Chapter XXIX · SOPHISTES — POLITIKUS. (continued 2)

Plato’s doctrine — That Non-Ens is nothing more than different from Ens.

When we say Non-Ens, therefore (continues Plato), we do not mean any thing contrary to Ens, but merely something different from Ens. When we say Not-great, we nothing do not mean any thing contrary to Great, but only something different from great. The negative generally, when annexed to any name, does not designate any thing contrary to what is meant by that name, but something different from it. The general nature or Form of difference is disseminated into a multitude of different parts or varieties according to the number of different things with which it is brought into communion: Not-great, Not-just, &c., are specific varieties of this general nature, and are just as much realities as great, just. And thus Non-Ens is just as much a reality as Ens being not contrary, but only that variety of the general nature of difference which corresponds to Ens. Non-Ens, Not-great, Not-just, &c., are each of them permanent Forms, among the many other Forms or Entia, having each a true and distinct nature of its own.118

I say nothing about contrariety (concludes Plato), or about any thing contrary to Ens; nor will I determine whether Non-Ens in this sense be rationally possible or not. What I mean by Non-Ens is a particular case under the general doctrine of the communion or combination of Forms: the combination of Ens with Diversum, composing that which is different from Ens, and which is therefore Non-Ens. Thus Ens itself, being different from all other Forms, is Non-Ens in reference to them all, or an indefinite number of times119 (i.e. an indefinite number of negative predications may be made concerning it).

Non-Ens being thus shown to be one among the many other Forms, disseminated among all the others, and entering into communion with Ens among the rest — we have next to enquire whether it enters into communion with the Form of Opinion and Discourse. It is the communion of the two which constitutes false opinion and false proposition: if therefore such communion be possible, false opinion and false proposition are possible, which is the point that Plato is trying to prove.120

Communion of Non-Ens with proposition — possible and explicable.

Now it has been already stated (continues Plato) that some Forms or Genera admit of communion with each other, others do not. In like manner some words admit of communion with each other — not others. Those alone admit of communion, which, when put together, make up a proposition significant or giving information respecting Essence or Existence. The smallest proposition must have a noun and a verb put together: the noun indicating the agent, the verb indicating the act. Every proposition must be a proposition concerning something, or must have a logical subject: every proposition must also be of a certain quality. Let us take (he proceeds) two simple propositions: Theætêtus is sitting down — Theætêtus is flying.121 Of both these two, the subject is the same: but the first is true, the second is false. The first gives things existing as they are, respecting the subject: the second gives respecting the subject, things different from those existing, or in other words things non-existent, as if they did exist.122 A false proposition is that which gives things different as if they were the same, and things non-existent as if they were existent, respecting the subject.123

Imperfect analysis of a proposition — Plato does not recognise the predicate.

The foregoing is Plato’s explanation of Non-Ens. Before we remark upon it, let us examine his mode of analysing a proposition. He conceives the proposition as consisting of a noun and a verb. The noun marks the logical subject, but he has no technical word equivalent to subject: his phrase is, that a proposition must be of something or concerning something. Then again, he not only has no word to designate the predicate, but he does not even seem to conceive the predicate as distinct and separable: it stands along with the copula embodied in the verb. The two essentials of a proposition, as he states them, are — That it should have a certain subject — That it should be of a certain quality, true or false.124 This conception is just, as far as it goes: but it does not state all which ought to be known about proposition, and it marks an undeveloped logical analysis. It indicates moreover that Plato, not yet conceiving the predicate as a distinct constituent, had not yet conceived the copula as such: and therefore that the substantive verb ἔστιν had not yet been understood by him in its function of pure and simple copula. The idea that the substantive verb when used in a proposition must mark existence or essence, is sufficiently apparent in several of his reasonings.

I shall now say a few words on Plato’s explanation of Non-Ens. It is given at considerable length, and was, in the judgment of Schleiermacher, eminently satisfactory to Plato himself. Some of Plato’s expressions125 lead me to suspect that his satisfaction was not thus unqualified: but whether he was himself satisfied or not, I cannot think that the explanation ought to satisfy others.

Plato’s explanation of Non-Ens is not satisfactory — Objections to it.

Plato here lays down the position — That the word Not signifies nothing more than difference, with respect to that other word to which it is attached. It does not signify (he says) what is contrary; but simply what is different. Not-great, Not-beautiful — mean what is different from great or beautiful: Non-Ens means, not what is contrary to Ens, but simply what is different from Ens.

