One of the pillars of Sir Karl Popper's philosophy is fallibilism, according to which there is no certain empirical knowledge. When this position is criticized, it is usually claimed that the scope of fallibilism is restricted, and that there are some areas where infallible knowledge is possible. In the paper we develop a different line of argument. We attempt to show that fallibilism is self-contradictory. Let us consider the following proposition: ""All propositions are fallible" is fallible" is infallible. We argue that a fallibilist is committed to hold this proposition to be true. In the paper we discuss consequences of this argument as well as some possible strategies of defense.