Finally, we get to the real question, the entire purpose of founding this city – where in it is justice located? (427d)
“So then, son of Ariston,” I said, “your city would now be founded. In the next place, get yourself an adequate light somewhere; and look yourself — and call in your brother and Polemarchus and the others — whether we can somehow see where the justice might be and where the injustice, in what they differ from one another, and which the man who’s going to be happy must possess, whether it escapes the notice of all gods and humans or not.”
“You’re talking nonsense,” said Glaucon. “You promised you would look for it because it’s not holy for you not to bring help to justice in every way in your power.”
“What you remind me of is true,” I said, “and though I must do so, you too have to join in.”
“We’ll do so,” he said.
“Now, then,” I said, “I hope I’ll find it in this way. I suppose our city — if, that is, it has been correctly founded — is perfectly good.”
“Necessarily,” he said.
“Plainly, then, it’s wise, courageous, moderate and just.”
“Plainly.”
“Isn’t it the case that whichever of them we happen to find will leave as the remainder what hasn’t been found?”
The city is identified as wise, courageous, moderate, and just. The procedure for investigation is that they will look for the first three of these virtues in the city, locating wisdom first, courage second, moderation third, and it presumes that justice will be that which is left over, that which remains. Is there a problem with this procedure? What is the underlying assumption? That there are four and only four virtues. If there are more than four virtues, say five, then once three of them are found, the remainder will be an amalgamation of those left over.
Are wisdom, courage, moderation, and justice the only virtues?