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.

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

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

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.

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.

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.

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

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 Ἄπειρον, Infinite, or Chaos: an object not real and absolute, but relative and variable according to the point of view of the subject.

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

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.

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.

CHAPTER XXVIII.

Subjects and personages in the Theætêtus.

The two persons who converse with Sokrates are, Theodôrus, an elderly man, eminent as a geometrician, astronomer, &c., and teaching those sciences — and Theætêtus, a young man of great merit and still greater promise: acute, intelligent, and inquisitive — high-principled and courageous in the field, yet gentle and conciliatory to all: lastly, resembling Sokrates in physiognomy and in the flatness of his nose. The dialogue is supposed to have taken place during the last weeks of the life of Sokrates, when his legal appearance as defendant is required to answer the indictment of Melêtus, already entered in the official record.1 The dialogue is here read aloud to Eukleides of Megara and his fellow-citizen Terpsion, by a slave of Eukleides: this last person had recorded it in writing from narrative previously made to him by Sokrates.2 It is prefaced by a short discourse between Eukleides and Terpsion, intended to attract our sympathy and admiration towards the youthful Theætêtus.

Question raised by Sokrates — What is knowledge or Cognition? First answer of Theætêtus, enumerating many different cognitions. Corrected by Sokrates.

In answer to the question put by Sokrates — What is Knowledge or Cognition? Theætêtus at first replies — That there are many and diverse cognitions:— of geometry, of arithmetic, of arts and trades, such as shoemaking, joinery, &c. Sokrates points out (as in the Menon, Hippias Major, and other dialogues) that such an answer involves a misconception of the question: which was general, and required a general answer, setting forth the characteristic common to all cognitions. No one can know what cognition is in shoemaking or any particular case — unless he first knows what is cognition generally.3 Specimens of suitable answers to general questions are then given (or of definition of a general term), in the case of clay — and of numbers square and oblong.4 I have already observed more than once how important an object it was with Plato to impress upon his readers an exact and adequate conception of the meaning of general terms, and the proper way of defining them. For this purpose he brings into contrast the misconceptions likely to arise in the minds of persons not accustomed to dialectic.

Preliminary conversation before the second answer is given. Sokrates describes his own peculiar efficacy — mental obstetric — He cannot teach, but he can evolve knowledge out of pregnant minds.

Theætêtus, before he attempts a second answer, complains how much the subject had embarrassed him. Impressed with what he had heard about the interrogatories of Sokrates, he had tried to solve this problem: but he had not been able to satisfy himself with any attempted solution — nor yet to relinquish the search altogether. “You are in distress, Theætêtus” (observes Sokrates), “because you are not empty, but pregnant.5 You have that within you, of which you need to be relieved; and you cannot be relieved without obstetric aid. It is my peculiar gift from the Gods to afford such aid, and to stimulate the parturition of pregnant minds which cannot of themselves bring forth what is within them.6 I can produce no truth myself: but I can, by my art inherited from my mother the midwife Phænaretê, extract truth from others, and test the answers given by others: so as to determine whether such answers are true and valuable, or false and worthless. I can teach nothing: I only bring out what is already struggling in the minds of youth: and if there be nothing within them, my procedure is unavailing. My most important function is, to test the answers given, how far they are true or false. But most people, not comprehending my drift, complain of me as a most eccentric person, who only makes others sceptical. They reproach me, and that truly enough, with always asking questions, and never saying any thing of my own: because I have nothing to say worth hearing.7 The young companions who frequent my society, often suffer long-continued pains of parturition night and day, before they can be delivered of what is within them. Some, though apparently stupid when they first come to me, make great progress, if my divine coadjutor is favourable to them: others again become tired of me, and go away too soon, so that the little good which I have done them becomes effaced. Occasionally, some of these impatient companions wish to return to me afterwards — but my divine sign forbids me to receive them: where such obstacle does not intervene, they begin again to make progress.”8

Ethical basis of the cross-examination of Sokrates — He is forbidden to pass by falsehood without challenge.

This passage, while it forcibly depicts the peculiar intellectual gift of Sokrates, illustrates at the same time the Platonic manner of describing, full of poetry and metaphor. Cross-examination by Sokrates communicated nothing new, but brought out what lay buried in the mind of the respondent, and tested the value of his answers. It was applicable only to minds endowed and productive: but for them it was indispensable, in order to extract what they were capable of producing, and to test its value when extracted. “Do not think me unkind,” (says Sokrates,) “or my procedure useless, if my scrutiny exposes your answers as fallacious. Many respondents have been violently angry with me for doing so: but I feel myself strictly forbidden either to admit falsehood, or to put aside truth.”9 Here we have a suitable prelude to a dialogue in which four successive answers are sifted and rejected, without reaching, even at last, any satisfactory solution.

Answer of Theætêtus — Cognition is sensible perception: Sokrates says that this is the same doctrine as the Homo Mensura laid down by Protagoras, and that both are in close affinity with the doctrines of Homer, Herakleitus, Empedoklês, &c., all except Parmenides.

The first answer given by Theætêtus is — “Cognition is sensation (or sensible perception)”. Upon this answer Sokrates remarks, that it is the same doctrine, though in other words, as what was laid down by Protagoras — “Man is the measure of all things: of things existent, that they exist: of things non-existent, that they do not exist. As things appear to me, so they are to me: as they appear to you, so they are to you.”10 Sokrates then proceeds to say, that these two opinions are akin to, or identical with, the general view of nature entertained by Herakleitus, Empedoklês, and other philosophers, countenanced moreover by poets like Homer and Epicharmus. The philosophers here noticed (he continues), though differing much in other respects, all held the doctrine that nature consisted in a perpetual motion, change, or flux: that there was no real Ens or permanent substratum, but perpetual genesis or transition.11 These philosophers were opposed to Parmenides, who maintained (as I have already stated in a previous chapter) that there was nothing real except Ens — One, permanent, and unchangeable: that all change was unreal, apparent, illusory, not capable of being certainly known, but only matter of uncertain opinion or estimation.