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Deeper than primes

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This is exactly Non-local (NXOR) reasoning where:

The truth table is:
Code:
P not-P  
F  F   T   
T  T   T

NXOR is the logic of sameness, where XOR is the logic of the difference (your table).

Sameness alone or difference alone are not researchable, so the researchable is at least Sameness\Difference logic.

Please explain how P and not-P can have the same value.
 
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Please explain how P and not-P can have the same value. Failing that, please explain what you mean by 'not'.

Not-P is the limitation of the existence of P (and vice versa).

By Sameness reasoning this limitation has no significance (P is [_]_).

By Difference reasoning this limitation has significance (P is [_];[ ]_).
 
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Exactly, and you do not understand what you read.

No you simply do not undestand what you claim.


If P is Non-local then:

a) P XOR not-P is a contradiction.

b) P NXOR not-P is consistent.

Code:
[B]P[/B] not-P  NXOR
F  F      T    (Non-locality)
F  T      F    (Locality)
T  F      F    (Locality)
T  T      T    (Non-locality)

If P is Local then:

a) P NXOR not-P is a contradiction.

b) P XOR not-P is consistent.

Code:
[B]P[/B] not-P  XOR
F  F      F    (Non-locality)
F  T      T    (Locality)
T  F      T    (Locality)
T  T      F    (Non-locality)


Bolding “P” does not eliminate the contradictions noted before. Remember “P” represented ‘non-local reasoning’ so you adding your “(Locality)” references when “P” (‘non-local reasoning’) is true simply adds another contradiction to each of your tables. You now have three contradictions in each table, but again we have come to understand that you simply adding contradictions is the hallmark of your OM.


You simply do not get Non-local reasoning, which is the negation of Local reasoning.

You simply do not get the meaning of negation.
 
Not-P is the limitation of the existence of P (and vice versa).

By Sameness reasoning this limitation has no significance (P is [_]_).

By Difference reasoning this limitation has significance (P is [_];[ ]_).

Thus by your “Sameness” “non-local reasoning”, ‘not’ or ‘non‘ “has no significance”. ‘Local reasoning’ is no different from ‘non-local reasoning’ as such a limitation of “local-only reasoning” “has no significance” when one is engaged in ‘non-local reasoning’. Once again you clearly affirm that when you accuse someone of “local-only reasoning” it is simply you engaging in “local-only reasoning” in order to assert any “limitation” by that ‘not non-local reasoning’ difference. Again no one can find any significance in your assertions of ‘non-local reasoning’ if you claim it “has no significance” when one is engaging in it.
 
You simply do not get the meaning of negation.
The Man said:
Thus by your “Sameness” “non-local reasoning”, ‘not’ or ‘non‘ “has no significance”. ‘Local reasoning’ is no different from ‘non-local reasoning’ as such a limitation of “local-only reasoning” “has no significance” when one is engaged in ‘non-local reasoning’. Once again you clearly affirm that when you accuse someone of “local-only reasoning” it is simply you engaging in “local-only reasoning” in order to assert any “limitation” by that ‘not non-local reasoning’ difference. Again no one can find any significance in your assertions of ‘non-local reasoning’ if you claim it “has no significance” when one is engaging in it.

No, you simply do not get the meaning of Sameness reasoning as shown in http://www.internationalskeptics.com/forums/showpost.php?p=5325048&postcount=6856, because your rasoning is closed under Difference reasoning.

As result you are unable the get Sameness\Difference Reasoning (NXOR\XOR Reasoninig) and Non-locality\Locality Linkage.

It is explained also in terms of Symmety\Asymmery Linkage in http://www.scribd.com/doc/21954904/UP but also this paper is beyond you Asymmetric-only reasoning.

Time after time it is shown that you get things only in terms of Local reasoning limitations and miss the real reasoning, which is not less than Sameness\Difference Reasoning.
 
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No, you simply do not get the meaning of Sameness reasoning as shown in http://www.internationalskeptics.com/forums/showpost.php?p=5325048&postcount=6856, because your rasoning is closed under Difference reasoning.

As result you are unable the get Sameness\Difference Reasoning (NXOR\XOR Reasoninig) and Non-locality\Locality Linkage.

Remember Doron

Not-P is the limitation of the existence of P (and vice versa).

By Sameness reasoning this limitation has no significance (P is [_]_).

By Difference reasoning this limitation has significance (P is [_];[ ]_).

Thus by your “Sameness reasoning” the “N” or “NOT” in “NXOR” “has no significance” making it just the same as “XOR” in your “Sameness reasoning” . Again simply demonstrating that your “Sameness reasoning” “has no significance” even just for you. Again no one is likely to consider your notions to be of any significance if you can not show that at least you consider them to have significance. In fact quite to the contrary you emphatically claim a specific lack of significance when your notion of “Sameness reasoning” is applied to your “Sameness\Difference Reasoning (NXOR\XOR Reasoninig) and Non-locality\Locality Linkage”.
 
Remember Doron



Thus by your “Sameness reasoning” the “N” or “NOT” in “NXOR” “has no significance” making it just the same as “XOR” in your “Sameness reasoning” . Again simply demonstrating that your “Sameness reasoning” “has no significance” even just for you. Again no one is likely to consider your notions to be of any significance if you can not show that at least you consider them to have significance. In fact quite to the contrary you emphatically claim a specific lack of significance when your notion of “Sameness reasoning” is applied to your “Sameness\Difference Reasoning (NXOR\XOR Reasoninig) and Non-locality\Locality Linkage”.
"NXOR" or "XOR" are just names exactly as "Sameness" or "Difference" are just names.

The important thing is to understand the notion of some name.

Since you see things only in terms of negation then Difference is the result of unitary negation (X;not-X), and Sameness is the result of double negation (X;not-not-X).

