PROTARCHUS: Very true.

SOCRATES: The art of the builder, on the other hand, which uses a number of measures and instruments, attains by their help to a greater degree of accuracy than the other arts.

PROTARCHUS: How is that?

SOCRATES: In ship-building and house-building, and in other branches of the art of carpentering, the builder has his rule, lathe, compa.s.s, 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 cla.s.s, 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 a.n.a.logy 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 surpa.s.s 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 surpa.s.sed 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 ma.s.s 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 I can hardly think that any other science or art has a firmer grasp of the truth than this.

SOCRATES: Do you say so because you observe that the arts in general and those engaged in them make use of opinion, and are resolutely engaged in the investigation of matters of opinion? Even he who supposes himself to be occupied with nature is really occupied with the things of this world, how created, how acting or acted upon. Is not this the sort of enquiry in which his life is spent?

PROTARCHUS: True.

SOCRATES: He is labouring, not after eternal being, but about things which are becoming, or which will or have become.

PROTARCHUS: Very true.

SOCRATES: And can we say that any of these things which neither are nor have been nor will be unchangeable, when judged by the strict rule of truth ever become certain?