Page - 923 - in The Complete Plato

power of guessing, which is commonly called art, and is perfected by attention and pains. PROTARCHUS: Nothing more, assuredly. SOCRATES: Music, for instance, is full of this empiricism; for sounds are harmonized, not by measure, but by skilful conjecture; the music of the flute is always trying to guess the pitch of each vibrating note, and is therefore mixed up with much that is doubtful and has little which is certain. PROTARCHUS: Most true. SOCRATES: And the same will be found to hold good of medicine and husbandry and piloting and generalship. 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, 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 923