Chapter XXVII: Parmenides (3)

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.

[Footnote 71: Aristot. Metaphys. iv. 1015-1017, ix. 1052, a. 15; Anal. Poster. ii. p. 92, b. 14. [Greek: to\ d' ei)=nai ou)k ou)si/a ou)deni/. ou) ga\r ge/nos to\ o)/n.]--Topica, iv. p. 127, a. 28. [Greek: plei/ô ga\r ta\ pa=sin e(po/mena; oi(=on to\ o)\n kai\ to\ e(\n tô=n pa=sin e(pome/nôn e)/stin], Physica, i. p. 185, b. 6.

Simplikius noted it as one among the differences between Plato and Aristotle--That Plato admitted Unum as having only one meaning, not being aware of the diversity of meanings which it bore; while Aristotle expressly pointed it out as a [Greek: pollakô=s lego/menon] (Schol. ad Aristot. Sophist. Elench. p. 320, b. 3, Brandis). Aristotle farther remarks that Plato considered [Greek: to\ ge/nos] as [Greek: e(\n a)rithmô=|], and that this was an error; we ought rather to say that Plato did not clearly discriminate [Greek: e(\n a)rithmô=|] from [Greek: e(\n ei)/dei] (Aristot. Topic. vi. 143, b. 30).

Simplikius farther remarks, that it was Aristotle who first rendered to Logic the important service of bringing out clearly and emphatically the idea of [Greek: to\ o(mô/numon]--the same word with several meanings either totally distinct and disparate, or ramifying in different directions from the same root, so that there came to be little or no affinity between many of them. It was Aristotle who first classified and named these distinctions ([Greek: sunô/numon--o(mô/numon], and the intermediate [Greek: kat' a)nalogi/an]), though they had been partially noticed by Plato and even by Sokrates. [Greek: e(/ôs A)ristote/lous ou) pa/mpan e)/kdêlon ê)=n to\ o(mô/numon; a)lla\ Pla/tôn te ê)/rxato peri\ tou/tou ê)\ ma=llon e)kei/nou Sôkra/tês], Schol. ad Aristot. Physic. p. 323, b. 24, Brandis.]

[Side-note: 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.

[Footnote 72: Plato, Parmenid. pp. 137 C, 142 B.]

[Footnote 73: This part of the argument is the extreme of dialectic subtlety, p. 139 C-D-E.]

[Side-note: 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]

[Footnote 74: Plato, Parmenid. p. 142 A.]

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 [Greek: Au)to\-E(\n] 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.

[Footnote 75: This is the main point of Demonstration 1, and is stated pp. 139 D, 140 A, compared with p. 137 C.]

[Footnote 76: Aristot. Metaph. A. 987, b. 20; A. 992, a. 8; B. 1001, a. 27; I. 1053, b. 18. Some ancient expositors thought that the purpose of Plato in the Parmenides was to demonstrate this [Greek: Au)to\-E(\n]; see Schol. ad Aristot. Metaph. p. 786, a. 10, Brandis.

It is not easy to find any common bearing between the demonstrations given in this dialogue respecting [Greek: E(\n] and [Greek: Polla\]--and the observations which Plato makes in the Philêbus upon [Greek: E(\n] and [Greek: Polla/]. Would he mean to include the demonstrations which we read in the Parmenides, in the category of what he calls in Philêbus "childish, easy, and irrational debates on that vexed question?" (Plato, Philêbus, p. 14 D). Hardly: for they are at any rate most elaborate as well as ingenious and suggestive. Yet neither do they suit the description which he gives in Philêbus of the genuine, serious, and difficult debates on the same question.]

[Side-note: 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 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]

[Footnote 77: Plato, Parmenid. p. 142 A. [Greek: Bou/lei ou)=n e)pi\ tê\n u(po/thesin pa/lin e)x a)rchê=s e)pane/lthômen, e)a/n ti ê(mi=n e)paniou=sin a)lloi=on phanê=|?]]

[Footnote 78: This shifting of the real hypothesis, though the terms remain unchanged, is admitted by implication a little afterwards, p. 142 B. [Greek: _nu=n de\_ ou)ch au(/tê e)/stin ê( u(po/thesis, _ei) e(\n e(\n_, ti/ chrê\ sumbai/nein, a)ll' _ei) e(\n e)/stin_.]]

[Footnote 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 [Greek: o(\ e)/stin e(\n] should be [Greek: polla\]--that [Greek: o(\ e)/stin o(/moion] should be [Greek: a)no/moion]. 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.]

