Protarchus: I think so, but I should like to be told by you.
Socrates: The argument has all along been seeking a parallel to pleasure, and true to that original design, has gone on to ask whether one sort of knowledge is purer than another, as one pleasure is purer than another.
Protarchus: Clearly; that was the intention.
Socrates: And has not the argument in what has preceded, already shown that the arts have different provinces, and vary in their degrees of certainty?
Protarchus: Very true.
Socrates: And just now did not the argument first designate a particular art by a common term, thus making us believe in the unity of that art; and then again, as if speaking of two different things, proceed to enquire whether the art as pursed by philosophers, or as pursued by non-philosophers, has more of certainty and purity?
Protarchus: That is the very question which the argument is asking.
Socrates: And how, Protarchus, shall we answer the enquiry?
Protarchus: O Socrates, we have reached a point at which the difference of clearness in different kinds of knowledge is enormous.
Socrates: Then the answer will be the easier.
Protarchus: Certainly; and let us say in reply, that those arts into which arithmetic and mensuration enter, far surpass all others; and that of these the arts or sciences which are animated by the pure philosophic impulse are infinitely superior in accuracy and truth.
Socrates: Then this is your judgment; and this is the answer which, upon your authority, we will give to all masters of the art of misinterpretation?
Protarchus: What answer?
Socrates: That there are two arts of arithmetic, and two of mensuration; and also several other arts which in like manner have this double nature, and yet only one name.
Protarchus: Let us boldly return this answer to the masters of whom you speak, Socrates, and hope for good luck.
Socrates: We have explained what we term the most exact arts or sciences.
Protarchus: Very good.
Socrates: And yet, Protarchus, dialectic will refuse to acknowledge us, if we do not award to her the first place.
Protarchus: And pray, what is dialectic?
Socrates: Clearly the science which has to do with all that knowledge of which we are now speaking; for I am sure that all men who have a grain of intelligence will admit that the knowledge which has to do with being and reality, and sameness and unchangeableness, is by far the truest of all. But how would you decide this question, Protarchus?
Protarchus: I have often heard Gorgias maintain, Socrates, that the art of persuasion far surpassed every other; this, as he says, is by far the best of them all, for to it all things submit, not by compulsion, but of their own free will. Now, I should not like to quarrel either with you or with him.
Socrates: You mean to say that you would like to desert, if you were not ashamed?
Protarchus: As you please.
Socrates: May I not have led you into a misapprehension?
Protarchus: How?