Soc. All that would be left for us would be to conjecture and to drill the perceptions by practice and experience, with the additional use of the powers of guessing,
 which are commonly called arts and acquire their efficacy by practice and toil. Pro. That is undeniable. Soc. Take music first; it is full of this; it attains harmony by guesswork based on practice, not by measurement; and flute music throughout tries to find the pitch of each note as it is produced by guess, so that the amount of uncertainty mixed up in it is great, and the amount of certainty small. Pro. Very true. Soc. And we shall find that medicine and agriculture and piloting and generalship are all in the same case. Pro. Certainly. Soc. But the art of building, I believe, employs the greatest number of measures and instruments which give it great accuracy and make it more scientific than most arts. Pro. In what way? Soc. In shipbuilding and house-building, and many other branches of wood-working. For the artisan uses a rule, I imagine, a lathe, compasses, a chalk-line,
 and an ingenious instrument called a vice. Pro. Certainly, Socrates; you are right. Soc. Let us, then, divide the arts, as they are called, into two kinds, those which resemble music, and have less accuracy in their works, and those which, like building, are more exact. Pro. Agreed. Soc. And of these the most exact are the arts which I just now mentioned first. Pro. I think you mean arithmetic and the other arts you mentioned with it just now. Soc. Certainly. But, Protarchus, ought not these to be divided into two kinds? What do you say? Pro. What kinds? Soc. Are there not two kinds of arithmetic, that of the people and that of philosophers? Pro. How can one kind of arithmetic be distinguished from the other? Soc. The distinction is no small one, Protarchus. For some arithmeticians reckon unequal units,
 for instance, two armies and two oxen and two very small or incomparably large units; whereas others refuse to agree with them unless each of countless units is declared to differ not at all from each and every other unit. Pro. You are certainly quite right in saying that there is a great difference between the devotees of arithmetic, so it is reasonable to assume that it is of two kinds. Soc. And how about the arts of reckoning and measuring as they are used in building and in trade when compared with philosophical geometry
 and elaborate computations—shall we speak of each of these as one or as two? Pro. On the analogy of the previous example, I should say that each of them was two. Soc. Right. But do you understand why I introduced this subject? Pro. Perhaps; but I wish you would give the answer to your question. Soc. This discussion of ours is now, I think, no less than when we began it, seeking a counterpart of pleasure,
 and therefore it has introduced the present subject and is considering whether there is one kind of knowledge purer than another, as one pleasure is purer than another. Pro. That is very clear; it was evidently introduced with that object. Soc. Well, had not the discussion already found in what preceded that the various arts had various purposes and various degrees of exactness? Pro. Certainly. Soc. And after having given an art a single name in what has preceded, thereby making us think that it was a single art,
 does not the discussion now assume that the same art is two and ask whether the art of the philosophers or that of the non-philosophers possesses the higher degree of clearness and purity? Pro. Yes, I think that is just the question it asks. Soc. Then what reply shall we make, Protarchus? Pro. Socrates, we have found a marvelously great difference in the clearness of different kinds of knowledge. Soc. That will make the reply easier, will it not? Pro. Yes, to be sure; and let our reply be this, that the arithmetical and metrical arts far surpass the others and that of these
 the arts which are stirred by the impulse of the true philosophers are immeasurably superior in accuracy and truth about measures and numbers. Soc. We accept that as our judgement, and relying upon you we make this confident reply to those who are clever in straining arguments— Pro. What reply? Soc. That there are two arts of arithmetic and two of measuring, and many other arts which, like these, are twofold in this way, but possess a single name in common. Pro. Let us give this answer, Socrates, to those who you say are clever; I hope we shall have luck with it. Soc. These, then, we say, are the most exact arts or sciences? Pro. Certainly. Soc. But the art of dialectic would spurn us, Protarchus, if we should judge that any other art is preferable to her. Pro. But what is the art to which this name belongs? Soc. Clearly anybody can recognize the art I mean; for I am confident that all men who have any intellect whatsoever believe that the knowledge which has to do with being, reality, and eternal immutability is the truest kind of knowledge. What do you think, Protarchus? Pro. I have often heard Gorgias constantly maintain that the art of persuasion surpasses all others for this, he said, makes all things subject to itself,
 not by force, but by their free will, and is by far the best of all arts; so now I hardly like to oppose either him or you. Soc. It seems to me that you wanted to speak and threw down your arms out of modesty. Pro. Very well; have it as you like. Soc. Is it my fault that you have misunderstood? Pro. Misunderstood what? Soc. My question, dear Protarchus, was not as yet what art or science surpasses all others
