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.1

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 alterna

This point is well brought out in F. A. Lange's Logische Untersuchungen.

tive 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.1 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 reason

1 Anal. Pr., I., xxxi.; Anal. Post., II., v.

ing, 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.

VII.

We have endeavoured to show that Aristotle's account of the syllogism is redundant on the one side and defective on the other, both errors being due to a false analysis of the reasoning process itself, combined with a false metaphysical philosophy. The same evil influences tell with much greater effect on his theory of applied reasoning. Here the fundamental division, corresponding to that between heaven and earth in the cosmos, is between demonstration and dialectic or experimental reasoning. The one starts with first principles of unquestionable validity, the other with principles the validity of which is to be tested by their consequences. Stated in its most abstract form, the distinction is sound, and very nearly prefigures the modern division between deduction and induction, the process by which general laws are applied, and the process by which they are established. Aristotle, however, committed two great mistakes; he thought that each method corresponded to an entirely different order of phenomena: and he thought that both were concerned for the most part with definitions. The Posterior Analytics, which contains his theory of demonstration, answers to the astronomical portion of his physics; it is the doctrine of eternal and necessary truth. And just as his ontology distinguishes between the Prime Mover himself uninoved and the eternal movement produced by his influence, so also his logic distinguishes between infallible first principles and the truths derived from them, the latter being, in his opinion, of inferior

value. Now, according to Aristotle, these first principles are definitions, and it is to this fact that their self-evident certainty is due. At the same time they are not verbal but real definitions-that is to say, the universal forms of things in themselves as made manifest to the eye of reason, or rather, stamped upon it like the impression of a signet-ring on wax. And, by a further refinement, he seems to distinguish between the concept as a whole and the separate marks which make it up, these last being the ultimate elements of all existence, and as much beyond its complex forms as Nous is beyond reasoned truth.

Such a view was essentially unfavourable to the progress of science, assigning, as it did, a higher dignity to meagre and very questionable abstractions than to the far-reaching combinations by which alone we are enabled to unravel the inmost texture of visible phenomena. Instead of using reason to supplement sense, Aristotle turned it into a more subtle and universal kind of sense; and if this disastrous assimilation was to a certain extent imposed upon him by the traditions of Athenian thought, it harmonised admirably with the descriptive and superficial character of his own intelligence. Much was also due to the method of geometry, which in his time had already assumed the form made familiar to us by Euclid's Elements. The employment of axioms side by side with definitions, might, indeed, have drawn his attention to the existence and importance of judgments which, in Kantian terminology, are not analytic but synthetic-that is, which add to the content of a notion instead of simply analysing it. But although he mentions axioms, and states that mathematical theorems are deduced from them, no suspicion of their essential difference from definitions, or of the typical significance which they were destined to assume in the theory of reasoning, seems ever to have crossed his mind; otherwise he could hardly have failed to ask how we come by our knowledge of them, and to what they correspond in Nature. On the whole,