Upon Cephalus' excusing himself from the conversation, Socrates funnily remarks that, since Polemarchus stands to inherit Cephalus' money, it follows logically that he has inherited the debate: What constitutes justice and how may it be defined?
Polemarchus essentially recapitulates his father's remarks in the previous friendly conversation: Justice, he says, is exemplified in "giving everyone what is due and proper to him." But Socrates is adamant in his refusal of the validity of such a definition, and he returns to his analogy of the friend and the sword. Surely, he says, this cannot be said to constitute justice.
Polemarchus agrees and then argues that justice may be defined as giving everyone what is "appropriate" to him and that it would be unjust to return a sword to a friend who is in a crazed condition. Then Polemarchus argues that it is appropriate to do good for one's friends and to do harm to one's enemies, and thus is justice attained.
But Socrates refuses this definition, too: By a series of analogies, he tries to illuminate the argument by showing that many classes of men engaged in various occupations might be said to be better, in given conditions, at doing good for friends and at harming enemies; in other words, there may be said to be infinite ways of accomplishing a "good" or a "bad," but all of these instances argued cannot be said to exemplify the accomplishment of justice. It is not the just man who is in any given instance best able to accomplish a given benefit or a harm. Justice, in fact, appears in these instances to be of no value.
