as a placeholder of different values is not A=B case.

"Any value" would include its negation. Why the redundancy?

By "A gets any value or its negation" we mean that any given A value is different than its negation, for example A=True or A=False where True\False are different values.

Classical logic stops here and does not ask "what is the basis of the reasoning, which enables A to be a placeholder of different values (for example: A=True or A=False)"?

OM reasoning is the answer to this question, by defining Non-locality in addition to Locality, and by defining Non-locality\Locality Linkage, which is not Local and not Non-local, (the un-manifested foundation of any given id or id's relations).

You seem to be coming to grips with the concept of "independent variables."

You seem to grips only the independence aspect among A\B variables, which are actually mutually-independent.

Mathematics, itself, has no such limitation or requirement.

1) Since Mathematical is not some external object out there, there is no such thing like "Mathematics, itself". If it was true then Mathematics was totally isolated of us, and it is obviously not the case.

2) Limitation or requirement are the local aspect of the mathematical science, in addition to the ability to be developed beyond some given limitations or requirements. Closeness\openness dynamic balance is the essence of this science, and because of this dynamic balance the mathematical science can be developed beyond the context-dependent deductive-only isolated frameworks, into a one organic form, which is non context-dependent, but it is a complex organ, which is developed by evolution (including mutations of already agreed\established notions, where "what is Definition"? is one of these notions).

Define? You have yet to define anything.

This is a typical conclusion of a person that thinks that there is such a thing like " Mathematics, itself", which has a one and only one method to define it.

All this accomplished is that you have shown "Rebmem" isn't the negation of "Member."

All this accomplished is that although "Rebmem" is the negation of "Member.", we do not get into contradiction is non-locality is logically defined among A\~A different values.

 

[doronshadmi]

A is to LOCAL as ~A is to ~LOCAL

Member=LOCAL

Rebmem=~LOCAL (the same as F=~T)

Member NXOR Rebmem.

Now we are using the True/False values as logical inputs that check Member NXOR Rebmem, and what we get is this truth table:

Member NXOR Rebmem
-------------------------------
F NXOR F --> T (Simultaneity of Member\Rebmem = Non-locality)
F NXOR T --> F (Non-simultaneity of Member\Rebmem = Locality)
T NXOR F --> F (Non-simultaneity of Member\Rebmem = Locality)
T NXOR T --> T (Simultaneity of Member\Rebmem = Non-locality)

Now let us check Member XOR Rebmem truth table:

Member XOR Rebmem
-------------------------------
F XOR F --> F (Simultaneity of Member\Rebmem = Non-locality)
F XOR T --> T (Non-simultaneity of Member\Rebmem = Locality)
T XOR F --> T (Non-simultaneity of Member\Rebmem = Locality)
T XOR T --> F (Simultaneity of Member\Rebmem = Non-locality)

In other words, NXOR or XOR are the Relation (Non-local aspect) and Member or Rebmem are the Element (Local aspect) or both truth tables.

 

[doronshadmi]

Ok, your inequality operator doesn't match the inequality operator in Mathematics. I can express the definition for A ≠ B as follows:
(A ≠ B) = ~(A = B)
How do you define your inequality operator?

Exactly as you do, which is: "A value is different than B value".

I ask: What enables to know it?

You do not ask this question. You just define (A ≠ B) = ~(A = B) without trying to under-stand it.

 

[doronshadmi]

Well that is because he is simultaneously in two states, agreeing with himself AND disagreeing with himself.

"agreeing with himself AND disagreeing with himself" is exactly the Local-only view of Non-locality\Locality Linkage.

There is no "himself" here (a one thing), there is Simultaneity of Member\Rebmem, which are different things.

 

[jsfisher]

Since ~ is "Anything but A" and A="{{2},banana}", then ~A is not necessarily the opposite of A, ~A is fist pf all different than A, and this is the important thing here.

Well, I see I cannot let the semantic quibble slide after all. Complementation (the operation represented by the tilde) does not mean "anything but". It means "everything but".

The complement of "all Greeks are liars" isn't any of many, many possibilities and you get to choose which one. It is exactly "not all Greeks are liars".

Under the implicit domain, the complement of the Earth is the entire universe with the Earth removed. Mars is not ~Earth, nor is Betelgeuse a possibility for ~Earth. ~Earth = Universe\Earth (where \ is the generalized difference operator).

Please stop making up stuff to cover you ignorance of Mathematics.

 

[The Man]

"agreeing with himself AND disagreeing with himself" is exactly the Local-only view of Non-locality\Locality Linkage.

There is no "himself" here (a one thing), there is Simultaneity of Member\Rebmem, which are different things.

Doron, it doesn’t matter much to me what you want to agree AND disagree with.