Paradox of Relativism:
 
Socrates: I am charmed with his [Protagoras's] doctrine, that what appears is to each one, but I wonder that he did not begin his book on Truth with a declaration that a pig or a dog-faced baboon, or some other yet stranger monster which has sensation, is the measure of all things; then he might have shown a magnificent contempt for our opinion of him by informing us at the outset that while we were reverencing him like a God for his wisdom he was no better than a tadpole, not to speak of his fellow-men-would not this have produced an over-powering effect? For if truth is only sensation, and no man can discern another's feelings better than he, or has any superior right to determine whether his opinion is true or false, but each, as we have several times repeated, is to himself the sole judge, and everything that he judges is true and right, why, my friend, should Protagoras be preferred to the place of wisdom and instruction, and deserve to be well paid, and we poor ignoramuses have to go to him, if each one is the measure of his own wisdom? Must he not be talking ad captandum in all this? I say nothing of the ridiculous predicament in which my own midwifery and the whole art of dialectic is placed; for the attempt to supervise or refute the notions or opinions of others would be a tedious and enormous piece of folly, if to each man his own are right; and this must be the case if Protagoras Truth is the real truth, and the philosopher is not merely amusing himself by giving oracles out of the shrine of his book.....
Self Refutation of Epistemic Relativism:
Socrates: Why, suppose that you determine in your own mind something to be true, and declare your opinion to me; let us assume, as he argues, that this is true to you. Now, if so, you must either say that the rest of us are not the judges of this opinion or judgment of yours, or that we judge you always to have a true opinion: But are there not thousands upon thousands who, whenever you form a judgment, take up arms against you and are of an opposite judgment and opinion, deeming that you judge falsely?

Theodorus: Yes, indeed, Socrates, thousands and tens of thousands, as Homer says, who give me a world of trouble.

Socrates: Well, but are we to assert that what you think is true to you and false to the ten thousand others?

Theodorus: No other inference seems to be possible.

Socrates: And how about Protagoras himself? If neither he nor the multitude thought, as indeed they do not think, that man is the measure of all things, must it not follow that the truth of which Protagoras wrote would be true to no one? But if you suppose that he himself thought this, and that the multitude does not agree with him, you must begin by allowing that in whatever proportion the many are more than one, in that proportion his truth is more untrue than true.

Theodorus: That would follow if the truth is supposed to vary with individual opinion.

Socrates: And the best of the joke is, that he acknowledges the truth of their opinion who believe his own opinion to be false; for he admits that the opinions of all men are true.

Theodorus: Certainly.

Socrates: And does he not allow that his own opinion is false, if he admits that the opinion of those who think him false is true?

Theodorus: Of course.

Socrates: Whereas the other side do not admit that they speak falsely?

Theodorus: They do not.

Socrates: And he, as may be inferred from his writings, agrees that this opinion is also true.

Theodorus: Clearly.

Socrates: Then all mankind, beginning with Protagoras, will contend, or rather, I should say that he will allow, when he concedes that his adversary has a true opinion-Protagoras, I say, will himself allow that neither a dog nor any ordinary man is the measure of anything which he has not learned-am I not right?

Theodorus: Yes.

Socrates: And the truth of Protagoras being doubted by all, will be true neither to himself to any one else?

Theodorus: I think, Socrates, that we are running my old friend [i. e. Protagoras] too hard.


The Wax Block:

Socrates: I would have you imagine, then, that there exists in the mind of man a block of wax, which is of different sizes in different men; harder, moister, and having more or less of purity in one than another, and in some of an intermediate quality.

Theaetetus: I see.

Socrates: Let us say that this tablet is a gift of Memory, the mother of the Muses; and that when we wish to remember anything which we have seen, or heard, or thought in our own minds, we hold the wax to the perceptions and thoughts, and in that material receive the impression of them as from the seal of a ring; and that we remember and know what is imprinted as long as the image lasts; but when the image is effaced, or cannot be taken, then we forget and do not know.

.....

Socrates: The only possibility of erroneous opinion is, when knowing you and Theodorus, and having on the waxen block the impression of both of you given as by a  seal, but seeing you imperfectly and at a distance, I try to assign the right impression of memory to the right visual impression, and to fit this into its own print: if I succeed, recognition will take place; but if I fad and transpose them, putting the foot into the wrong shoe-that is to say, putting the vision of either of you on to the wrong impression, or if my mind, like the sight in a mirror, which is transferred from right to left, err by reason of some similar affection, then "heterodoxy" and false opinion ensues.


.....
How False Opinion is possible with perception:

 
Socrates: And the origin of truth and error is as follows:-When the wax in the soul of any one is deep and abundant, and smooth and perfectly tempered, then the impressions which pass through the senses and sink into the heart of the soul, as Homer says in a parable, meaning to indicate the likeness of the soul to wax (Kerh Kerhos); these, I say, being pure and clear, and having a sufficient depth of wax, are also lasting, and minds, such as these, easily learn and easily retain, and are not liable to confusion, but have true thoughts, for they have plenty of room, and having clear impressions of things, as we term them, quickly distribute them into their proper places on the block. And such men are called wise. Do you agree?

