I. Plato assumes, that there will be critics who blame the two dialogues as too long and circuitous; excessive in respect of prolixity. In replying to those objectors,[1] he enquires, What is meant by long or short — excessive or deficient — great or little? Such expressions denote mensuration or comparison. But there are two varieties of mensuration. We may measure two objects one against the other: the first will be called great or greater, in relation to the second — the second will be called little or less in relation to the first. But we may also proceed in a different way. We may assume some third object as a standard, and then measure both the two against it: declaring the first to be great, greater, excessive, &c., because it exceeds the standard — and the second to be little, less, deficient, &c., because it falls short of the standard. Here then are two judgments or estimations altogether different from each other, and yet both denoted by the same words great and little: two distinct essences (in Platonic phrase) of great and little, or of greatness and littleness.[2] The art of mensuration has thus two varieties. One includes arithmetic and geometry, where we simply compare numbers and magnitudes with each other, determining the proportions between them: the other assumes some independent standard; above which is excess, and below which is deficiency. This standard passes by different names according to circumstances: the Moderate, Becoming, Seasonable, Proper, Obligatory, &c.[3] Such a standard is assumed in every art — in every artistic or scientific course of procedure. Every art has an end to be attained, a result to be produced; which serves as the standard whereby each preparatory step of the artist is measured, and pronounced to be either excessive or deficient, as the case may be.[4] Unless such a standard be assumed, you cannot have regular art or science of any kind; neither in grave matters, nor in vulgar matters — neither in the government of society, nor in the weaving of cloth.[5]
[1] The treatment of this subject begins, Politik. p. 283 C, where Plato intimates that the coming remarks are of wide application.
[2] Plato, Politik. p. 283 E. δίττας ἄρα ταύτας οὐσίας καὶ κρίσεις τοῦ μεγάλου καὶ τοῦ σμικροῦ θετέον.
[3] Plato, Politik. p. 284 E. τὸ μέτριον, τὸ πρέπον, τὸν καιρόν, τὸ δέον, &c.
The reader will find these two varieties of mensuration, here distinguished by Plato, illustrated in the “two distinct modes of appreciating weight” (the Absolute and the Relative), described and explained by Professor Alexander Bain in his work on The Senses and The Intellect, 3rd edition, p. 93. This explanation forms an item in the copious enumeration given by Mr. Bain of the fundamental sensations of our nature.
[4] Plato, Politik. p. 283 D. κατὰ τὴν τῆς γενέσεως ἀναγκαίαν οὐσίαν. — 284 A-C. πρὸς τὴν τοῦ μετρίου γένεσιν.
[5] Plato, Politik. p. 284 C.
Purpose in the Sophistês and Politikus is — To attain dialectic aptitude. This is the standard of comparison whereby to judge whether the means employed are suitable.
Now what is the end to be attained, by this our enquiry into the definition of a Statesman? It is not so much to solve the particular question started, as to create in ourselves dialectic talent and aptitude, applicable to every thing. This is the standard with reference to which our enquiry must be criticised — not by regard to the easy solution of the particular problem, or to the immediate pleasure of the hearer. And if an objector complains, that our exposition is too long or our subject-matters too vulgar — we shall require him to show that the proposed end might have been attained with fewer words and with more solemn illustrations. If he cannot show this, we shall disregard his censure as inapplicable.[6]
[6] Plato, Politik. pp. 286 D, 287 A. Compare Plato, Philêbus, p. 36 D.