284
Str. Then just as in the case of the sophist Plat. Soph. 235 we forced the conclusion that not-being exists, since that was the point at which we had lost our hold of the argument, so now we must force this second conclusion, that the greater and the less are to be measured in relation, not only to one another, but also to the establishment of the standard of the mean, must we not? For if this is not admitted, neither the statesman nor any other man who has knowledge of practical affairs can be said without any doubt to exist.
284
Y. Soc. Then we must by all means do now the same that we did then.
284
Str. This, Socrates, is a still greater task than that was; and yet we remember how long that took us; but it is perfectly fair to make about them some such assumption as this.
284
Y. Soc. As what?
284
Str. That sometime we shall need this principle of the mean for the demonstration of absolute precise truth. But our belief that the demonstration is for our present purpose good and sufficient is, in my opinion, magnificently supported by this argument—that we must believe that all the arts alike exist and that the greater and the less are measured in relation not only to one another but also to the establishment of the standard of the mean. For if this exists, they exist also, and if they exist, it exists also, but neither can ever exist if the other does not.
284
Y. Soc. That is quite right. But what comes next?
284
Str. We should evidently divide the science of measurement into two parts in accordance with what has been said. One part comprises all the arts which measure number, length, depth, breadth, and thickness in relation to their opposites; the other comprises those which measure them in relation to the moderate, the fitting, the opportune, the needful, and all the other standards that are situated in the mean between the extremes.
284
Y. Soc. Both of your divisions are extensive, and there is a great difference between them.
