Parmenides now proceeds to his second demonstration: professing to take up again the same hypothesis — Si Unum est — from which he had started in the first[77] — but in reality taking up a different hypothesis under the same words. In the first hypothesis, Si Unum est, was equivalent to, Si Unum est Unum: nothing besides Unum being taken into the reasoning, and est serving merely as copula. In the second, Si Unum est, is equivalent to, Si Unum est Ens, or exists: so that instead of the isolated Unum, we have now Unum Ens.[78] Here is a duality consisting of Unum and Ens: which two are considered as separate or separable factors, coalescing to form the whole Unum Ens, each of them being a part thereof. But each of these parts is again dual, containing both Unum and Ens: so that each part may be again divided into lesser parts, each of them alike dual: and so on ad infinitum. Unum Ens thus contains an infinite number of parts, or is Multa.[79] But even Unum itself (Parmenides argues), if we consider it separately from Ens in which it participates, is not Unum alone, but Multa also. For it is different from Ens, and Ens is different from it. Unum therefore is not merely Unum but also Diversum: Ens also is not merely Ens but Diversum. Now when we speak of Unum and Ens — of Unum and Diversum — or of Ens and Diversum — we in each case speak of two distinct things, each of which is Unum. Since each is Unum, the two things become three — Ens, Diversum, Unum — Unum, Diversum, Unum — Unum being here taken twice. We thus arrive at two and three — twice and thrice — odd and even — in short, number, with its full extension and properties. Unum therefore is both Unum and Multa — both Totum and Partes — both finite and infinite in multitude.[80]
[77] Plato, Parmenid. p. 142 A. Βούλει οὖν ἐπὶ τὴν ὑπόθεσιν πάλιν ἐξ ἀρχῆς ἐπανέλθωμεν, ἐάν τι ἡμῖν ἐπανιοῦσιν ἀλλοῖον φανῇ;
[78] This shifting of the real hypothesis, though the terms remain unchanged, is admitted by implication a little afterwards, p. 142 B. νῦν δὲ οὐχ αὕτη ἔστιν ἡ ὑπόθεσις, εἰ ἓν ἓν, τί χρὴ συμβαίνειν, ἀλλ’ εἰ ἓν ἔστιν.
[79] Plato, Parmenid. pp. 142-143. This is exactly what Sokrates in the early part of the dialogue (p. 129 B-D) had pronounced to be utterly inadmissible, viz.: That ὃ ἔστιν ἓν should be πολλὰ — that ὃ ἔστιν ὅμοιον should be ἀνόμοιον. The essential characteristic of the Platonic Ideas is here denied. However, it appears to me that Plato here reasons upon two contradictory assumptions; first, that Unum Ens is a total composed of two parts separately assignable — Unum and Ens; next, that Unum is not assignable separately from Ens, nor Ens from Unum. Proceeding upon the first, he declares that the division must be carried on ad infinitum, because you can never reach either the separate Ens or the separate Unum. But these two assumptions cannot be admitted both together. Plato must make his election; either he takes the first, in which case the total Unum Ens is divisible, and its two factors, Unum and Ens, can be assigned separately; or he takes the second, in which case Unum and Ens cannot be assigned separately — are not distinguishable factors, — so that Unum Ens instead of being infinitely divisible, is not divisible at all.
The reasoning as it now stands is, in my judgment, fallacious.
[80] Plato, Parmen. pp. 144 A-E, 145 A.
It ends in demonstrating Both, of that which the first Demonstration had demonstrated Neither.
Parmenides proceeds to show that Unum has beginning, middle, and end — together with some figure, straight or curved: and that it is both in itself, and in other things: that it is always both in motion and at rest:[81] that it is both the same with itself and different from itself — both the same with Cætera, and different from Cætera:[82] both like to itself, and unlike to itself — both like to Cætera, and unlike to Cætera:[83] that it both touches, and does not touch, both itself and Cætera:[84] that it is both equal, greater, and less, in number, as compared with itself and as compared with Cætera:[85] that it is both older than itself, younger than itself, and of the same age with itself — both older than Cætera, younger than Cætera, and of the same age as Cætera — also that it is not older nor younger either than itself or than Cætera:[86] that it grows both older and younger than itself, and than Cætera.[87] Lastly, Unum was, is, and will be; it has been, is, and will be generated: it has had, has now, and will have, attributes and predicates: it can be named, and can be the object of perception, conception, opinion, reasoning, and cognition.[88]
[81] Plato, Parmenid. p. 146 A-B.
[82] Plato, Parmenid. pp. 146-147 C.