Does Socrates give a convincing account of justice in the first four books of "The Republic"?
This is a very interesting question! The answer will depend upon whether you agree with Socrates' definition of justice in the first four books. Then, you will have to decide whether he adequately addresses the necessity for justice. First, let's explore his main points in all four books.
In Book One, Socrates tries to define justice. In this book, three definitions of justice are discussed. The first one (voiced by Cephalus) is the traditional Greek concept of justice: honesty in all transactions and diligence in paying off one's debts. The second definition of justice (voiced by Cephalus' son, Polemarchus) involves giving to everyone his/her just due. Thus, the enemy is owed retribution, while the friend is owed loyalty and protection.
Here, Thrasymachus chimes in and argues that these two definitions of justice are lacking. He proposes a third definition of justice that takes into account the advantage dominant individuals have over others. Thrasymachus sees the conventional definitions of justice as limiting and unnatural; he believes that true justice allows the dominant man to claim what is rightfully his. Thus, Thrasymachus proposes justice as a "might makes right" concept. Meanwhile, Socrates argues in support of the just life in the conventional sense.
In Book Two, Glaucon and Adeimantus argue that justice is sought for its benefits and that, if justice offered no practical benefits of any consequence, no one would seek it. They challenge Socrates to prove that justice should be sought for itself. So, Socrates must defend his belief that people are happier being just than unjust. He proceeds to show how a just city can be used as an analogy to describe the benefits of being a just individual. In Socrates' fictionalized just city, every individual knows his/her place. In order to protect this "good" society, warriors must be stationed around it. These soldiers are to be carefully chosen and carefully taught the rudiments of being good warriors. They must be gentle with the innocent and absolutely ruthless with the enemy.
In Book Three, Socrates maintains that these soldiers or "auxiliaries" must be well-educated in order to preside over and to protect a just city. The auxiliaries themselves must be just; they must read only poetry or works that promote self-discipline, humility, honesty, and obedience. Above all, they must receive adequate training in the arts of war. Socrates also proposes that the rulers or "guardians" of the just city should be chosen from the auxiliary class. Ultimately, Socrates' point is that a just society is made up of just individuals.
In Book Four, Socrates continues to argue that a just life is a happy life, regardless of whether it brings about practical or material benefits. In this book, Socrates proposes that a just city is ruled by three important elements: wisdom, courage, and self-discipline. Thus, for a city to be just, wisdom must rest in its ruling (guardian) class, courage must rest in its warrior (auxiliary) class, and self-restraint must rest in its citizen (producer) class. Justice is thus rendered when each class performs its prescribed functions to perfection.
Socrates then equates the just city to the just individual, wherein resides the three concepts of wisdom, courage, and self-discipline in harmony. To Socrates, a just soul is a balanced soul (and also a happy one).
So, there you have it! Now, you must decide whether Socrates gives a convincing account of justice. Do you agree with his hypothesis that justice should be sought for itself rather than for its practical benefits? Essentially, do you agree with Socrates' argument that a just soul is a happy soul, regardless of time, place, or circumstance? Your answer to these two questions will decide your response to your original question.