First, then, even if we admit that Non-Ens has this latter meaning and nothing beyond — yet when we turn to Plato’s own definition of Ens, we shall find it so all-comprehensive, that there can be absolutely nothing different from Ens:— these last words can have no place and no meaning. Plato defines Ens so as to include all that is knowable, conceivable, thinkable.126 One portion of this total differs from another: but there can be nothing which differs from it all. The Form or nature of Diversum (to use Plato’s phrase) as it is among the knowable or conceivable, is already included in the total of Ens, and comes into communion (according to the Platonic phraseology) with one portion of that total as against another portion. But with Ens as a whole, it cannot come into communion, for there is nothing apart from Ens. Whenever we try to think of any thing apart from Ens, we do by the act of thought include it in Ens, as defined by Plato. Different from great — different from white (i.e. not great, not white, sensu Platonico) is very intelligible: but Different from Ens, is not intelligible: there is nothing except the inconceivable and incomprehensible: the words professing to describe it, are mere unmeaning sound. Now this is just127 what Parmenides said about Non-Ens. Plato’s definition of Ens appears to me to make out the case of Parmenides about Non-Ens; and to render the Platonic explanation — different from Ens — open to quite as many difficulties, as those which attach to Non-Ens in the ordinary sense.

Secondly, there is an objection still graver against Plato’s explanation. When he resolves negation into an affirmation of something different from what is denied, he effaces or puts out of sight one of the capital distinctions of logic. What he says is indeed perfectly true: Not-great, Not-beautiful, Non-Ens, are respectively different from great, beautiful, Ens. But this, though true, is only a part of the truth; leaving unsaid another portion of the truth which, while equally essential, is at the same time special and characteristic. The negative not only differs from the affirmative, but has such peculiar meaning of its own, as to exclude the affirmative: both cannot be true together. Not-great is certainly different from great: so also, white, hard, rough, just, valiant, &c, are all different from great. But there is nothing in these latter epithets to exclude the co-existence of great. Theætêtus is great — Theætêtus is white; in the second of these two propositions I affirm something respecting Theætêtus quite different from what I affirm in the first, yet nevertheless noway excluding what is affirmed in the first.128 The two propositions may both be true. But when I say — Theætêtus is dead — Theætêtus is not dead: here are two propositions which cannot both be true, from the very form of the words. To explain not-great, as Plato does, by saying that it means only something different from great,129 is to suppress this peculiar meaning and virtue of the negative, whereby it simply excludes the affirmative, without affirming any thing in its place. Plato is right in saying that not-great does not affirm the contrary of great, by which he means little.130 The negative does not affirm any thing: it simply denies. Plato seems to consider the negative as a species of affirmative:131 only affirming something different from what is affirmed by the term which it accompanies. Not-Great, Not-Beautiful, Not-Just — he declares to be Forms just as real and distinct as Great, Beautiful, Just: only different from these latter. This, in my opinion, is a conception logically erroneous. Negative stands opposed to affirmative, as one of the modes of distributing both terms and propositions. A purely negative term cannot stand alone in the subject of a proposition: Non-Entis nulla sunt prædicata — was the scholastic maxim. The apparent exceptions to this rule arise only from the fact, that many terms negative in their form have taken on an affirmative signification.

Plato’s view of the negative is erroneous. Logical maxim of contradiction.

The view which Plato here takes of the negative deserves the greater notice, because, if it were adopted, what is called the maxim of contradiction would be divested of its universality. Given a significant proposition with the same subject and the same predicate, each taken in one and the same signification — its affirmative and its negative cannot both be true. But if by the negative, you mean to make a new affirmation, different from that contained in the affirmative — the maxim just stated cannot be broadly maintained as of universal application: it may or may not be valid, as the case happens to stand. The second affirmation may be, as a matter of fact, incompatible with the first: but this is not to be presumed, from the mere fact that it is different from the first: proof must be given of such incompatibility.

Examination of the illustrative propositions chosen by Plato — How do we know that one is true, the other false?

We may illustrate this remark by looking at the two propositions which Plato gives as examples of true and false. Theætêtus is sitting down — Theætêtus is flying. Both the examples are of affirmative propositions: and it seems clear that Plato, in all this reasoning, took no account of negative propositions: those which simply deny, affirming nothing. The second of these propositions (says Plato) affirms what is not, as if it were, respecting the subject But how do we know this to be so? In the form of the second proposition there is nothing to show it: there is no negation of any thing, but simply affirmation of a different positive attribute. Although it happens, in this particular case, that the two attributes are incompatible, and that the affirmation of the one includes the negation of the other — yet there is nothing in the form of either proposition to deny the other:— no formal incompatibility between them. Both are alike affirmative, with the same subject, but different predicates. These two propositions therefore do not serve to illustrate the real nature of the negative, which consists precisely in this formal incompatibility. The proper negative belonging to the proposition — Theætêtus is sitting down — would be, Theætêtus is not sitting down. Plato ought to maintain, if he followed out his previous argument, that Not-Sitting down is as good a Form as Sitting-down, and that it meant merely — Different from Sitting down. But instead of doing this Plato gives us a new affirmative proposition, which, besides what it affirms, conceals an implied negation of the first proposition. This does not serve to illustrate the purpose of his reasoning — which was to set up the formal negative as a new substantive attribute, different from its corresponding affirmative. As between the two, the maxim of contradiction applies: both cannot be true. But as between the two propositions given in Plato, that maxim has no application: they are two propositions with the same subject, but different predicates; which happen in this case to be, the one true, the other false — but which are not formally incompatible. The second is not false because it differs from the first; it has no essential connection with the first, and would be equally false, even if the first were false also.

