[10] Plato, Sophist. p. 227 B; Politik. p. 266 D; also Theætêt. p. 174 D.
Both the Platonic Sokrates, and the Xenophontic Sokrates, frequently illustrate the education of men by comparison with the bringing up of young animals as well as with the training of horses: they also compare the educator of young men with the trainer of young horses. Indeed this comparison occurs so frequently, that it excites much displeasure among various modern critics (Forchhammer, Köchly, Socher, &c.), who seem to consider it as unseemly and inconsistent with “the dignity of human nature”. The frequent allusions made by Plato to the homely arts and professions are noted by his interlocutors as tiresome.
See Plato, Apolog. Sokr. p. 20 A. ὦ Καλλία, εἰ μέν σου τὼ υἱέε πώλω ἢ μόσχω ἐγενέσθην, &c.
The Zoological works of Aristotle exhibit a memorable example of scientific intelligence, overcoming all the contempt and disgust usually associated with minute and repulsive organisms. To Plato, it would be repugnant to arrange in the same class the wolf and the dog. See Sophist. p. 231 A.
Parmenides now produces various objections against the Platonic variety of dualism: the two distinct but partially inter-communicating worlds — one, of separate, permanent, unchangeable, Forms or Ideas — the other, of individual objects, transient and variable; participating in, and receiving denomination from, these Forms.
Objections of Parmenides — How can objects participate in the Ideas. Each cannot have the whole Idea, nor a part thereof.
1. How (asks Parmenides) can such participation take place? Is the entire Form in each individual object? No: for one and the same Form cannot be at the same time in many distant objects. A part of it therefore must be in one object; another part in another. But this assumes that the Form is divisible — or is not essentially One. Equality is in all equal objects: but how can a part of the Form equality, less than the whole, make objects equal? Again, littleness is in all little objects: that is, a part of the Form littleness is in each. But the Form littleness cannot have parts; because, if it had, the entire Form would be greater than any of its parts, — and the Form littleness cannot be greater than any thing. Moreover, if one part of littleness were added to other parts, the sum of the two would be less, and not greater, than either of the factors. It is plain that none of these Forms can be divisible, or can have parts. Objects therefore cannot participate in the Form by parts or piecemeal. But neither can each object possess the entire Form. Accordingly, since there remains no third possibility, objects cannot participate in the Forms at all.[11]
[11] Plato, Parmenid. p. 131. A similar argument, showing the impossibility of such μέθεξις, appears in Sextus Empiric. adv. Arithmeticos, sect. 11-20, p. 334 Fab., p. 724 Bek.
Comparing the Idea with the sensible objects partaking in the Idea, there is a likeness between them which must be represented by a higher Idea — and so on ad infinitum.