Aristotle calls Antisthenes and his followers ἀπαίδευτοι, in the passage cited in the preceding [note].
Precepts and examples of logical partition, illustrated in the Sophistês.
The long and varied predicamental series, given in the Sophistês, illustrates the process of logical partition, as Plato conceived it, and the definition of a class-name founded thereupon. You take a logical whole, and you subtract from it part after part until you find the quæsitum isolated from every thing else.[156] But you must always divide into two parts (he says) wherever it can be done: dichotomy or bipartition is the true logical partition: should this be impracticable, trichotomy, or division into the smallest attainable number of parts, must be sought for.[157] Moreover, the bipartition must be made according to Forms (Ideas, Kinds): the parts which you recognise must be not merely parts, but Forms: every form is a part, but every part is not a form.[158] Next, you must draw the line of division as nearly as you can through the middle of the dividendum, so that the parts on both sides may be nearly equal: it is in this way that your partition is most likely to coincide with forms on both sides of the line.[159] This is the longest way of proceeding, but the safest. It is a logical mistake to divide into two parts very unequal: you may find a form on one side of the line, but you obtain none on the other side. Thus, it is bad classification to distribute the human race into Hellênes + Barbari: the Barbari are of infinite number and diversity, having no one common form to which the name can apply. It is also improper to distribute Number into the myriad on side, and all other numbers on the other — for a similar reason. You ought to distribute the human race into the two forms, Male — Female: and number into the two, Odd — Even.[160] So also, you must not divide gregarious creatures into human beings on one side, and animals on the other; because this last term would comprise numerous particulars utterly disparate. Such a classification is suggested only by the personal feeling of man, who prides himself upon his intelligence. But if the classification were framed by any other intelligent species, such as Cranes,[161] they would distinguish Cranes on the one side from animals on the other, including Man as one among many disparate particulars under animal.
[156] Plato, Politikus, p. 268 D. μέρος ἀεὶ μέρους ἀφαιρουμένους ἐπ’ ἄκρον ἐφικνεῖσθαι τὸ ζητούμενον.
Ueberweg thinks that Aristotle, when he talks of αἱ γεγραμμέναι διαιρέσεις alludes to these logical distributions in the Sophistês and Politikus (Aechtheit der Platon. Schr. pp. 153-154).
[157] Politik. p. 287 C.
[158] Politik. p. 263 C.
[159] Politik. pp. 262 B, 265 A. δεῖ μεσοτομεῖν ὡς μάλιστα, &c.
[160] Politikus, p. 262 D-E.
[161] Politikus, p. 262 D. σεμνῦνον αὑτὸ ἑαυτό, &c.