The function of the negative is to deny. Now denial is not a species of affirmation, but the reversal or antithesis of affirmation: it nullifies a belief previously entertained, or excludes one which might otherwise be entertained, — but it affirms nothing. In particular cases, indeed, the denial of one thing may be tantamount to the affirmation of another: for a man may know that there are only two suppositions possible, and that to shut out the one is to admit the other. But this is an inference drawn in virtue of previous knowledge possessed and contributed by himself: another man without such knowledge would not draw the same inference, nor could he learn it from the negative proposition per se. Such then is the genuine meaning of the negative; from which Plato departs, when he tells us that the negative is a kind of affirmation, only affirming something different — and when he illustrates it by producing two affirmative propositions respecting the same subject, affirming different attributes, the one as matter of fact incompatible with the other.

Necessity of accepting the evidence of sense.

But how do we know that the first proposition — Theætêtus is sitting down — affirms what is:— and that the second proposition — Theætêtus is flying — affirms what is not? If present, our senses testify to us the truth of the first, and the falsehood of the second: if absent, we have the testimony of a witness, combined with our own past experience attesting the frequency of facts analogous to the one, and the non-occurrence of facts analogous to the other. When we make the distinction, then, — we assume that what is attested by sense or by comparisons and inductions from the facts of sense, is real, or is: and that what is merely conceived or imagined, without the attestation of sense (either directly or by way of induction), is not real, or is not. Upon this assumption Plato himself must proceed, when he takes it for granted, as a matter of course, that the first proposition is true, and the second false. But he forgets that this assumption contradicts the definition which, in this same dialogue,132 he had himself given of Ens — of the real or the thing that is. His definition was so comprehensive, as to include not only all that could be seen or felt, but also all that had capacity to be known or conceived by the mind: and he speaks very harshly of those who admit the reality of things perceived, but refuse to admit equal reality to things only conceived. Proceeding then upon this definition, we can allow no distinction as to truth or falsehood between the two propositions — Theætêtus is sitting down — Theætêtus is flying: the predicate of the second affirms what is, just as much as the predicate of the first: for it affirms something which, though neither perceived nor perceivable by sense, is distinctly conceivable and conceived by the mind. When Plato takes for granted the distinction between the two, that the first affirms what is, and the second what is not — he unconsciously slides into that very recognition of the testimony of sense (in other words, of fact and experience), as the certificate of reality, which he had so severely denounced in the opposing materialist philosophers: and upon the ground of which he thought himself entitled, not merely to correct them as mistaken, but to reprove them as wicked and impudent.133

Errors of Antisthenes — depended partly on the imperfect formal logic of that day.

I have thus reviewed a long discussion — terminating in a conclusion which appears to me unsatisfactory — of the meaning and function of the negative. I hardly think that Plato would have given such an explanation of it, if he had had the opportunity of studying the Organon of Aristotle. Prior to Aristotle, the principles and distinctions of formal logic were hardly at all developed; nor can we wonder that others at that time fell into various errors which Plato scornfully derides, but very imperfectly rectifies. For example, Antisthenes did not admit the propriety of any predication, except identical, or at most essential, predication: the word ἔστιν appeared to him incompatible with any other. But we perceive in this dialogue, that Plato also did not conceive the substantive verb as performing the simple function of copula in predication: on the contrary he distinguishes ἔστιν, as marking identity between subject and predicate — from μετέχει, as marking accidental communion between the two. Again, there were men in Plato’s day who maintained that Non-Ens (τὸ μὴ ὂν) was inconceivable and impossible. Plato, in refuting these philosophers, gives a definition of Ens (τὸ ὂν), which puts them in the right — fails in stating what the true negative is — and substitutes, in place of simple denial, a second affirmation to overlay and supplant the first.

Doctrine of the Sophistês — contradicts that of other Platonic dialogues.

