Monday, May 11, 2020

[sygtrmyz] Fun with the rule of the excluded middle

For all statements P, either P is true or P is false.  ("Either ... or" means exclusive or.)

Paradox: let P = "This statement is false."  This causes a problem because P is a statement that is neither true nor false, so violates the rule of the excluded middle, meaning the rule is not always valid.

I think the resolution of the paradox is that the rule does not apply to all statements, but only to some subset of "well formed" statements.  What is a good definition of well formed for the rule?  ("Good" mught be subjective.)  Forbidding self-reference is not enough, e.g., Quine's Paradox.

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