In this passage, Socrates accuses Protagoras's "man is the measure" doctrine of being self-contradictory. Because this purports to be a general claim about truth and falsity (that what is and is true for each person is just what appears to her to be and to be true), Socrates says that Protagoras must be committed to the following contradiction: His own Measure Doctrine will be both true and false, since it is true for him, but he admits it will be false for at least some others, and their view that it is false is equally true relative to them and their own appearances. So Protagoras will have to admit that both he and others are correct in their conflicting views about the Measure Doctrine.
Unless I'm missing something, this is a bad argument. If you're careful about relativizing each claim to the proper individual's perspective, there is no contradiction here. From Protagoras's perspective, he is right about the Measure Doctrine, and others are wrong. Of course, from the others' perspective, they are right that the Measure Doctrine is false, and Protagoras is wrong. But at least on the surface, relativism is entirely consistent with a certain kind of absolutism, even intolerance: Protagoras can vigorously assert and argue for his own general, relativistic theory (if that's what it is) without pain of contradiction precisely because, as a relativist, he acknowledges that he is bound by his own perspective on these things. If there is really no way of making someone else's truth your own, because we are each bound by our own "measure," then it must be that Protagoras means for his theory to be understood as being true for him. He can of course recognize that other perspectives might exist, but by his lights, these other perspectives are all incorrect. What is true in these other perspectives is true only for those people, and false for him, but by his own lights, he's right. So I don't think the self-refutation objection here is entirely successful.
(Note also that this meta-relativistic move doesn't threaten the generality of the Measure Doctrine: Protagoras can continue to claim that, by his (Protagoras's) lights, each person is the measure of his or her own truth and reality. And anyone who thinks differently is wrong.)
Happy reading!
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