[103] Plato, Parmenid. p. 164 B. Ἄλλα μέν που δεῖ αὐτὰ εἶναι· εἰ γὰρ μηδὲ ἄλλα ἐστίν, οὐκ ἂν περὶ τῶν ἄλλων λέγοιτο.
[104] Plato, Parmenid. p. 164 D. Οὐκοῦν πολλοὶ ὄγκοι ἔσανται, εἶς ἕκαστος φαινόμενος, ὢν δὲ οὔ, εἴπερ ἓν μὴ ἔσται. Οὕτως.
[105] Plato, Parmenid. p. 165 A. Ὅτι ἀεὶ αὐτῶν ὅταν τίς τι λάβῃ τῇ διανοίᾳ ὥς τι τούτων ὅν, πρό τε τῆς ἀρχῆς ἄλλη ἀεὶ φαίνεται ἀρχή, μετά τε τὴν τελευτὴν ἑτέρα ὑπολειπομένη τελευτή, ἕν τε τῷ μέσῳ ἄλλα μεσαίτερα τοῦ μέσου, σμικρότερα δὲ διὰ τὸ μὴ δύνασθαι ἑνὸς αὐτῶν ἑκάστου λαμβάνεσθαι, ἄτε οὐκ ὄντος τοῦ ἑνός.
[106] Plato, Parmenid. p. 165 E. Compare p. 158 E. τοῖς ἄλλοις δὴ τοῦ ἑνὸς.… ἡ δὲ αὐτῶν φύσις καθ’ ἑαυτὰ ἀπειρίαν (πάρεσχε).
Demonstration VIII. is very subtle and Zenonian.
This Demonstration 8, with its strange and subtle chain of inferences, purporting to rest upon the admission of Cætera without Unum, brings out the antithesis of the Apparent and the Real, which had not been noticed in the preceding demonstrations. Demonstration 8 is in its character Zenonian. It probably coincides with the proof which Zeno is reported (in the earlier half of this dialogue) to have given against the existence of any real Multa. If you assume Multa (Zeno argued), they must be both like and unlike, and invested with many other opposite attributes; but this is impossible; therefore the assumption is untrue.[107] Those against whom Zeno reasoned, contended for real Multa, and against a real Unum. Zeno probably showed, and our eighth Demonstration here shows also, — that Multa under this supposition are nothing real, but an assemblage of indefinite, ever-variable, contradictory appearances: an Ἄπειρον, Infinite, or Chaos: an object not real and absolute, but relative and variable according to the point of view of the subject.
[107] Plato, Parmenid. p. 127 E; compare this with the close of the eighth Demonstration, p. 165 E — εἰ ἑνὸς μὴ ὄντος πολλὰ ἔστιν.
Demonstration IX. Neither following Both.
To the eighth Demonstration, ingenious as it is, succeeds a countervailing reversal in the ninth: the Neither following the Both. The fundamental supposition is in terms the same. Si Unum non est, what is to become of Cætera? Cætera are not Unum: yet neither are they Multa: for if there were any Multa, Unum would be included in them. If none of the Multa were Unum, all of them would be nothing at all, and there would be no Multa. If therefore Unum be not included in Cætera, Cætera would be neither Unum nor Multa: nor would they appear to be either Unum or Multa: for Cætera can have no possible communion with Non-Entia: nor can any of the Non-Entia be present along with any of Cætera — since Non-Entia have no parts. We cannot therefore conceive or represent to ourselves Non-Ens as along with or belonging to Cætera. Therefore, Si Unum non est, nothing among Cætera is conceived either as Unum or as Multa: for to conceive Multa without Unum is impossible. It thus appears, Si Unum non est, that Cætera neither are Unum nor Multa. Nor are they conceived either as Unum or Multa — either as like or as unlike — either as the same or as different — either as in contact or as apart. — In short, all those attributes which in the last preceding Demonstration were shown to belong to them in appearance, are now shown not to belong to them either in appearance or in reality.[108]
[108] Plato, Parmenid. p. 166 A-B. Ἓν ἄρα εἰ μὴ ἔστι, τἄλλα οὔτε ἔστιν οὔτε δοξάζεται ἓν οὔτε πολλά.… Οὔδ’ ἄρα ὅμοια οὐδὲ ἀνόμοια.… Οὐδὲ μὴν τὰ αὐτά γε οὐδ’ ἕτερα, οὐδὲ ἁπτόμενα οὐδὲ χωρίς, οὐδὲ ἄλλ’ ὅσα ἐν τοῖς πρόσθεν διήλθομεν (compare διελθεῖν, p. 165 E) ὡς φαινόμενα αὐτά, τούτων οὔτε τι ἔστιν οὔτε φαίνεται τἄλλα, ἓν εἰ μὴ ἔστιν.