“Eine arge Täuschung ist es, zu glauben, dass das principium identitatis et contradictionis oberstes logisches Princip des Plato sei … Es ist gerade eine Hauptaufgabe, welche sich Plato stellen musste, die Coexistenz der Gegensätze nachzuweisen, wie diess bekanntlich im Philebus und besonders im Parmenides geschieht.”
According to this view, the Antinomies in the Parmenides are all of them good proofs, and the conclusions of all of them, summed up as they are in the final sentence of the dialogue, constitute an addition to the positive knowledge of Sokrates. I confess that this to me is unintelligible. I understand these Antinomies as ἀπορίαι to be cleared up, but in no other character.
Prantl speaks (p. 73) of “die antinomische Begründung der Ideenlehre im Parmenides,” &c. This is the same language as that used by Zeller, upon which I have already remarked.
Demonstration third — Attempt to reconcile the contradiction of Demonstrations I. and II.
How can this be possible? How can these four propositions all be true — Unum est Unum — Unum est Multa — Unum non est Unum — Unum non est Multa? Plato suggests a way out of the difficulty, in that which he gives as Demonstration 3. It has been shown that Unum “partakes of time” — was, is, and will be. The propositions are all true, but true at different times: one at this time, another at that time.[90] Unum acquires and loses existence, essence, and other attributes: now, it exists and is Unum — before, it did not exist and was not Unum: so too it is alternately like and unlike, in motion and at rest. But how is such alternation or change intelligible? At each time, whether present or past, it must be either in motion or at rest: at no time, neither present nor past, can it be neither in motion nor at rest. It cannot, while in motion, change to rest — nor, while at rest, change to motion. No time can be assigned for the change: neither the present, nor the past, nor the future: how then can the change occur at all?[91]
[90] This is a distinction analogous to that which Plato points out in the Sophistes (pp. 242-243) between the theories of Herakleitus and Empedoklês.
[91] Plato, Parmenid. p. 156.
Plato’s imagination of the Sudden or Instantaneous — Breaches or momentary stoppages in the course of time.
To this question the Platonic Parmenides finds an answer in what he calls the Sudden or the Instantaneous: an anomalous nature which lies out of, or apart from, the course of time, being neither past, present, nor future. That which changes, changes at once and suddenly: at an instant when it is neither in motion nor at rest. This Suddenly is a halt or break in the flow of time:[92] an extra-temporal condition, in which the subject has no existence, no attributes — though it revives again forthwith clothed with its new attributes: a point of total negation or annihilation, during which the subject with all its attributes disappears. At this interval (the Suddenly) all predicates may be truly denied, but none can be truly affirmed.[93] Unum is neither at rest, nor in motion — neither like nor unlike — neither the same with itself nor different from itself — neither Unum nor Multa. Both predicates and Subject vanish. Thus all the negations of the first Demonstration are justified. Immediately before the Suddenly, or point of change, Unum was in motion — immediately after the change, it is at rest: immediately before, it was like — equal — the same with itself — Unum, &c. — immediately after, it is unlike — unequal — different from itself — Multa, &c. And thus the double and contradictory affirmative predications, of which the second Demonstration is composed, are in their turn made good, as successive in time. This discovery of the extra-temporal point Suddenly, enables Parmenides to uphold both the double negative of the first Demonstration, and the double affirmative of the second.
[92] Plato, Parmenid. p. 156 E. ἀλλ’ ἡ ἐξαίφνης αὕτη φύσις ἄτοπός τις ἐγκάθηται μεταξὺ τῆς κινήσεώς τε καὶ στάσεως, ἐν χρόνῳ οὐδενὶ οὖσα, καὶ εἰς ταύτην δὴ καὶ ἐκ ταύτης τό τε κινούμενον μεταβάλλει ἐπὶ τὸ ἑστάναι, καὶ τὸ ἑστὸς ἐπὶ τὸ κινεῖσθαι.… καὶ τὸ ἓν δή, εἴπερ ἕστηκέ τε καὶ κινεῖται, μεταβάλλοι ἂν ἐφ’ ἑκάτερα· μόνως γὰρ ἂν οὕτως ἀμφότερα ποιοῖ· μεταβάλλον δ’ ἐξαίφνης μεταβάλλει, καὶ ὅτε μεταβάλλει, ἐν οὐδενὶ χρόνῳ ἂν εἴη, οὐδὲ κινοῖτ’ ἂν τότε, οὐδ’ ἂν σταίη.