VI.

We now pass to the consideration of Aristotle’s most important achievement—his system of logic. And as, here also, we shall find much to criticise, it is as well to begin by saying that, in our opinion, his contributions to the science are the most valuable ever made, and perhaps have done more to advance it than all other writings on the same subject put together.

The principal business of reason is, as we have seen, to form abstract ideas or concepts of things. But before the time of Aristotle it had already been discovered that concepts, or rather the terms expressing them, were capable of being united in propositions which might be either true or false, and whose truth might be a matter either of certainty or of simple opinion. Now, in modern psychology, down to the most recent times, it has always been assumed that, just as there is an intellectual faculty or operation called abstraction corresponding to the terms of which a proposition is composed, so also there is a faculty or operation called judgment corresponding to the entire proposition. Sometimes, again, the third operation, which consists in linking propositions together to form syllogisms, is assigned to a distinct faculty called reason; sometimes all three are regarded as ascending steps in a single fundamental process. Neither Plato nor Aristotle, however, had thought out the subject so scientifically. To both the framing, or rather the discovery, of concepts was by far the most important business of a philosopher, judgment and reasoning being merely subsidiary to it. Hence, while in one part of their logic they were realists and conceptualists, in other parts they were nominalists. Abstract names and the definitions unfolding their connotation corresponded to actual entities in Nature—the eternal Ideas of the one and the substantial forms of the other—as well as to mental representations about whose existence they were agreed, while ascribing to them a different origin. But they did not in like manner treat propositions as the expression of natural laws without, or of judgments within, the mind; while reasoning they regarded much more as an art of thinking, a method for the discovery of ideas, than as the Systematisation of a process spontaneously performed by every human being without knowing it; and, even as such, their tendency is to connect it with the theory of definition rather than with the theory of synthetic propositions. Some approach to a realistic view is, indeed, made by both. The restless and penetrating thought of Plato had, probably towards the close of his career, led him to enquire into the mutual relations of those Ideas which he had at first been inclined to regard as absolutely distinct. He shows us in the _Sophist_ how the most abstract notions, such as Being, Identity, and so forth, must, to a certain extent, partake of each other’s nature; and when their relationship does not lie on the surface, he seeks to establish it by the interposition of a third idea obviously connected with both. In the later books of the _Republic_ he also points to a scheme for arranging his Ideas according to a fixed hierarchy resembling the concatenation of mathematical proofs, by ascending and descending whose successive gradations the mind is to become familiarised with absolute truth; and we shall presently see how Aristotle, following in the same track, sought for a counterpart to his syllogistic method in the objective order of things. Nevertheless, with him, as well as with his master, science was not what it is with us, a study of laws, a perpetually growing body of truth, but a process of definition and classification, a systematisation of what had already been perceived and thought.

It was from the initiative of Socrates that logic received this direction. By insisting on the supreme importance of definition, he drew away attention from the propositions which add to our knowledge, and concentrated it on those which only fix with precision the meaning of words. Yet, in so doing he was influenced quite as much by the spirit of the older physical philosophy, which he denounced, as by the necessities of the new humanistic culture, which he helped to introduce. His definitions were, in truth, the reproduction, on a very minute scale, of those attempts to formulate the whole universe which busied the earliest Ionian speculation. Following the natural tendency of Greek thought, and the powerful attraction of cosmic philosophy, an effort was speedily made to generalise and connect these partial definitions until they grew into a system of universal classification. It was when, under the influence of a new analysis, this system threatened to fall to pieces, that a rudimentary doctrine of judgment first made its appearance. The structure of a grammatical sentence was used to explain how objective ideas could, in a manner, overlap and adhere to one another. Hence propositions, which, as the expression of general truths, were destined to become the beginning and end of thought, remained at first strictly subordinated to the individual concepts that they linked and reconciled.

With Aristotle propositions assumed a new importance. He looked on them as mediating, not only between concepts, but also between conception and reasoning. Still, neither as a psychologist nor as a logician did he appreciate them at their real value. A very brief consideration is given to judgment in his work on the soul, and we are left in doubt whether it is a function of Nous alone or of Nous combined with some other faculty. Setting aside the treatise on Interpretation, which is probably spurious, and, at any rate, throws no new light on the subject, we may gather from his logical writings half a dozen different suggestions towards a classification of propositions, based partly on their form and partly on their import. In all we find an evident tendency to apply, here also, his grand fundamental distinction between the sphere of uniformity and the sphere of change and opposition. All propositions are either universal or particular; either positive or negative; either necessary or actual or contingent; either reciprocating or not reciprocating; either essential or accidental; either answering to the first question in the categories, or to one of the other nine.[273] But nowhere is any attempt made to combine and systematise these various points of view.

In the theory of reasoning the simple proposition is taken as a starting-point; but instead of deducing the syllogism from the synthesis of two premises, Aristotle reaches the premises through the conclusion. He tells us, indeed, that reasoning is a way of discovering from what we know, something that we did not know before. With him, however, it is really a process not of discovery but of proof. He starts with the conclusion, analyses it into predicate and subject or major and minor, and then, by a further analysis, introduces a middle term connecting the two. Thus, we begin with the proposition, ‘Caius is mortal,’ and prove it by interpolating the notion humanity between its two extremes. From this point of view the premises are merely a temporary scaffolding for bringing the major and minor into connexion with the middle term; and this is also the reason why Aristotle recognises three syllogistic figures only, instead of the four admitted by later logicians. For, the middle may either be contained in one extreme and contain the other, which gives us the first figure; or it may contain both, which gives the second figure; or be contained in both, which gives the third; and this is an exhaustive enumeration of the possible combinations.[274]

We have here, also, the secret of that elaborate machinery devised for the very unnecessary purpose of converting syllogisms of the second and third figure into syllogisms of the first, which is one of the Stagirite’s principal contributions to logic. For it is only in the first figure that the notion by which the extremes are either united or held apart is really a middle term, that is to say, really comes between the others. The distinction between perfect and imperfect syllogisms also serves to illustrate Aristotle’s systematic division between the necessary and the contingent. The method of proof by inclusion corresponds in its unconditioned and independent validity to the concentric arrangement of the supernal spheres; the second and third figures, with their conversions and reductions, to the sublunary sphere in its helpless dependence on the celestial revolutions, and its transformations of the elements into one another.

