i. 3, 12): "Learners ought to go through logical exercises

silently and by themselves: for it will be thought both ridiculous and absurd, for a man to use such language publicly". Proklus tells us, that the difficulty of the [Greek: gumnasi/a], here set out by the Platonic Parmenides, is so prodigious, that no one after Plato employed it. (Prok. ad Parmen. p. 801, Stallb.)]

[Side-note: Parmenides elects his own theory of the _Unum_, as the topic for exhibition--Aristoteles becomes respondent.]

It is especially on this ground--the small number and select character of the auditors--that Parmenides suffers himself to be persuaded to undertake what he calls "amusing ourselves with a laborious pastime".[46] He selects, as the subject of his dialectical exhibition, his own doctrine respecting the One. He proceeds to trace out the consequences which flow, first, from assuming the affirmative thesis, _Unum Est_: next, from assuming the negative thesis, or the Antithesis, _Unum non Est_. The consequences are to be deduced from each hypothesis, not only as regards _Unum_ itself, but as regards _Cætera_, or other things besides _Unum_. The youngest man of the party, Aristoteles, undertakes the duty of respondent.

[Footnote 46: Plato, Parmenid. p. 137 A. [Greek: dei= ga\r chari/zesthai, _e)peidê\_ kai\ o(\ Zê/nôn le/gei, _au)toi/ e)smen_ . . . ê)\ bou/lesthe _e)peidê/per dokei= pragmateiô/dê paidia\n pai/zein_,] &c.]

[Side-note: Exhibition of Parmenides--Nine distinct deductions or Demonstrations, first from _Unum Est_--next from _Unum non Est_.]

The remaining portion of the dialogue, half of the whole, is occupied with nine distinct deductions or demonstrations given by Parmenides. The first five start from the assumption, _Unum Est_: the last four from the assumption, _Unum non Est_. The three first draw out the deductions from _Unum Est_, in reference to _Unum_: the fourth and fifth draw out the consequences from the same premiss, in reference to _Cætera_. Again, the sixth and seventh start from _Unum non Est_, to trace what follows in regard to _Unum_: the eighth and ninth adopt the same hypothesis, and reason it out in reference to _Cætera_.

[Side-note: The Demonstrations in antagonising pairs, or Antinomies. Perplexing entanglement of conclusions given without any explanation.]

Of these demonstrations, one characteristic feature is, that they are presented in antagonising pairs or Antinomies: except the third, which professes to mediate between the first and second, though only by introducing new difficulties. We have four distinct Antinomies: the first and second, the fourth and fifth, the sixth and seventh, the eighth and ninth, stand respectively in emphatic contradiction with each other. Moreover, to take the demonstrations separately--the first, fifth, seventh, ninth, end in conclusions purely negative: the other four end in double and contradictory conclusions. The purpose is formally proclaimed, of showing that the same premisses, ingeniously handled, can be made to yield these contradictory results.[47] No attempt is made to reconcile the contradictions, except partially by means of the third, in reference to the two preceding. In regard to the fourth and fifth, sixth and seventh, eighth and ninth, no hint is given that they can be, or afterwards will be, reconciled. The dialogue concludes abruptly at the end of the ninth demonstration, with these words: "We thus see that--whether Unum exists or does not exist--Unum and Cætera both are, and are not, all things in every way--both appear, and do not appear, all things in every way--each in relation to itself, and each in relation to the other".[48] Here is an unqualified and even startling announcement of double and contradictory conclusions, obtained from the same premisses both affirmative and negative: an announcement delivered too as the fulfilment of the purpose of Parmenides. Nothing is said at the end to intimate how the demonstrations are received by Sokrates, nor what lesson they are expected to administer to him: not a word of assent, or dissent, or surprise, or acknowledgment in any way, from the assembled company, though all of them had joined in entreating Parmenides, and had expressed the greatest anxiety to hear his dialectic exhibition. Those who think that an abrupt close, or an abrupt exordium, is sufficient reason for declaring a dialogue not to be the work of Plato (as Platonic critics often argue), are of course consistent in disallowing the Parmenides. For my part, I do not agree in the opinion. I take Plato as I find him, and I perceive both here and in the Protagoras and elsewhere, that he did not always think it incumbent upon him to adapt the end of his dialogues to the beginning. This may be called a defect, but I do not feel called upon to make out that Plato's writings are free from defects; and to acknowledge nothing as his work unless I can show it to be faultless.

