A paradox is a statement or event that seems to contradict itself, though it is still true, or at least makes sense.
Paradoxes are common in literature. Consider the "rule" painted on the barn in George Orwell's Animal Farm: "All animals are equal, but some are more equal than others." The idea of being "more equal" is paradoxical, but that doesn't stop Napoleon from using that rule to oppress the other farm animals.
Consider also the paradox of Captain Beatty in Ray Bradbury's Fahrenheit 451. Books have been banned, and Beatty's job is to destroy any books he finds, but he is obviously well-read because he surrounds himself with quotations from great literature that he uses to convince people that destroying books is the right thing to do.