Correction: Socrates, as represented by Plato, did not conclude that he knew nothing. In the Apology Socrates' argument is not that he knows nothing, but that while he lacks the specific knowledge of poets or craftsmen, unlike them he does not lay claim to knowledge he does not have. Ergo, Socrates says that he does have one type of knowledge: that he knows that he does not know things that he does not know. The distinction is epistemologically important, in that Socrates neither denies knowledge, but also does not deny that he could learn the things that he does not know. In fact, Socrates in the Apology outright says that if you want to learn natural philosophy you can buy Anaxagoras' books for cheap and learn it that way. Socrates himself does not know Anaxagoras' natural philosophy, but could learn it if he read the same books. But Socrates' unique knowledge is a sort of self-knowledge, not a knowledge of skills or external phenomena--in the Apology Socrates is implicitly forced to admit that the oracle was correct, and that he is the wisest, because his examinations have yielded nobody else who possesses this form of knowledge!

This is in direct contrast with the sophists, who teach things that they do not necessarily know anything about. Many of Plato's early and middle dialogues deal with the problem of virtue and of τέχνη, namely how virtue can be defined and whether it is a τέχνη that can be taught. Often Socrates' sophistic interlocutors demonstrate that they either do not know what virtue is, in which case they cannot teach it, or cannot show that virtue can be taught at all. That ἀπορία of the interlocutor is how Socrates claims to have discovered that unlike everybody else he knows that he does not know what he does not know, since he can consistently force the other party into demonstrating that he doesn't actually know what he's talking about. Nowhere in Plato, however, does Socrates seem firmly to deny that virtue is a τέχνη or that it can be taught--in the Protagoras he actually takes up both views at different points, that it can be taught and that it cannot be taught.