[Footnote 47: See the connecting words between the first and second demonstration, pp. 142 A, 159. [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?_] Also p. 163 B.]

[Footnote 48: Plato, Parmenid. ad fin. [Greek: Ei)rê/sthô toi/nun tou=to/ te kai\ o(/ti, ô(s e)/oiken, e(\n ei)/t' e)/stin ei)/te mê\ e)/stin, au)to/ te kai\ ta)/lla kai\ pro\s au(ta\ kai\ pro\s a)/llêla pa/nta pa/ntôs e)sti/ te kai\ ou)k e)sti kai\ phai/netai/ te kai\ ou) phai/netai.]]

[Side-note: Different judgments of Platonic critics respecting the Antinomies and the dialogue generally.]

The demonstrations or Antinomies in the last half of the Parmenides are characterised by K. F. Hermann and others as a masterpiece of speculative acuteness. Yet if these same demonstrations, constructed with care and labour for the purpose of proving that the same premisses will conduct to double and contradictory conclusions, had come down to us from antiquity under the name either of the Megaric Eukleides, or Protagoras, or Gorgias--many of the Platonic critics would probably have said of them (what is now said of the sceptical treatise remaining to us under the name of Gorgias) that they were poor productions worthy of such Sophists, who are declared to have made a trade of perverting truth. Certainly the conclusions of the demonstrations are specimens of that "Both and Neither," which Plato (in the Euthydemus[49]) puts into the mouth of the Sophist Dionysodorus as an answer of slashing defiance--and of that intentional evolution of contradictions which Plato occasionally discountenances, both in the Euthydemus and elsewhere.[50] And we know from Proklus[51] that there were critics in ancient times, who depreciated various parts of the Parmenides as sophistical. Proklus himself denies the charge with some warmth. He as well as the principal Neo-Platonists between 200-530 A.D. (especially his predecessors and instructors at Athens, Jamblichus, Syrianus, and Plutarchus) admired the Parmenides as a splendid effort of philosophical genius in its most exalted range, inspired so as to become cognizant of superhuman persons and agencies. They all agreed so far as to discover in the dialogue a sublime vein of mystic theology and symbolism: but along with this general agreement, there was much discrepancy in their interpretation of particular parts and passages. The commentary of Proklus attests the existence of such debates, reporting his own dissent from the interpretations sanctioned by his venerated masters, Plutarchus and Syrianus. That commentary, in spite of its prolixity, is curious to read as a specimen of the fifth century, A.D., in one of its most eminent representatives. Proklus discovers a string of theological symbols and a mystical meaning throughout the whole dialogue: not merely in the acute argumentation which characterises its middle part, but also in the perplexing antinomies of its close, and even in the dramatic details of places, persons, and incidents, with which it begins.[52]

[Footnote 49: Plato, Euthydem. p. 300 C. [Greek: A)ll' ou) tou=to e)rôtô=, a)lla\ ta\ pa/nta siga=| ê)\ le/gei? _Ou)de/tera kai\ a)mpho/tera_, e)/phê u(pharpa/sas o( Dionuso/dôros; eu)= ga\r oi)=da o(/ti tê=| a)pokri/sei ou)ch e(/xeis o(/, ti chrê=|.]]

[Footnote 50: Plato, Sophist. p. 259 B. [Greek: ei)/te ô(s ti chalepo\n katanenoêkô\s chai/rei, tote\ me\n e)pi\ tha/tera tote\ d' e)pi\ tha/tera tou\s lo/gous e(/lkôn, ou)k a)/xia pollê=s spoudê=s e)spou/daken, ô(s oi( nu=n lo/goi phasi/n.]--Also p. 259 D. [Greek: To\ de\ tau)to\n e(/teron a)pophai/nein a(mê=| ge/ pê|, kai\ to\ tha/teron tau)to/n, kai\ to\ me/ga smikro/n, kai\ to\ o(/moion a)no/moion, kai\ chai/rein ou(/tô ta)nanti/a a)ei\ prophe/ronta e)n toi=s lo/gois, ou)/ te/ tis e)/legchos ou(=tos a)lêthino/s, a)/rti te tô=n o)/ntôn tino\s e)phaptome/nou dê=los neogenê\s ô)/n.]]

[Footnote 51: Proklus, ad Platon. Parmen. p. 953, ed. Stallb.; compare p. 976 in the last book of the commentary, probably composed by Damaskius. K. F. Hermann, Geschichte und System der Platon. Philos. p. 507.]