[Footnote 80: Plato, Parmen. pp. 144 A-E, 145 A.]

[Side-note: 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]

[Footnote 81: Plato, Parmenid. p. 146 A-B.]

[Footnote 82: Plato, Parmenid. pp. 146-147 C.]

[Footnote 83: Plato, Parmenid. p. 148 A-D.]

[Footnote 84: Plato, Parmenid. p. 149 A-D.]

[Footnote 85: Plato, Parmenid. pp. 150-151 D.]

[Footnote 86: Plato, Parmen. pp. 152-153-154 A.]

[Footnote 87: Plato, Parmenid. pp. 154 B, 155 C. [Greek: kata\ dê\ pa/nta tau=ta, to\ e(\n au)to/ te au(tou= kai\ tô=n a)/llôn presbu/teron kai\ neô/teron e)/sti te kai\ gi/gnetai, kai\ ou(/te presbu/teron ou(/te neô/teron ou(/t' e)/stin ou(/te gi/gnetai ou(/te au(tou= ou(/te tô=n a)/llôn.]]

[Footnote 88: Plato, Parmenid. p. 155 C-D.]

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.

[Side-note: 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]

[Footnote 89: Prantl (in his Geschichte der Logik, vol. i. s. 3, pp. 70-71-73) maintains, if I rightly understand him, not only that Plato did not adopt the _principium identitatis et contradictionis_ as the basis of his reasonings, but that one of Plato's express objects was to demonstrate the contrary of it, partly in the Philêbus, but especially in the Parmenides:--

"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 [Greek: a)pori/ai] 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.]

[Side-note: 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]

[Footnote 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.]

[Footnote 91: Plato, Parmenid. p. 156.]

[Side-note: 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.

[Footnote 92: Plato, Parmenid. p. 156 E. [Greek: a)ll' ê( _e)xai/phnês au(/tê phu/sis a)/topo/s tis e)gka/thêtai metaxu\ tê=s kinê/seô/s te kai\ sta/seôs_, e)n chro/nô| ou)deni\ ou)=sa, kai\ ei)s tau/tên dê\ kai\ e)k tau/tês to/ te kinou/menon metaba/llei e)pi\ to\ e(sta/nai, kai\ to\ e(sto\s e)pi\ to\ kinei=sthai. . . . kai\ to\ e(\n dê/, ei)/per e(/stêke/ te kai\ kinei=tai, metaba/lloi a)\n e)ph' e(ka/tera; mo/nôs ga\r a)\n ou(/tôs a)mpho/tera poioi=; metaba/llon d' e)xai/phnês metaba/llei, kai\ o(/te metaba/llei, e)n ou)deni\ chro/nô| a)\n ei)/ê, ou)de\ kinoi=t' a)\n to/te, ou)d' a)\n stai/ê.]

[Greek: To\ e)xai/phnês--ê( e)xai/phnês phu/sis a)/topo/s tis]--may be compared to an infinitesimal; analogous to what is recognised in the theory of the differential calculus.]

[Footnote 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 [Greek: to\ nu=n] as [Greek: mêde/n]--and nothing in time to be real except [Greek: to\ parô|chêko\s] and [Greek: to\ me/llon] (Plutarch, De Commun. Notitiis contra Stoicos, p. 1081 D).]

[Side-note: 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.

[Side-note: 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 ([Greek: to\ e)xai/phnês, a)/topo/s tis phu/sis]) 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 [Greek: to\ e)xai/phnês]) 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.

[Footnote 94: Steinhart represents this idea of [Greek: to\ e)xai/phnês]--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.]

[Footnote 95: Aristotel. Physic. p. 235, b. 32, with the Scholion of Simplikius, p. 410, b. 20, Brandis.

The discussion occupies two or three pages of Aristotle's Physica. In regard to [Greek: a)lloi/ôsis] or qualitative change, he recognised what he called [Greek: a)thro/an metabolê/n]--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_.

[Side-note: 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]

[Footnote 96: Plato, Parmenid. pp. 160-161 A. [Greek: ei)=nai me\n dê\ tô=| e(ni\ ou)ch oi(=o/n te, ei)/per ge mê\ e)/sti, mete/chein de\ pollô=n ou)de\n kôlu/ei, a)lla\ kai\ a)na/gkê, ei)/per to/ ge e(\n e)kei=no kai\ mê\ a)/llo mê\ e)/stin. ei) me/ntoi mê/te to\ e(\n mê/t' _e)kei=no_ mê\ e)/stai, a)lla\ peri\ a)/llou tou o( lo/gos, ou)de\ phthe/ggesthai dei= ou)de/n; ei) de\ to\ e(\n e)kei=no kai\ mê\ a)/llo u(pokei=tai mê\ ei)=nai, kai\ tou= _e)kei/nou_ kai\ a)/llôn pollô=n a)na/gkê au)tô=| metei=nai.]]

