Plato argues, at Theaetetus 170e-171c, that Protagoras’ relativism is self-refuting. This argument, known as the ‘exquisite argument’, and its merits have been the subject of much controversy over the past few decades. Burnyeat (1976b) has argued in defense of Plato’s argument, but his reconstruction of the argument has been criticized as question-begging. After offering an interpretation of Protagoras’ relativism, I argue that the exquisite argument is successful, for reasons that Burnyeat hints at but fails to develop sufficiently. I consider Protagorean relativism under both of the two possible readings with respect to its scope: global relativism, according to which all truths are only relatively true, and qualified relativism, according to which the relativistic thesis itself is excepted. Taking into consideration some contemporary work on relativism and self-refutation, I show that Plato’s argument succeeds on both of these readings. Given that Protagoras could avoid self-contradiction simply by denying that an enduring subject exists, I argue that the exquisite argument is best understood as confronting Protagoras with a dilemma between self-contradiction and self-defeat of various sorts, all of which lead to the same result, that Protagoras violates the requirements of rational discourse in such a way that he becomes an absurd figure who has nothing to say to us.