The rules which Aristotle gives us for the conversion of propositions are no doubt highly instructive, and throw great light on their meaning; but one cannot help observing that such a process as conversion ought, on his own principles, to have been inadmissible. With Plato, the copulation of subject and predicate corresponded to an almost mechanical juxtaposition of two self-existent ideas. It was, therefore, a matter of indifference in what order they were placed. Aristotle, on the other hand, after insisting on the restoration of the concrete object, and reducing general notions to an analysis of its

## particular aspects, could not but make the predicate subordinate to,

and dependent on, the subject—a relation which altogether excludes the logical possibility of making them interchangeable with one another.[275]

The antithetical structure of the whole system is reproduced even in the first syllogistic figure, where there is a similar opposition between the first mood, by which alone universal affirmatives can be obtained, and the remaining three, whose conclusions are either negative or particular, or both. And the complicated rules for testing the validity of those syllogisms in which the premises are distinguished as necessary, actual, and possible, are still more obviously based on Aristotle’s false metaphysical distinctions; so that with the overthrow of those distinctions large portions of the _Analytics_ lose their entire value for modern students.

On the other hand, a theory of reasoning based on the relations of concepts, instead of on the relations of judgments, necessarily leaves out of account the whole doctrine of hypothetical and disjunctive propositions, together with that of the syllogisms based on them; since the elements of which they are composed are themselves propositions. And this inevitable omission is the more remarkable because alternative and, to a less extent, hypothetical arguments form the staple of Aristotle’s own dialectic; while categorical reasoning never occurs in it at all. His constant method is to enumerate all possible views of a subject, and examine them one after the other, rejecting those which are untenable, and resting content with the remainder. In other words, he reaches his positive conclusions through a series of negative premises representing a process of gradual elimination. The _First Analytics_ is itself an admirable instance of his favourite method. Every possible combination of terms is discussed, and the valid moods are sifted out from a much greater number of illegitimate syllogisms. The dialectic of Socrates and Plato followed the same procedure. It was essentially experimental—a method of trial, elimination, and selection. On going back still further, we find that when there is any reasoning at all in Homer, it is conducted after the same fashion. Hector, in his soliloquy before the Scaean Gate, imagines three alternative courses, together exhausting the possibilities of the situation. He may either retreat within the walls, or offer terms of peace to Achilles, or fight. The first two alternatives being rejected, nothing remains but the third. This is the most elaborate example; but on many other occasions Homer’s actors are represented as hesitating between two courses, and finally deciding on one of them.

Disjunction is, in truth, the primordial form of all reasoning, out of which the other forms are successively evolved; and, as such, it is common to man with the lower animals. You are taking a walk in the country with your dog. You come to a stream and jump over it. On measuring the distance with his eye, the animal is afraid to follow you. After waiting a little, he first runs up stream in search of a crossing, and, finding none, returns to look for one in the opposite direction. Failing there also, he comes back once more, and either ventures on the leap or makes his way home by some other route. Now, on considering the matter a little more closely, we shall find that hypothetical reasoning takes its rise from the examination of each separate alternative presented by a disjunctive premise. A plurality of courses being open to us, we consider what will ensue on the acceptance or rejection of each. The dog in our illustration thinks (after a canine fashion) that if he jumps he may fall in; if he does not, he will be left behind. Hector will not take refuge within the walls, because, if he does, Polydamas will triumph over him; nor will he offer terms of peace, because, if he does, Achilles will refuse them. Once more, categorical reasoning is developed out of hypothetical reasoning by the necessity of deducing consequences from a general rule. Hector must have argued from the known characters of Polydamas and Achilles, that in certain circumstances they would act after a certain manner. We may add, that this progress of conscious reasoning is a reproduction of the unconscious logic according to which life itself is evolved. All sorts of combinations are spontaneously produced, which, in consequence of the struggle for existence, cannot all survive. Those adapted to the conditions of life are selected, on trial, at the expense of the rest; and their adaptation or non-adaptation is determined in accordance with categorical laws. Furthermore, the framing of a disjunctive proposition necessitates the systematic distribution of possibilities under mutually exclusive heads, thus involving the logical processes of definition, division, and classification. Dialectic, as Plato understood it, consisted almost entirely in the joint performance of these operations;—a process which Aristotle regards as the immediate but very imperfect precursor of his own syllogistic method.[276] You cannot, he says, prove anything by dividing, for instance, all living things into the two classes, mortal and immortal; unless, indeed, you assume the very point under discussion—to which class a particular species belongs. Yet this is how he constantly reasons himself; and even demonstrative reasoning, as he interprets it, implies the possession of a ready-made classification. For, according to him, it consists exclusively of propositions which predicate some essential attribute of a thing—in other words, some attribute already included in the definition of the subject; and a continuous series of such definitions can only be given by a fixed classification of things.