You said that Zeus had sent justice and respect to mankind, and furthermore it was frequently stated in your discourse that justice, temperance, holiness and the rest were all but one single thing, virtue: pray, now proceed to deal with these in more precise exposition, stating whether virtue is a single thing, of which justice and temperance and holiness are parts, or whether the qualities I have just mentioned are all names of the same single thing. This is what I am still hankering after. (329c-d)
Protagoras replies that this is an easy question: justice, temperance, and the like are all parts of virtue. Socrates asks whether they are parts of virtue that are all different from each other, like the parts of a face, or parts of virtue that are the same as each other. When Protagoras says that they are different from each other, however, Socrates is able to argue in response that this yields strange results -- we end up having to say that piety, for instance, is not just, or that justice is not pious. Protagoras is unconvinced, so Socrates tries a different tack. If two things share the same opposite for the same reason, it seems that they must be in some way the same kind of thing. But folly, for instance, is the opposite of both wisdom and temperance, and it seems for the same reason.
Protagoras by this point is starting to get irritated. They argue a bit about the way they should proceed, with Protagoras not wanting to get involved in question and answer, and Socrates preparing to leave because, he says, he cannot follow long speeches very well at all. The others intervene, however, with Callias arguing that Protagoras should be able to argue in his style just as much as Socrates, and Alcibiades jumping in (as had been noted at the beginning of the dialogue) to say that Socrates already concedes that Protagoras is better at long speeches, so if Protagoras really wants to concede that Socrates is better at discussion than he is, he should feel free to do so. After this, several others put in their two cents, with Prodicus and Hippias making sure to show off a bit in doing so. Socrates eventually proposes that Protagoras ask the questions, and this is accepted at large.
Protagoras attempts to shift the discussion back on his ground by starting to ask Socrates questions about a poem by Simonides about whether it is difficult to be virtuous -- poetry being a major part of what Protagoras has previously said is education in virtue, and Protagoras no doubt being very familiar with the poem in question. Socrates claims he was dazzled by Protagoras' argument, and to buy time, he started a discussion with Prodicus. Prodicus, of course, is happy to be able to put one over Protagoras himself, and plays along, helping Socrates argue that Protagoras has misinterpreted the poem. Socrates, in his turn, plays Prodicus off of Protagoras, but then agrees with Protagoras that that interpretation might not be right. He proposes to give his own thought about what Simonides really intends, and Protagoras agrees to the proposal.
Socrates argues then that philosophy is associated with laconic utterance -- the very opposite of the speechifying of the Sophists:
Now philosophy is of more ancient and abundant growth in Crete and Lacedaemon than in any other part of Greece, and sophists are more numerous in those regions: but the people there deny it and make pretence of ignorance, in order to prevent the discovery that it is by wisdom that they have ascendancy over the rest of the Greeks, like those sophists of whom Protagoras was speaking; they prefer it to be thought that they owe their superiority to fighting and valor, conceiving that the revelation of its real cause would lead everyone to practise this wisdom....[Y]ou can tell that what I say is true and that the Spartans have the best education in philosophy and argument by this: if you choose to consort with the meanest of Spartans, at first you will find him making a poor show in the conversation; but soon, at some point or other in the discussion, he gets home with a notable remark, short and compressed—a deadly shot that makes his interlocutor seem like a helpless child. (342a-b, d-e)
This is confirmed by the fact that the wisdom associated with the Seven Sages of Greece consists entirely of short little maxims like 'Know Thyself'. Thus, says Socrates, what Simonides really was trying to do was to outdo Pittacus, whom he quotes, by coming up with something more clever, and interprets Simonides as arguing that Pittacus's maxim, 'Virtue is difficult', is inaccurate: continually being virtuous is actually impossible, being a divine thing. He likewise takes Simonides to imply that nobody willingly does something bad.
This interpretation is probably no more serious than his attribution of philosophy to Sparta (and may just be to put into question the possibility that poetry could have the role in moral education Protagoras claims), but by this point Hippias is feeling left out, and offers to give everyone his own speech about Simonides' poem. He's stymied by Alcibiades, though, who points out that Protagoras and Socrates are not yet finished, because they were supposed to do some question-and-answer. Socrates says he's willing to do what Protagoras deems best, but suggests that they leave off talking about poems, which he dismisses as an excuse not to discuss. Protagoras seems to refuse to say what he wants to do, but Alcibiades jumps in again by asking Callias whether it is really appropriate for Protagoras to refuse to answer, thus shaming Protagoras into saying that he would be willing to answer whatever questions Socrates wished to put to him.
