If you are ignorant of [what a Sophist really is], you cannot know to whom you are entrusting your soul—whether it is to something good or to something evil.
In this passage (312c), Socrates is exploring precisely why Hippocrates is so eager to study with Protagoras that he would wake him in the early morning. Socrates's caution to Hippocrates lays out the importance of the subject of the dialogue that is about to take place. Education, when it concerns in particular the teaching of virtue, involves the alteration of the soul. Before we have been taught what virtue is, we have no way of determining whether the teacher who claims to be able to teach it to us can indeed do this. To be educated is to submit to instruction in a state of ignorance. If we were not ignorant, after all, we would not need to be educated. But this paradox is no mere logical trick. It concerns the future state of our soul, a matter which—as Socrates points out to Hippocrates—is of the utmost importance.
When it comes to consideration of how to do well in running the city, which must proceed entirely through justice and soundness of mind, [the Athenians] are right to accept advice from anyone, since it is incumbent on everyone to share in that sort of excellence, or else there can be no city at all.
Socrates is not the only speaker in the Protagoras, nor is he the only speaker who expresses important theories. Here (322e-323a), Protagoras summarizes his theory of political relations towards the end of his long fable about the creation of the world. The ability to live in social harmony makes communities possible; therefore, all those who live in a community must have some share in the civic virtues. Protagoras's argument continues on to a more extreme position, however. From this argument that all people have some basic awareness of justice and good sense, he then advocates democracy as the best political system. In a democracy like Athens, living within the community is not just a matter of abiding by the laws, but also of actively participating in making those laws. Protagoras concludes that all people should play a part in making political decisions, because all people have a god-given notion of fairness and common sense. However, this conclusion does not properly follow from its premise. The ability to make political decisions does not necessarily accompany the ability to live in a community, at least within the principles that Protagoras expounds. Like many of Protagoras's arguments, this apparently persuasive theory relies on some shoddy logic. Nonetheless, this passage does raise important questions about the philosophical basis for democracy.
No intelligent man believes that anybody ever willingly errs or willingly does base and evil deeds; they are well aware that all who do base and evil things to them unwillingly.
In the middle of his analysis of Simonides's poem (345e), Socrates gives this clear statement of his doctrine that it is impossible to want to commit an evil action. However, Socrates is being ironical when he states that other people who were renowned for wisdom also held this view. The case was, in fact, quite the contrary: Socrates's theory was generally thought to be completely absurd. Undoubtedly, it is counter-intuitive: people quite willingly steal, murder, lie and so on all the time. However, this idea becomes harder to dismiss once we understand what Socrates takes an evil action to be. If, as he argues, to do something that is evil is the same thing as doing something in a state of ignorance, any action that is evil is an action whose character and effects are not properly understood. When we lie, for instance, we do not fully understand the damage we are doing. If we did understand, we would not lie: in this sense, no-one knowingly and willingly ever commits an evil act. How this gels with Socrates's patent falsehood in this sentence—that his opinions are shared by other wise men—is unclear.
Let us hold our discussion together in our own persons, making trial of the truth and of ourselves.
As Socrates prepares to begin his turn at asking Protagoras questions (348a), he gives a concise statement of what he perceives the purpose of philosophy to be. Philosophical thinking is not merely a search for truth, nor is it only a way of testing the self. Rather, it should unite both these aspects. Discussions can only take place between people, and this simple fact should shape the form those discussions take. In arguing with someone, we should not merely argue with their opinions, but with those opinions as that person embodies them. Using a poem as a medium between the two interlocutors—as Protagoras does—interrupts this confrontation of true personalities.
But there is a harsh irony here, for Plato himself argues through characters in the dialogues. Instead of holding a discussion in his own person, Plato uses masks to represent his opinions. Socrates's belief in the importance of the unvarnished truth immediately spoken by a person appears in a very mediated form, itself spoken in a hypothetical dialogue written down half a century after it is supposed to have taken place.
The art of measurement by showing us the truth would have brought our soul into the repose of abiding by the truth, and so would have saved our life.
Socrates's assertion that evil is nothing other than ignorance is one of the most important theories articulated in the Protagoras. Here (356d-e), midway through his deconstruction of Protagoras's concept of virtue, he declares that virtue can indeed be taught because it is a form of knowledge. Learning is then of the utmost importance, because it can reform the soul and remold it into a better state. The type of learning required, however, is not that which is taught by Protagoras. Rather, we can overcome ignorance by acquiring the art of measurement, a kind of moral corrective that will allow us to assess accurately the competing merits of various courses of action. For Socrates, such a perspective will ensure that we will always do the right thing, for it will allow us to determine what is right, and it is impossible for us to do wrong while knowing what is right. The art of moral measurement then allows us to penetrate through the deceptions of appearance, and arrive at truth. For Socrates, nothing could be more important, so he concludes that possessing such an art "would have saved our life."
You, Socrates, began by saying that virtue can't be taught, and now you are insisting on the opposite, trying to show that all things are knowledge, justice, soundness of mind, even courage, from which it would follow that virtue most certainly can be taught.
At the end of the dialogue (361b), Socrates is here addressing himself ('You, Socrates') from the perspective of the discussion itself, as if he were speaking for the god of philosophy or dialectic. Socrates notes how topsy-turvy the course of the argument has become. He and Protagoras have switched positions. Socrates is arguing that virtue can be taught, but he began by arguing the opposite; Protagoras, arguing against him, began by arguing that virtue can be taught, and ends by arguing that some forms of virtue are not a knowledge or science. However, for all the ground that has been covered in the argument, the audience (and the reader) is still not entirely sure who is right.
But this passage points to a more interesting end than this inconclusive reversal of positions. The strange conclusion—or rather, the failure to arrive at a conclusion—accuses and mocks the two philosophers "like some human person." Thus, the discussion has become a character in the discussion. Socrates and Protagoras have therefore done more in this dialogue than fail to achieve a solid result. Between them, they have given rise to something that is superior to both of them. The fact that the discussion can, after all, accuse them of their failure and track the vicissitudes of their arguments shows that they have given birth to something new. Here, the dialogue folds in on itself to become a dialectic capable of revising its own argument.