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Self-Referential statements

  1. Sep 10, 2006 #1

    Alkatran

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    I've been doing some thinking on self-referencing statements and the problems they imply. For example:
    THIS=TRUE is both true and false
    THIS=FALSE is neither true nor false
    THIS>TRUE is both true and false
    THIS>FALSE is neither true nor false
    THIS > X implies itself and x (using the fact that THIS = (THIS > X))
    etc...

    I was wondering if the people here could shoot down this idea:
    A self referential statement is true if and only if it implies itself.
    THAT(written) = (THAT(value) > THAT(written))

    Given this, we would get:
    (THIS=TRUE) = (THAT > THAT=TRUE) = TRUE > TRUE = TRUE
    (THIS=FALSE) = (THAT > THAT=FALSE) = FALSE
    and we wouldn't be able to imply X using (THIS > X) because once we get THIS = (THIS > X) we have change it to THAT = (THAT > (THAT = (THAT > THAT))) before we can evaluate it.

    I suppose what I'm looking for here are interesting statements that break this rule. I know it doesn't handle indirect self-reference.
     
    Last edited: Sep 11, 2006
  2. jcsd
  3. Sep 11, 2006 #2

    CRGreathouse

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    "(THIS=THIS) and false" would be a counterexample, although it doesn't show that your method is wrong (perhaps you need a stronger form of "self-referential" to exclude this).
     
  4. Sep 11, 2006 #3

    Hurkyl

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    You're hitting a seam in a common abuse of language, I think.

    Statements don't have inherent truth value -- what you're really saying here is that you can (consistently) label "this = true" with either truth value, and that you cannot (consistently) label "this = false" with either truth value.



    Logically, any statement implies itself:

    P --> P

    is a tautology.
     
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