papal infallibility
The Catholic belief that the Pope is infallible; that is, he cannot err whenever he defines a doctrine of faith and morals, since he is guided by the Holy Ghost.
Papal infallibility is a paradox; at one point in time the non-infallible Pope declared himself infallible. But if he was not infallible when he declared himself to be so, then how can he make himself infallible all of a sudden?