Of the twenty one people who are specifically said to be present, three are famous sophists. In addition to Protagoras himself, there are Hippias of Elis and Prodicus of Ceos. Two of the sons of Pericles are said to be there, Paralus and Xanthippus. With the exception of Aristophanes, all of Socrates' named friends from the Symposium are in attendance: Eryximachus the doctor, and Phaedrus are there, and so are the lovers Pausanias and Agathon (who is said to be a mere boy at this point), and Alcibiades. Not part of the official head-count are unnamed (and unnumbered) foreigners who Protagoras is said to have picked up in his travels and a servant (a eunuch) in the employ of Callias.
The company in attendance links this dialogue not only with the Symposium, but also with the Apology. The gathering is at the home of Callias, the man who Socrates disparages in the Apology as having wasted a good deal of money on over-priced, arrogant sophists. Two of the honored guests, Prodicus and Hippias, are men Socrates mentioned in the Apology as examples of intellectual pretentiousness.
Twenty-one is a significant number, because it is a triple multiple of seven, which Greek tradition holds as the traditional number of wise men: Thales, Pittacus, Bias, Solon, Cleobulus, Myson, and Chilon (Protag. 343a).
The dialogue begins with an unnamed friend of Socrates asking him how his pursuit of the young Alcibiades, just now reputed to be getting the beard, was proceeding. Socrates says, "What of it?" He explains that while he has just been in the company of Alcibiades, his mind is now on more interesting matters. He says that Protagoras, the wisest man alive, is in town. Socrates relates the story of how his young friend, Hippocrates, son of Apollodorus, came knocking on his door before daybreak and rousted him out of bed. Hippocrates was in a big hurry to be present when Protagoras held court, as he was expected to do, at the home of Callias.
This gathering of sophists has multigenerational implications. Socrates is presently associating with Hippocrates, son of Apollodorus, who, when he was himself a young disciple of Socrates, recites the Symposium to Glaucon. Glaucon's son Charmides is also present now at the home of Callias, pressumeably with Critias, who is his cousin and guardian in the dialogue named after him.
Socrates warns the excitable Hippocrates that sophists are dangerous. He tells him that the words of the sophists go straight into the mind ("psyche") and can corrupt a person straightaway. Socrates says that buying wisdom from a sophist is different from buying food and drink at the market. With food and drink, you never know what you're getting, but you can consult experts for advice before consuming anything that might be dangerous (313a-314c).
Socrates' cautionary advice not only falls on deaf ears, it also comes out of an equivocating mouth. Socrates says he regards Prodicus as a man of inspired genius (316a). In another dialogue, he expresses the same admiration for Prodicus. He says in the Theaetetus (151b), that he has arranged "love matches" between Prodicus and several boys who wanted to become wiser. Nevertheless, Prodicus seems to be a second-class sophist. (Socrates will note later that Prodicus was assigned to sleep in a storage room that his host had cleaned out for the visit (315d). Protagoras presumeably got the real guest room.)
Socrates accompanies Hippocrates to the home of Callias, and they stand in the doorway chatting about "some point which had come up along the road," apparently overheard by the eunuch doorman (314c). The eunuch opened the door, took one look at them, guessed they were sophists, and slammed the door in their faces (314d). They knocked again, and this time assured the porter they were not sophists, but only wanted to visit with Protagoras. The porter let them in, and it is at this point that Socrates recites the list of guests.
Protagoras does not deny being a sophist, and claims that it is an ancient and honorable art, the same art practiced by Homer and Hesiod. These poets, he says, used the arts as a screen, a front, to protect themselves from the charge. He says that he is better than the ancient artists, trainers, and musicians in frankly admitting that he is an educator. Protagoras says he is old enough now to be the father of any of the men present, and would like now to address himself to the whole company of people in the house. Socrates assumed that Prodicus would not want to miss the lecture, and so Callias and Alcibiades were sent to roust him out of his bed (317c-e).
