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You, Socrates, began by saying that virtue can't be taught, and now you are insisting on the opposite, trying to show that all things are knowledge, justice, soundness of mind, even courage, from which it would follow that virtue most certainly can be taught.
At the end of the dialogue (361b), Socrates is here addressing himself ("You, Socrates") from the perspective of the discussion itself, as if he were speaking for the god of philosophy or dialectic. Socrates notes how topsy-turvy the course of the argument has become. He and Protagoras have switched positions. Socrates is arguing that virtue can be taught, but he began by arguing the opposite; Protagoras, arguing against him, began by arguing that virtue can be taught, and ends by arguing that some forms of virtue are not a knowledge or science. However, for all the ground that has been covered in the argument, the audience (and the reader) is still not entirely sure who is right.
But this passage points to a more interesting end than this inconclusive reversal of positions. The strange conclusion—or rather, the failure to arrive at a conclusion—accuses and mocks the two philosophers "like some human person." Thus, the discussion has become a character in the discussion. Socrates and Protagoras have therefore done more in this dialogue than fail to achieve a solid result. Between them, they have given rise to something that is superior to both of them. The fact that the discussion can, after all, accuse them of their failure and track the vicissitudes of their arguments shows that they have given birth to something new. Here, the dialogue folds in on itself to become a dialectic capable of revising its own argument.
Ace your assignments with our guide to Protagoras!