Analysis of Thrasymachus' Argument in The Republic

Thrasymachus has just stated, "Justice is nothing other than the advantage of the stronger", and is now, at the request of Socrates, clarifying his statement.

"'Don't you know that some cities are ruled by tyranny, some by a democracy, and some by an aristocracy?'

'Of Course.'

'And in each city this element is stronger, namely, the ruler?'

'Certainly.'

'And each makes laws to its own advantage. Democracy makes democratic laws, tyranny makes tyrannical laws, and so on with the others. And they declare what they have made - what is to their own advantage - to be just for their subjects, and they punish anyone who goes against this as lawless and unjust. This, then, is what I say justice is, the same in all cities, the advantage of the established rule. Since the established rule is surely stronger, anyone who reasons correctly will conclude that the just is the same everywhere, namely, the advantage of the stronger.'" Plato, Republic, Book 1, 338

Thrasymachus, tired of holding his tongue back, barges into the argument and asks Socrates exactly what justice is; since Socrates cannot answer Thrasymachus offers his perception:

Thrasymachus starts off by stating his conclusion: justice is the advantage of the stronger. He then gives Socrates two premises that he uses to arrive at his conclusion first that rulers of cities are stronger than their subjects and second that rulers declare what is just and unjust by making laws for their subjects to follow. Since justice is declared by the stronger then it must surely be a tool for the stronger.

Now that I have reconstructed the argument and distinguished the premises from the conclusions, I will explain the logical structure of the argument. By asserting that that rulers of cities are stronger than their subjects and that rulers declare what is just and unjust Thrasymachus is using a conjunction as his argument form in which both premises of the argument must be true for the conclusion to be true. According to Thrasymachus both these premises are true therefore the conclusion is also true; later in the discussion Thrasymachus is proved wrong by Socrates.

I will argue that the characters have good reason to accept the first premise because rulers must be stronger than their subjects or else they wouldn't have reached the position of ruler. And if there is a case where a subject is stronger than the ruler himself, then the ruler can easily quiet that particular subject using the powers he has been given as a ruler.