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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.
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.
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