Socrates asks Protagoras “in respect to what” will Hippocrates improve by associating with him, in the manner that by associating himself to a doctor he would improve in medicine (318d). Protagoras begins his discourse with the statement that a good sophist can make his students into good citizens. Socrates says that this is fine and good, but that he personally believes that this is not feasible since 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 points to the fact that while in matters concerning specialised labour one would only take advice from the appropriate specialist, like for example builders (???????? ) about construction, in matters of state everyone’s opinions is considered, which proves that political virtue is within everyone, or that at least that is what Athenians in their democratic ideals believe. Another example is that Pericles did not manage to impart his wisdom to his sons (319e).
Socrates’ uses a similar example in the Meno. He then adds 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 give more examples, but thinks his point is sufficiently established. Protagoras says his claim that virtue can be taught is better made by a story than by reasoned arguments, and he recounts a myth about the origins of living things.
He says that Epimetheus (whose name means “Afterthought”) who 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 from Hephaestus and practical wisdom from Athena and gave them to man. However, man was never granted civic wisdom which belonged to Zeus 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 states 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 notes 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 lays out a thought experiment where a hypothetical city state is resting its survival as such to the skill of flute playing. Being the most important thing for that society, parents would be eager to teach the skill to their sons.
Not everyone would be successful though, as we can imagine, as some would have a greater natural inclination than others and often the son of a good flute player would turn out bad and vica versa. Any of them however, even the bad ones, would be better than an average citizen in the real world which might have never been taught how to play. Same goes for virtue, it is considered so important that everyone is taught to a certain degree, to the point that it seems like a part of human nature while it is not. (327b-d).