Proklus observes in his commentary on the dialogue — ὁ γὰρ Σωκράτης ἄγαται τὰς ἀπορίας, &c. (L. v. p. 252).
[59] Xenoph. Memor. iv. 2, ad fin.
[60] Plato, Parmenid. pp. 136 C, 137 A. Hobbes remarks (Computatio sive Logica, Part I, ch. iii. s. 12), “Learners ought to go through logical exercises silently and by themselves: for it will be thought both ridiculous and absurd, for a man to use such language publicly”.
Proklus tells us, that the difficulty of the γυμνασία here enjoined by the Platonic Parmenides is so prodigious, that no one after Plato employed it (Prokl. ad Parmenid. p. 306, p. 801, Stallb.).
εἰ μὲν οὖν πλείους ἦμεν, οὐκ ἂν ἄξιον ἦν δεῖσθαι. ἀπρεπῆ γὰρ τὰ τοιαῦτα πολλῶν ἐναντίον λέγειν, ἄλλως τε καὶ τηλικούτῳ· ἀγνοοῦσι γὰρ οἱ πολλοὶ ὅτι ἀνευ ταύτης τῆς διὰ πάντων διεξόδου καὶ πλάνης ἀδύνατον ἐντυχόντα τῷ ἀληθεῖ νοῦν σχεῖν.
[61] Plato, Parmenides, p. 137 B; compare Sophistes, p. 217 D.
To understand the force of this remark of Parmenides, we should contrast it with the precepts given by Aristotle in the Topica for dialectic debate: precepts teaching the questioner how to puzzle, and the respondent how to avoid being puzzled. Such precautions are advised to the respondent by Aristotle, not merely in the Topica but also in the Analytica — χρὴ δ’ ὅπερ φυλάττεσθαι παραγγέλλομεν ἀποκρινομένους, αὐτοὺς ἐπιχειροῦντας πειρᾶσθαι λανθάνειν (Anal. Priora, ii. p. 66, a. 33).
The exercises exhibited by Parmenides are exhibited only as illustrative specimens of a method enjoined to be applied to many other Antinomies.
We must remark farther, that the two hypotheses here handled at length by Parmenides are presented by him only as examples of a dialectical process which he enjoins the lover of truth to apply equally to many other hypotheses.[62] As he shows that in the case of Unum, each of the two assumptions (Unum est — Unum non est) can be traced through different threads of deductive reasoning so as to bring out double and contradictory results — Both and Neither: so also in the case of those other assumptions which remain to be tested afterwards in like manner, antinomies of the same character may be expected: antinomies apparent at least, if not real — which must be formally propounded and dealt with, before we can trust ourselves as having attained reasoned truth. Hence we see that, negative and puzzling as the dialogue called Parmenides is, even now — it would be far more puzzling if all that it prescribes in general terms had been executed in detail. While it holds out, in the face of an aspirant in philosophy, the necessity of giving equal presumptive value to the affirmative and negative sides of each hypothesis, and deducing with equal care, the consequences of both — it warns him at the same time of the contradictions in which he will thereby become involved. These contradictions are presented in the most glaring manner: but we must recollect a striking passage in the Republic, where Plato declares that to confront the aspirant with manifest contradictions, is the best way of provoking him to intellectual effort in the higher regions of speculation.[63]
[62] Plato, Parmenid. p. 136 B.