Dialogues

help to a greater degree of accuracy than the other arts. Protarchus How is that? Socrates In shipbuilding and house-building, and in other branches of the art of carpentering, the builder has his rule, lathe, compass, line, and a most ingenious machine for straightening wood. Protarchus Very true, Socrates. Socrates Then now let us divide the arts of which we were speaking into two kinds⁠—the arts which, like music, are less exact in their results, and those which, like carpentering, are more exact. Protarchus Let us make that division. Socrates Of the latter class, the most exact of all are those which we just now spoke of as primary. Protarchus I see that you mean arithmetic, and the kindred arts of weighing and measuring. Socrates Certainly, Protarchus; but are not these also distinguishable into two kinds? Protarchus What are the two kinds? Socrates In the first place, arithmetic is of two kinds, one of which is popular, and the other philosophical. Protarchus How would you distinguish them? Socrates There is a wide difference between them, Protarchus; some arithmeticians reckon unequal units; as for example, two armies, two oxen, two very large things or two very small things. The party who are opposed to them insist that every unit in ten thousand must be the same as every other unit. Protarchus Undoubtedly there is, as you say, a great difference among the votaries of the science; and there may be reasonably supposed to be two sorts of arithmetic. Socrates And when we compare the art of mensuration which is used in building with philosophical geometry, or the art of computation which is used in trading with exact calculation, shall we say of either of the pairs that it is one or two? Protarchus On the analogy of what has preceded, I should be of opinion that they were severally two. Socrates Right; but do you understand why I have discussed the subject? 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? Socrates Dear Protarchus, I never asked which was the greatest or best or usefullest of arts or sciences, but which had clearness and accuracy, and the greatest amount of truth, however humble and little useful an art. And as for Gorgias, if you do not deny that his art has the advantage in usefulness to mankind, he will not quarrel with you for saying that the study of which I am speaking is superior in this particular of essential truth; as in the comparison of white colours, a little whiteness, if that little be only pure, was said to be superior in truth to a great mass which is impure. And now let us give our best attention and consider well, not the comparative use or reputation of the sciences, but the power or faculty, if there be such, which the soul has of loving the truth, and of doing all things for the sake of it; let us search into the pure element of mind and intelligence, and then we shall be able to say whether the science of which I have been speaking is most likely to possess the faculty, or whether there be some other which has higher claims. Protarchus Well, I have been considering, and