[Footnote 52: This commentary is annexed to Stallbaum's edition of the Parmenides. Compare also the opinion of Marinus (disciple and biographer of Proklus) about the Parmenidês--Suidas v. [Greek: Mari=nos]. Jamblichus declared that Plato's entire theory of philosophy was embodied in the two dialogues, Parmenides and Timæus: in the Parmenides, all the intelligible or universal Entia were deduced from [Greek: to\ e(/n]: in the Timæus, all cosmical realities were deduced from the Demiurgus. Proklus ad Timæeum, p. 5 A, p. 10 Schneider.

Alkinous, in his Introduction to the Platonic Dialogues (c. 6, p. 159, in the Appendix Platonica attached to K. F. Hermann's edition of Plato) quotes several examples of syllogistic reasoning from the Parmenides, and affirms that the ten categories of Aristotle are exhibited therein.

Plotinus (Ennead. v. 1, 8) gives a brief summary of what he understood to be contained in the Antinomies of the Platonic Parmenides; but the interpretation departs widely from the original.

I transcribe a few sentences from the argument of Ficinus, to show what different meanings may be discovered in the same words by different critics. (Ficini Argum. in Plat. Parmen. p. 756.) "Cum Plato per omnes ejus dialogos totius sapientiæ semina sparserit, in libris De Republicâ cuncta moralis philosophiæ instituta collegit, omnem naturalium rerum scientiam in Timæo, universam in Parmenide complexus est Theologiam. Cumque in aliis longo intervallo cæteros philosophos antecesserit, in hoc tandem seipsum superasse videtur. Hic enim divus Plato de ipso Uno subtilissimé disputat: quemadmodum Ipsum Unum rerum omnium principium est, super omnia, omniaque ab illo: quo pacto ipsum extra omnia sit et in omnibus: omniaque ex illo, per illud, atque ad illud. Ad hujus, quod super essentiam est, Unius intelligentiam gradatim ascendit. In iis quæ fluunt et sensibus subjiciuntur et sensibilia nominantur: In iis etiam quas semper eadem sunt et sensibilia nuncupantur, non sensibus amplius sed solâ mente percipienda: Nec in iis tantum, verum etiam supra sensum et sensibilia, intellectumque et intelligibilia:--ipsum Unum existit.--Illud insuper advertendum est, quod in hoc dialogo cum dicitur _Unum_, Pythagoreorum more quæque substantia a materiâ penitus absoluta significari potest: ut Deus, Mens, Anima. Cum vero dicitur Aliud et Alia, tam materia, quam illa quæ in materiâ fiunt, intelligere licet."

The Prolegomena, prefixed by Thomson to his edition of the Parmenides, interpret the dialogue in the same general way as Proklus and Ficinus: they suppose that by Unum is understood Summus Deus, and they discover in the concluding Antinomies theological demonstrations of the unity, simplicity, and other attributes of God. Thomson observes, very justly, that the Parmenides is one of the most difficult dialogues in Plato (Prolegom. iv.-x.) But in my judgment, his mode of exposition, far from smoothing the difficulties, adds new ones greater than those in the text.]

The various explanations of it given by more recent commentators may be seen enumerated in the learned Prolegomena of Stallbaum,[53] who has also set forth his own views at considerable length. And the prodigious opposition between the views of Proklus (followed by Ficinus in the fifteenth century), who extols the Parmenides as including in mystic phraseology sublime religious truths--and those of the modern Tiedemann, who despises them as foolish subtleties and cannot read them with patience--is quite sufficient to inspire a reasonable Platonic critic with genuine diffidence.

[Footnote 53: Stallbaum, Prolegg. in Parmen. ii. 1, pp. 244-265. Compare K. F. Hermann, Gesch. und Syst. der Platon. Phil. pp. 507-668-670.

To the works which he has there enumerated, may be added the Dissertation by Dr. Kuno Fischer, Stuttgart, 1851, De Parmenide Platonico, and that of Zeller, Platonische Studien, p. 169 seqq.

Kuno Fischer (pp. 102-103) after Hegel (Gesch. der Griech. Phil. I. p. 202), and some of the followers of Hegel, extol the Parmenides as a masterpiece of dialectics, though they complain that "der philosophirende Pöbel" misunderstand it, and treat it as obscure. Werder, Logik, pp. 92-176, Berlin, 1841. Carl Beck, Platon's Philosophie im Abriss ihrer genetischen Entwickelung, p. 75, Reutlingen, 1852. Marbach, Gesch. der Griech. Phil. sect. 96, pp. 210-211.]

