The Republic: Paradox 1 key example

When Socrates asks "how can any one answer who knows and says that he knows, just nothing," he is identifying a flaw in Thrasymachus's reasoning. Socrates asserts that he knows nothing about the definition of justice, and to prohibit that answer is to prohibit Socrates from telling the truth and thus providing an answer to Thrasymachus's question. The wording of this quotation is quite similar to one of the most famous Socrates quotations on wisdom from The Apology. In The Apology, Socrates claims that he is the wisest man because he knows that he knows nothing, whereas everyone else thinks they know something but are incorrect (and in fact they know nothing). By playing on the idea of knowledge in claiming to know that he knows nothing, Socrates highlights a paradox that results from Thrasymachus's challenge specifically and from quests for knowledge more generally.

And yet, Socrates does have a reply for Thrasymachus, Thrasymachus simply doesn't like that reply (and has thus preemptively forbidden it). The fact that Thrasymachus has told Socrates not to utter his "faint notions" once more limits the pursuit of knowledge that Socrates and his interlocutors are embarking on. The seemingly paradoxical bind Thrasymachus has placed Socrates in highlights Thrasymachus's role as a sophist as opposed to a philosopher—someone who persuades through rhetoric instead of pursuing wisdom.