In Theaetetus, Plato set to give arguments against Protagoras'(c 490-c. 421 B.C) epistemological relativism namely “Man is the measure of all things” or Whatever a person believes to be true is true, or that every person’s opinion is correct. Plato records the following dialogue between Socrates’ discussion with Protagoras:
Socrates: ” So you believe that each man’s opinion is as good as anyone else’s.”
Protagoras: “That’s correct.”
Socrates: “How do you make a living?”
Protagoras: “I am a teacher”
Socrates: “I find this very puzzling. You admit you earn money teaching, but I cannot imagine what you could possibly teach anyone. After all, you admit that each person’s opinion is as good as anyone else’s. This means that what your students believe is as good as anything you could possibly teach them. Once they learn that each person is the measure of all things, what possible reason would they have to pay you for any further lessons? How can you possibly teach them anything once they learn that their opinions are as true as yours?”
In short, Plato shows how self-refuting epistemological relativism is. The opinion P is Q and P is not-Q as “Man is the measure of all things” and ” Man is not the measure of all things” are equally correct in epistemological relativism which is absurd.
What to conclude then: When faced with two contradicting opinions, Either one is false or both are. Both can not be true. POW! A bullet in Epistemological relativism head.