> Thrasymachus’s cynicism is so compelling that Socrates spends the rest of the “Republic” trying to prove that justice is better than injustice by trying to refute the apparent success of unjust people by making metaphysical claims about the effects of injustice on the soul. Socrates is thus only able to counter cynicism in the visible world through faith in the existence of an invisible world, an invisible world that he argues is more real than the visible world. In other words, it is Thrasymachus’s cynicism that forces Socrates to reveal his nihilism.
The logic seems to be that such an invisible world is obviously false - so obviously false that not even Socrates himself could believe it. But the absurdity of calling Socrates a nihilist is easy to see as soon as you give that invisible world a little credibility, even if only to say that Socrates could have found the idea plausible.