Platos work Theaetetus is written in the conventional form of a dialogue between Socrates and his opponent. Socrates argues with Theaetetus, a young mathematician, who is proponent of Protagoras ideas. The main point of philosophical dispute is the nature of knowledge, so in the course of this dispute, Socrates attempts to refute arguments posed by Theaeteus in order to state what knowledge is not.
In the second point of discussion, Theaetetus claims that knowledge is in the first place related to perception. "It seems to me that one who knows something is perceiving the thing he knows, and, so far as I can see at present, knowledge is nothing but perception" (151d). When reacting to the youngsters words, Socrates points out that he recognizes a well-known Protagoras idea in his speech, which is just formulated in a different way. In fact, Protagoras claimed that "man is the measure of all things" (152a). This famous saying has been disputed over the years because there were at least two different interpretations of what he possibly meant. Some philosophers thought that he meant an individual human, while others believed that he meant humanity in general, or at least some collective social groups. The problem behind this controversy is the specifics of Greek language, where the two concepts are marked by the same word. Other works of Protagoras do not cast light on whether he meant either of the two concepts; moreover, both variants find reference in his texts. Anyway, for the sake of dispute Socrates takes the first perspective, when an individual person is claimed to be a measure of all things.
First of all, Socrates gives an example which demonstrates that perception is individual and under such circumstances each persons knowledge would be different and subjective:
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SOCRATES Let us try to understand him: the same wind is blowing, and yet one of us may be cold and the other not, or one may be slightly and the other very cold? THEAETETUS: Quite true. SOCRATES: Now is the wind, regarded not in relation to us but absolutely, cold or not; or are we to say, with Protagoras, that the wind is cold to him who is cold, and not to him who is not? (151d-152c).
With this example, Socrates demonstrates the difference between absolute and relative knowledge, which proves his point of view that an individual person cannot be a measure of all things because his perception is limited. Further on, he gives several objections that refute Theaetetus argument that knowledge is perception. He argues that any person can be in different states of mind at times, which can affect his perception dramatically. For example, a healthy and an ill person can treat the same object differently because they are in a different physical, mental and emotional states. In a similar way, when a person is mentally ill, the reality is perceived differently by them than by a healthy person. Even when a person is asleep, his/ her visions are different than those of a person who is awake. However, when he states that he himself is two individual personalities when he is ill and healthy, or when he is awake and asleep, it is made clear that the opposition to Protagoras becomes less dramatic because Socrates seems to claim that a man might be a measure of all things, but only to himself and only in the aspect of perception, not knowledge.
Further on, Socrates adds new arguments to dispute Theaetetusstatements. Thus, he believes that it would be wrong to identify the capacity of human beings only with their ability to perceive things. In that case, it would be fair to recognize that many animals have sharper and more developed organs of perception, but this would mean that animals can judge about knowledge more accurately than humans. Yet, it is true that it is not exactly so and that knowledge is not equal to perception. Instead, Socrates believes that knowledge is not the very perception but the ability to judge consciously about what is perceived. So, it involves intellect, not only the biological tools of human mind. Thirdly, Socrates states that according to Protagoras argument, those people who believe that Protagoras is wrong have their own knowledge, which is different from Protagoras one: 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. ... That is to say, he would acknowledge his own belief to be false, if he admits that the belief of those who think him wrong is true." (171b)
Thus, the dialogue is structured in the way to cast light on Protagoras position first and then to refute it by using several arguments. First of all, Socrates objects that an individual person can be a measure of all things because even one persons perception can vary depending on his mental or physical state, which is always changing. Hence, perception can be changing but knowledge cannot be such, so it would be wrong to identify these two concepts. Further on, he points out that ability to perceive is not knowledge but just function, while knowledge is rather a mental ability to judge about perception in a sound and adequate way. Finally, he argues that according to Protagoras, his opponents are right when believing him wrong because he gives them such a right by his own definition of knowledge.