What appears to be so to me is true for me, and what appears to be so to you is true for you. It follows that everyone’s perceptions are equally true. This of course is the extreme form of relativism that Protagoras claims when he asserts that man is the measure of all things in regards to truth. It seems that if all perceptions (e.g. judgments and beliefs) are equally true, there can be no room for expertise. But what is Protagoras to say of our natural inclination that such things as wisdom and the wise really do exist among individuals? If Protagoras’ relativism is to be accepted, he must explain how expertise is possible. Protagoras does not deny that some men are wiser than others, but he disagrees that some men are right while others are wrong. Though some men may appear to be wiser than others, it does not follow that their beliefs or judgments are truer than men who lack expertise in the given field; rather, and this is an important distinction that Protagoras makes, the judgments and beliefs of the wise are to be understood as being better (not truer) than those who lack expertise. For Protagoras, the wise man is the man “who can change the appearances—the man who in any case where bad things both appear and are for one of us, works a change and makes good things appear and be for him” (166d).
Before we attempt to unpack Protagoras’ definition of the wise, as stated above, I think it is important at this time that we give a brief historical account of what led Protagoras to speak of ‘better’ opinions and states. At one point in the Theatetus Socrates attempts to refute Protagoras by arguing somewhere between these lines: Let M be defined as the ‘man is the measure’ doctrine; 1) assuming M to be true, all perceptions must be true; 2) the majority of men think that M is false; 3) all of our judgments, including the judgment that M is false, must be true according to the very principles of M; 4) we can infer that M is false;
References: Plato: Theatetus. M.J. Levett, rev. Myles Burnyeat. Hackett Publishing Company (1997).