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Socrates: The opening words of [Protagoras'] treatise [Truth Knockdown Arguments: "man is the measure of all things, of what is that it is and of what is not that it is not"] surprise me.
In general, I am delighted with his statement that what seems to anyone also is, but I am surprised that he did not begin his Truth with the words, The measure of all things is the pig, or the baboon, or some sentient creature still more uncouth. There would have been something magnificent in so disdainful an opening, telling us that all the time, while we were admiring him for a wisdom more than mortal, he was in fact no wiser than a tadpol, to say nothing of any other human being.
What else can we say, Theodorus: If what every man believes as a result of perception is indeed to be true for him; if, just as no one is to be a better judge of what another experiences, so no one is better entitled to consider whether what another thinks is true or false, and, as we have said more than once, every man is to have his own beliefs for himself alone and they are all right and true--then, my friend, where is the wisdom of Protagoras, to justify his setting up to teach others and to be handsomely paid for it, and where is our comparative ignorance or the need for us to go and sit at his feet, when each of us is himself the measure of his own wisdom: Must we not suppose that Protagoras speaks in this way to flatter the ears of the public? I say nothing of my own case or of the ludicrous predicament to which my art of midwifery is brought, and, for that matter, this whole business of philosophical conversation, for to set about overhauling and testing one another's notions and opinions when those of each and every one are right, is a tedious and monstrous display of folly, if the Truth of Protagoras is really truthful and not amusing herself with oracles delivered from the unapproachable shrine of his book.
Theaetetus 161c3-6
Socrates: [The observation] involves a really exquisite conclusion. Protagoras, for his part, admitting as he does that everybody's opinion is true, must acknowledge the truth of his opponents' belief about his own belief, where they think he is wrong.
Theodorus: Certainly.
Socrates: That is to say, he would acknowledge his own belief to be false, if he admits that the belif of those who think him wrong is true?
Theodorus: Necessarily.
Socrates: But the others, on their side, do not admit to themselves that they are wrong.
Theodorus: No.
Socrates: Whereas Protagoras, once more, according to what he has written, admits that this opinion of theirs is as true as any other.
Theodorus: Evidently.
Socrates: On all hands, then, Protagoras included, his opinion will be disputed, or rather Protagoras will join in the general consent--when he admits to an opponent the truth of his contrary opinion, from that moment Protagoras himself will be admitting that a dog or the man in the street is not a measure of anything whatever that he does not understand. Isn't that so?
Theodorus: Yes.
Socrates: Then, since it is disputed by everyone, the Truth of Protagoras is true to nobody--to himself no more than to anyone else.
Theaetetus 171b-c