liar paradox.
Semantic paradox, known in antiquity, focus of much recent work. Jack says ‘I am now speaking falsely’, referring to the words he is then uttering. If Jack speaks truly when he says he is speaking falsely, he is speaking falsely. If he is speaking falsely when this is what he says is going on, he is speaking truly. So what he says is true if, and only if, it is false; which seems absurd. One response claims that Jack says nothing true and nothing false. But a variant makes trouble: Jill says ‘I am now not speaking truly’. If Jill is not speaking truly when this is what she says she is up to, she is speaking truly. If she is speaking truly, then she must be doing what she says, that is, not speakingly truly. So, it seems, what she says is true if, and only if, it is not true.... ...
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