[Side-note: No dogmatical solution or purpose is wrapped up in the dialogue. The purpose is negative, to make a theorist keenly feel all the difficulties of theorising.]

In so far as these different expositions profess, each in its own way, to detect a positive dogmatical result or purpose in the Parmenides,[54] none of them carry conviction to my mind, any more than the mystical interpretations which we read in Proklus. If Plato had any such purpose, he makes no intimation of it, directly or indirectly. On the contrary, he announces another purpose not only different, but contrary. The veteran Parmenides, while praising the ardour of speculative research displayed by Sokrates, at the same time reproves gently, but distinctly, the confident forwardness of two such immature youths as Sokrates and Aristotle in laying down positive doctrines without the preliminary exercise indispensable for testing them.[55] Parmenides appears from the beginning to the end of the dialogue as a propounder of doubts and objections, not as a doctrinal teacher. He seeks to restrain the haste of Sokrates--to make him ashamed of premature affirmation and the false persuasion of knowledge--to force upon him a keen sense of real difficulties which have escaped his notice. To this end, a specimen is given of the exercise required. It is certainly well calculated to produce the effect intended--of hampering, perplexing, and putting to shame, the affirmative rashness of a novice in philosophy. It exhibits a tangled skein of ingenious contradiction which the novice must somehow bring into order, before he is in condition to proclaim any positive dogma. If it answers this purpose, it does all that Parmenides promises. Sokrates is warned against attaching himself exclusively to one side of an hypothesis, and neglecting the opposite: against surrendering himself to some pre-conception, traditional, or self-originated, and familiarising his mind with its consequences, while no pains are taken to study the consequences of the negative side, and bring them into comparison. It is this one-sided mental activity, and premature finality of assertion, which Parmenides seeks to correct. Whether the corrective exercises which he prescribes are the best for the purpose, may be contested: but assuredly the malady which he seeks to correct is deeply rooted in our human nature, and is combated by Sokrates himself, though by other means, in several of the Platonic dialogues. It is a rare mental endowment to study both sides of a question, and suspend decision until the consequences of each are fully known.

[Footnote 54: I agree with Schleiermacher, in considering that the purpose of the Parmenides is nothing beyond [Greek: gumnasi/a], or exercise in the method and perplexities of philosophising (Einl. p. 83): but I do not agree with him, when he says (pp. 90-105) that the objections urged by Parmenides (in the middle of the dialogue) against the separate substantiality of Forms or Ideas, though noway answered in the dialogue itself, are sufficiently answered in other dialogues (which he considers later in time), especially in the Sophistes (though, according to Brandis, Handb. Gr.-Röm. Phil. p. 241, the Sophistes is earlier than the Parmenides). Zeller, on the other hand, denies that these objections are at all answered in the Sophistes; but he maintains that the second part of the Parmenides itself clears up the difficulties propounded in the first part. After an elaborate analysis (in the Platon. Studien, pp. 168-178) of the Antinomies or contradictory Demonstrations in the concluding part of the dialogue, Zeller affirms the purpose of them to be "die richtige Ansicht von den Ideen als der Einheit in dem Mannichfaltigen der Erscheinung dialektisch zu begründen, die Ideenlehre möglichen Einwürfen und Missverständnissen gegenüber dialektisch zu begründen" (pp. 180-182). This solution has found favour with some subsequent commentators. See Susemihl, Die genetische Entwickelung der Platon. Philosophie, pp. 341-353; Heinrich Stein, Vorgeschichte und System des Platonismus, pp. 217-220.

To me it appears (what Zeller himself remarks in p. 188, upon the discovery of Schleiermacher that the objections started in the Parmenides are answered in the Sophistes) that it requires all the acuteness of so able a writer as Zeller to detect any such result as that which he here extracts from the Parmenidean Antinomies--from what Aristeides calls (Or. xlvii. p. 430) "the One and Many, the multiplied twists and doublings, of this divine dialogue". I confess that I am unable to perceive therein what Zeller has either found or elicited. Objections and misunderstandings (Einwürfe und Missverständnisse), far from being obviated or corrected, are accumulated from the beginning to the end of these Antinomies, and are summed up in a formidable total by the final sentence of the dialogue. Moreover, none of these objections which Parmenides had advanced in the earlier part of the dialogue are at all noticed, much less answered, in the concluding Antinomies.

