This is a summary of what I wrote earlier about why Glaucon thinks it is impossible to persuade somebody who refuses to listen and what he could do:

Listening is one of the most important concepts in politics. The power to grant or withhold listening is one of the most fundamental ways in which power is exercised. The opposite side of the same coin is the power to command listening. The imperative, "Listen!" or "You listen to me!" is a way of asserting authority.

The first element of justice is the opportunity to be heard. To be denied that opportunity is almost universally agreed to be a fundamental injustice.

At the beginning of the Republic Socrates appears to be caught in a classic confrontation with the superior force of the many. This is the typical situation of the individual threatened by the majority. It is the typical situation of the weak in the face of the strong. If Polemarchus and Glaucon are right, that there is no way to persuade in the face of a refusal to listen, then we must conclude that persuasion is always powerless in the face of threatened coercion. That should give us some sense of what is at stake here, at the beginning of the Republic: If Polemarchus and Glaucon are right, politics -- and justice -- are impossible.

What might Socrates have said, if he disagreed with Glaucon’s answer to Polemarchus? If we think about this we may see why Socrates might have kept silent at this point, even if he disagreed with Glaucon. For Socrates could have answered Polemarchus by saying, “Perhaps I can't persuade you if you won't listen, but I think I can get you to listen.”

But if that is what Socrates thought, why would he say it? Suppose Socrates said to Polemarchus, “I am going to show you that I can make you listen to me, even if you refuse to listen.” Would saying this to Polemarchus help in making Polemarchus listen? Probably not. Which is why Plato has Socrates keep silent at this point. One lesson of this is that, for a wise man, sometimes the best thing to do is to keep silent.

The next question to consider is, why does Glaucon answer in the way he does? We could simply say, “Well, maybe that’s just what most people would think.” After all, it appears that most readers of Plato’s Republic, if they have thought about this at all, have tended to agree with Glaucon. (Mainly because most readers of the Republic think that this whole conversation is just an unimportant introduction and that the real discussion that makes up the dialogue has not yet begun.)

But let us consider the possibility that another answer to the question might have been given, and then ask what might be motivating Glaucon to give this answer and not another. Polemarchus, after all, did not ask, "Could you persuade if we don't hear you?" He said, "Could you persuade if we don’t listen."

Intentionally not listening, is a very different thing from not hearing, especially in this case where Polemarchus has explicitly spoken this intention. Intentionally not listening is a declaration with respect to some future utterance. It is an intention that may or may not be carried out. So the correct answer to P.'s question is, Even if you refuse to listen, I think there is a good chance that I could persuade you to listen anyway. Another way to put it is to say that refusing to listen is a part of an ongoing conversation. It says, I expect I will hear that you are saying something to me and I am telling you that I will be intentionally not paying attention to what you are saying
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Now let us ask what might be motivating Glaucon to respond in the way he does. In Xenophon’s Socrates, Leo Strauss summarizes a passage from Xenophon which may help us to understand why Glaucon does not see that he has any alternative:

"At about the same age at which the young Alkibiades cross-examined the great Pericles regarding law without making himself in the least ridiculous, Glaukon, son of Ariston, tried to address the Assembly, eager as he was to be a leading man in the city, was dragged from the speaker's stand, and made himself ridiculous. No one could stop him; Socrates alone, who was well-disposed toward him for the sake of Charmides the son of Glaukon and for the sake of Plato, stopped him. How he stopped him Xenophon shows by the present conversation. Socrates gained Glaukon's attention by setting before him the resplendent rewards which he could expect if he succeeded in becoming the leading man in Athens. He asks him then from where he would start benefitting the city, such benefitting being necessary if he wished to become honored. Glaukon is reduced to silence since he had not apparently given any thought to what would be, in the language of our time, his first priority. Sensing how Glaukon feels, Socrates asks him whether he would try to increase the city's wealth just as, if he wished to increase the estate of a friend, he would attempt to make him richer: increase of the estate or the wealth of the city is for Glaukon of course the goal. It appears that Glaukon had not given any thought to the present revenues and expenditures of the city; the revenues might have to be increased and the expenditures to be decreased. Glaukon defends himself by having recourse to the indubitable fact that one can enrich the city at the expense of its foreign enemies. But only, Socrates warns, if one is stronger than the enemies. He asks him, therefore, about the military power of the city and that of her enemies. Glaukon proves again to be utterly ignorant. The same result is reached when he is asked about the defense of the country and the silver mines. When speaking of the silver mines, Socrates openly makes fun of Glaukon....Socrates finally points out to Glaukon his ignorance regarding the grain supply of the city. He refers again to the parallel of the city and the household: just as the manager of the household must know all its needs and take care that they are supplied, the manager of the city must know all her needs and take care that they are supplied; but the city consists of more than ten thousand houses: should not a beginner like Glaukon first try to manage a single household, say, that of his uncle Charmides, which is badly in need of competent management? Glaukon would gladly try his hand at it BUT HIS UNCLE WILL NOT LISTEN TO HIM: how can you, unable as you are to persuade your uncle, imagine that you will be able to persuade all the Athenians, your uncle included, to accept your counsels?"

