In the Protagoras Plato does not treat the question of virtue itself, but rather Protagoras’ claim that he knows what virtue is and that he is able to teach it. The structure of argumentation in the Protagoras, particularly Socrates’ long introductory dialogue with Hippocrates to dissuade him from attending Protagoras’ school, Socrates’ repeated attempts to end the conversation, his frequent digressions from the guidelines of the argumentation, and his countless logical failures and adaptations concerning the meanings of various terms lead to the conclusion that Socrates is not interested in discovering the nature of virtues, but rather in demonstrating that Protagoras is incapable of teaching it.