To complete the examination of this doctrine of the Sophistês, respecting Non-Ens, we must compare it with the doctrine on the same subject laid down in other Platonic dialogues. It will be found to contradict, very distinctly, the opinion assigned by Plato to Sokrates both in the Theætêtus and in the fifth Book of the Republic:134 where Sokrates deals with Non-Ens in its usual sense as the negation of Ens: laying down the position that Non-Ens can be neither the object of the cognizing Mind, nor the object of the opining (δοξάζων) or cogitant Mind: that it is uncognizable and incogitable, correlating only with Non-Cognition or Ignorance. Now we find that this doctrine (of Sokrates, in Theætêtus and Republic) is the very same as that which is affirmed, in the Sophistês, to be taken up by the delusive Sophist: the same as that which the Eleate spends much ingenuity in trying to refute, by proving that Non-Ens is not the negation of Ens, but only that which differs from Ens, being itself a particular variety of Ens. It is also the same doctrine as is declared, both by the Eleate in the Sophistês and by Sokrates in the Theætêtus, to imply as an undeniable consequence, that the falsehood of any proposition is impossible. “A false proposition is that which speaks the thing that is not (τὸ μὴ ὄν). But this is an impossibility. You can neither know, nor think, nor speak, the thing that is not. You cannot know without knowing something: you cannot speak without speaking something (i. e. something that is).” Of this consequence — which is expressly announced as included in the doctrine, both by the Eleate in the Sophistês and by the Platonic Sokrates in the Theætêtus — no notice is taken in the Republic.135

Again, the doctrine maintained by the Eleate in the Sophistês respecting Ens, as well as respecting Ideas or Forms, is in other ways inconsistent with what is laid down in other Platonic dialogues. The Eleate in the Sophistês undertakes to refute two different classes of opponents; first, the Materialists, of whom he speaks with derision and antipathy — secondly, others of very opposite doctrines, whom he denominates the Friends of Ideas or Forms, speaking of them in terms of great respect. Now by these Friends of Forms or Ideas, Schleiermacher conjectures that Plato intends to denote the Megaric philosophers. M. Cousin, and most other critics (except Ritter), have taken up this opinion. But to me it seems that Socher is right in declaring the doctrine, ascribed to these Friends of Ideas, to be the very same as that which is laid down by Plato himself in other important dialogues — Republic, Timæus, Phædon, Phædrus, Kratylus, &c. — and which is generally understood as that of the Platonic Ideas.136 In all these dialogues, the capital contrast and antithesis is that between Ens or Entia on one side, and Fientia (the transient, ever generated and ever perishing), on the other: between the eternal, unchangeable, archetypal Forms or Ideas — and the ever-changing flux of particulars, wherein approximative likeness of these archetypes is imperfectly manifested. Now it is exactly this antithesis which the Friends of Forms in the Sophistês are represented as upholding, and which the Eleate undertakes to refute.137 We shall find Aristotle, over and over again, impugning the total separation or demarcation between Ens and Fientia (εἴδη — γένεσις — χωριστά), both as the characteristic dogma, and the untenable dogma, of the Platonic philosophy: it is exactly the same issue which the Eleate in the Sophistês takes with the Friends of Forms. He proves that Ens is just as full of perplexity, and just as difficult to understand, as Non-Ens:138 whereas, in the other Platonic dialogues, Ens is constantly spoken of as if it were plain and intelligible. In fact, he breaks down the barrier between Ens and Fientia, by including motion, change, the moving or variable, among the world of Entia.139 Motion or Change belongs to Fieri; and if it be held to belong to Esse also (by recognising a Form or Idea of Motion or Change, as in the Sophistês), the antithesis between the two, which is so distinctly declared in other Platonic dialogues, disappears.140

The persons whom Plato here attacks as Friends of Forms are those who held the same doctrine as Plato himself espouses in Phædon, Republic, &c.