[Footnote 97: Plato, Parmenid. p. 161 C-D.]

[Footnote 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]

[Footnote 99: Plato, Parmenid. pp. 163-164 A.]

[Side-note: Demonstration VII. is founded upon the genuine doctrine of Parmenides.]

These two last counter-demonstrations (6 and 7), forming the third Antinomy, deserve attention in this respect--That the seventh is founded upon the genuine Parmenidean or Eleatic doctrine about Non-Ens, as not merely having no attributes, but as being unknowable, unperceivable, unnameable: while the sixth is founded upon a different apprehension of Non-Ens, which is explained and defended by Plato in the Sophistes, as a substitute for, and refutation of, the Eleatic doctrine.[100] According to Number 7, when you deny, of Unum, the predicate existence, you deny of it also all other predicates: and the name Unum is left without any subject to apply to. This is the Eleatic dogma. Unum having been declared to be Non-Ens, is (like Non-Ens) neither knowable nor nameable. According to Number 6, the proposition _Unum est non-Ens_, does not carry with it any such consequences. Existence is only one predicate, which may be denied of the subject Unum, but which, when denied, does not lead to the denial of all other predicates--nor, therefore, to the loss of the subject itself. Unum still remains Unum, knowable, and different from other things. Upon this first premiss are built up several other affirmations; so that we thus arrive circuitously at the affirmation of existence, in a certain way: _Unum_, though non-existent, does nevertheless exist _quodam modo_. This coincides with that which the Eleatic stranger seeks to prove in the Sophistes, against Parmenides.

[Footnote 100: Plato, Sophistes, pp. 258-259.]

[Side-note: Demonstrations VI. and VII. considered--Unwarrantable steps in the reasoning--The fundamental premiss differently interpreted, though the same in words.]

If we compare the two foregoing counter-demonstrations (7 and 6), we shall see that the negative results of the seventh follow properly enough from the assumed premisses: but that the affirmative results of the sixth are not obtained without very unwarrantable jumps in the reasoning, besides its extreme subtlety. But apart from this defect, we farther remark that here also (as in Numbers 1 and 2) the fundamental principle assumed is in terms the same, in signification materially different. The signification of _Unum non est_, as it is construed in Number 7, is the natural one, belonging to the words: but as construed in Number 6, the meaning of the predicate is altogether effaced (as it had been before in Number 1): we cannot tell what it is which is really denied about Unum. As, in Number 1, the proposition _Unum est_ is so construed as to affirm nothing except _Unum est Unum_--so in Number 7, the proposition _Unum non est_ is so construed as to deny nothing except _Unum non est Unum_, yet conveying along with such denial a farther affirmation--_Unum non est Unum, sed tamen est aliquid scibile, differens ab aliis_.[101] Here this _aliquid scibile_ is assumed as a substratum underlying _Unum_, and remaining even when Unum is taken away: contrary to the opinion--that Unum was a separate nature and the fundamental Subject of all--which Aristotle announces as having been held by Plato.[102] There must be always some meaning (the Platonic Parmenides argues) attached to the word Unum, even when you talk of _Unum non Ens_: and that meaning is equivalent to _Aliquid scibile, differens ab aliis_. From this he proceeds to evolve, step by step, though often in a manner obscure and inconclusive, his series of contradictory affirmations respecting Unum.

[Footnote 101: Plato, Parmenid. p. 160 C.]

[Footnote 102: Aristot. Metaph. B. 1001, a. 6-20.]

The last couple of Demonstrations--8 and 9--composing the fourth Antinomy, are in some respects the most ingenious and singular of all the nine. Si _Unum non est_, what is true about Cætera? The eighth demonstrates the _Both_ of the affirmative predicates, the ninth proves the _Neither_.

[Side-note: Demonstrations VIII. and IX.--Analysis of Demonstration VIII.]

