Protagoras's Relativism as Explained by Plato

In Plato's dialogue Theaetetus Socrates described Protagoras's theory, "As each thing appears to me, so it is for me, and as it appears to you, so it is for you - you and I each being a man (152a, pg.14)." Socrates goes on to say that, in "this expression 'it appears' means 'he perceives it'."(152b pg.14) Every judgment based on perception itself is true in relation to the person whose judgment it is. The example that Socrates uses is the temperature of the wind. If one man feels the wind and says it is cold and another feels the wind and says it is warm, which one is correct? According to Protagoras's theory of relativism, both are correct.

However, claims such as "X is Y" cannot be made, but must instead be "X is Y relative to the Perceiver." When Theaetetus is told to define knowledge he states, "Knowledge is simply perception," which Socrates then argues using Protagoras's Measure Doctrine. Nothing can be stated as a fact, because no facts can be proven true. If two men were sitting in a room staring at a wall and one perceived it to be white (A) and the other perceived it to be blue (B), it could be said that, "The wall is white relative to A," as well as, "The wall is blue relative to B." It could not be stated that the wall is white or blue because it is neither; the property of the wall is relative to each person's perception and judgment. Each man perceives the wall to be a different color, but they are both correct relative to their perceptions.

Protagoras's relativist view, as described by Plato, allows everyone to be right, and so there is no chance for argument or discussion. There is no point in arguing about an opinion or "fact" because they do not exist. Everyone is correct because truth is relative to his or her own judgment. Because there are no opinions or argument there's no reason to move forwards. Everyone is correct with his or her own judgments and there can be no defined societal "truth" to any one statement. This also means that there can be no scientific advancement because science itself is the pursuit of a whole truth, not individual truth.

Socrates discussed the ideas of dreaming and insanity in relation to the Measure Doctrine and stated that, "It is by no means true that everything is to each man which appears to him; on the contrary, nothing is which appears (158a)." In the case of dreaming, it is impossible for both the subconscious dream and reality to coincide. When someone is asleep, their dream is what they perceive and what they believe to be true. As soon as they wake up their dream is over, and they know that it is not truth, even though it was perceived to be.

If everyone, besides Protagoras himself, believed the Measure Doctrine to be false, it would be false relative to them; but it would be true relative to Protagoras. This statement is refuting Protagoras's Measure Doctrine that, "Man is the measure of all things." If man is the measure of all things, but only Protagoras himself believes this to be true, then the doctrine would be relative to only Protagoras. It would instead have to be written as, "It is true for Protagoras that every perception and judgment is true for the person whose judgment it is," which although that may be an entirely true statement, it is irrelevant for anyone besides Protagoras.