If we examine the reasoning of the Eleate, in the Sophistês, against the persons whom he calls the Friends of Forms, we shall see that these latter are not Parmenideans only, but also Plato himself in the Phædon, Republic, and elsewhere. We shall also see that the ground, taken up by the Eleate, is much the same as that which was afterwards taken up by Aristotle against the Platonic Ideas. Plato, in most of his dialogues, declares Ideas, Forms, Entia, to be eternal substances distinct and apart from the flux and movement of particulars: yet he also declares, nevertheless, that particulars have a certain communion or participation with the Ideas, and are discriminated and denominated according to such participation. Aristotle controverts both these doctrines: first, the essential separation of the two, which he declares to be untrue: next, the participation or coming together of the two separate elements — which he declares to be an unmeaning fiction or poetical metaphor, introduced in order to elude the consequences of the original fallacy.141 He maintains that the two (Entia and Fientia — Universals and Particulars) have no reality except in conjunction and implication together; though they are separable by reason (λόγῳ χωριστὰ — τῷ εἰναι, χωριστά) or abstraction, and though we may reason about them apart, and must often reason about them apart.142 Now it is this implication and conjunction of the Universal with its particulars, which is the doctrine of the Sophistês, and which distinguishes it from other Platonic dialogues, wherein the Universal is transcendentalized — lodged in a separate world from particulars. No science or intelligence is possible (says the Eleate in the Sophistês) either upon the theory of those who pronounce all Ens to be constant and unchangeable, or upon that of those who declare all Ens to be fluent and variable. We must recognise both together, the constant and the variable, as equally real and as making up the totality of Ens.143 This result, though not stated in the language which Aristotle would have employed, coincides very nearly with the Aristotelian doctrine, in one of the main points on which Aristotle distinguishes his own teaching from that of his master.

The Sophistês recedes from the Platonic point of view, and approaches the Aristotelian.

That the Eleate in the Sophistes recedes from the Platonic point of view and approaches towards the Aristotelian, will be seen also if we look at the lesson of logic which he gives to Theætêtus. In his analysis of a proposition — and in discriminating such conjunctions of words as are significant, from such as are insignificant — he places himself on the same ground as that which is travelled over by Aristotle in the Categories and the treatise De Interpretatione. That the handling of the topic by Aristotle is much superior, is what we might naturally expect from the fact that he is posterior in time. But there is another difference between the two which is important to notice. Aristotle deals with this topic, as he does with every other, in the way of methodical and systematic exposition. To expound it as a whole, to distribute it into convenient portions each illustrating the others, to furnish suitable examples for the general principles laid down — are announced as his distinct purposes. Now Plato’s manner is quite different. Systematic exposition is not his primary purpose: he employs it up to a certain point, but as means towards another and an independent purpose — towards the solution of a particular difficulty, which has presented itself in the course of the dialogue. — “Nosti morem dialogorum.” Aristotle is demonstrative: Plato is dialectical. In our present dialogue (the Sophistês), the Eleate has been giving a long explanation of Non-Ens; an explanation intended to prove that Non-Ens was a particular sort of Ens, and that there was therefore no absurdity (though Parmenides had said that this was absurdity) in assuming it as a passable object of Cognition, Opination, Affirmation. He now goes a step further, and seeks to show that it is, actually and in fact, an object of Opination and Affirmation.144 It is for this purpose, and for this purpose only, that he analyses a proposition, specifies the constituent elements requisite to form it, and distinguishes one proposition from another.

Accordingly, the Eleate, — after pointing out that neither a string of nouns repeated one after the other, nor a string of verbs so repeated, would form a significant proposition, — declares that the conjunction of a noun with a verb is required to form one; and that opination is nothing but that internal mental process which the words of the proposition express. The smallest proposition must combine a noun with a verb:— the former signifying the agent, the latter, the action or thing done.145 Moreover, the proposition must be a proposition of something; and it must be of a certain quality. By a proposition of something, Plato means, that what is called technically the subject of the proposition (in his time there were no technical terms of logic) must be something positive, and cannot be negative: by the quality of the proposition, he means that it must be either true or false.146

Aristotle assumes without proof, that there are some propositions true, others false.

This early example of rudimentary grammatical or logical analysis, recognising only the two main and principal parts of speech, is interesting as occurring prior to Aristotle; by whom it is repeated in a manner more enlarged, systematic,147 and instructive. But Aristotle assumes, without proof and without supposing that any one will dispute the assumption — that there are some propositions true, other propositions false: that a name or noun, taken separately, is neither true nor false:148 that propositions (enunciations) only can be true or false.

Plato in the Sophistês has undertaken an impossible task — He could not have proved, against his supposed adversary, that there are false propositions.

