The discussion occupies two or three pages of Aristotle’s Physica. In regard to ἀλλοίωσις or qualitative change, he recognised what he called ἀθρόαν μεταβολήν — a change all at once, which occupied no portion of time. It is plain, however, that even his own scholars Theophrastus and Eudemus had great difficulty in accepting the doctrine; see Scholia, pp. 409-410-411, Brandis.
The two last Antinomies, or four last Demonstrations, have, in common, for their point of departure, the negative proposition, Si Unum non est: and are likewise put together in parallel couples (6-7, 8-9), a Demonstration and a Counter-Demonstration — a Both and a Neither: first with reference to the subject Unum — next with reference to the subject Cætera.
Review of the two last Antinomies. Demonstrations VI. and VII.
Si Unum est — Si Unum non est. Even from such a proposition as the first of these, we might have thought it difficult to deduce any string of consequences — which Plato has already done: from such a proposition as the second, not merely difficult, but impossible. Nevertheless the ingenious dialectic of Plato accomplishes the task, and elicits from each proposition a Both, and a Neither, respecting several predicates of Unum as well as of Cætera. When you say Unum non est (so argues the Platonic Parmenides in Demonstration 6), you deny existence respecting Unum: but the proposition Unum non est, is distinguishable from Magnitudo non est — Parvitudo non est — and such like: propositions wherein the subject is different, though the predicate is the same: so that Unum non Ens is still a Something knowable, and distinguishable from other things — a logical subject of which various other predicates may be affirmed, though the predicate of existence cannot be affirmed.[96] It is both like and unlike, equal and unequal — like and equal to itself unlike and unequal to other things.[97] These its predicates being all true, are also real existences: so that Unum partakes quodam modo in existence: though Unum be non-Ens, nevertheless, Unum non-Ens est. Partaking thus both of non-existence and of existence, it changes: it both moves and is at rest: it is generated and destroyed, yet is also neither generated nor destroyed.[98]
[96] Plato, Parmenid. pp. 160-161 A. εἶναι μὲν δὴ τῷ ἑνὶ οὐχ οἷόν τε, εἴπερ γε μὴ ἔστι, μετέχειν δὲ πολλῶν οὐδὲν κωλύει, ἀλλὰ καὶ ἀνάγκη, εἴπερ τό γε ἓν ἐκεῖνο καὶ μὴ ἄλλο μὴ ἔστιν. εἰ μέντοι μήτε τὸ ἓν μήτ’ ἐκεῖνο μὴ ἔσται, ἀλλὰ περὶ ἄλλου του ὁ λόγος, οὐδὲ φθέγγεσθαι δεῖ οὐδέν· εἰ δὲ τὸ ἓν ἐκεῖνο καὶ μὴ ἄλλο ὑποκεῖται μὴ εἶναι, καὶ τοῦ ἐκείνου καὶ ἄλλων πολλῶν ἀνάγκη αὐτῷ μετεῖναι.
[97] Plato, Parmenid. p. 161 C-D.
[98] Plato, Parmenid. pp. 162-163 A.
The steps by which these conclusions are made out are extremely subtle, and hardly intelligible to me.
Having thus deduced from the fundamental principle this string of Both opposite predicates, the Platonic Parmenides reverts (in Demonstration 7) to the same principium (Si Unum non est) to deduce by another train of reasoning the Neither of these predicates. When you say that Unum non est, you must mean that it does not partake of existence in any way — absolutely and without reserve. It therefore neither acquires nor loses existence: it is neither generated nor destroyed: it is neither in motion nor at rest: it partakes of nothing existent: it is neither equal nor unequal — neither like nor unlike — neither great nor little — neither this, nor that: neither the object of perception, nor of knowledge, nor of opinion, nor of naming, nor of debate.[99]
[99] Plato, Parmenid. pp. 163-164 A.