The general view taken by Zeller of the Platonic Parmenides, is repeated by him in his Phil. der Griech. vol. ii. pp. 394-415-429, ed. 2nd. In the first place, I do not think that he sets forth exactly (see p. 415) the reasoning as we read it in Plato; but even if that were exactly set forth, still what we read in Plato is nothing but an assemblage of difficulties and contradictions. These are indeed suggestive, and such as a profound critic may meditate with care, until he finds himself put upon a train of thought conducting him to conclusions sound and tenable in his judgment. But the explanations, sufficient or not, belong after all not to Plato but to the critic himself. Other critics may attach, and have attached, totally different explanations to the same difficulties. I see no adequate evidence to bring home any one of them to Plato; or to prove (what is the main point to be determined) that any one of them was present to his mind when he composed the dialogue.

Schwegler also gives an account of what he affirms to be the purpose and meaning of the Parmenides--"The positive meaning of the antinomies contained in it can only be obtained by inferences which Plato does not himself expressly enunciate, but leaves to the reader to draw" (Geschichte der Philosophie im Umriss, sect. 14, 4 c. pp. 52-53, ed. 5).

A learned man like Schwegler, who both knows the views of other philosophers, and has himself reflected on philosophy, may perhaps find affirmative meaning in the Parmenides; just as Sokrates, in the Platonic Protagoras, finds his own ethical doctrine in the song of the poet Simonides. But I venture to say that no contemporary reader of Plato could have found such a meaning in the Parmenides; and that if Plato intended to communicate such a meaning, the whole structure of the dialogue would be only an elaborate puzzle calculated to prevent nearly all readers from reaching it.

By assigning the leadership of the dialogue to Parmenides (Schwegler says) Plato intends to signify that the Platonic doctrine of Ideas is coincident with the doctrine of Parmenides, and is only a farther development thereof. How can this be signified, when the discourse assigned to Parmenides consists of a string of objections against the doctrine of Ideas, concluding with an intimation that there are other objections, yet stronger, remaining behind?

The fundamental thought of the Parmenides (says Schwegler) is, that the One is not conceivable in complete abstraction from the Many, nor the Many in complete abstraction from the One,--that each reciprocally supposes and serves as condition to the other. Not so: for if we follow the argumentation of Parmenides (p. 131 E), we shall see that what he principally insists upon, is the entire impossibility of any connection or participation between the One and the Many--there is an impassable gulf between them.

Is the discussion of [Greek: to\ e(\n] (in the closing Antinomies) intended as an example of dialectic investigation--or is it _per se_ the special object of the dialogue? This last is clearly the truth (says Schwegler). "otherwise the dialogue would end without result, and its two portions would be without any internal connection". Not so; for if we read the dialogue, we find Parmenides clearly proclaiming and singling out [Greek: to\ e(\n] as only one among a great many different notions, each of which must be made the subject of a bilateral hypothesis, to be followed out into its consequences on both sides (p. 136 A). Moreover, I think that the "internal connection" between the first and the last half of the dialogue, consists in the application of this dialectic method, and in nothing else. If the dialogue ends without result, this is true of many other Platonic dialogues. The student is brought face to face with logical difficulties, and has to find out the solution for himself; or perhaps to find out that no solution can be obtained.]

[Footnote 55: Plato, Parmenid. p. 135 C.]

[Side-note: This negative purpose is expressly announced by Plato himself. All dogmatical purpose, extending farther, is purely hypothetical, and even inconsistent with what is declared.]

Such, in my judgment, is the drift of the contradictory demonstrations here put into the mouth of Parmenides respecting Unum and Cætera. Thus far at least, we are perfectly safe: for we are conforming strictly to the language of Plato himself in the dialogue: we have no proof that he meant anything more. Those who presume that he must have had some ulterior dogmatical purpose, place themselves upon hypothetical ground: but when they go farther and attempt to set forth what this purpose was, they show their ingenuity only by bringing out what they themselves have dropped in. The number of discordant hypotheses attests[56] the difficulty of the problem. I agree with those early Platonic commentators (mentioned and opposed by Proklus) who could see no other purpose in these demonstrations than that of dialectical exercise. In this view Schleiermacher, Ast, Strümpell, and others mainly concur: the two former however annexing to it a farther hypothesis--which I think improbable--that the dialogue has come to us incomplete; having once contained at the end (or having been originally destined to contain, though the intention may never have been realised) an appendix elucidating the perplexities of the demonstrations.[57] This would have been inconsistent with the purpose declared by Parmenides: who, far from desiring to facilitate the onward march of Sokrates by clearing up difficulties, admonishes him that he is advancing too rapidly, and seeks to keep him back by giving him a heap of manifest contradictions to disentangle. Plato conceives the training for philosophy or for the highest exercise of intellectual force, to be not less laborious than that which was required for the bodily perfections of an Olympic athlete. The student must not be helped out of difficulties at once: he must work his own way slowly out of them.

