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.)