What would Glaucon have to do in this situation in order to get his uncle to listen to him? From Xenophon’s account we see that Glaucon was very much attached to a particular idea of himself. He apparently thinks that he already possesses the qualities needed in a ruler or manager. With regard to the people as a whole it seems he is ignorant of the fact that the people do not share his opinion of himself — or he thinks that their opinion is unimportant. But in the case of his uncle Charmides, Glaucon at some level knows that Charmides does not share Glaucon’s opinion of himself. At least that is a plausible way to interpret Glaucon’s complaint that his uncle will not listen to him. Although the text does not say so, based on common experience of conversations between adults and adolescents we may imagine that Glaucon has already experienced from Charmides the latter’s unwillingness to accept as valid his nephew’s pretensions to have already achieved maturity and competence as a leader or manager. This does not mean that Charmides will refuse to hear anything that Glaucon says. It does not mean that Charmides does not like Glaucon or that he would refuse to grant what he perceives as a reasonable request from Glaucon. It just means, most likely, that Charmides refuses to treat Glaucon in the way that Glaucon wants to be treated, as a mature person already in possession of competence as a leader or manager.

How, then, could Glaucon get Charmides to listen to him?

The following answer is based on a simple observation: Everybody listens in a particular way. In other words, all of us listen based on what we expect (or fear) and what we are interested in. And all experienced and successful speakers know, more or less instinctively in most cases, that if you want to capture somebody’s attention you must address your words to that person’s interests, concerns or expectations. The difficulty comes when we want others to accept us, from the outset, in the way that we see ourselves. If a person is very strongly attached to a certain image of himself that others do not share, and insists on that as a condition for starting a conversation, the likely result is that he will experience others as being unwilling to listen to him. He will feel that the others are demanding that, in order to begin a conversation, he should give up being who he is in some essential way.

For Glaucon, being an already mature person and an already competent leader is, we might say, part of his identity. Therefore, to the question, what would Glaucon have to do in order to get his uncle to listen to him, the answer seems to be that he would have to be willing to give up his identity. In other words, Glaucon would have to be willing to appear to be somebody other than the person he wants people to take him to be. He would have to give up his identity. This might help us to understand why Glaucon, and all of us, might find this situation so threatening and so impossible. In order to get somebody to listen to us it seems we might actually have to sacrifice who we are, which looks like a terrible loss and an injustice, since the person being listened to would then be somebody else and our “true identity” would thereby be suppressed and rendered invisible.

In the present day there is an enormous amount of agreement with and sympathy for what we will call Glaucon’s problem. It is said that people have a right to be accepted in terms of their own identity, and anything else is unjust. But as we read this and think about the difficulty and injustice of Glaucon’s problem, it might be instructive if we were also to think about Plato's choice as a writer. As a writer, Plato chose to give up his own identity. He never speaks in his own voice. And yet he has always been listened to.

As for Glaucon (who was Plato’s brother), the answer to the question of how he could get his uncle to listen to him is now evident: If he wants his uncle to listen to him he needs to speak into the listening that his uncle already has for him. And that means he has to give up, at least for the present, insisting that his uncle listen to him as a big man who is already capable of leading the city. Instead he needs to speak to the listening that his uncle already has for him as his young nephew.

I said earlier: “I think that the speculative suggestion I offered about how Glaucon could get his uncle to listen to him will turn out to be essentially correct as a description of what Socrates did in order to get Polemarchus to listen to him.”

What I have written just above is a summary of what I that "speculative suggestion." If I am right about that, then we should find that Socrates got Polemarchus to listen to him by speaking into the listening of Polemarchus. So next we should look again at the text to see if that turns out to be the case.

Lance

Meanwhile, I want to thank you profusely for your comments on Glaucon's identity problems because they have advanced my thinking considerably regarding youthful identity crises, the dynamics of listening and obtuseness and family conflict.

Andrew, thank you for your comments. This slow reading of the Republic is not intended to be a monologue. I will carry on speaking into silence if that is what there is to speak into, because I have some thoughts about the Republic that I want to express. But my preference is always to have a more interactive conversation.  

In the theater of my imagination, I see Polemarchus reacting, not only to the apparent repudiation of Cephalus' assertion about t he nature of justice but to an insinuation about the soundness of Cephalus' reasoning that could be inferred from the content of Socrates' question as to the validity of Cephalus' definition in the case where the party requesting return of hie property is not in his right mind. And the quality of Cephalus' reasoning is very much in question, if he is basing his reason for calmness at the anticipation of death on an incorrect definition of justice.
The translation I'm reading (Jowett) shows Socrates underlining Polemarchus' status as heir, and to my mind that makes a difference in how I understand Polemarchus' expressions (or demonstrations) of his interests.  So, I find myself wondering why do the various interpretations differ on this point.