STRANGER: Then we must suppose that the great and small exist and are discerned in both these ways, and not, as we were saying before, only relatively to one another, but there must also be another comparison of them with the mean or ideal standard; would you like to hear the reason why? YOUNG SOCRATES: Certainly. STRANGER: If we assume the greater to exist only in relation to the less, there will never be any comparison of either with the mean. YOUNG SOCRATES: True. STRANGER: And would not this doctrine be the ruin of all the arts and their creations; would not the art of the Statesman and the aforesaid art of weaving disappear? For all these arts are on the watch against excess and defect, not as unrealities, but as real evils, which occasion a difficulty in action; and the excellence or beauty of every work of art is due to this observance of measure. YOUNG SOCRATES: Certainly. STRANGER: But if the science of the Statesman disappears, the search for the royal science will be impossible. YOUNG SOCRATES: Very true. STRANGER: Well, then, as in the case of the Sophist we extorted the inference that not-being had an existence, because here was the point at which the argument eluded our grasp, so in this we must endeavour to show that the greater and less are not only to be measured with one another, but also have to do with the production of the mean; for if this is not admitted, neither a statesman nor any other man of action can be an undisputed master of his science. YOUNG SOCRATES: Yes, we must certainly do again what we did then. STRANGER: But this, Socrates, is a greater work than the other, of which we only too well remember the length. I think, however, that we may fairly assume something of this sort-- YOUNG SOCRATES: What? STRANGER: That we shall some day require this notion of a mean with a view to the demonstration of absolute truth; meanwhile, the argument that the very existence of the arts must be held to depend on the possibility of measuring more or less, not only with one another, but also with a view to the attainment of the mean, seems to afford a grand support and satisfactory proof of the doctrine which we are maintaining; for if there are arts, there is a standard of measure, and if there is a standard of measure, there are arts; but if either is wanting, there is neither. YOUNG SOCRATES: True; and what is the next step? STRANGER: The next step clearly is to divide the art of measurement into two parts, as we have said already, and to place in the one part all the arts which measure number, length, depth, breadth, swiftness with their opposites; and to have another part in which they are measured with the mean, and the fit, and the opportune, and the due, and with all those words, in short, which denote a mean or standard removed from the extremes. YOUNG SOCRATES: Here are two vast divisions, embracing two very different spheres.