Relativism, as espoused by Protagoras, is a theory about the relativity of knowledge and sense perception. It is the position that truth does not exist independently of a perceiver and perceiver’s assertion that something is true. To exemplify this stance, Protagoras said that, “Man is the measure of all things.” What this means is that reality is only knowable, interpreted, through a medium: ourselves. And so Man determines what all things are. And because everybody is different, the medium through which we interpret the world is different and therefore reality will be different for each person.
Relativism says that all knowledge is a posteriori. It says that anything known is only gained empirically. But empirical knowledge can sometimes be proven incorrect over time if suddenly contradictory knowledge is gained. For instance, if Bob told Greg his mother’s name was Hilga, Greg would assume Greg’s mother’s name was Hilga. Twenty years later Bob finally meets Greg’s mom and greets her using the name Hilga. Greg’s mom tells Bob that her name is not Hilga, but Gertrude. This shows that the truth (Greg’s mom’s name is Hilga) can be, at some later point, proven wrong. Even if Greg’s mom had responded and said her name is Hilga, it is still possible that she is lying.
What this means is that we are sometimes mistaken in our empirical knowledge. If we are sometimes mistaken in our empirical knowledge, then it is logically possible that we are always mistaken in our empirical knowledge. If it is logically possible that we are always mistaken, then we never know if any of our empirical knowledge is true.
Socrates agreed with the sophists insofar as that empirical knowledge is flawed and relative. But for Socrates true knowledge was gained through the use of reason. He believed that all true knowledge was actually a priori knowledge merely forgotten when the soul entered the mortal body. Therefore true knowledge, gained through reason, was really gained through a process he called anamnesis. Socrates said that through reason you were just “remembering” the truth. He said that this was true knowledge and that everything not gained through reason was merely true opinion.
To prove his point, Socrates used the example of teaching a young slave boy rudimentary geometry. He could guide the boy step by step through geometrical proofs and the boy could understand them, even though he had no prior understanding of geometry, because, through reason, he was merely recollecting geometrical truths. Socrates also used many other mathematical tools to prove his point. The square root of four is logically always two, no matter who is doing the math. It is through this process of finding logical truths that Socrates finds universal Truth.