Note here, unlike Charmides, we move from rhetoric to ethics, unlike a move from ethics to epistemology.
Start by asking Gorgias: what art has Gorgias mastered, by analogy with shipbuilders who can make ships, etc.? Gorgias' answer is that rhetoric is the mastery of speech about the greatest of human concerns, which seems to amount to persuasion. And this art supposed to be morally neutral--the use to which it is put is something extra.
Note the historical background against which we're to understand this: Gorgias gave Helen's defense speech, arguing that compulsion by words equivalent to physical compulsion.
Another provocative example: an audience will prefer a rhetorician's answer to how to cure a patient to a doctor's in a debate.
Socrates wants to know whether Gorgias can also teach good, to avoid the bad use of rhetorical skill. Note Plato here makes Gorgias more like Protagoras (who did say he could teach the good) than the historical Gorgias, who doesn't appear to have made that claim.
But now Gorgias is in a bind. Rhetoric was supposed to be knowledge of the greatest of human concerns. But now it looks like rhetoric is persuasive speech in the absence of knowledge, i.e. rhetoric seems to be the art of getting people to make mistakes.
Next: Polus asks for Socrates' definition of rhetoric, and Socrates replies that it's not an art at all (the pastry chef/dietitian example).
Polus' objection: if rhetoric gives us absolute power, who cares if it can't tell us what we really ought to do?
Socrates' response: true power is being able to do what's good for you; rhetorician tyrants aren't truly powerful.
So: better to suffer wrongdoing than to do wrong oneself.
Polus' objection: no one agrees with this!
P1 Justice is a good thing; injustice, badCombining this with the earlier point vs Gorgias about rhetoric as lack of knowledge of what's good, get another argument for Socrates' virtue is knowledge claim--i.e., virtue is knowing how to get what's in fact good. People who lack virtue are ones who do not know what is good for them. [Hence, better to suffer wrongdoing than inflict it? But surely can agree that inflicting wrongdoing is harmful because unjust, but still say that suffering wrongdoing is also harmful, so that it's not yet clear whether it's better to suffer wrongdoing than to inflict it.]
P2 Things are good because pleasant, beneficial, or both
P3 Justice is not pleasant
C1 If justice is good, justice is beneficial
P4 Things are bad because unpleasant, harmful, or both
P5 Injustice is not unpleasant
C2 If injustice is bad, injustice is harmful
C3 Justice is beneficial; injustice, harmful.
And, of course, worse for you to have great power if you have little knowledge--inflict harm on everyone, including yourself.
Objection: is it odd to say that the reason to be virtuous is for our benefit? Virtue seems to be tied with welfare of others being at least as important as our own. But maybe the answer here is just that Socrates appealing here to premises that Polus would accept.
Callicles' challenge. The accusation: Socrates exploits Gorgias' and Polus' shame which leads them to admit that rhetoric should be able to teach good, and that injustice bad, justice good.
Callicles' strategy is to deny P1, i.e. say that justice is bad; injustice, good.
P1 Justice is a set of conventional rules to keep the strongest in line, i.e. to protect the interests of the weaker.Note this resembles Nietzchean critique of morality.
P2 The law of nature says that the strongest should get power, pleasure (i.e. what's naturally good).
C1 Justice deprives the strong of what's rightfully (by natural right) theirs.
C2 Justice contradicts the law of nature.
C3 Justice is bad; injustice, good.
Socrates focuses on hedonistic tenor of Callicles' reply: his objection is that the life Callicles describes is slavery, not mastery. Reply by allegory: soul as jar. The hedonistic jar is full of leaks, and needs continual replenishment; water rushes out even as poured in. The temperate jar is sealed, never loses its contents. So hedonism requires continual trouble.
Callicles' reply: he's good with the hedonistic jar! Socrates tries to push the idea that as much pain in the hedonistic life as pleasure. But Callicles has a separate objection: that the life of the sealed jar is the "life of a stone".
Plato possibly here drawing attention to the limits of Socratic dialogue: if no common ground, or if common ground taken back, then no way to get purchase to refute a consistent immoralist (or indeed a radical skeptic).