Thursday, January 22, 2009

Vacuous Truth

From my post in a topic in the xkcd forums:

"Every woman currently living on Pluto is male."

"Every true falsity is false."
"Every false truth is true."

"Every circular square is neither circular nor square." (This one almost makes an intuitive sense... but then, it really doesn't, when we consider that every circular square is also circular and square.)

"Every present King of France is simultaneously bald and not bald."

By the mathematical/logical principle that propositions are vacuously true when their subject does not exist, no matter what is predicated of that subject, the above statements should be considered true.

This relates to the problem of negative existentials in the philosophy of language, but I don't have more to say about it at the moment. May investigate further.

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