Such negative element, manifested as it is in so many of the Platonic dialogues, has its extreme manifestation in the Parmenidês. When we see it here applied to a doctrine which Plato in other dialogues insists upon as truth, we must call to mind (what sincere believers are apt to forget) that a case may always be made out against truth as well as in its favour: and that its privilege as a certified portion of “reasoned truth,” rests upon no better title than the superiority of the latter case over the former. It is for testing the two cases — for determining where the superiority lies — and for graduating its amount — that the process of philosophising is called for, and that improvements in the method thereof become desirable. That Plato should, in one of his many diversified dialogues, apply this test to a doctrine which, in other dialogues, he holds out as true — is noway inconsistent with the general spirit of these compositions. Each of his dialogues has its own point of view, worked out on that particular occasion; what is common to them all, is the process of philosophising applied in various ways to the same general topics.
Those who, like Socher, deny Plato’s authorship of the Parmenidês, on the ground of what is urged therein against the theory of Ideas, must suppose, either that he did not know that a negative case could be made out against that theory; or that knowing it, he refrained from undertaking the duty.[27] Neither supposition is consistent with what we know both of his negative ingenuity, and of his multifarious manner of handling.
[27] Plato, Philêbus, p. 14, where the distinction taken coincides accurately enough with that which we read in Plato, Parmenid. p. 129 A-D.
Strümpell thinks that the Parmenidês was composed at a time of Plato’s life when he had become sensible of the difficulties and contradictions attaching to his doctrine of self-existent Forms or Ideas, and when he was looking about for some way of extrication from them: which way he afterwards thought that he found in that approximation to Pythagorism — that exchange of Ideas for Ideal numbers, &c. — which we find imputed to him by Aristotle (Gesch. der Griech. Phil. sect. 96, 3). This is not impossible; but I find no sufficient ground for affirming it. Nor can I see how the doctrine which Aristotle ascribes to Plato about the Ideas (that they are generated by two στοιχεῖα or elements, τὸ ἕν along with τὸ μέγα καὶ τὸ μικρόν) affords any escape from the difficulties started in the Parmenidês.
Strümpell considers the dialogue Parmenidês to have been composed “ganz ausdrücklich zur dialektischen Uebung,” ib. s. 96, 2, p. 128.
Force of the negative case in the Parmenidês. Difficulties about participation of sensible objects in the world of Ideas.
The negative case, made out in the Parmenidês against the theory of Ideas, is indeed most powerful. The hypothesis of the Ideal World is unequivocally affirmed by Sokrates, with its four principal characteristics. 1. Complete essential separation from the world of sense. 2. Absolute self-existence. 3. Plurality of constituent items, several contrary to each other. 4. Unchangeable sameness and unity of each and all of them. — Here we have full satisfaction given to the Platonic sentiment, which often delights in soaring above the world of sense, and sometimes (see Phædon) in heaping contemptuous metaphors upon it. But unfortunately Sokrates cannot disengage himself from this world of sense: he is obliged to maintain that it partakes of, or is determined by, these extra-sensible Forms or Ideas. Here commence the series of difficulties and contradictions brought out by the Elenchus of Parmenides. Are all sensible objects, even such as are vulgar, repulsive, and contemptible, represented in this higher world? The Platonic sentiment shrinks from the admission: the Platonic sense of analogy hesitates to deny it. Then again, how can both assertions be true — first that the two worlds are essentially separate, next, that the one participates in, and derives its essence from, the other? How (to use Aristotelian language[28]) can the essence be separated from that of which it is the essence? How can the Form, essentially One, belong at once to a multitude of particulars?
[28] Arist. Met. A. 991, b. 1. ἀδύνατον, χωρὶς εἶναι τὴν οὐσίαν καὶ οὖ ἡ οὐσία.
Two points deserve notice in this debate respecting the doctrine of Ideas:—
Difficulties about the Cognizability of Ideas. If Ideas are absolute, they cannot be cognizable: if they are cognizable, they must be relative. Doctrine of Homo Mensura.