Why does Thrasymachus blush? How might this tell us the nature of justice?.
I feel that in order to understand the scenes with Thrasymachus, one first has to see the differences between Socrates and Thyrasymachus. The dialogue plainly shows that the key difference between the two is in their respective approaches. Thrasymachus is a realist; Socrates, an idealist. Thrasymachus tries to find the definition of justice by the laws of the city. He felt that rulers possess their own advantage. Socrates however brought about the idea that way before cities came along, there was justice in the mind of human beings. Obviously the many attempts of humans to make laws that somehow embody justice may not always hit the mark. Justice should be ideally guiding the city laws, but the notion of justice sought out by Socrates is prior to any city laws. Basically Socrates is looking for an answer outside of the city's laws and regulations, which is what will be Thrasymacus's downfall and in turn, make him blush.
If you read the passages prior to 350d, it's clear that both Socrates and Thrasymacus are doomed to talk each other's ears off because of their differences of opinion. Every argument that Thrasymacus makes on what justice is Socrates has a counter attack. For instance, "Justice is the advantage of the stronger". Socrates is able to reply to this definition by saying that the disadvantage of the stronger could also be looked at as just with the ideas that everyone makes mistakes, even rulers. Thrasymachus later readjusts his definition by stating that injustice is stronger, freer, and more beneficial. Socrates is then able to trick Thrasymachus to admit that injustice is virtue and justice is vice. Socrates is able to wear Thrasymachus down after every round of arguments. I feel that this is where Thrasymachus blushes.
Blushing can insinuate many things. The day was extremely hot, and when you are participating in a mentally agonizing conversation, I'm sure you would get red in the face from aggravation and being tired.