These Platonic Antinomies are more formidable than any of the sophisms or subtleties broached by the Megaric philosophers.

I have already had occasion, when I touched upon the other viri Socratici, contemporaneous with or subsequent to Plato, to give some account of the Zenonian and Megaric dialecticians, and of their sophisms or logical puzzles, which attracted so much attention from speculative men, in the fourth and third centuries B.C. These Megarics, like the Sophists, generally receive very harsh epithets from the historian of philosophy. They took the negative side, impugned affirmative dogmas, insisted on doubts and difficulties, and started problems troublesome to solve. I have tried to show, that such disputants, far from deserving all the censure which has been poured upon them, presented one indispensable condition to the formation of any tolerable logical theory.64 Their sophisms were challenges to the logician, indicating various forms of error and confusion, against which a theory of reasoning, in order to be sufficient, was required to guard. And the demonstrations given by Plato in the latter half of the Parmenides are challenges of the same kind: only more ingenious, elaborate, and effective, than any of those (so far as we know them) proposed by the Megarics — by Zeno, or Eukleides, or Diodorus Kronus. The Platonic Parmenides here shows, that in regard to a particular question, those who believe the affirmative, those who believe the negative, and those who believe neither — can all furnish good reasons for their respective conclusions. In each case he gives the proof confidently as being good: and whether unimpeachable or not, it is certainly very ingenious and subtle. Such demonstrations are in the spirit of Sextus Empiricus, who rests his theory of scepticism upon the general fact, that there are opposite and contradictory conclusions, both of them supported by evidence equally good: the affirmative no more worthy of belief than the negative.65 Zeno (or, as Plato calls him, the Eleatic Palamêdes66) did not profess any systematic theory of scepticism; but he could prove by ingenious and varied dialectic, both the thesis and the antithesis on several points of philosophy, by reasons which few, if any, among his hearers could answer. In like manner the Platonic Parmenides enunciates his contradictory demonstrations as real logical problems, which must exercise the sagacity and hold back the forward impulse of an eager philosophical aspirant. Even if this dilemma respecting Unum Est and Unum non Est, be solved, Parmenides intimates that he has others in reserve: so that either no tenable positive result will ever be attained — or at least it will not be attained until after such an amount of sagacity and patient exercise as Sokrates himself declares to be hardly practicable.67 Herein we may see the germ and premisses of that theory which was afterwards formally proclaimed by Ænesidemus and the professed Sceptics: the same holding back (ἐποχὴ), and protest against precipitation in dogmatising,68 which these latter converted into a formula and vindicated as a system.

In order to understand fully the Platonic Antinomies, we ought to have before us the problems of the Megarics and others. Uselessness of searching for a positive result.

Schleiermacher has justly observed,69 that in order to understand properly the dialectic manœuvres of the Parmenides, we ought to have had before us the works of that philosopher himself, of Zeno, Melissus, Gorgias, and other sceptical reasoners of the age immediately preceding — which have unfortunately perished. Some reference to these must probably have been present to Plato in the composition of this dialogue.70 At the same time, if we accept the dialogue as being (what it declares itself to be) a string of objections and dialectical problems, we shall take care not to look for any other sort of merit than what such a composition requires and admits. If the objections are forcible, the problems ingenious and perplexing, the purpose of the author is satisfied. To search in the dialogue for some positive result, not indeed directly enunciated but discoverable by groping and diving — would be to expect a species of fruit inconsistent with the nature of the tree. Ζητῶν εὑρήσεις οὐ ῥόδον ἀλλὰ βάτον.

Assumptions of Parmenides in his Demonstrations convey the minimum of determinate meaning. Views of Aristotle upon these indeterminate predicates, Ens, Unum, &c.

It may indeed be useful for the critic to perform for himself the process which Parmenides intended Sokrates to perform; and to analyse these subtleties with a view to measure their bearing upon the work of dogmatic theorising. We see double and contradictory conclusions elicited, in four separate Antinomies, from the same hypothesis, by distinct chains of interrogatory deduction; each question being sufficiently plausible to obtain the acquiescence of the respondent. The two assumptions successively laid down by Parmenides as principia for deduction — Si Unum est — Si Unum non est — convey the very minimum of determinate meaning. Indeed both words are essentially indeterminate. Both Unum and Ens are declared by Aristotle to be not univocal or generic words,71 though at the same time not absolutely equivocal: but words bearing several distinct transitional meanings, derived either from each other, or from some common root, by an analogy more or less remote. Aristotle characterises in like manner all the most indeterminate predicates, which are not included in any one distinct category among the ten, but are made available to predication sometimes in one category, sometimes in another: such as Ens, Unum, Idem, Diversum, Contrarium, &c. Now in the Platonic Parmenides, the two first among these words are taken to form the proposition assumed as fundamental datum, and the remaining three are much employed in the demonstration: yet Plato neither notices nor discriminates their multifarious and fluctuating significations. Such contrast will be understood when we recollect that the purpose of the Platonic Parmenides is, to propound difficulties; while that of Aristotle is, not merely to propound, but also to assist in clearing them up.

