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fubarobfusco comments on Rationality Quotes September 2012 - Less Wrong
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If someone tells you the opposite of the truth in order to deceive you, and you believe the opposite of what they say because you know they are deceitful, then you believe the truth. (A knave is as good as a knight to a blind bat.) The problem is, a clever liar doesn't lie all the time, but only when it matters.
It's more likely that they're a stupid liar than that they got it all wrong by chance.
Another problem is that for many interesting assertions X, opposite(opposite(X)) does not necessarily equal X. Indeed, opposite(opposite(X)) frequently implies NOT X.
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 this is true.
If I end up saying "I'm indifferent to you" and you decide to believe the opposite of that... well, what do you believe?
Of course, simply negating the truth ("I don't love you") is unambiguously arrived at, and can be thought of as an opposite... though in practice, that's often not what I actually do when I want to deceive someone, unless I've been specifically accused of the truth. ("We're not giant purple tubes from outer space!")