Si _Unum non est_ (is the argument of the eighth), Cætera must nevertheless somehow still be Cætera: otherwise you could not talk about Cætera.[103] (This is an argument like that in Demonstration 6: What is talked about must exist, somehow.) But if Cætera can be named and talked about, they must be different from something,--and from something, which is also different from them. What can this Something be? Not certainly Unum: for Unum, by the Hypothesis, does not exist, and cannot therefore be the term of comparison. _Cætera_ therefore must be different among themselves and from each other. But they cannot be compared with each other by units: for Unum does not exist. They must therefore be compared with each other by heaps or multitudes: each of which will appear at first sight to be an unit, though it be not an unit in reality. There will be numbers of such heaps, each in appearance one, though not in reality:[104] numbers odd and even, great and little, in appearance: heaps appearing to be greater and less than each other, and equal to each other, though not being really so. Each of these heaps will appear to have a beginning, middle, and end, yet will not really have any such: for whenever you grasp any one of them in your thoughts, there will appear another beginning before the beginning,[105] another end after the end, another centre more centrical than the centre,--minima ever decreasing because you cannot reach any stable unit. Each will be a heap without any unity; looking like one, at a distance,--but when you come near, each a boundless and countless multitude. They will thus appear one and many, like and unlike, equal and unequal, at rest and moving, separate and coalescing: in short, invested with an indefinite number of opposite attributes.[106]

[Footnote 103: Plato, Parmenid. p. 164 B. [Greek: A)/lla me/n pou dei= au)ta\ ei)=nai; ei) ga\r mêde\ a)/lla e)sti/n, ou)k a)\n peri\ tô=n a)/llôn le/goito.]]

[Footnote 104: Plato, Parmenid. p. 164 D. [Greek: Ou)kou=n polloi\ o)/gkoi e)/santai, ei)=s e(/kastos phaino/menos, ô)\n de\ ou)/, ei)/per e(\n mê\ e)/stai. Ou(/tôs.]]

[Footnote 105: Plato, Parmenid. p. 165 A. [Greek: O(/ti a)ei\ au)tô=n o(/tan ti/s ti la/bê| tê=| dianoi/a| ô(/s ti tou/tôn o(/n, pro/ te tê=s a)rchê=s a)/llê a)ei\ phai/netai a)rchê/, meta/ te tê\n teleutê\n e(te/ra u(poleipome/nê teleutê/, e(/n te tô=| me/sô| a)/lla mesai/tera tou= me/sou, smikro/tera de\ dia\ to\ mê\ du/nasthai e(no\s au)tô=n e(ka/stou lamba/nesthai, a)/te ou)k o)/ntos tou= e(no/s.]]

[Footnote 106: Plato, Parmenid. p. 165 E. Compare p. 158 E. [Greek: toi=s a)/llois dê\ tou= e(no\s. . . . ê( de\ au)tô=n phu/sis kath' e(auta\ a)peiri/an (pa/resche).]]

[Side-note: Demonstration VIII. is very subtle and Zenonian.]

This Demonstration 8, with its strange and subtle chain of inferences, purporting to rest upon the admission of Cætera without Unum, brings out the antithesis of the Apparent and the Real, which had not been noticed in the preceding demonstrations. Demonstration 8 is in its character Zenonian. It probably coincides with the proof which Zeno is reported (in the earlier half of this dialogue) to have given against the existence of any real Multa. If you assume Multa (Zeno argued), they must be both like and unlike, and invested with many other opposite attributes; but this is impossible; therefore the assumption is untrue.[107] Those against whom Zeno reasoned, contended for real Multa, and against a real Unum. Zeno probably showed, and our eighth Demonstration here shows also,--that Multa under this supposition are nothing real, but an assemblage of indefinite, ever-variable, contradictory appearances: an [Greek: A)/peiron], Infinite, or Chaos: an object not real and absolute, but relative and variable according to the point of view of the subject.

[Footnote 107: Plato, Parmenid. p. 127 E; compare this with the close of the eighth Demonstration, p. 165 E--[Greek: ei) e(no\s mê\ o)/ntos polla\ e)/stin].]

[Side-note: Demonstration IX. _Neither_ following _Both_.]

To the eighth Demonstration, ingenious as it is, succeeds a countervailing reversal in the ninth: the Neither following the Both. The fundamental supposition is in terms the same. _Si Unum non est_, what is to become of _Cætera_? _Cætera_ are not _Unum_: yet neither are they _Multa_: for if there were any Multa, Unum would be included in them. If none of the Multa were Unum, all of them would be nothing at all, and there would be no Multa. If therefore Unum be not included in Cætera, Cætera would be neither Unum nor Multa: nor would they appear to be either Unum or Multa: for Cætera can have no possible communion with Non-Entia: nor can any of the Non-Entia be present along with any of Cætera--since Non-Entia have no parts. We cannot therefore conceive or represent to ourselves Non-Ens as along with or belonging to Cætera. Therefore, _Si Unum non est_, nothing among _Cætera_ is conceived either as Unum or as Multa: for to conceive Multa without Unum is impossible. It thus appears, _Si Unum non est_, that Cætera neither are Unum nor Multa. Nor are they conceived either as Unum or Multa--either as like or as unlike--either as the same or as different--either as in contact or as apart.--In short, all those attributes which in the last preceding Demonstration were shown _to belong to them_ in appearance, are now shown _not to belong_ to them either in appearance or in reality.[108]