[Footnote 56: Proklus ad Platon. Parmen. I. pp. 482-485, ed. Stallb.; compare pp. 497-498-788-791, where Proklus is himself copious upon the subject of exercise in dialectic method.

Stallbaum, after reciting many different hypothetical interpretations from those interpreters who had preceded him, says (Prolegg. p. 265), "En lustravimus tandem varias interpretum de hoc libro opiniones. Quid igitur? verusne fui, quum suprà dicerem, tantam fuisse hominum eruditorum in eo explicando fluctuationem atque dissensionem, ut quamvis plurimi de eo disputaverint, tamen ferè alius aliter judicaverit? Nimirum his omnibus cognitis, facilè alicui in mentem veniat Terentianum illud--_Fecisti propé, multo sim quam dudum incertior_."

Brandis (Handbuch Gr.-Röm. Phil. s. 105, pp. 257-258) cannot bring himself to believe that dialectical exercise was the only purpose with which Plato composed the Parmenides. He then proceeds to state what Plato's ulterior purpose was, but in such very vague language, that I hardly understand what he means, much less can I find it in the Antinomies themselves. He has some clearer language, p. 241, where he treats these Antinomies as preparatory [Greek: a)pori/ai].]

[Footnote 57: Ast, Platon's Leben und Schriften, pp. 239-244; Schleiermacher, Einleit. zum Parmen. pp. 94-99; Strümpell, Geschichte der Theoretischen Philosophie der Griechen, sect. 96, pp. 128-129.

I do not agree with Socher's conclusion, that the Parmenides is not a Platonic composition. But I think he is quite right in saying that the dialogue as it now stands performs all that Parmenides promises, and leaves no ground for contending that it is an unfinished fragment (Socher, Ueber Platon's Schriften, p. 286), so far as philosophical speculation is concerned. The dialogue as a dramatic or literary composition undoubtedly lacks a proper close; it is [Greek: a)/pous] or [Greek: kolobo\s] (Aristot. Rhetor. iii. 8), sinning against the strict exigence which Plato in the Phædrus applies to the discourse of Lysias.]

[Side-note: The Demonstrations or Antinomies considered. They include much unwarranted assumption and subtlety. Collection of unexplained perplexities or [Greek: a)pori/ai].]

That the demonstrations include assumption both unwarranted and contradictory, mingled with sophistical subtlety (in the modern sense of the words), is admitted by most of the commentators: and I think that the real amount of it is greater than they admit. How far Plato was himself aware of this, I will not undertake to say. Perhaps he was not. The reasonings which have passed for sublime and profound in the estimation of so many readers, may well have appeared the same to their author. I have already remarked that Plato's ratiocinative force is much greater on the negative side than on the positive: more ingenious in suggesting logical difficulties than sagacious in solving them. Impressed, as Sokrates had been before him, with the duty of combating the false persuasion of knowledge, or premature and untested belief,--he undertook to set forth the pleadings of negation in the most forcible manner. Many of his dialogues manifest this tendency, but the Parmenides more than any other. That dialogue is a collection of unexplained [Greek: a)pori/ai] (such as those enumerated in the second book of Aristotle's Metaphysica) brought against a doctrine which yet Plato declares to be the indispensable condition of all reasoning. It concludes with a string of demonstrations by which contradictory conclusions (Both and Neither) are successively proved, and which appear like a _reductio ad absurdum_ of all demonstration. But at the time when Plato composed the dialogue, I think it not improbable that these difficulties and contradictions appeared even to himself unanswerable: in other words, that he did not himself see any answers and explanations of them. He had tied a knot so complicated, that he could not himself untie it. I speak of the state of Plato's mind when he wrote the Parmenides. At the dates of other dialogues (whether earlier or later), he wrote under different points of view; but no key to the Parmenides does he ever furnish.

[Side-note: Even if Plato himself saw through these subtleties, he might still choose to impose and to heap up difficulties in the way of a forward affirmative aspirant.]