The proceeding of Plato in the Sophistês is different. He supposes a Sophist who maintains that no proposition either is false or can be false, and undertakes to prove against him that there are false propositions: he farther supposes this antagonist to reject the evidence of sense and visible analogies, and to acknowledge no proof except what is furnished by reason and philosophical deduction.149 Attempting, under these restrictions, to prove his point, Plato’s Eleatic disputant rests entirely upon the peculiar meaning which he professes to have shown to attach to Non-Ens. He applies this to prove that Non-Ens may be predicated as well as Ens: assuming that such predication of Non-Ens constitutes a false proposition. But the proof fails. It serves only to show that the peculiar meaning ascribed by the Eleate to Non-Ens is inadmissible. The Eleate compares two distinct propositions — Theætêtus is sitting down — Theætêtus is flying. The first is true: the second is false. Why? Because (says the Eleate) the first predicates Ens, the second predicates Non-Ens, or (to substitute his definition of Non-Ens) another Ens different from the Ens predicated in the first.150 But here the reason assigned, why the second proposition is false, is not the real reason. Many propositions may be assigned, which predicate attributes different from the first, but which are nevertheless quite as much true as the first. I have already observed, that the reason why the second proposition is false is, because it contradicts the direct testimony of sense, if the persons debating are spectators: if they are not spectators, then because it contradicts the sum total of their previous sensible experience, remembered, compared, and generalised, which has established in them the conviction that no man does or can fly. If you discard the testimony of sense as unworthy of credit (which Plato assumes the Sophist to do), you cannot prove that the second proposition is false — nor indeed that the first proposition is true. Plato has therefore failed in giving that dialectic proof which he promised. The Eleate is forced to rely (without formally confessing it), on the testimony of sense, which he had forbidden Theætêtus to invoke, twenty pages before.151 The long intervening piece of dialectic about Ens and Non-Ens is inconclusive for his purpose, and might have been omitted. The proposition — Theætêtus is flying — does undoubtedly predicate attributes which are not as if they were,152 and is thus false. But then we must consult and trust the evidence of our perception: we must farther accept are not in the ordinary sense of the words, and not in the sense given to them by the Eleate in the Platonic Sophistês. His attempt to banish the specific meaning of the negative particle, and to treat it as signifying nothing more than difference, appears to me fallacious.153

What must be assumed in all dialectic discussion.

In all reasoning, nay in all communication by speech, you must assume that your hearer understands the meaning of what is spoken: that he has the feelings of belief and disbelief, and is familiar with those forms of the language whereby such feelings are expressed: that there are certain propositions which he believes — in other words, which he regards as true: that there are certain other propositions which he disbelieves, or regards as false: that he has had experience of the transition from belief to disbelief, and vice versâ — in other words, of having fallen into error and afterwards come to perceive that it was error. These are the mental facts realised in each man and assumed by him to be also realised in his neighbours, when communication takes place by speech. If a man could be supposed to believe nothing, and to disbelieve nothing; — if he had no forms of speech to express his belief, disbelief, affirmation, and denial — no information could be given, no discussion would be possible. Every child has to learn this lesson in infancy; and a tedious lesson it undoubtedly is.154 Antisthenes (who composed several dialogues) and the other disputants of whom we are now speaking, must have learnt the lesson as other men have: but they find or make some general theory which forbids them to trust the lesson when learnt. It was in obedience to some such theory that Antisthenes discarded all predication except essential predication, and discarded also the form suited for expressing disbelief — the negative proposition: maintaining, That to contradict was impossible. I know no mode of refuting him, except by showing that his fundamental theory is erroneous.

Discussion and theorising presuppose belief and disbelief, expressed in set forms of words. They imply predication, which Antisthenes discarded.

Discussion and theorising can only begin when these processes, partly intellectual, partly emotional, have become established and reproducible portions of the train of mental association. As processes, they are common to all men. But though two persons agree in having expressed the feeling of belief, and in expressing that feeling by one form of proposition — also in having the feeling of disbelief, and in expressing it by another form of proposition — yet it does not follow that the propositions which these two believe or disbelieve are the same. How far such is the case must be ascertained by comparison — by appeal to sense, memory, inference from analogy, induction, feeling, consciousness, &c. The ground is now prepared for fruitful debate: for analysing the meaning, often confused and complicated, of propositions: for discriminating the causes, intellectual and emotional, of belief and disbelief, and for determining how far they harmonise in one mind and another: for setting out general rules as to sequence, or inconsistency, or independence, of one belief as compared with another. To a certain extent, the grounds of belief and disbelief in all men, and the grounds of consistency or inconsistency between some beliefs and others, will be found to harmonise: they can be embodied in methodical forms of language, and general rules can be laid down preventing in many cases inadvertence or erroneous combination. It is at this point that Aristotle takes up rational grammar and logic, with most profitable effect. But he is obliged to postulate (what Antisthenes professed to discard) predication, not merely identical, but also accidental as well as essential — together with names and propositions both negative and affirmative.155 He cannot avoid postulating thus much: though he likewise postulates a great deal more, which ought not to be granted.

Precepts and examples of logical partition, illustrated in the Sophistês.

