Cont: Deeper than primes - Continuation 2

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doronshadmi said:
Well, it is an example of jsfisher's logic that forces OR to be XOR.
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Not at all. This issue is whether the expression x OR ~x is in any way different from x XOR ~x.

According to you, Doronshadmi, they are different. Real Mathematics doesn't agree.
 
doronshadmi said:
Please demonstrate your argument by using T ~T as seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11294564&postcount=1579.
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That would be one of the many posts where you treat x and ~x as independent variables. They are not. Both the expression x OR ~x and the expression x XOR ~x are expressions of one free variable (x, in case you missed it), not two.

The variable x can be either valued true or false.

If x is true then ~x is false and x OR ~x is true and so is x XOR ~x.
If x is false then ~x is true and x OR ~x is true and so is x XOR ~x.

The two expressions are indistinguishable.
 
jsfisher said:
That would be one of the many posts where you treat x and ~x as independent variables. They are not. Both the expression x OR ~x and the expression x XOR ~x are expressions of one free variable (x, in case you missed it), not two.

The variable x can be either valued true or false.

If x is true then ~x is false and x OR ~x is true and so is x XOR ~x.
If x is false then ~x is true and x OR ~x is true and so is x XOR ~x.

The two expressions are indistinguishable.
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Unlike in XOR logical connective, OR logical connective enables x or ~x to be optional properties of a given primitive, for example:

Code: 
x OR ~x
-------
T     T ---> T

In other words, your "real math" is too weak in order to realize it.

As about the issue at hand, being a successor OR not being a successor are both optional properties of primitive {X}, but jsfisher's "real math" can't realize that since it is stuck at XOR that prevents them of being both optional properties of primitive {X}.

More generally, being optional is not an option by jsfisher's "real math".
 
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jsfisher said:
I could not have summarized doronetics any better, Doron: self-contradicting. Thank you.
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You still do do not understated that being an option OR its negation of a given primitive does not mean that an option AND its negation are used do define the relations of that primitive with another primitive.

For example: ({X} IsSuccessorOf X is a true option) OR ({X} ~IsSuccessorOf X is a true option) and this is exactly the meaning of
Code: 
x OR ~x
-------
T     T ---> T

Since being optional is not an option by jsfisheretics he simply misses the issue at hand.

Moreover, jsfisheretics actually fails to comprehend what he calls "real math" as seen in the following part:
In logic, or by itself means the inclusive or, distinguished from an exclusive or, which is false when both of its arguments are true, while an "or" is true in that case.
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(https://en.wikipedia.org/wiki/Logical_disjunction)

Forthermore, according to jsfisheretics the following truth tables are indistinguishable:

Code: 
 T OR ~T
~T    ~T --> ~T
~T     T -->  T
 T    ~T -->  T
 T     T -->  T

Code: 
 T XOR ~T
~T     ~T --> ~T
~T      T -->  T
 T     ~T -->  T
 T      T --> ~T
 
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doronshadmi said:
You still do do not understated that being an option OR its negation of a given primitive does not mean that an option AND its negation are used do define the relations of that primitive with another primitive.
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I never said it was. What I said was that ~x is not independent of x. If x is true, then ~x must be false. If x is false, then ~x must be true. The truth table for the expression x OR ~x is very simple and has only two lines, not four:
[table=heading]x |:| x OR ~x
T |:|
T​
|
F |:|
T​
[/table]​

The expression x XOR ~x has exactly the same true table.
 
jsfisher said:
I never said it was. What I said was that ~x is not independent of x.
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What you say is irrelevant to ({X} IsSuccessorOf X is a true option) OR ({X} ~IsSuccessorOf X is a true option) and this is exactly the meaning of
Code: 
x OR ~x
-------
T     T ---> T
which is a part of four lines truth table

Code: 
 x OR ~x
~T    ~T --> ~T
~T     T -->  T
 T    ~T -->  T
 T     T -->  T
 
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abaddon said:
That isn't a definition.
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({X}$X) OR ({X}~$X) ($ is an optional property of {X}) is an exact definition of an optional property.

jsfisheretics, abaddonetics and Little_10_Toesetics have the same built_in non useful restrictions that prevent the comprehension of optional properties.
 
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