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.