Τὸ ἐξαίφνης — ἡ ἐξαίφνης φύσις ἄτοπός τις — may be compared to an infinitesimal; analogous to what is recognised in the theory of the differential calculus.
[93] This appears to be an illustration of the doctrine which Lassalle ascribes to Herakleitus; perpetual implication of negativity and positivity — des Nichtseins mit dem Sein: perpetual absorption of each particular into the universal; and perpetual reappearance as an opposite particular. See the two elaborate volumes of Lassalle upon Herakleitus, especially i. p. 358, ii. p. 258. He scarcely however takes notice of the Platonic Parmenides.
Some of the Stoics considered τὸ νῦν as μηδέν — and nothing in time to be real except τὸ παρῳχηκὸς and τὸ μέλλον (Plutarch, De Commun. Notitiis contra Stoicos, p. 1081 D).
Review of the successive pairs of Demonstrations or Antinomies in each, the first proves the Neither, the second proves the Both.
The theory here laid down in the third Demonstration respecting this extra-temporal point — the Suddenly — deserves all the more attention, because it applies not merely to the first and second Demonstration which precede it, but also to the fourth and fifth, the sixth and seventh, the eighth and ninth, which follow it. I have already observed, that the first and second Demonstration form a corresponding pair, branching off from the same root or hypothetical proposition (at least the same in terms), respecting the subject Unum; and destined to prove, one the Neither, the other the Both, of several different predicates. So also the fourth and fifth form a pair applying to the subject Cætera; and destined to prove, that from the same hypothetical root — Si Unum est — we can deduce the Neither as well as the Both, of various predicates of Cætera. When we pass on to the four last Demonstrations, we find that in all four, the hypothesis Si Unum non est is substituted for that of Si Unum est: but the parallel couples, with the corresponding purpose, are still kept up. The sixth and seventh apply to the subject Unum, and demonstrate respecting that subject (proceeding from the hypothesis Si Unum non est) first the Both, then the Neither, of various predicates: the eighth and ninth arrive at the same result, respecting the subject Cætera. And a sentence at the close sums up in few words the result of all the four pairs (1-2, 4-5, 6-7, 8-9, that is, of all the Demonstrations excepting the third) — the Neither and the Both respecting all of them.
The third Demonstration is mediatorial but not satisfactory — The hypothesis of the Sudden or Instantaneous found no favour.
To understand these nine Demonstrations properly, therefore, we ought to consider eight among them (1-2, 4-5, 6-7, 8-9) as four Antinomies, or couples establishing dialectic contradictions: and the third as a mediator satisfactory between the couples — announced as if it reconciled the contradictions of the first Antinomy, and capable of being adapted, in the same character with certain modifications, to the second, third, and fourth Antinomy. Whether it reconciles them successfully — in other words, whether the third Demonstration will itself hold good — is a different question. It will be found to involve the singular and paradoxical (Plato’s own phrase) doctrine of the extra-temporal Suddenly — conceiving Time as a Discretum and not a Continuum. This doctrine is intended by Plato here as a means of rendering the fact of change logically conceivable and explicable. He first states briefly the difficulty (which we know to have been largely insisted on by Diodorus Kronus and other Megarics) of logically explaining the fact of change — and then enunciates this doctrine as the solution. We plainly see that it did not satisfy others — for the puzzle continued to be a puzzle long after — and that it did not even satisfy Plato, except at the time when he composed the Parmenides — since neither the doctrine itself (the extra-temporal break or transition) nor the very peculiar phrase in which it is embodied (τὸ ἐξαίφνης, ἄτοπός τις φύσις) occur in any of his other dialogues. If the doctrine were really tenable, it would have been of use in dialectic, and as such, would have been called in to remove the theoretical difficulties raised among dialectical disputants, respecting time and motion. Yet Plato does not again advert to it, either in Sophistes or Timæus, in both of which there is special demand for it.[94] Aristotle, while he adopts a doctrine like it (yet without employing the peculiar phrase τὸ ἐξαίφνης) to explain qualitative change, does not admit the same either as to quantitative change, or as to local motion, or as to generation and destruction.[95] The doctrine served the purpose of the Platonic Parmenides, as ingenious, original, and provocative to intellectual effort: but it did not acquire any permanent footing in Grecian dialectics.
[94] Steinhart represents this idea of τὸ ἐξαίφνης — the extra-temporal break or zero of transition — as an important progress made by Plato, compared with the Theætêtus, because it breaks down the absoluten Gegensatz between Sein and Werden, Ruhe and Bewegung (Einleitung zum Parmen. p. 309).
Surely, if Plato had considered it a progress, we should have seen the same idea repeated in various other dialogues — which is not the case.
[95] Aristotel. Physic. p. 235, b. 32, with the Scholion of Simplikius, p. 410, b. 20, Brandis.