Now let us use NXOR\XOR logic without Not.

Sameness=S ; D=Difference and we are talking about S\D Logic.

R=Result

Sameness Result is:
Code:
S D  R 
F F  T  S
F T  F  D
T F  F  D
T T  T  S
Difference Result is:
Code:
S D  R 
F F  F  S
F T  T  D
T F  T  D
T T  F  S

Both S and D are the aspects of a one logical framework, called S\D Logic, where S\D complement each other.
 
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In general:

Not unitary logical connective actually used as a limit that things are compared to it.

For example:

Let Not be [ ]

There are things that [ ] is a limit for them such that [_] [ ]_

There are things that [ ] is transparent for them such that [_]_

S\D Logic is the complement framework of both things.

EDIT: As you see limit AND transperency framework is more interesting than limit-only framework.
 
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So, the logical operator, NOT, means "any value at all independent of".

Thus, P and NOT P can both be true. How useless.
 
So, the logical operator, NOT, means "any value at all independent of".

Thus, P and NOT P can both be true. How useless.

It is very useful, since only NOT is an isolation of things form each other such that there is no connection between them, for example:

X is a place holder for an element and we have only NOT framework:

... X NOT X NOT X NOT X NOT ...

In the only NOT system any X is totally isolated and there is no framework.

In an only YES system we also do not have a framework, as follows:

X is a place holder for an element and we have only YES framework:

... X YES X YES X YES X YES ...

In the only YES system any X is totally connected and there is no framework.

So the minimal useful framework is X that is comparable by connection, such that X is not total isolation and the connector is not total connection.

All along this thread I am talking about a researchable framework, which is weaker than total connectivity (only YES state) and stronger than total isolation (only NOT state).

Also classical Logic is based on YES\NOT linkage, but classical logicians are focused only on the weak NOT side of YES\NOT linkage, without ask themselves how it is possible to compare X with NOT-X, in the first place.

OM asks this question, and the answer is the weak YES side of YES\NOT linkage, which enables the comparison of X with NOT-X, in order to conclude that X in not NOT-X.

The logic of YES under YES\NOT linkage is a weak version of only-Sameness (total connectivity).

The logic of NOT under YES\NOT linkage is a weak version of only-Difference (total isolation).

No total state is a researchable framework, but in Classical Logic the logicians are using NOT without the understanding that they are actually using the weak version of NOT, which is weak exactly because it is under YES\NO linkage logical framework.

So once again:

Total NOT is resulted at least as a point.

Total YES is resulted at least as an endless (edgeless) straight Line.

No one of these total states is researchable (a point in itself is too weak and a line in itself is too strong).

Only a segment (ray is included) is researchable exactly because it is the result of YES\NO linkage logical framework, such that the NOT aspect of the linkage is transparent to the line aspect of the linkage (and we have the connection of X with NOT-X that enables the comparison under YES\NOT linkage) and the NOT aspect of the linkage is sealed to the point aspect of the linkage (and we have the isolation of X from NOT-X that enables the identity under YES\NOT linkage).

If the YES aspect of YES\NOT linkage is dominant, then we have superposition of Ids.

If the NOT aspect of YES\NOT linkage is dominant, then we have unique Ids.

Organic Numbers express exactly this.
 
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Please explain how the logical operator 'Not' can be a pair of brackets with a space between them.

We do not need a pair of brackets, for example:

Let NOT be |

There are things that | is a limit for them such that __|__

There are things that | is transparent for them such that _|_
 
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"NXOR" or "XOR" are just names exactly as "Sameness" or "Difference" are just names.

The important thing is to understand the notion of some name.

Apparently why you think just ascribing names to things somehow imbues them with some characteristic by virtue of simply your ascribed name. The important thing (as I have said before Doron) is to actually learn the concepts you base your arguments upon.


Since you see things only in terms of negation then Difference is the result of unitary negation (X;not-X), and Sameness is the result of double negation (X;not-not-X).

Since I do not “see things only in terms of negation” your assertions are as ludicrous as ever. The only negation difference requires is that something is not the same. The same as “Sameness” requires that it is not different.


Now let us use NXOR\XOR logic without Not.

Meaning you are just using “XOR”


Sameness=S ; D=Difference and we are talking about S\D Logic.

R=Result

Sameness Result is:
Code:
S D  R 
F F  T  S
F T  F  D
T F  F  D
T T  T  S
Difference Result is:
Code:
S D  R 
F F  F  S
F T  T  D
T F  T  D
T T  F  S


Nope you stuck the “Not” back in there for "NXOR", otherwise your “Difference Result” would not have been, well, different.

Both S and D are the aspects of a one logical framework, called S\D Logic, where S\D complement each other.

What a joke, you’ve employed no “logical framework” your are just playing games with your F, T, S and D letters as you think such arrangements of letters somehow imbues your so “called S\D Logic” with some form of, well, logic.
 
In general:

Not unitary logical connective actually used as a limit that things are compared to it.

For example:

Let Not be [ ]

There are things that [ ] is a limit for them such that [_] [ ]_

There are things that [ ] is transparent for them such that [_]_

S\D Logic is the complement framework of both things.

EDIT: As you see limit AND transperency framework is more interesting than limit-only framework.

This does not help you Doron. By your “difference reasoning” that “difference reasoning” is not different than, well, your “difference reasoning”. By your “sameness reasoning” “not” is “insignificant” thus you have no basis to claim by your “sameness reasoning” that your “difference reasoning” is “not” the same as your “sameness reasoning” (or even your “complement framework of both things“). As a consequence of your own expressed nature of your “sameness reasoning” having a “complement framework of both things” is the same as your “difference reasoning” since the additional inclusion of your “sameness reasoning” can make no, well, difference.
 
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