Theaetetus: Entirely.

Socrates: But when the heart of any one is shaggy-a quality which the all-wise poet commends, or muddy and of impure wax, or very soft, or very hard, then there is a corresponding defect in the mind -the soft are good at learning, but apt to forget; and the hard are the reverse; the shaggy and rugged and gritty, or those who have an admixture of earth or dung in their composition, have the impressions indistinct, as also the hard, for there is no depth in them; and the soft too are indistinct, for their impressions are easily confused and effaced. Yet greater is the indistinctness when they are all jostled together in a little soul, which has no room. These are the natures which have false opinion; for when they see or hear or think of anything, they are slow in assigning the right objects to the right impressions-in their stupidity they confuse them, and are apt to see and hear and think amiss-and such men are said to be deceived in their knowledge of objects, and ignorant.

But false Opinion not possible with conceptions involving no perceptions
Socrates: Then do we not come back to the old difficulty? For he who makes such a mistake does think one thing which he knows to be another thing which he knows; but this, as we said, was impossible, and afforded an irresistible proof of the non-existence of false opinion, because otherwise the same person would inevitably know and not know the same thing at the same time.

Theaetetus: Most true.

Socrates: Then false opinion cannot be explained as a confusion of thought and sense, for in that case we could not have been mistaken about pure conceptions of thought; and thus we are obliged to say, either that false opinion does not exist, or that a man may not know that which he knows;-which alternative do you prefer?

Aviary analogy:
Socrates: We may suppose that the birds are kinds of knowledge, and that when we were children, this receptacle was empty; whenever a man has gotten and detained in the enclosure a kind of knowledge, he may be said to have learned or discovered the thing which is the subject of the knowledge: and this is to know.

Theaetetus: Granted.

Socrates: And further, when any one wishes to catch any of these knowledges or sciences, and having taken, to hold it, and again to let them go, how will he express himself?-will he describe the "catching" of them and the original "possession" in the same words?

...
Socrates: Then shall we say that about names we care nothing?-any one may twist and turn the words "knowing" and "learning" in any way which he likes, but since we have determined that the possession of knowledge is not the having or using it, we do assert that a man cannot not possess that which he possesses; and, therefore, in no case can a man not know that which he knows, but he may get a false opinion about it; for he may have the knowledge, not of this particular thing, but of some other;-when the various numbers and forms of knowledge are flying about in the aviary, and wishing to capture a certain sort of knowledge out of the general store, he takes the wrong one by mistake, that is to say, when he thought eleven to be twelve, he got hold of the ringdove which he had in his mind, when he wanted the pigeon.

Knowledge is True Opinion with a Rational Explanation:
Socrates: Let me give you, then, a dream in return for a dream: I thought I too had a dream, and I heard in my dream that the primeval letters or elements out of which you and I and all other things are compounded, have no reason or explanation; you can only name them, but no predicate can be either affirmed or denied of them, for in the one case existence, in the other non-existence is already implied, neither of which must be added, if you mean to speak of this or that thing by itself alone. It should not be called itself, or that, or each, or alone, or this, or the like; for these go about everywhere and are applied to all things, but are distinct from them; whereas, if the first elements could be described, and had a definition of their own, they would be spoken of apart from all else. But none of these primeval elements can be defined; they can only be named, for they have nothing but a name, and the things which are compounded of them, as they are complex, are expressed by a combination of names, for the combination of names is the essence of a definition. Thus, then, the elements or letters are only objects of perception, and cannot be defined or known; but the syllables or combinations of them are known and expressed, and are apprehended by true opinion. When, therefore, any one forms the true opinion of anything without rational explanation, you may say that his mind is truly exercised, but has no knowledge; for he who cannot give and receive a reason for a thing, has no knowledge of that thing; but when he adds rational explanation, then, he is perfected in knowledge and may be all that I have been denying of him. Was that the form in which the dream appeared to you?
Rational Explanation requires knowing the "difference and distinguishing characteristics" of the object of knowledge:
Socrates: Understand why:-the reason is, as I was just now saying, that if you get at the difference and distinguishing characteristic of each thing, then, as many persons affirm, you will get at the definition or explanation of it; but while you lay hold only of the common and not of the characteristic notion, you will only have the definition of those things to which this common quality belongs.

Theaetetus: I understand you, and your account of definition is in my judgment correct.

Socrates: But he, who having right opinion about anything, can find out the difference which distinguishes it from other things will know that of which before he had only an opinion.


But that means we have to know those characteristics, making the definition circular:

Socrates: And so, when the question is asked, What is knowledge? this fair argument will answer "Right opinion with knowledge,"-knowledge, that is, of difference, for this, as the said argument maintains, is adding the definition.

Theaetetus: That seems to be true.

Socrates: But how utterly foolish, when we are asking what is knowledge, that the reply should only be, right opinion with knowledge of difference or of anything! And so, Theaetetus, knowledge is neither sensation nor true opinion, nor yet definition and explanation accompanying and added to true opinion?