The long and varied predicamental series, given in the Sophistês, illustrates the process of logical partition, as Plato conceived it, and the definition of a class-name founded thereupon. You take a logical whole, and you subtract from it part after part until you find the quæsitum isolated from every thing else.156 But you must always divide into two parts (he says) wherever it can be done: dichotomy or bipartition is the true logical partition: should this be impracticable, trichotomy, or division into the smallest attainable number of parts, must be sought for.157 Moreover, the bipartition must be made according to Forms (Ideas, Kinds): the parts which you recognise must be not merely parts, but Forms: every form is a part, but every part is not a form.158 Next, you must draw the line of division as nearly as you can through the middle of the dividendum, so that the parts on both sides may be nearly equal: it is in this way that your partition is most likely to coincide with forms on both sides of the line.159 This is the longest way of proceeding, but the safest. It is a logical mistake to divide into two parts very unequal: you may find a form on one side of the line, but you obtain none on the other side. Thus, it is bad classification to distribute the human race into Hellênes + Barbari: the Barbari are of infinite number and diversity, having no one common form to which the name can apply. It is also improper to distribute Number into the myriad on side, and all other numbers on the other — for a similar reason. You ought to distribute the human race into the two forms, Male — Female: and number into the two, Odd — Even.160 So also, you must not divide gregarious creatures into human beings on one side, and animals on the other; because this last term would comprise numerous particulars utterly disparate. Such a classification is suggested only by the personal feeling of man, who prides himself upon his intelligence. But if the classification were framed by any other intelligent species, such as Cranes,161 they would distinguish Cranes on the one side from animals on the other, including Man as one among many disparate particulars under animal.

Recommendation of logical bipartition.

The above-mentioned principle — dichotomy or bipartition into two equal or nearly equal halves, each resting upon a characteristic form — is to be applied as far as it will go. Many different schemes of partition upon this principle may be found, each including forms subordinated one to the other, descending from the more comprehensive to the less comprehensive. It is only when you can find no more parts which are forms, that you must be content to divide into parts which are not forms. Thus after all the characteristic forms, for dividing the human race, have been gone through, they may at last be partitioned into Hellênes and Barbari, Lydians and non-Lydians, Phrygians and non-Phrygians: in which divisions there is no guiding form at all, but only a capricious distribution into fractions with separate names162 — meaning by capricious, a distribution founded on some feeling or circumstance peculiar to the distributor, or shared by him only with a few others; such as the fact, that he is himself a Lydian or a Phrygian, &c.

Precepts illustrated by the Philêbus.

These precepts in the Sophistês and Politikus, respecting the process of classification, are illustrated by an important passage of the Philêbus:163 wherein Plato tells us that the constitution of things includes the Determinate and the Indeterminate implicated with each other, and requiring study to disengage them. Between the highest One, Form, or Genus — and the lowest array of indefinite particulars — there exist a certain number of intermediate Ones or Forms, each including more or fewer of these particulars. The process of study or acquired cognition is brought to bear upon these intermediate Forms: to learn how many there are, and to discriminate them in themselves as well as in their position relative to each other. But many persons do not recognise this: they apprehend only the Highest One, and the Infinite Many, not looking for any thing between: they take up hastily with some extreme and vague generality, below which they know nothing but particulars. With knowledge thus imperfect, you do not get beyond contentious debate. Real, instructive, dialectic requires an understanding of all the intermediate forms. But in descending from the Highest Form downwards, you must proceed as much as possible in the way of bipartition, or if not, then of tripartition, &c.: looking for the smallest number of forms which can be found to cover the whole field. When no more forms can be found, then and not till then, you must be content with nothing better than the countless indeterminate particulars.

This instructive passage of the Philêbus — while it brings to view a widespread tendency of the human mind, to pass from the largest and vaguest generalities at once into the region of particulars, and to omit the distinctive sub-classes which lie between — illustrates usefully the drift of the Sophistês and Politikus. In these two last dialogues it is the method itself of good logical distribution which Plato wishes to impress upon his readers: the formal part of the process.164 With this view, he not only makes the process intentionally circuitous and diversified, but also selects by preference matters of common sensible experience, though in themselves indifferent, such as the art of weaving,165 &c.

Importance of founding logical Partition on resemblances perceived by sense.

The reasons given for this preference deserve attention. In these common matters (he tells us) the resemblances upon which Forms are founded are perceived by sense, and can be exhibited to every one, so that the form is readily understood and easily discriminated. The general terms can there be explained by reference to sense. But in regard to incorporeal matters, the higher and grander topics of discussion, there is no corresponding sensible illustration to consult. These objects can be apprehended only by reason, and described only by general terms. By means of these general terms, we must learn to give and receive rational explanations, and to follow by process of reasoning from one form to another. But this is more difficult, and requires a higher order of mind, where there are no resemblances or illustrations exposed to sense. Accordingly, we select the common sensible objects as an easier preparatory mode of a process substantially the same in both.166

Province of sensible perception — is not so much narrowed by Plato here as it is in the Theætêtus.

