Theology Geek NZ lists a dozen or so statements which are, in philosopher-speak, self-referentially incoherent - i.e. they're self-refuting. If they're true they must be false. Here are a few of them:
- Truth does not exist (Is that a true statement?)
- Nothing is absolute (Is that absolutely true?)
- I do not exist (You must exist to deny that you exist)
- Science is the only way to know (Can you scientifically prove that?)
There are more at the link. Meanwhile, here a couple of my all-time favorites:
A quote from the famous evidentialist William Clifford: "It is wrong always and everywhere for anyone to believe anything on insufficient evidence." If that's true then we shouldn't believe it for there's no evidence that warrants it.
Then there is the verification principle of the logical positivists: "Only those statements which can be empirically verified are meaningful." Since there's no way to verify this statement is it therefore meaningless?
HT: Dangerous IdeaRLC