Could you give an example? I would have thought this happens with Not(opposite(X)); for example, "I don't hate you" is different than "I love you", and in fact implies that I don't. But I would have thought "opposite" was symmetric, so opposite(opposite(X)) = X.
Well, OK. So suppose (to stick with your example) I love you, and I want to deceive you about it by expressing the opposite of what I feel. So what do I say?
You seem to take for granted that opposite("I love you") = "I hate you." And not, for example, "I am indifferent to you." Or "You disgust me." Or various other assertions. And, sure, if "I love you" has a single, unambiguous opposite, and the opposite also has a single, unambiguous opposite, then my statement is false. But it's not clear to me that thi...
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