Socrates suggests that Protagoras’ relativism doctrine is self-refuting. For, even if Protagoras agrees with the doctrine, Socrates does not. Thus it will be true for Socrates that Protagoras’ doctrine is false. Indeed, since this follows from Protagoras’ doctrine, it will even be true for Protagoras that for Socrates the doctrine is false (171b). Thus Protagoras is bound by his own doctrine to admit that his doctrine is false.
