Note 13 — Chapter XXVII · PARMENIDES.

Plato, Parmenid. p. 132 A. See this process, of comparing the Form with particular objects denominated after the Form, described in a different metaphysical language by Mr. John Stuart Mill, System of Logic, book iv. ch. 2, sect. 3. “As the general conception is itself obtained by a comparison of particular phenomena, so, when obtained, the mode in which we apply it to other phenomena is again by comparison. We compare phenomena with each other to get the conception; and we then compare those and other phenomena with the conception. We get the conception of an animal by comparing different animals, and when we afterwards see a creature resembling an animal, we compare it with our general conception of an animal: and if it agrees with our general conception, we include it in the class. The conception becomes the type of comparison. We may perhaps find that no considerable number of other objects agree with this first general conception: and that we must drop the conception, and beginning again with a different individual case, proceed by fresh comparisons to a different general conception.”

The comparison, which the argument of the Platonic Parmenides assumes to be instituted, between τὸ εἶδος and τὰ μετέχοντα αὐτοῦ, is denied by Proklus; who says that there can be no comparison, nor any κοινότης, except between τὰ ὁμοταγῆ: and that the Form is not ὁμοταγὲς with its participant particulars. (Proklus ad Parmenidem, p. 125, p. 684 ed. Stallbaum.)

This argument of Parmenides is the memorable argument known under the name of ὁ τρίτος ἄνθρωπος. Against the Platonic εἴδη considered as χωριστά, it is a forcible argument. See Aristot. Metaphys. A. 990, b. 15 seq., where it is numbered among οἱ ἀκριβέστεροι τῶν λόγων. We find from the Scholion of Alexander (p. 566 Brandis), that it was advanced in several different ways by Aristotle, in his work Περὶ Ἰδεῶν: by his scholar Eudemus ἐν τοῖς περὶ Λέξεως: and by a contemporary σοφιστὴς named Polyxenus, as well as by other Sophists.