This explanation given by Plato, in itself just, deserves to be compared with his view of sensible objects as knowable, and of sense as a source of knowledge. I noticed in a preceding chapter the position which Sokrates is made to lay down in the Theætêtus,167 — That (αἴσθησις) sensible perception reaches only to the separate impressions of sense, and does not apprehend the likeness and other relations between them. I have also noticed the contrast which he establishes elsewhere between Esse and Fieri: i.e., between Ens which alone (according to him) is knowable, and the perpetual flux of Fientia which is not knowable at all, but is only matter of opinion or guess-work. Now in the dialogue before us, the Politikus, there is no such marked antithesis between opinion and knowledge. Nor is the province of αἴσθησις so strictly confined: on the contrary, Plato here considers sensible perception as dealing with Entia, and as appreciating resemblances and other relations between them. It is by an attentive study and comparison of these facts of sense that Forms are detected. “When a man (he says) has first perceived by sense the points of communion between the Many, he must not desist from attentive observation until he has discerned in that communion all the differences which reside in Forms: and when he has looked at the multifarious differences which are visible among these Many, he must not rest contented until he has confined all such as are really cognate within one resemblance, tied together by the essence of one common Form.”168

Comparison of the Sophistês with the Phædrus.

These passages may be compared with others of similar import in the Phædrus.169 Plato here considers the Form, not as an Entity per se separate from and independent of the particulars, but as implicated in and with the particulars: as a result reached by the mind through the attentive observation and comparison of particulars: as corresponding to what is termed in modern language abstraction and generalisation. The self-existent Platonic Ideas do not appear in the Politikus:170 which approximates rather to the Aristotelian doctrine:— that is, the doctrine of the universal, logically distinguishable from its particulars, but having no reality apart from them (χωριστὰ λόγῳ μόνον). But in other dialogues of Plato, the separation between the two is made as complete as possible, especially in the striking passages of the Republic: wherein we read that the facts of sense are a delusive juggle — that we must turn our back upon them and cease to study them — and that we must face about, away from the sensible world, to contemplate Ideas, the separate and unchangeable furniture of the intelligible world — and that the whole process of acquiring true Cognition, consists in passing from the higher to the lower Forms or Ideas, without any misleading illustrations of sense.171 Here, in the Sophistês and Politikus, instead of having the Universal behind our backs when the particulars are before our faces, we see it in and amidst particulars: the illustrations of sense, instead of deluding us, being declared to conduce, wherever they can be had, to the clearness and facility of the process.172 Here, as well as in the Phædrus, we find the process of Dialectic emphatically recommended, but described as consisting mainly in logical classification of particulars, ascending and descending divisions and conjunctions, as Plato calls them173 — analysis and synthesis. We are enjoined to divide and analyse the larger genera into their component species until we come to the lowest species which can no longer be divided: also, conversely, to conjoin synthetically the subordinate species until the highest genus is attained, but taking care not to omit any of the intermediate species, in their successive gradations.174 Throughout all this process, as described both in the Phædrus and in the Politikus, the eye is kept fixed upon the constituent individuals. The Form is studied in and among the particulars which it comprehends: the particulars are looked at in groups put together suitably to each comprehending Form. And in both dialogues, marked stress is laid upon the necessity of making the division dichotomous; as well as according to Forms, and not according to fractions which are not legitimate Forms.175 Any other method, we are told, would be like the wandering of a blind man.

What distinguishes the Sophistês and Politikus from most other dialogues of Plato, is, that the method of logical classification is illustrated by setting the classifier to work upon one or a few given subjects, some in themselves trivial, some important. Though the principles of the method are enunciated in general terms, yet their application to the special example is kept constantly before us; so that we are never permitted, much less required, to divorce the Universal from its Particulars.

Comparison of the Politikus with the Parmenidês.

As a dialogue illustrative of this method, the Politikus (as I have already pointed out) may be compared to the Phædrus: in another point of view, we shall find instruction in comparing it to the Parmenidês. This last too is a dialogue illustrative of method, but of a different variety of method.

Variety of method in dialectic research — Diversity of Plato.

What the Sophistês and Politikus are for the enforcement of logical classification, the Parmenidês is for another part of the philosophising process — laborious evolution of all the consequences deducible from the affirmative as well as from the negative of every hypothesis bearing upon the problem. And we note the fact, that both in the Politikus and Parmenidês, Plato manifests the consciousness that readers will complain of him as prolix, tiresome, and wasting ingenuity upon unprofitable matters.176 In the Parmenidês, he even goes the length of saying that the method ought only to be applied before a small and select audience; to most people it would be repulsive, since they cannot be made to comprehend the necessity for such circuitous preparation in order to reach truth.177