The Thrasymachus section breaks down into five parts:
Justice is the advantage of the stronger.
Justice is obedience to the laws.
What if the rulers make mistakes regarding their advantage?
The ruler in the precise sense always knows correctly.
Every artist serves the one he works for, not himself.
Notice Thrasymachus makes a claim that justice is founded in knowledge, however distorted it may be. Thus, we have had as a foundation of justice the following three things:
Desire in Cephalus’s account
Spiritedness in Polemarchus’s account
Reason in Thrasymachus’s account