2. Parmenides now passes to a second argument. The reason why you assume that each one of these Forms exists, is — That when you contemplate many similar objects, one and the same ideal phantom or Concept is suggested by all.[12] Thus, when you see many great objects, one common impression of greatness arises from all. Hence you conclude that The Great, or the Form of Greatness, exists as One. But if you take this Form of Greatness, and consider it in comparison with each or all the great individual objects, it will have in common with them something that makes it great. You must therefore search for some higher Form, which represents what belongs in common both to the Form of Greatness and to individual great objects. And this higher Form again, when compared with the rest, will have something in common which must be represented by a Form yet higher: so that there will be an infinite series of Forms, ascending higher and higher, of which you will never reach the topmost.[13]
[12] Plato, Parmenid. p. 132. Οἶμαι σε ἐκ τοῦ τοιοῦδε ἓν ἕκαστον εἶδος οἴεσθαι εἶναι. Ὅταν πόλλ’ ἄττα μεγάλα σοι δόξῃ εἶναι, μία τις ἴσως δοκεῖ ἰδέα ἡ αὐτὴ εἶναι ἐπὶ πάντα ἰδόντι, ὅθεν ἓν τὸ μέγα ἡγεῖ εἶναι.
[13] 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.
Are the Ideas conceptions of the mind, and nothing more? Impossible.
3. Perhaps (suggests Sokrates) each of these Forms is a Conception of the mind and nothing beyond: the Form is not competent to exist out of the mind.[14] How? (replies Parmenides.) There cannot be in the mind any Conception, which is a Conception of nothing. Every Conception must be of something really existing: in this case, it is a Conception of some one thing, which you conceive as belonging in common to each and all the objects considered. The Something thus conceived as perpetually One and the same in all, is, the Form. Besides, if you think that individual objects participate in the Forms, and that these Forms are Conceptions of the mind, — you must suppose, either that all objects are made up of Conceptions, and are therefore themselves Concipients: or else that these Forms, though Conceptions, are incapable of conceiving. Neither one nor the other is admissible.[15]
[14] Plato, Parmenid. p. 132 B. μὴ τῶν εἰδῶν ἕκαστον ᾖ τούτων νοήμα, καὶ οὐδαμοῦ αὐτῷ προσήκη ἐγγίγνεσθαι ἄλλοθι ἢ ἐν ψυχαῖς.… Τί οὖν; φάναι, ἓν ἕκαστόν ἐστι τῶν νοημάτων, νόημα δὲ οὐδενός; Ἀλλ’ ἀδύνατον, εἰπεῖν. Ἀλλὰ τινός; Ναί. Ὄντος ἢ οὐκ ὄντος; Ὄντος. Οὐχ ἑνός τινος, ὃ ἐπὶ πᾶσιν ἐκεῖνο τὸ νόημα ἐπὸν νοεῖ, μίαν τινὰ οὖσαν ἰδέαν; Ναί.
Aristotle (Topic. ii. 113, a. 25) indicates one way of meeting this argument, if advanced by an adversary in dialectic debate — εἰ τὰς ἰδέας ἐν ἡμῖν ἔφησεν εἶναι.
[15] Plato, Parmenid. p. 132 D. οὐκ ἀνάγκη, εἰ τἄλλα φῂ τῶν εἰδῶν μετέχειν, ἢ δοκεῖν σοι ἐκ νοήματα ὄντα ἀνόητα εἶναι; Ἀλλ’ οὐδὲ τοῦτο, φάναι, ἔχει λόγον.