The chief purpose of this lecture is to set forth the full challenge Socrates faced to defend justice. We turn first to the conclusion to Thrasymachus’s powerful and vehement argument against the goodness of justice, as well as Socrates’s attempts to rebut it. Socrates himself states that he is not satisfied with what has been said, however, because they have been proceeding without a clear definition of “justice.” Yet before they can arrive at such a definition, Socrates first entertains two somewhat different but quite riveting attacks on justice from none other than Glaucon and Adeimantus, Plato’s brothers, who admire justice greatly. But they have been hearing for some time arguments against justice, of the kind the group has just heard from Thrasymachus, and they are eager to have Socrates refute them once and for all. Accordingly, each delivers the strongest case he can against justice because they, in contrast to Thrasymachus, want to hear the strongest case for justice.