Protagoras begins his speechmaking with the proclamation that a good sophist can make his students into good citizens. Socrates says this is fine and good, but that he personally thinks that virtue cannot be taught (319b). He adds that technical thinking can be imparted to students by teachers, but that wisdom cannot be. By way of example, Socrates says that Pericles did not manage to impart his wisdom to his sons (319e). These men, who are presumably present at this conversation, do not defend themselves. He says that Clinias, younger brother of Alcibiades, was taken from the family for fear that Alcibiades would corrupt him, and he was given back as a hopeless case. Socrates says he could multiply examples, but thinks his point is sufficiently established. It might be noted that this is not the first time that Socrates maligns Pericles' parenting. In the Meno he trots out the sons of Pericles as examples of the unteachability of virtue by implying that they are inferior to their father (Meno 94a,b).
Protagoras says his claim that virtue can be taught is better made by a story than by reasoned arguments, and he tells a fable about the origins of living things. He says that Epimetheus (whose name means "Afterthought") was assigned the task of passing out the assets for survival, forgot to give mankind anything so his twin brother Prometheus (whose name means "Forethought") stole fire and practical wisdom for man. However, man was never granted civic wisdom or the art of politics, so the race was initially in danger of extinction. Zeus, however, sent Hermes to distribute shame and justice equally among human beings. To Protagoras, this answers Socrates's question why people think that wisdom about architecture or medicine is limited to the few while wisdom about justice and politics is thought to be more broadly understood (322d).
Protagoras says that he has two good pieces of evidence that people agree with him. First, people do not rebuke the ugly, dwarfish, and weak, but pity them, because they cannot help being as they are (323d). Second, they do instruct people who are unjust and irreligious, hoping to impart goodness in them. He says that parents begin with their children from earliest childhood, and teachers carry on the task. Protagoras states that none of this is surprising, but what would be surprising is if this were not the case (326e). He closes by addressing Socrates's question why, if virtue is teachable, the sons of virtuous men often lack virtue. Protagoras points out that a skilled flute player could fail to teach his son to play the flute well, because the son may not be naturally inclined to music. The children of the flute player would be more skilled than those who had never studied the flute, but they would be inferior to their parents. The same applies to the teaching of virtue (327b-d).
Socrates complains that Protagoras is long-winded, like a gong that booms when you strike it and won't stop until you lay a hand on it. Socrates then peppers Protagoras with questions aimed at the problem of whether virtue is one thing or many, like the parts of a face (329d). Protagoras begins to bristle at this. Socrates says that their styles are opposite. He personally doesn't like long-winded speeches like the one Protagoras just delivered, because he is forgetful and cannot follow the train of thought (334d), and Protagoras does not like to be peppered with questions that seem to lead them off track. Socrates gets up to leave, grousing that companionable talk is one thing and public speaking another (336b). Finally, the men agree to compromise their styles so the discussion can continue.
The conversation then takes several digressions. First they analyze some poetry, and discuss the difference between being and becoming, and then Socrates praises the Spartans as the best people in the world at concealing their sophistical skills. He says you might think Spartans are unimpressive speakers, but just at the right moment, they can fire off a smart remark (342e). He adds that Laconic brevity was the earliest characteristic of philosophy (343b). Socrates finally brings the conversation around to whether virtue is knowledge. He tries to establish that virtue is connected to knowledge of wise choices in pleasure and pain. Wrong choices, that is to say, ignorance, in these matters lead to evildoing (357c-358d).
Socrates draws the conclusion of the discussion of the debate: that Socrates and Protagoras are an absurd pair (361a). He says by way of explanation that Socrates began by saying that virtue is not teachable, and then tried to show that virtue is knowledge, in which case it is teachable, and that Protagoras, who tried to argue that virtue is teachable, wanted to argue that it is not knowledge, in which case virtue would not be teachable. Each man shoots himself in the foot when virtue becomes a matter of cognition/knowledge.
Protagoras' theme is also being dealt in the dialogue of Meno, where, Plato finally puts Socrates to conclude with the opposite conclusion 'That virtue cannot be taught.'