In the Platonic Demonstrations the same proposition in words is made to bear very different meanings.

Certainly, in Demonstrations 1 and 2 (as well as 4 and 5), the foundation assumed is in words the same proposition — Si Unum est: but we shall find this same proposition used in two very different senses. In the first Demonstration, the proposition is equivalent to Si Unum est Unum:72 in the second, to Si Unum est Ens, or Si Unum existit. In the first the proposition is identical and the verb est serves only as copula: in the second, the verb est is not merely a copula but implies Ens as a predicate, and affirms existence. We might have imagined that the identical proposition — Unum est Unum — since it really affirms nothing — would have been barren of all consequences: and so indeed it is barren of all affirmative consequences. But Plato obtains for it one first step in the way of negative predicates — Si Unum est Unum, Unum non est Multa: and from hence he proceeds, by a series of gentle transitions ingeniously managed, to many other negative predications respecting the subject Unum. Since it is not Multa, it can have no parts, nor can it be a whole: it has neither beginning, middle, nor end: it has no boundary, or it is boundless: it has no figure, it is neither straight nor circular: it has therefore no place, being neither in itself, nor in anything else: it is neither in motion nor at rest: it is neither the same with anything else, nor the same with itself:73 it is neither different from any thing else, nor different from itself: it is neither like, nor unlike, to itself, nor to anything else: it is neither equal, nor unequal, to itself nor to any thing else: it is neither older nor younger, nor of equal age, either with itself or with anything else: it exists therefore not in time, nor has it any participation with time: it neither has been nor will be, nor is: it does not exist in any way: it does not even exist so as to be Unum: you can neither name it, nor reason upon it, nor know it, nor perceive it, nor opine about it.

First demonstration ends in an assemblage of negative conclusions. Reductio ad Absurdum, of the assumption — Unum non Multa.

All these are impossibilities (concludes Plato). We must therefore go back upon the fundamental principle from which we took our departure, in order to see whether we shall not obtain, on a second trial, any different result.74

Here then is a piece of dialectic, put together with ingenuity, showing that everything can be denied, and that nothing can be affirmed of the subject — Unum. All this follows, if you concede the first step, that Unum is not Multa. If Unum be said to have any other attribute except that of being Unum, it would become at once Multa. It cannot even be declared to be either the same with itself, or different from any thing else; because Idem and Diversum are distinct natures from Unum, and if added to it would convert it into Multa.75 Nay it cannot even be affirmed to be itself: it cannot be named or enunciated: if all predicates are denied, the subject is denied along with them: the subject is nothing but the sum total of its predicates — and when they are all withdrawn, no subject remains. As far as I can understand the bearing of this self-contradictory demonstration, it appears a reductio ad absurdum of the proposition — Unum is not Multa. Now Unum which is not Multa designates the Αὐτὸ-Ἓν or Unum Ideale; which Plato himself affirmed, and which Aristotle impugned.76 If this be what is meant, the dialogue Parmenides would present here, as in other places, a statement of difficulties understood by Plato as attaching to his own doctrines.

Second Demonstration.

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 first77 — 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

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

Here Parmenides finishes the long Demonstratio Secunda, which completes the first Antinomy. The last conclusion of all, with which it winds up, is the antithesis of that with which the first Demonstration wound up: affirming (what the conclusion of the first had denied) that Unum is thinkable, perceivable, nameable, knowable. Comparing the second Demonstration with the first, we see — That the first, taking its initial step, with a negative proposition, carries us through a series of conclusions every one of which is negative (like those of the second figure of the Aristotelian syllogism):— That whereas the conclusions professedly established in the first Demonstration are all in Neither (Unum is neither in itself nor in any thing else — neither at rest nor in motion — neither the same with itself nor different from itself, &c.), the conclusions of the second Demonstration are all in Both (Unum is both in motion and at rest, both in itself and in other things, both the same with itself and different from itself):— That in this manner, while the first Demonstration denies both of two opposite propositions, the second affirms them both.

Startling paradox — Open offence against logical canon — No logical canon had then been laid down.

Such a result has an air of startling paradox. We find it shown, respecting various pairs of contradictory propositions, first, that both are false — next, that both are true. This offends doubly against the logical canon, which declares, that of two contradictory propositions, one must be true, the other must be false. We must remember, that in the Platonic age, there existed no systematic logic — no analysis or classification of propositions — no recognised distinction between such as were contrary, and such as were contradictory. The Platonic Parmenides deals with propositions which are, to appearance at least, contradictory: and we are brought, by two different roads, first to the rejection of both, next to the admission of both.89

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

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.

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.