(2) Perception yields contradictory impressions. The same object appears large when near, small when removed to a distance. Compared with some things it is light, with others heavy. In one light it is white, in another green, and in the dark it has no colour at all. Looked at from one angle this piece of paper seems square, from another it appears to be a rhombus. Which of all these impressions is true? To know which is true, we must be able to exercise a choice among these varying impressions, to prefer one to another, to discriminate, to accept this and reject that. But if knowledge is perception, then we have no right to give one perception preference over another. For all perceptions are knowledge. All are true.
(3) This doctrine renders all teaching, all discussion, proof, or disproof, impossible. Since all perceptions are equally true, the child's perceptions must be just as much the truth as those of his teachers. His teachers, [{179}] therefore, can teach him nothing. As to discussion and proof, the very fact that two people dispute about anything implies that they believe in the existence of an objective truth. Their impressions, if they contradict each other, cannot both be true. For if so, there is nothing to dispute about. Thus all proof and refutation are rendered futile by the theory of Protagoras.
(4) If perception is truth, man is the measure of all things, in his character as a percipient being. But since animals are also percipient beings, the lowest brute must be, equally with man, the measure of all things.
(5) The theory of Protagoras contradicts itself. For Protagoras admits that what appears to me true is true. If, therefore, it appears to me true that the doctrine of Protagoras is false, Protagoras himself must admit that it is false.
(6) It destroys the objectivity of truth, and renders the distinction between truth and falsehood wholly meaningless. The same thing is true and false at the same time, true for you and false for me. Hence it makes no difference at all whether we say that a proposition is true, or whether we say that it is false. Both statements mean the same thing, that is to say, neither of them means anything. To say that whatever I perceive is true for me merely gives a new name to my perception, but does not add any value to it.
(7) In all perception there are elements which are not contributed by the senses. Suppose I say, "This piece of paper is white." This, we might think, is a pure judgment of perception. Nothing is stated except what I perceive by means of my senses. But on consideration it turns out that this is not correct. First of all I must [{180}] think "this piece of paper." Why do I call it paper? My doing so means that I have classified it. I have mentally compared it with other pieces of paper, and decided that it is of a class with them. My thought, then, involves comparison and classification. The object is a compound sensation of whiteness, squareness, etc. I can only recognise it as a piece of paper by identifying these sensations, which I have now, with sensations received from other similar objects in the past. And not only must I recognize the sameness of the sensations, but I must recognize their difference from other sensations. I must not confound the sensations I receive from paper with those which I receive from a piece of wood. Both identities and differences of sensations must be known before I can say "this piece of paper." The same is true when I go on to say that it "is white." This is only possible by classifying it with other white objects, and differentiating it from objects of other colours. But the senses themselves cannot perform these acts of comparison and contrast. Each sensation is, so to speak, an isolated dot. It cannot go beyond itself to compare itself with others. This operation must be performed by my mind, which acts as a co-ordinating central authority, receiving the isolated sensations, combining, comparing, and contrasting them. This is particularly noticeable in cases where we compare sensations of one sense with those of another. Feeling a ball with my fingers, I say it feels round. Looking at it with my eyes, I say it looks round. But the feel is quite a different sensation from the look. Yet I use the same word, "round," to describe both. And this shows that I have identified the two sensations. This [{181}] cannot be done by the senses themselves. For my eyes cannot feel, and my fingers cannot see. It must be the mind itself, standing above the senses, which performs the identification. Thus the ideas of identity and difference are not yielded to me by my senses. The intellect itself introduces them into things. Yet they are involved in all knowledge, for they are involved even in the simplest acts of knowledge, such as the proposition, "This is white." Knowledge, therefore, cannot consist simply of sense-impressions, as Protagoras thought, for even the simplest propositions contain more than sensation.
If knowledge is not the same as perception, neither is it, on the other hand, the same as opinion. That knowledge is opinion is the second false theory that Plato seeks to refute. Wrong opinion is clearly not knowledge. But even right opinion cannot be called knowledge. If I say, without any grounds for the statement, that there will be a thunderstorm next Easter Sunday, it may chance that my statement turns out to be correct. But it cannot be said that, in making this blind guess, I had any knowledge, although, as it turned out, I had right opinion. Right opinion may also be grounded, not on mere guess-work, but on something which, though better, is still not true understanding. We often feel intuitively, or instinctively, that something is true, though we cannot give any definite grounds for our belief. The belief may be quite correct, but it is not, according to Plato, knowledge. It is only right opinion. To possess knowledge, one must not only know that a thing is so, but why it is so. One must know the reasons. Knowledge must be full and complete understanding, rational comprehension, and not mere instinctive belief. [{182}] It must be grounded on reason, and not on faith. Right opinion may be produced by persuasion and sophistry, by the arts of the orator and rhetorician. Knowledge can only be produced by reason. Right opinion may equally be removed by the false arts of rhetoric, and is therefore unstable and uncertain. But true knowledge cannot be thus shaken. He who truly knows and understands cannot be robbed of his knowledge by the glamour of words. Opinion, lastly, may be true or false. Knowledge can only be true.
These false theories being refuted, we can now pass to the positive side of the theory of knowledge. If knowledge is neither perception nor opinion, what is it? Plato adopts, without alteration, the Socratic doctrine that all knowledge is knowledge through concepts. This, as I explained in the lecture on Socrates, gets rid of the objectionable results of the Sophistic identification of knowledge with perception. A concept, being the same thing as a definition, is something fixed and permanent, not liable to mutation according to the subjective impressions of the individual. It gives us objective truth. This also agrees with Plato's view of opinion. Knowledge is not opinion, founded on instinct or intuition. Knowledge is founded on reason. This is the same as saying that it is founded upon concepts, since reason is the faculty of concepts.
But if Plato, in answering the question, "What is knowledge?" follows implicitly the teaching of Socrates, he yet builds upon this teaching a new and wholly un-Socratic metaphysic of his own. The Socratic theory of knowledge he now converts into a theory of the nature of reality. This is the subject-matter of Dialectic.