Recommendation of logical bipartition.
The above-mentioned principle — dichotomy or bipartition into two equal or nearly equal halves, each resting upon a characteristic form — is to be applied as far as it will go. Many different schemes of partition upon this principle may be found, each including forms subordinated one to the other, descending from the more comprehensive to the less comprehensive. It is only when you can find no more parts which are forms, that you must be content to divide into parts which are not forms. Thus after all the characteristic forms, for dividing the human race, have been gone through, they may at last be partitioned into Hellênes and Barbari, Lydians and non-Lydians, Phrygians and non-Phrygians: in which divisions there is no guiding form at all, but only a capricious distribution into fractions with separate names[162] — meaning by capricious, a distribution founded on some feeling or circumstance peculiar to the distributor, or shared by him only with a few others; such as the fact, that he is himself a Lydian or a Phrygian, &c.
[162] Politikus, p. 262 E. Λυδοὺς δὲ ἢ Φρύγας ἤ τινας ἑτέρους πρὸς ἅπαντας τάττων ἀπόσχιζοι τότε, ἡνίκα ἀποροῖ γένος ἄμα καὶ μέρος εὑρίσκειν ἑκάτερον τῶν σχισθέντων.
Precepts illustrated by the Philêbus.
These precepts in the Sophistês and Politikus, respecting the process of classification, are illustrated by an important passage of the Philêbus:[163] wherein Plato tells us that the constitution of things includes the Determinate and the Indeterminate implicated with each other, and requiring study to disengage them. Between the highest One, Form, or Genus — and the lowest array of indefinite particulars — there exist a certain number of intermediate Ones or Forms, each including more or fewer of these particulars. The process of study or acquired cognition is brought to bear upon these intermediate Forms: to learn how many there are, and to discriminate them in themselves as well as in their position relative to each other. But many persons do not recognise this: they apprehend only the Highest One, and the Infinite Many, not looking for any thing between: they take up hastily with some extreme and vague generality, below which they know nothing but particulars. With knowledge thus imperfect, you do not get beyond contentious debate. Real, instructive, dialectic requires an understanding of all the intermediate forms. But in descending from the Highest Form downwards, you must proceed as much as possible in the way of bipartition, or if not, then of tripartition, &c.: looking for the smallest number of forms which can be found to cover the whole field. When no more forms can be found, then and not till then, you must be content with nothing better than the countless indeterminate particulars.
[163] Plato, Philêbus, pp. 16-17.
The notes of Dr. Badham upon this passage in his edition of the Philêbus, p. 11, should be consulted as a just correction of Stallbaum in regard to πέρας and τῶν ἓν ἐκείνων.
This instructive passage of the Philêbus — while it brings to view a widespread tendency of the human mind, to pass from the largest and vaguest generalities at once into the region of particulars, and to omit the distinctive sub-classes which lie between — illustrates usefully the drift of the Sophistês and Politikus. In these two last dialogues it is the method itself of good logical distribution which Plato wishes to impress upon his readers: the formal part of the process.[164] With this view, he not only makes the process intentionally circuitous and diversified, but also selects by preference matters of common sensible experience, though in themselves indifferent, such as the art of weaving,[165] &c.
[164] He states this expressly, Politik. p. 286 D.
[165] Plato, Politik. p. 285 D.