Book1 (Republic)

The setting for the discussion that leads to the rest of the republic. Book1 begins the quest for a definition of justice.

Two main definitions are offered in book1. The first is that justice is doing right by one's friends, and repaying one's debts. This fails to satisfy those involved.

More notably, we are introduced to Thrasymachus, a sophist. Thrasymachus is not presented with much kindness to us, and it is obvious that Plato thinks little of his ideas.
What Thrasymachus argues is that justice is merely those rules that are imposed upon citizens by those in power. The individuals in positions of power thus create rules that they believe will be to their benefit, regardless of how just or unjust these rules may be for the citizens they rule over. It would seem then that what Thrasymachus is really saying is that there is no such thing as justice- that the standards of good and bad vary with the people in power.
As he tells is the sheepherder is concerned withe sheep only for the benefits he can get from the sheep. If he could get the same benefits by killing the sheep or making their lives miserable, the ruler would, and that would be justice.
Socrates of course disagrees with this approach, countering that :1. those in power do not always know what is in their best interest, so anything they do is not therefore just. 2. that only behaving in accordance with actual standards of justice will be in the best interest of the rulers, since it is in everyone's best interest.
Notice that there are two contradicting claims here, and that Socrates' argument depends on him being able to prove that it is better to be just (in accordance to standards of justice that are objectively true) than to be unjust.
WHich is exactly what Glaucon, in book2 two, challenges Sorcrates to demonstrate.

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