With a number of compliments to Protagoras, Socrates returns the discussion to the original question: Are the virtues all somehow one thing, or are particular virtues parts of virtue different from each other? Protagoras responds by arguing that courage (andreia) is very different from other virtues, since one can be courageous and yet also unjust. (An argument, incidentally, that people regularly still make.) Socrates points out that this gets us odd results again, however: Protagoras has said that he teaches virtue, and the virtue is a wholly good thing; further, it seems clear that in every situation those people behave most courageously who know what they are doing. All of this suggests, though, that wisdom is courage.
Socrates goes on to get Protagoras to tell him whether the pleasant and the good are the same thing, and seems to try to press him to say it is. This has puzzled some commentators, since Socrates in other dialogues quite clearly denies that pleasure and goodness are the same, but I think it's pretty clear what Socrates is doing: if the pleasant and the good are the same, Protagoras has made a mistake somewhere. We see this by how he goes about his argument. Having raised the question of whether the pleasant and the good are the same, he immediately goes on to talk about knowledge, noting that most people regard knowledge as unable to guarantee action. He gets Protagoras to agree that knowledge is not like this (as, indeed, Protagoras must say if he also claims to teach virtue). He then indirectly leads Protagoras into an argument with the many (polloi), who claim that people can be led to do things they know are bad by being overcome with pleasure. The many are also committed to saying that good things can be painful or unpleasant. In the course of this indirect argument, Protagoras does, in fact, commit himself to the claim that the pleasant and the good are the same. If this is the case, however, nobody willingly does wrong (notice how Socrates was preparing for this in his previous discussion of the poem), because then if we 'do wrong' because we are overcome with pleasure, this would be the same as saying that we do wrong because we are led by the good.
If, however, virtue comes down to making the right choice of pleasure and pain, the result is that the measurement of these things, "study of their excess and defect and equality in relation to each other" (357b). This makes virtue a matter of knowledge: the reason people make bad choices is nothing other than ignorance, which the Sophists claim to cure. Socrates asks all three Sophists if they agree with this, and they all three agree.
Then Socrates springs the trap. If all of this is so, it seems to follow that virtue, including courage, is all one thing: wisdom or knowledge. Protagoras, of course, gets sulky at this and stops cooperating, so Socrates wraps it up by insisting that he is not simply trying to put one over on Protagoras, but has uncovered a real puzzle. Socrates had originally doubted that virtue is teachable, but then ended up arguing that virtue is knowledge, which suggests that it is teachable; whereas Protagoras had originally insisted that virtue was teachable, but in the course of the discussion has argued that virtue is not all one thing, which means that it is not all knowledge, which seems to indicate that some parts of virtue are not actually teachable. And he ends by saying that he would like to go through the whole thing more closely.
At this, Protagoras replies by complimenting Socrates on the quality of his argument and saying that it is his view that Socrates would one day likely have a very high reputation for wisdom; but, he says (no doubt due to his assessment of what going through the matter even more closely would be like), they should probably end the discussion and do other things. And thus it comes to an end, and Socrates leaves.
* Prodicus's little speech urging Protagoras and Socrates to go on seems clearly to be a parody of Prodicus's style; Prodicus we know from elsewhere was famous for making lots of distinctions in terms, and that fits what we get here. It is likely the little bit by Hippias immediately afterward is also a parody of Hippias's style of speaking.
* The claim that Sparta is more philosophical than Athens and that all the typical Spartan characteristics are really attempts by Sparta to keep its philosophy a secret is certainly comedic, and would not doubt have been regarded as such.
* Note that Socrates explicitly goes out of his way to insist that among the philosophical Spartans women are educated, too.
* Plato at 343a is one of the sources for the traditional list of the Seven Sages of Greece: Thales of Miletus, Pittacus of Mytilene, Bias of Priene, Solon of Athens, Cleobulus of Lindus, Myson of Chen, and Chilon of Sparta. However, on most other lists, Periander of Corinth or Anacharsis the Scythian takes the place of Myson of Chen. Plato makes it sound as if the list of the seven were already widely known in his day.
* John Stuart Mill, who knew Plato very well (since he had been reading Plato in the original Greek since he was only a few years old), points to Socrates' argument at the end of this dialogue as an example of (classical) utilitarianism. It seems clear, though, that Socrates develops the utilitarian-sounding parts of the argument in the person of the Sophists, since he explicitly claims to be speaking for them. If this is so, the overall thrust of the argument seems to be that this utilitarian-sounding theory is really incoherent.
* Note that in both Parmenides and Protagoras, the Socratic dialogues with the earliest dramatic dates, in which Socrates is at his youngest (about nineteen or twenty in the first and in his mid-thirties in the second) the eminent Grand Old Man of the dialogue compliments Socrates' skill at argument and remarks on his potential to do great things with it.
[The quotations from the dialogue in this second post are from the Perseus Project. They are currently just standing in for the main translation I've been using, because I've been having car trouble, which has shifted my schedule so that I don't currently have access to the translation I originally read and used, and which was quoted in the first part. I'll replace all the quotations with those from the right translation as soon as I have a chance.]