The Liar paradox arises when we ask ourselves whether the following sentence, called a “Liar sentence”, is true or not:
This sentence is not true.
The sentence just above this line says of itself, so to speak, that it is not true. If we suppose that the sentence is true, then what the sentence says (that it is not true) must be the case and, thus, the sentence is not true. But if we suppose that the sentence is not true, then what the sentence says (again, that it is not true) turns out to be the case and, hence, the sentence is true after all.
The Liar paradox was already known by the ancient Greeks and, after more than 2000 years, is yet to be solved.