[Footnote 108: Plato, Parmenid. p. 166 A-B. [Greek: E(\n a)/ra ei) mê\ e)/sti, ta)/lla ou)/te e)/stin ou)/te doxa/zetai e(\n ou)/te polla/. . . . Ou)/d' a)/ra o(/moia ou)de\ a)no/moia. . . . Ou)de\ mê\n ta\ au)ta/ ge ou)d' e(/tera, ou)de\ a(pto/mena ou)de\ chôri/s, _ou)de\ a)/ll' o(/sa e)n toi=s pro/sthen diê/lthomen_] (compare [Greek: dielthei=n], p. 165 E) [Greek: _ô(s phaino/mena au)ta/, tou/tôn ou)/te ti e)/stin ou)/te phai/netai ta)/lla, e(\n ei) mê\ e)/stin_.]]

[Side-note: Concluding words of the Parmenides--Declaration that he has demonstrated the Both and the Neither of many different propositions.]

Here we find ourselves at the close of the Parmenides. Plato announces his purpose to be, to elicit contradictory conclusions, by different trains of reasoning, out of the same fundamental assumption.[109] He declares, in the concluding words, that--on the hypothesis of _Unum est_, as well as on that of _Unum non est_--he has succeeded in demonstrating the Both and the Neither of many distinct propositions, respecting Unum and respecting Cætera.

[Footnote 109: Compare, with the passage cited in the last note, another passage, p. 159 B, at the beginning of Demonstration 5.

[Greek: Ou)kou=n tau=ta me\n ê)/dê e)ô=men ô(s phanera/, e)piskopô=men de\ pa/lin, e(\n ei) e)/stin, a)=ra _kai\ ou)ch ou(/tôs e)/chei ta)/lla tou= e(no\s ê)\ ou(/tô mo/non_?]

Here the purpose to prove [Greek: _ou)ch ou(/tôs_], immediately on the heels of [Greek: _ou(/tôs_], is plainly enunciated.]

[Side-note: Comparison of the conclusion of the Parmenides to an enigma of the Republic. Difference. The constructor of the enigma adapted its conditions to a foreknown solution. Plato did not.]

The close of the Parmenides, as it stands here, may be fairly compared to the enigma announced by Plato in his Republic--"A man and no man, struck and did not strike, with a stone and no stone, a bird and no bird, sitting upon wood and no wood".[110] This is an enigma, propounded for youthful auditors to guess: stimulating their curiosity, and tasking their intelligence to find it out. As far as I can see, the puzzling antinomies in the Parmenides have no other purpose. They drag back the forward and youthful Sokrates from affirmative dogmatism to negative doubt and embarrassment. There is however this difference between the enigma in the Republic, and the Antinomies in the Parmenides. The constructor of the enigma had certainly a preconceived solution to which he adapted the conditions of his problem: whereas we have no sufficient ground for asserting that the author of the Antinomies had any such solution present or operative in his mind. How much of truth Plato may himself have recognised, or may have wished others to recognise, in them, we have no means of determining. We find in them many equivocal propositions and unwarranted inferences--much blending of truth with error, intentionally or unintentionally. The veteran Parmenides imposes the severance of the two, as a lesson, upon his youthful hearers Sokrates and Aristoteles.

[Footnote 110: Plato, Republ. v. 479 C. The allusion was to an eunuch knocking down a bat seated upon a reed. [Greek: Ai)no/s tis e)/stin ô(s a)nê/r te kou)k a)nê/r, O)/rnitha/ te kou)k o)/rnith' i)dô/n te kou)k i)dô/n, E)pi\ xu/lou te kou) xu/lou kathême/nên Li/thô| te kou) li/thô| ba/loi te kou) ba/loi.]

I read with astonishment the amount of positive philosophy which a commentator like Steinhart extracts from the concluding enigma of the Parmenides, and which he even affirms that no attentive reader of the dialogue can possibly miss (Einleitung zum Parmenides, pp. 302-303).]