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Hurkyl
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#14
Mar19-12, 03:53 PM
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Quote Quote by lugita15 View Post
But rather we should analyze it as follows. P = (P --> not P) = P & (P --> not P) = P & not P = false.
I was referring to the semantics you had described in your post: that you interpret the phrase "this statement is false" as being a statement P with the property
P = (P --> not P)
(because you kept describing it as implicitly meaning "if this statement is true, then ...")

That part of my post doesn't apply to Prior's version, where he interprets it as a P satisfying
P = P and not P
This version suffers from the criticism I made in my first half of my post: no matter what proposition Q is, because we have interpreted it as satisfying
Q = Q and <something else>
we can assign the truth value "false" to Q.