These political concerns about Sophistry may, at first, appear to be remote from the central subject of Protagoras, the question of whether virtue is teachable or not. This question, and the related one of what virtue is, echo throughout Protagoras, even at those points where the topic being discussed has apparently little to do with virtue. While Protagoras asserts that he can teach young men how to administrate their estates, Socrates never challenges this claim. Instead, the two thinkers battle over whether Protagoras can teach political virtue, whether he can educate citizens to become good citizens. But Socrates and Protagoras have different ideas about what is involved in being a good citizen. Is citizenship simply a matter of obeying the laws, or is something more involved?

In the course of his questioning, Socrates reveals that Protagoras is operating with an unexamined concept of virtue, and the dialogue as a whole can be interpreted as a clarification and analysis of this tricky concept. In this, Protagoras is typical of the early dialogues. Like Meno and Laches, Protagoras sets out to arrive at a firm definition of virtue; also like the other two dialogues, it fails to accomplish this task.

However, these repeated failures do not lead to the conclusion that the question of virtue is not worth pursuing, or that it will inevitably fail. In Protagoras, this question about virtue takes the form of a lengthy attempt by Socrates to prove that what are commonly thought of as separate virtues—courage, temperance, holiness, justice and wisdom—are in fact simply different names for the same thing. It might seem somewhat irrelevant whether virtue is one thing, or a conglomeration of different things; however, Socrates has a very definite aim in mind when trying to prove that virtue is singular. Virtue, for Socrates, is not only an indivisible thing. As he argues in Protagoras, virtue is the same as knowledge. Learning how to be virtuous means learning a specific type of knowledge or science. But this means that we need to understand properly what knowledge is.