A paradox by the German mathematician Martin Löb:
Let A be any sentence. Let B be the sentence: ‘If this sentence is true, then A.’ Then a contradiction arises.
Here’s the contradiction. B makes the assertion “If B is true, then A.” Now consider this argument. Assume B is true. Then, by B, since B is true, A is true. This argument shows that, if B is true, then A. But that’s exactly what B had asserted! So B is true. And therefore, by B, since B is true, A is true. And thus every sentence is true, which is impossible.
(Lan Wen, “Semantic Paradoxes as Equations,” Mathematical Intelligencer 23:1 [December 2001], 43-48.)