The Politikus by itself, apart from the Sophistês

I have examined in the preceding sections both that which the Sophistês and Politikus present in common—(viz. a lesson, as well as a partial theory, of the logical processes called Definition and Division)—and that which the Sophistês presents apart from the Politikus. I now advert to two matters which we find in the Politikus, but not in the Sophistês. Both of them will be found to illustrate the Platonic mode of philosophising.

Views of Plato on mensuration. Objects measured against each other. Objects compared with a common standard. In each Art, the purpose to be attained is the standard

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, 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.