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Socrates informs Protagoras that Hippocrates and Socrates want to talk to him about whether he can help fulfill Hippocrates's ambition to achieve prominence within the public affairs of Athens. Protagoras immediately launches into a lengthy exposition on the relation between sophistry and public scrutiny. Many Sophists, he asserts, have "disguised" their sophistic art "in a decent dress" (316d), fearful of the reaction from those who are concerned about the Sophists's influence over their students. Poets, prophets, musicians and track coaches have all hidden their secret sophistry behind their ostensible professions, but Protagoras declares that he is different: he is proud of being a sophist. He therefore proposes that the three hold their discussion before the others, and consequently the room is arranged as a miniature theatre and the debate begins.
Protagoras invites Socrates to repeat the topic under discussion, and Socrates does so, thus officially inaugurating the dialogue. What benefit, he asks, will Hippocrates recieve from becoming Protagoras's pupil? Protagoras answers that Hippocrates will become a better man every day he studies under him. But, as Socrates notes, this comparative "better" presumes a notion of "good" that has not been examined, and he demonstrates this presumption by exploring a series of parallel, analogous cases, as was the fashion in Socratic dialogues. Socrates says that painters teach their pupils to become better painters; flautists teach their pupils how to play the flute better. At what, specifically, can Hippocrates hope to improve if he studies with Protagoras?
Protagoras's answer is to the point: he states that he can teach Hippocrates "good judgment" in both his personal affairs and civic issues. As Socrates re-phrases it, Protagoras claims to be able to teach political science so that his students will become good citizens. This, Socrates says, is something that Socrates did not know could be taught, and in consequence he poses one of the central questions of the dialogue: is virtue teachable? There are good reasons for thinking that virtue cannot be taught, Socrates explains. The Athenians allow all citizens to participate in political decision-making, thereby implying that statecraft is not a skill (techne) like construction or ship-building, possessed only by the few who have undergone the necessary technical apprenticeship. According to Socrates, this indicates that virtue is neither teachable nor learnable. Further, Socrates notes, even some of the most virtuous citizens—men like Pericles—are "unable to transmit this excellence of theirs to others" (319e). On these grounds, asserting that civic virtue can be taught seems counter-intuitive, and Socrates challenges Protagoras to demonstrate that virtue can indeed be taught.
This section performs two important tasks that inform each other in complex ways. First, it explicitly lays out the grounds of inquiry for the text as a whole: what is virtue, can it be acquired, and if so, how is it best taught? Second, it frames the form this inquiry will take, and does so in a way that calls attention to questions of form. Protagoras's opening expository spiel stands in glaring contrast both to Socrates's probing questions and to Socrates's arguments, which operate through a series of analogous examples. If this dialogue will be a debate between different philosophical positions, it will be even more a debate between different philosophical methods. If Socrates's method (the elenchus) is a means of exploring and extending the limits of his interlocutors's arguments, Plato's method in writing his dialogues aims to explore and extend the limits of argument itself.
The connections between the form and content of Protagoras can best be understood in this section by considering the relationship between sophistry and the key notion of "civic virtue." Note that Protagoras's claim to be capable of teaching wise management of one's personal affairs is not challenged here, nor will it be at any point throughout the entire text. Protagoras states that he can teach "how best to order his own home" (318e-319a), but Socrates pointedly ignores this. The argument henceforth will concern only civic behavior and public business, and questions concerning private virtue will be treated as if they are irrelevant.
On the one hand, this means that the rest of the dialogue will be played out on territory Protagoras has claimed as his. It is precisely this distinction between public and private, after all, that Protagoras uses to set himself apart from the tradition of sophistry. Previous sophists have taught secretly, in private, masking their teachings with a deceitful appearance; he teaches openly, and the text that we read is proof of this. When asked by Socrates whether he wishes to talk in private or before the others, he seizes the opportunity to speak openly, and the discussion takes place before an audience. This audience (the men who occupy the benches around Socrates and Protagoras) exists within the text, but there is an audience external to the text as well: by reading the text, we ourselves guarantee the openness that Protagoras seeks.
On the other hand, while the dialogue places so much formal emphasis on its open, public and civic character, it is concerned thematically with the question of whether this public form of discussion and decision-making can be secured and passed down. How can a functioning civic order be guaranteed for future generations? In this sense, the question of whether virtue can be taught is inseparable from the question, "what makes dialogues like this possible?" The teaching of virtue is related to the possibility of uninhibited philosophical debate. Through this interweaving of the theme of the debate and the carefully composed form in which that debate is represented, Plato therefore opens up the explicit questions addressed by the text into that most fundamental philosophical question, "what is philosophy?"