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Non trivial logic

  1. Apr 19, 2004 #1
    Complementary Logic universe ( http://www.geocities.com/complementarytheory/BFC.pdf ) is an ordered logical forms that existing between a_XOR_b and a_AND_b.

    For example:

    Let XOR be #

    Let AND be &

    Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:

    Code (Text):
     
                  Uncertainty
      <-Redundancy->^
        d  d  d  d  |
        #  #  #  #  |
        c  c  c  c  |
        #  #  #  #  |
        b  b  b  b  |
        #  #  #  #  |
       {a, a, a, a} V
        .  .  .  .
        |  |  |  |
        |  |  |  |
        |  |  |  | <--(First 4-valued logical form)
        |  |  |  |
        |  |  |  |
        |&_|&_|&_|_
        |
        ={x,x,x,x}


       {a, b, c, d}
        .  .  .  .
        |  |  |  |
        |#_|  |  |
        |     |  | <--(Last 4-valued logical form)
        |#____|  |      
        |        |
        |#_______|
        |
        ={{{{x},x},x},x}

    [b]
    ============>>>

                    Uncertainty
      <-Redundancy->^
        d  d  d  d  |          d  d             d  d
        #  #  #  #  |          #  #             #  #        
        c  c  c  c  |          c  c             c  c
        #  #  #  #  |          #  #             #  #  
        b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
        #  #  #  #  |    #  #  #  #             #  #       #  #  #  #  
       {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |  |  |  |       |&_|_ |  |       |#_|  |  |       |&_|_ |&_|_
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |&_|&_|&_|_      |&____|&_|_      |&____|&_|_      |&____|____
        |                |                |                |
        {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}    
     
                                          c  c  c
                                          #  #  #      
              b  b                        b  b  b          b  b
              #  #                        #  #  #          #  #        
       {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |#_|  |&_|_      |#_|  |#_|       |  |  |  |       |&_|_ |  |
        |     |          |     |          |  |  |  |       |     |  |
        |     |          |     |          |&_|&_|_ |       |#____|  |
        |     |          |     |          |        |       |        |
        |&____|____      |&____|____      |#_______|       |#_______|
        |                |                |                |
        {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x}

       {a, b, c, d}
        .  .  .  .
        |  |  |  |
        |#_|  |  |
        |     |  |  
        |#____|  |      
        |        |
        |#_______|
        |    
        {{{{x},x},x},x}
    [/b]                
     
    A 2-valued logic is:

    Code (Text):

        b   b
        #   #    
        a   a    
        .   .  
        |   |  
        |&__|_  
        |
       
        [B]a   b    
        .   .  
        |   |  <--- (Standard Math logical system fundamental building-block)
        |#__|  
        |[/B]
     
    We can see the triviality of Standard Math logical system,
    when each n has several ordered logical forms between a_AND_b and a_XOR_b?


    Please look at these ordered information forms http://www.geocities.com/complementarytheory/ETtable.pdf , but instead of numbers please look at them as infinitely many unique and ordered logical forms that are "waiting" to be explored and used by us.

    I hope that it is understood that the flexibility of any language (including Math language) can be seen, when we examine it from the level of the information concept.
     
    Last edited: Apr 19, 2004
  2. jcsd
  3. Apr 19, 2004 #2

    matt grime

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    Sorry if anyone thinks I'm fanning the flames. But in the last bit of code you seem to imply that those structures must correspond to the ordinary logical operations of xor, and and. I can see that the second one is axorb, but I don't see how even to read the first one as it looks like (a xor b)and(a xor b), which isn't a and b (consider a true b false).
     
  4. Apr 19, 2004 #3

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    Hi,

    Maybe a,b,c,... are not true/false pairs but some version of multi-valued logic: http://en.wikipedia.org/wiki/Multi-valued_logic

    you know, like probabilities in a QM wave function before it collapses to some certain state.
     
    Last edited: Apr 19, 2004
  5. Apr 19, 2004 #4

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    I thought about it, I think we can explain (a xor b) and (a xor b) like this:

    (a xor b) and (a xor b) can hold if we do not have yet a (certain result a) xor (certain result b).

    After we have some certain result then (a xor b) and (a xor b) collapsed to (a xor b) where each notation is a well defined logical state, which is our unique result.
     
    Last edited: Apr 19, 2004
  6. Apr 19, 2004 #5

    matt grime

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    No, Organic, or WWW or whatever you choose to call yourself today, (a xor b) and(a xor b) iff (a xor b). It's not a hard thing to show that X and X is equivalent to X.
     
  7. Apr 20, 2004 #6

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    X and X is X but X has different degrees of probabilities when X = (a xor b) and (a xor b),
    or when X = (a xor b).

