Cont: Deeper than primes - Continuation 2

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Little 10 Toes said:
Let's see if you understand truth tables.

I assume you know what direction North is. Can you face North and South at the same time?

North OR ~North = true
North AND ~North = false
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There are two possible options: x OR the negation of x, notated as ~x.

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

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

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

It is T to claim that there are two possible options (written as T OR T --> T)

So the truth table of x OR ~x is:

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

OR logical connective guarantees that the two possible options are not simultaneously considered, so the contradiction is avoided.

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

More details of its mathematical usefulness (using the optional with the non-optional in the same mathematical framework) are already given in http://www.internationalskeptics.com/forums/showpost.php?p=11294638&postcount=1581.
 
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So then you don't understand my example. It's ok. Let's take this one step at a time.

Can you face North and face another direction at the same time?

Edit: doron, you keep making things more complicated than they are. I got myself confused.

You are misusing OR when you should be using or. In my example the question is are you facing North. Simple answer, yes/no, true/false.
 
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doronshadmi said:
In the real world there are optional or non-optional things, but your reasoning forces everything to be non-optional.
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Then you don't understand my reasoning.

What I was saying was that both options can't be true at the same time (contradictions are false), so your OR is effectively a XOR.

XOR still presents options, you know.

And don't quote my 'and' again; that was not part of a logic statement. Clearly you didn't understand what I wrote, or deliberately misrepresent.
 
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MetalPig said:
What I was saying was that both options can't be true at the same time (contradictions are false), so your OR is effectively a XOR.
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OR logical connective (unlike AND logical connective) guarantees that the two possible options are not simultaneously considered, so the contradiction is avoided.
 
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Little 10 Toes said:
Can you face North and face another direction at the same time?
Click to expand...

MetalPig said:
Please look at the last line of your table. You have both x and ~x set to true. Why do you think that is a valid option?
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Please take the standpoint of a dove.

By using OR logical connective it simply aware of the fact that there are two opposite directions, but it can't use this knowledge in order to simultaneously flying at both opposite directions (which is the determination derived by AND logical connective).

By using XOR logical connective it simply aware of a given one of the two possible opposite directions.
 
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MetalPig said:
Please look at the last line of your table. You have both x and ~x set to true. Why do you think that is a valid option?
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I believe Doron's departure from mathematical norms is really a language issue. Not English vs. some native tongue as is the case for some, but English vs. Mathematics.

Doron interprets "X OR ~X" as a literal statement in English, "X is true or not X is true." The OR is taken as a conjunction, not a dyadic boolean operator.

This is the theory that is mine and belongs to me. It does account for quite a bit.
 
jsfisher said:
The OR is taken as a conjunction, not a dyadic boolean operator.
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OR is exactly a dyadic boolean operator between two possible options (including opposite options) that are not taken simultaneously.

Therefore T OR T ---> T also in case of x OR ~x.

jsfisher said:
This is the theory that is mine and belongs to me. It does account for quite a bit.
Click to expand...

More generally, http://www.internationalskeptics.com/forums/showpost.php?p=11337788&postcount=1723 is not in the scope of jsfisheretics.
 
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doronshadmi said:
OR is exactly a dyadic boolean operator between two possible options (including opposite options) that are not taken simultaneously.

Therefore T OR T ---> T also in case of x OR ~x.
Click to expand...

Mathematics would disagree. No instantiation of x OR ~x yields T OR T.
 
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