What does Thrasymachus believe is the natural ordering of society based upon individual capacities? What distinguishes the stronger individual from the weak?
Thrasymachus operates as a foil to Socrates in the opening book of The Republic. Whereas Socrates operates as the thinker in pursuit of the transcendent, Thrasymachus is shown to operate in the realm of the contingent. Being the Sophist, Thrasymachus advocates a notion of justice that is temporal, the foil position against which Socrates argues.
For Thrasymachus, the individual capacity to possess power is what defines justice. Those in the position of power can embody justice by virtue of their claim to power:
No artist or sage or ruler err at the time when he is what his name implies; though he is commonly said to err, and I adopted the common mode of speaking. But to be perfectly accurate, since you are such a lover of accuracy, we should say that the ruler, in so far as he is the ruler, is unerring, and, being unerring, always commands that which is for his own interest; and the subject is required to execute his commands; and therefore, as I said at first and now repeat, justice is the interest of the stronger.
Thrasymachus believes that temporal notions of power define individual capacities. This ability to hold and possess power is where justice lies. Thrasymachus's ideas are shown to be relative and flexible to human capacity. They are not transcendental or universal. It is in this where the stronger individual is distinguished from the weak: "Thus, Socrates, injustice on a sufficiently large scale is a stronger, freer, and a more masterful thing than justice, and, as I said in the beginning, it is the advantage of the stronger that is the just, while the unjust is what profits man's self and is for his advantage." Plato has constructed Thrasymachus's character as reflective of the contingent, evident in his demanding for payment before he speaks: "What, and no payment! a pleasant notion!" Power is the ordering principle in Thrasymachus's vision when he suggests that the unjust person is more “mightier, freer, and more masterful than justice."
This position establishes Socrates's entire function in The Republic. He must assert the universality and transcendence of justice as well as its intrinsic good. It is done in contrast to the position that Thrasymachus articulates. The social and political order that Thrasymachus operates from this position of fundamental difference than the one that Socrates will articulate. To be able to assert a definition of strength and justice in stark opposition to Thrasymachus's relativist and contingent position represents Socrates's starting point.