    For example:

    X is a quantum element, which is a wave/particle duality.

    a= wave

    b= particle

    X=(a xor b) and (a xor b) is X BOFORE it is collapsed to X=(a xor b)

    If X=(a and b) then logically X cannot collapse to (a xor b).

    If X=(a xor b) then logically X does not have a wave/particle duality.

    The only way to show logically that X has a wave/particle duality that can collapse to (wave xor particle) is by this model:

    ( ((a xor b)and(a xor b)) xor (a xor b) )
     
    Last edited: Apr 20, 2004
  8. Apr 20, 2004 #7

    matt grime

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    Seeing as you were attempting to explain how it modelled boolean logic in the degenerate case your argument is vacuous.
     
  9. Apr 20, 2004 #8

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    Can you use boolean logic to show a logical model of wave/particle duality, as I show in the previous post?
     
  10. Apr 20, 2004 #9

    matt grime

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    DO you mean: can you write out a series of speciously linked words with no argument that makes no sense and still adheres to some alleged logical system? And for that to be boolean? As long as I'm allowed to draw whatever conclusion I wish without justification like you did then the answer must be yes, mustn't it?
     
  11. Apr 20, 2004 #10

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    Show us how you construct a model of X=wave/particle element that can collapse to (wave xor particle) state.
     
  12. Apr 20, 2004 #11

    matt grime

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    As I don't believe you've done that, I don't see why I should. If you want just write out that thing you wrote above with its self referential circular logic in it and we'll call it boolean shall we?

    Or how about

    let A be the statement: X displays wave-like properties, let B be the statement X display particle-lke properties, then If X is say a photon, then Aand B is true...

    i've no idea what you mean by model in this sense, and i suspect you couldn't tell me either
     
    Last edited: Apr 20, 2004
  13. Apr 20, 2004 #12

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    It is not fine what you write because:

    If X=(wave and particle) then (wave and no-particle) or (no-wave and particle) --> no-X.
     
  14. Apr 20, 2004 #13

    matt grime

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    did i say that displaying wave like properties means it is a wave? no i didn't. try reading it more carefully, i didn't say x is a wave nor did i say it was a particle, i said ti displayed proerties of both.
     
  15. Apr 20, 2004 #14

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    I know.

    And this is exactly why I wrote:

    If X=(wave and particle) then (wave and no-particle) or (no-wave and particle) --> no-X.

    What I show is that your model cannot describe X because by your model if one of the properties does not exist then (a and b)=0 --> X does not exist.

    But as you know X can also be (a xor b).
     
  16. Apr 20, 2004 #15

    matt grime

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    But I qualifed what X is, i said if it were a photon, for example, then... and you a and b are not the A and B that i have, reread the post and think....
     
  17. Apr 20, 2004 #16

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    You ignore the meaning of (A and B) properties, because these two properties are prevent/complement each other.

    Therefore:
    (A and B) are both 0(=prevent) and 1(=complement) --> ( ((A and B)=0) and ((A and B)=1) ), which does not hold in Boolean Logic.

    The only way to show logically that X has a wave/particle duality that can collapse to (wave xor particle) is by this logical model:

    ( ((a xor b)and(a xor b)) xor (a xor b) )
     
    Last edited: Apr 20, 2004
  18. Apr 20, 2004 #17

    matt grime

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    No they don't prevent each other, there is nothing necessarily stopping something displaying (some of) the properties of a wave and of a particle. for pity's sake a photon does that which means it is not a wave and it is not a particle it displays properties of both. according to you then the photon doesn't exist. displaying wave like properties does not preclude it displaying particle like properties, we have something that proves this is possible for heaven's sake.
     
    Last edited: Apr 20, 2004
  19. Apr 20, 2004 #18

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    Again you think trough Boolean Logic where any middle state is excluded.

    A and B properties preventing each other existence not immediately but according
    to our experiment.

    Therefore A and B as Boolean model of X is a trivial logical system that does not hold, in this case.
     
    Last edited: Apr 20, 2004
  20. Apr 20, 2004 #19

    matt grime

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    No, organic, doron, www, read what my statement A is, you don't appear to understand it. it displays wavelike properties. not it is a wave, but that it displays wavelike properties. a photon does that so that statement is true for a photon. or are you going to say that diffraction does happen. it also displays particle like properties as we know from einstein's experiment on the photovoltaic effect, therefore the assertion that a photon displays particle like properties is true. there for A and B is true in boolean logic... you seem to have it completely backwards, but that's true of a lot of your logic.
     
  21. Apr 20, 2004 #20

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    You know what?

    Use Boolean Logic to say that X exists, but is this really all you want to Know about X?

    Can you show us how you use Boolean Logic to explore a non-exluded-middle element like a photon for examlpe?
     
    Last edited: Apr 20, 2004
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