Plato’s defence of the Politikus against critics. Necessity that the critic shall declare explicitly what his standard of comparison is.
The above-mentioned distinction between the two varieties of mensuration or comparison, is here given by Plato, simply to serve as a defence against critics who censured the peculiarities of the Politikus. It is not pursued into farther applications. But it deserves notice, not merely as being in itself just and useful, but as illustrating one of the many phases of Plato’s philosophy. It is an exhibition of the relative side of Plato’s character, as contra-distinguished from the absolute or dogmatical: for both the two, opposed as they are to each other, co-exist in him and manifest themselves alternately. It conveys a valuable lesson as to the apportionment of praise and blame. “When you blame me” (he says to his critics), “you must have in your mind some standard of comparison upon which the blame turns. Declare what that standard is:— what you mean by the Proper, Becoming, Moderate, &c. There is such a standard, and a different one, in every different Art. What is it here? You must choose this standard, explain what it is, and adhere to it when you undertake to praise or blame.” Such an enunciation (thoroughly Sokratic[7]) of the principle of relativity, brings before critics the fact — which is very apt to be forgotten — that there must exist in the mind of each some standard of comparison, varying or unvarying, well or ill understood: while at the same time it enforces upon them the necessity of determining clearly for themselves, and announcing explicitly to others, what that standard is. Otherwise the propositions, affirming comparison, can have no uniform meaning with any two debaters, nor even with the same man at different times.
[7] Xenophon, Memorab. iii. 8, 7, iii. 10, 12.
Comparison of Politikus with Protagoras, Phædon, Philêbus, &c.
To this relative side of Plato’s mind belong his frequent commendations of measurement, numbering, computation, comparison, &c. In the Protagoras,[8] he describes the art of measurement as the main guide and protector of human life: it is there treated as applicable to the correct estimation of pleasures and pains. In the Phædon,[9] it is again extolled: though the elements to be calculated are there specified differently. In the Philêbus, the antithesis of Πέρας and Ἄπειρον (the Determinant or Limit, and the Indeterminate or Infinite) is one of the leading points of the dialogue. We read in it moreover a bipartite division of Mensuration or Arithmetic,[10] which is quite different from the bipartite division just cited out of the Politikus. Plato divides it there (in the Philêbus) into arithmetic for theorists, and arithmetic for practical life: besides which, he distinguishes the various practical arts as being more or less accurate, according as they have more or less of measurement and sensible comparison in them. Thus the art of the carpenter, who employs measuring instruments such as the line and rule — is more accurate than that of the physician, general, pilot, husbandman, &c., who have no similar means of measuring. This is a classification quite different from what we find in the Politikus; yet tending in like manner to illustrate the relative point of view, and its frequent manifestation in Plato. In the Politikus, he seeks to refer praise and blame to a standard of measurement, instead of suffering them to be mere outbursts of sentiment unsystematic and unanalysed.
[8] Plato, Protagor. p. 357 B.
[9] Plato, Phædon, p. 69 B.
[10] Plato, Philêbus, pp. 25 C, 27 D, 57. δύο ἀριθμητικαὶ καὶ δύο μετρητικαί … τὴν διδυμότητα ἔχουσαι ταύτην, ὀνόματος δὲ ἑνὸς κεκοινωμέναι.
This same bipartition, however, is noticed in another passage of the Politikus, p. 258 D-E.
Definition of the statesman, or Governor. Scientific competence. Sokratic point of departure. Procedure of Plato in subdividing.