Contradictions do not exist. Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong.
Francisco says this to Dagny in Part One, Chapter VII, when she challenges him for squandering his talent as a worthless playboy. Dagny asks him how he can be such a paradox, how a man as capable, brilliant, and accomplished as he is can also choose to be a worthless playboy. It does not seem possible that he can be both, and yet he seems to be. In asking her to check her premises, Francisco suggests that it is indeed not possible. He cannot be both things at once, because contradictions cannot exist. A thing is what it is, not something else entirely. Therefore, there must be another answer that Dagny has not seen yet. Hugh Akston (who had been Francisco’s teacher) says something similar to Dagny when she meets him at the diner where he works as a short-order cook. He tells her this in response to her disbelief over why a famous philosopher would choose to work in a diner, or why a motor with the power to revolutionize industry would be abandoned in ruins. He urges her to look beyond her assumptions in the search for an answer that could make sense.