 by being the greatest and best and most useful to us: what I am trying to find out at present is which art, however little and of little use, has the greatest regard for clearness, exactness, and truth. See; you will not make Gorgias angry if you grant that his art is superior for the practical needs of men, but say that the study of which I spoke is superior in the matter of the most perfect truth, just as I said in speaking about the white that if it was small and pure it was superior to that which was great
 but impure. Now, therefore, with careful thought and due consideration, paying attention neither to the usefulness nor to the reputation of any arts or sciences, but to that faculty of our souls, if such there be, which by its nature loves the truth and does all things for the sake of the truth, let us examine this faculty and say whether it is most likely to possess mind and intelligence in the greatest purity, or we must look for some other faculty
 which has more valid claims. Pro. I am considering, and I think it is difficult to concede that any other science or art cleaves more closely to truth than this. Soc. In saying that, did you bear in mind that the arts in general, and the men who devote themselves to them,
 make use of opinion and persistently investigate things which have to do with opinion? And even if they think they are studying nature, they are spending their lives in the study of the things of this world, the manner of their production, their action, and the forces to which they are subjected. Is not that true? Pro. Yes, it is. Soc. Such thinkers, then, toil to discover, not eternal verities, but transient productions of the present, the future, or the past? Pro. Perfectly true. Soc. And can we say that any of these things becomes certain, if tested by the touchstone of strictest truth,
 since none of them ever was, will be, or is in the same state? Pro. Of course not. Soc. How can we gain anything fixed whatsoever about things which have no fixedness whatsoever? Pro. In no way, as it seems to me. Soc. Then no mind or science which is occupied with them possesses the most perfect truth. Pro. No, it naturally does not. Soc. Then we must dismiss the thought of you and me and Gorgias and Philebus, and make this solemn declaration
 on the part of our argument. Pro. What is the solemn declaration? Soc. That fixed and pure and true and what we call unalloyed knowledge has to do with the things which are eternally the same without change or mixture, or with that which is most akin to them; and all other things are to be regarded as secondary and inferior. Pro. Very true. Soc. And of the names applied to such matters, it would be fairest to give the finest names to the finest things, would it not? Pro. That is reasonable. Soc. Are not mind, then, and wisdom the names which we should honor most? Pro. Yes. Soc. Then these names are applied most accurately and correctly to cases of contemplation of true being. Pro. Certainly. Soc. And these are precisely the names which I brought forward in the first place as parties to our suit. Pro. Yes, of course they are, Socrates. Soc. Very well. As to the mixture of wisdom and pleasure,
 if anyone were to say that we are like artisans, with the materials before us from which to create our work, the simile would be a good one. Pro. Certainly. Soc. And is it, then, our next task to try to make the mixture? Pro. Surely. Soc. Would it not be better first to repeat certain things and recall them to our minds? Pro. What things? Soc. Those which we mentioned before. I think the proverb we ought to repeat twice and even three times that which is good 
 is an excellent one. Pro. Surely. Soc. Well then, in God’s name; I think this is the gist of our discussion. Pro. What is it? Soc. Philebus says that pleasure is the true goal of every living being and that all ought to aim at it, and that therefore this is also the good for all, and the two designations good and pleasant are properly and essentially one; Socrates, however, says that they are not one,
 but two in fact as in name, that the good and the pleasant differ from one another in nature, and that wisdom’s share in the good is greater than pleasure’s. Is not and was not that what was said, Protarchus? Pro. Yes, certainly. Soc. And furthermore, is not and was not this a point of agreement among us? Pro. What? Soc. That the nature of the good differs from all else in this respect. Pro. In what respect? Soc. That whatever living being possesses the good always, altogether, and in all ways, has no further need of anything, but is perfectly sufficient. We agreed to that? Pro. We did. Soc. And then we tried in thought to separate each from the other and apply them to individual lives, pleasure unmixed with wisdom and likewise wisdom which had not the slightest alloy of pleasure? Pro. Yes. Soc. And did we think then that either of them would be sufficient for any one? Pro. By no means. Soc. And if we made any mistake at that time, let any one now take up the question again. Assuming that memory, wisdom, knowledge, and true opinion belong to the same class, let him ask whether anyone would wish to have or acquire anything whatsoever without these not to speak of pleasure, be it never so abundant or intense, if he could have no true opinion that he is pleased, no knowledge whatsoever
 of what he has felt, and not even the slightest memory of the feeling. And let him ask in the same way about wisdom, whether anyone would wish to have wisdom without any, even the slightest, pleasure rather than with some pleasures, or all pleasures without wisdom rather than with some wisdom. Pro. That is impossible, Socrates; it is useless to ask the same question over and over again.