Cont: Deeper than primes - Continuation 2

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jsfisher said:
It is not math. It warrants no other reply.
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It is nonsense to claim that contradiction (A AND ~A) or tautology (A OR ~A) is not Math, just because you do not understand that by A OR ~A, A and its negation are not taken simultaneously, or that by A AND ~A, A and its negation are taken simultaneously.
 
jsfisher said:
Attempting to give those typographic squiggles some deep set theoretic meaning is neither mathematics nor completely rational.
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Ignoring the formalization of outer braces that logically define them as tautology, or by ignoring the formalization of the void between the braces that logically defines it as contradiction, is neither mathematics nor completely rational.

Because of your neither mathematical nor completely rational approach about the issue at hand you can't deal with ~contradiction AND ~tautology as formal definition of being a member.

Moreover, http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900 and its related links are not interact with your neither mathematical nor completely rational approach about the issue at hand.

Furthermore, you continue the exclude mathematicians as factors of Mathematics, and by doing this you demonstrate your ignorance of how Mathematics is actually discovered OR invented.

jsfisher, please do not lose your effective criticism.

http://www.internationalskeptics.com/forums/showpost.php?p=11361086&postcount=1920 is not an effective criticism, so please try again.
 
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MetalPig said:
We are talking about this:
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Actually our last discassion was about AND logical connective, as seen in http://www.internationalskeptics.com/forums/showpost.php?p=11360788&postcount=1915 and in my corrected reply to you in http://www.internationalskeptics.com/forums/showpost.php?p=11360932&postcount=1917.

MetalPig said:
You claim contradictions can be true.

And now:

You claim contradictions can not be true.

So which is it?
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If you read very carefully http://www.internationalskeptics.com/forums/showpost.php?p=11360932&postcount=1917, you can realize that I do not claim that contradiction can be true.

What I claim is that A AND ~A means that A and its negation are taken simultaneously, and the result is contradiction.

On the contrary I claim that A OR ~A means that A and its negation are not taken simultaneously, and the result is tautology.
 
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MetalPig said:
We are talking about this:


Then you claimed ~A is the negation of A
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Let's use OR.

In http://www.internationalskeptics.com/forums/showpost.php?p=11359187&postcount=1901 ~A is defined such that no options are defined.

In that case A OR ~A ---> T (tautology) since A,~A are not simultaneously taken.

Now let's define ~A by the claims about the defined options.

In case of OR, It is T to claim that the two defined options are not simultaneously taken (written as T(for one option) OR T(for the other option) --> T(for not simultaneously be taken)) and since they are not simultaneously taken, indeed A OR ~A ---> T (tautology) exactly as claimed about the defined options by T OR T --> T.

Also let's correct what was written about the claims about the defined options in case of A OR ~A truth table:

By using OR logical connective between the defined options, the truth table is as follows:

It is ~T to claim that no one of the defined options is possible (written as ~T OR ~T --> ~T)

It is T to claim that at least one of the defined options is possible (written as T OR ~T --> T, ~T OR T --> T)

It is T to claim that the two defined options are not simultaneously taken (written as T OR T --> T)

So the truth table of A OR ~A is:

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

OR logical connective guarantees that the two defined options are not simultaneously taken, so the contradiction avoided (A OR ~A --> T (tautology)).
 
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jsfisher said:
Nope. The expression, A OR ~A, is a formula of only one free variable. It has only two instantiations, not four.
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If A's options are considered, then the formula is not of only one free variable.

In other words, there are four cases, as given in http://www.internationalskeptics.com/forums/showpost.php?p=11361427&postcount=1925, that logically are not simultaneously taken, where not simultaneously taken is the essence of OR logical connective.

Simultaneously taken is the essence of AND logical connective, but it does not change the fact that if A's options are considered, then the formula is not of only one free variable, as given in http://www.internationalskeptics.com/forums/showpost.php?p=11360932&postcount=1917.
 
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jsfisher said:
If you ignore Mathematics, sure. Most of us, though, would prefer not to.
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Your reasoning ignores A's two options, no less no more, simply because option is not optional by your reasoning.
 
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jsfisher said:
What I said was that ~x is not independent of x. If x is true, then ~x must be false.
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EDIT:

No one claims that ~x is independent of x.

What is claimed is that x has two options, where x is not a free variable.

In order to be clearer: given x, x has at least two options, being x, not being x, where x is not a free variable.

being x AND not being x is contradiction exactly because x two options are simultaneously taken.

being x OR not being x is tautology exactly because x two options are not simultaneously taken.

By not ignoring x two options, one enables to define the straightforward connection between OR and AND truths tables of four rows and the fact that x OR ~x is tautology, where x AND ~x is contradiction.

More details are given in http://www.internationalskeptics.com/forums/showpost.php?p=11362031&postcount=1928.
 
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doronshadmi said:
Your reasoning ignores A's two options, no less no more, simply because option is not optional by your reasoning.
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I have never indicated that A had anything other than two possible values. The mere fact it is (in context) a boolean variable guarantees it.
 
jsfisher said:
Let me know when you correct the two lines that followed it.
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Here it is:

No one claims that ~x is independent of x.

What is claimed is that x has two options, where x is not a free variable.

In order to be clearer: given x, x has at least two options, being x, not being x, where x is not a free variable.

being x AND not being x is contradiction exactly because x two options are simultaneously taken.

being x OR not being x is tautology exactly because x two options are not simultaneously taken.

By not ignoring x two options (where x is not a free variable) one enables to define the straightforward connection between OR and AND truths tables of four rows and the fact that x OR ~x is tautology, where x AND ~x is contradiction.

More details are given in http://www.internationalskeptics.com/forums/showpost.php?p=11362031&postcount=1928 (any place where "free variable" is written, has to be changed to " not a free variable").
 
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jsfisher said:
You'd be wrong to claim that. X is a free variable in the expression X OR ~X.
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By your reasoning.

By my reasoning X is not a free variable.

Once again, in order to be clearer: given X, X has at least two options, being X, not being X, where X is not a free variable.

Please pay attention that since no binary logical connective is used, "being X, not being X" is simply X two options.
 
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