In Book I, Socrates entertains two distinct definitions of justice. The first is provided by Polermarchus, who suggests that justice is "doing good to your friends and harm to your enemies." The definition, which is a version of conventionally morality, is considered. Very soon though, its faults are clearly apparent.
It is far to relative to serve as a formulation of the justice.
Moreover, its individual terms are vulnerable; that is to say, how does one know who is a friend and who an enemy? And are not friends as much as enemies capable of evil? And when a friend acts wickedly, should he not be punished? And next, what does it mean that an action is good or bad? The perils of giving credence to false appearances is introduced early on as a major theme. It will be dealt with at length in the succeeding books.
Thus surely an idea as noble as justice will not stand on such precarious ground. Socrates is dissatisfied.
A second definition, offered by Thrasymachus, endorses tyranny. "Obedience to the interest of the stronger," is likewise mined for its value, shown to be deficient, and discarded.
Tyranny, Socrates demonstrates employing several analogies, inevitably results in the fragmentation of the soul. Benevolent rule, on the other hand, ensures a harmonious life for both man and State. Justice is its means and good is its end.
That "justice is the excellence of the soul" is Socrates' main conclusion. But there are too many presumptions. Although his auditors have troubled refuting his claims, Socrates knows he has been too vague and that should they truly wish to investigate the question of justice, he will have to be more specific.
Book I ends with yet another question. Is the just life more pleasurable, more rewarding than the unjust? Rather all at once the philosophers have inundated themselves.
But the first book has succeeded in one major way. It has established the territory of the over-arching argument of the entire work.