If however we suppose that Plato must have had the key present to his own mind, he might still think it right to employ, in such a dialogue, reasonings recognised by himself as defective. It is the task imposed upon Sokrates to find out and expose these defective links. There is no better way of illustrating how universal is the malady of human intelligence--unexamined belief and over-confident affirmation--as it stands proclaimed to be in the Platonic Apology. Sokrates is exhibited in the Parmenides as placed under the screw of the Elenchus, and no more able than others to extricate himself from it, when it is applied by Parmenides: though he bears up successfully against Zeno, and attracts to himself respectful compliments, even from the aged dialectician who tests him. After the Elenchus applied to himself, Sokrates receives a farther lesson from the "Neither and Both" demonstrations addressed by Parmenides to the still younger Aristotle. Sokrates will thus be driven, with his indefatigable ardour for speculative research, to work at the problem--to devote to it those seasons of concentrated meditation, which sometimes exhibited him fixed for hours in the same place and almost in the same attitude[58]--until he can extricate himself from such difficulties and contradictions. But that he shall not extricate himself without arduous mental effort, is the express intention of Parmenides: just as the Xenophontic Sokrates proceeds with the youthful Euthydemus and the Platonic Sokrates with Lysis, Theætetus, and others. Plausible subtlety was not unsuitable for such a lesson.[59] Moreover, in the Parmenides, Plato proclaims explicitly that the essential condition of the lesson is to be strictly private: that a process so roundabout and tortuous cannot be appreciated by ordinary persons, and would be unseemly before an audience.[60] He selects as respondent the youngest person in the company, one still younger than Sokrates: because (he says) such a person will reply with artless simplicity, to each question as the question may strike him--not carrying his mind forward to the ulterior questions for which his reply may furnish the handle--not afraid of being entangled in puzzling inconsistencies--not solicitous to baffle the purpose of the interrogator.[61] All this betokens the plan of the dialogue--to bring to light all those difficulties which do not present themselves except to a keen-sighted enquirer.

[Footnote 58: Plato, Symposion, p. 220 C-D: compare pp. 174-175.

In the dialogue Parmenides (p. 130 E), Parmenides himself is introduced as predicting that the youthful Sokrates will become more and more absorbed in philosophy as he advances in years.

Proklus observes in his commentary on the dialogue--[Greek: o( ga\r Sôkra/tês a)/gatai ta\s a)pori/as], &c. (L. v. p. 252).]

[Footnote 59: Xenoph. Memor. iv. 2, ad fin.]

[Footnote 60: Plato, Parmenid. pp. 136 C, 137 A. Hobbes remarks (Computatio sive Logica, Part I, ch. iii. s. 12), "Learners ought to go through logical exercises silently and by themselves: for it will be thought both ridiculous and absurd, for a man to use such language publicly".

Proklus tells us, that the difficulty of the [Greek: gumnasi/a] here enjoined by the Platonic Parmenides is so prodigious, that no one after Plato employed it (Prokl. ad Parmenid. p. 306, p. 801, Stallb.).

[Greek: ei) me\n ou)=n plei/ous ê)=men, ou)k a)\n a)/xion ê)=n dei=sthai. a)prepê= ga\r ta\ toiau=ta pollô=n e)nanti/on le/gein, a)/llôs te kai\ têlikou/tô|; a)gnoou=si ga\r oi( polloi\ o(/ti a)neu tau/tês tê=s dia\ pa/ntôn diexo/dou kai\ pla/nês a)du/naton e)ntucho/nta tô=| a)lêthei= nou=n schei=n.]]

[Footnote 61: Plato, Parmenides, p. 137 B; compare Sophistes, p. 217 D.

To understand the force of this remark of Parmenides, we should contrast it with the precepts given by Aristotle in the Topica for dialectic debate: precepts teaching the questioner how to puzzle, and the respondent how to avoid being puzzled. Such precautions are advised to the respondent by Aristotle, not merely in the Topica but also in the Analytica--[Greek: chrê\ d' o(/per phula/ttesthai paragge/llomen a)pokrinome/nous, au)tou\s e)picheirou=ntas peira=sthai lantha/nein] (Anal. Priora, ii. p. 66, a. 33).]

[Side-note: The exercises exhibited by Parmenides are exhibited only as illustrative specimens of a method enjoined to be applied to many other Antinomies.]

We must remark farther, that the two hypotheses here handled at length by Parmenides are presented by him only as examples of a dialectical process which he enjoins the lover of truth to apply equally to many other hypotheses.[62] As he shows that in the case of Unum, each of the two assumptions (Unum est--Unum non est) can be traced through different threads of deductive reasoning so as to bring out double and contradictory results--Both and Neither: so also in the case of those other assumptions which remain to be tested afterwards in like manner, antinomies of the same character may be expected: antinomies apparent at least, if not real--which must be formally propounded and dealt with, before we can trust ourselves as having attained reasoned truth. Hence we see that, negative and puzzling as the dialogue called Parmenides is, even now--it would be far more puzzling if all that it prescribes in general terms had been executed in detail. While it holds out, in the face of an aspirant in philosophy, the necessity of giving equal presumptive value to the affirmative and negative sides of each hypothesis, and deducing with equal care, the consequences of both--it warns him at the same time of the contradictions in which he will thereby become involved. These contradictions are presented in the most glaring manner: but we must recollect a striking passage in the Republic, where Plato declares that to confront the aspirant with manifest contradictions, is the best way of provoking him to intellectual effort in the higher regions of speculation.[63]

[Footnote 62: Plato, Parmenid. p. 136 B.]

[Footnote 63: Plato, Repub. vii. p. 524 E, and indeed the whole passage, pp. 523-524.]

[Side-note: 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 Palamêdes[66]) 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 ([Greek: e)pochê\]), and protest against precipitation in dogmatising,[68] which these latter converted into a formula and vindicated as a system.

[Footnote 64: Among the commentators on the Categories of Aristotle, there were several whose principal object it was to propound all the most grave and troublesome difficulties which they could think of. Simplikius does not commend the style of these men, but he expresses his gratitude to them for the pains which they had taken in the exposition of the negative case, and for the stimulus and opportunity which they had thus administered to the work of affirmative exposition (Simplikius, Schol. ad Categ. Aristot. p. 40, a. 22-30; Schol. Brandis). David the Armenian, in his Scholia on the Categories (p. 27, b. 41, Brandis), defends the Topica of Aristotle as having been composed [Greek: gumnasi/as cha/rin, i(/na thlibome/nê ê( psuchê\ e)k tô=n e)ph' e(ka/tera e)picheirêma/tôn a)pogennê/sê| to\ tê=s a)lêthei/as phô=s.]]

[Footnote 65: Sext. Emp. Pyrrh. Hypot. i. 8-12. [Greek: E)/sti de\ ê( skeptikê\ du/namis a)ntithetikê\ phainome/nôn te kai\ nooume/nôn kath' oi(ondê/pote tro/pon, a)ph' ê(=s e)rcho/metha, dia\ tê\n e)n toi=s a)ntikeime/nois pra/gmasi kai\ lo/gois i)sosthe/neian, to\ me\n prô=ton ei)s e)pochê\n to\ de\ meta\ tou=to ei)s a)taraxi/an . . . _i)sosthe/neian_ de\ le/gomen tê\n kata\ pi/stin kai\ a)pisti/an i)so/têta, ô(s mêde/na mêdeno\s prokei=sthai tô=n machome/nôn lo/gôn ô(s pisto/teron . . . susta/seôs de\ tê=s skeptikê=s e)stin a)rchê\ ma/lista _to\ panti\ lo/gô| lo/gon i)/son a)ntikei=sthai_.]]

[Footnote 66: Plato, Phædrus, p. 261 D.]

[Footnote 67: Plato, Parmenid. p. 136 C-D.]

[Footnote 68: Sext. Emp. Pyrrh. Hyp. i. 20-212. [Greek: tê\n tô=n dogmatikô=n prope/teian--tê\n dogmatikê\n prope/teian.]]

[Side-note: 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 manoeuvres 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. [Greek: Zêtô=n eu(rê/seis ou) r(o/don a)lla\ ba/ton.]

[Footnote 69: Schleiermacher, Einleitung zum Parmen. pp. 97-99.]

[Footnote 70: Indeed, the second demonstration, among the nine given by Parmenides (pp. 143 A, 155 C), coincides to a great degree with the conclusion which Zeno is represented as having maintained in his published dissertation (p. 127 E); and shows that the difficulties and contradictions belong to the world of invisible Ideas, as well as to that of sensible particulars, which Sokrates had called in question (p. 129 C-E).

The Aristotelian treatise (whether by Aristotle, Theophrastus, or any other author) De Zenone, Melisso, Xenophane, et Gorgiâ--affords some curious comparisons with the Parmenides of Plato. Aristotel. p. 974 seq. Bekk.; also Fragmenta Philosophorum Græcorum, ed. Didot, pp. 278-309.]

[Side-note: 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.

[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).]