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is not bridged by the function of νοῦς in relation to “induction.” What is known is not real, and what is real is not known. The Knowledge and reality. nodus^[1] has its cause in the double sense of the word “universal” and a possible solution in the doctrine of εἶδος. The “form” of a thing constitutes it what it is, and at the same time, therefore, is constitutive of the group to which it belongs. It has both individual and universal reference. The individual is known in the εἶδος, which is also the first universal in which by analysis higher universals are discoverable. These are predicates of the object known, ways of knowing it, rather than the object itself. The suggested solution removes certain difficulties, but scarcely all. On seeing Callias my perception is of man, not Callias, or even man-Callias. The recognition of the individual is a matter of his accidents, to which even sex belongs, and the gap from lowest universal to individual may still be conceived as unbridged. It is in induction, which claims to start from particulars and end in universals,^[2] that we must, if anywhere within the confines of logical inquiry, expect to find the required bridge. The Aristotelian conception of induction, however, is somewhat ambiguous. He had abandoned for the most part Conclusions as to induction. the Platonic sense of the corresponding verb, viz. to lead forward to the as yet unknown, and his substitute is not quite clear. It is scarcely the military metaphor. The adducing of a witness for which he uses the verb^[3] is not an idea that covers all the uses.^[4] Perhaps confrontation with facts is the general meaning. But how does he conceive of its operation? There is in the first place the action of the psychological mechanism in the process from discriminative sense upwards wherein we realize “first” universals.^[5] This is clearly an unreflective, prelogical process, not altogether lighted up by our retrojection upon it of our view of dialectical induction based thereon. The immanent rationality of this first form, in virtue of which at the stage when intelligence acts freely on the occasion of the datum supplied it recognizes continuity with its own self-conscious process, is what gives the dialectical type its meaning. Secondly we have this dialectical “induction as to particulars by grouping of similars”^[6] whose liability to rebuttal by an exception has been already noted in connexion with the limits of dialectic. This is the incomplete induction by simple enumeration which has so often been laughed to scorn. It is a heuristic process liable to failure, and its application by a nation of talkers even to physics where non-expert opinion is worthless somewhat discredited it. Yet it was the fundamental form of induction as it was conceived throughout the scholastic period. Thirdly we have the limiting cases of this in the inductive syllogism διὰ πάντων,^[7] a syllogism in the third figure concluding universally, and yet valid because the copula expresses equivalence, and in analogy^[8] in which, it has been well said, instances are weighed and not counted. In the former it has been noted^[9] that Aristotle’s illustration does not combine particular facts into a lowest concept, but specific concepts into a generic concept, and^[10] that in the construction of definite inductions the ruling thought with Aristotle is already, though vaguely, that of causal relation. It appears safer, notwithstanding, to take the less subtle interpretation^[11] that dialectical induction struggling with instances is formally justified only at the limit, and that this, where we have exhausted and know that we have exhausted the cases, is in regard to individual subjects rarely and accidentally reached, so that we perforce illustrate rather from the definite class-concepts falling under a higher notion. After all, Aristotle must have had means by which he reached the conclusions that horses are long-lived and lack gall. It is only then in the rather mystical relation of νοῦς to the first type of induction as the process of the psychological mechanism that an indication of the direction in which the bridge from individual being to universal knowledge is to be found can be held to lie.

Enough has been said to justify the great place assigned to Aristotle in the history of logic. Without pressing metaphysical formulae in logic proper, he analysed formal implication grounded implication as a mode of knowledge in the rationality of the real, and developed a justificatory Summary. metaphysic. He laid down the programme which the after history of logic was to carry out. We have of course abandoned particular logical positions. This is especially to be noted in the theory of the proposition. The individualism with which he starts, howsoever afterwards mitigated by his doctrine of τὸ τὶ ἦν εἰναι or εἶδος constituting the individual in a system of intelligible relations, confined him in an inadmissible way to the subject-attribute formula. He could not recognize such vocables as the impersonals for what they were, and had perforce to ignore the logical significance of purely reciprocal judgments, such as those of equality. There was necessarily a “sense” or direction in every proposition, with more than the purely psychological import that the advance was from the already mastered and familiar taken as relatively stable, to the new and strange. Many attributes, too, were predicable, even to the end, in an external and accidental way, not being derivable from the essence of the subject. The thought of contingency was too easily applied to these attributes, and an unsatisfactory treatment of modality followed. It is indeed the doctrine of the intractability of matter to form that lies at the base of the paradox as to the disparateness of knowledge and the real already noted. On the one hand Aristotle by his doctrine of matter admitted a surd into his system. On the other, he assigned to νοῦς with its insight into rationality too high a function with regard to the concrete in which the surd was present, a power to certify the truth of scientific principles. The example of Aristotle’s view of celestial physics as a science of pure forms exhibits both points. On the Copernican change the heavenly bodies were recognized as concrete and yet subject to calculable law. Intelligence had warranted false principles. The moral is that of the story of the heel of Achilles.

To return to logic proper. The Aristotelian theory of the universal of science as secure from dependence on its instances and the theory of linking in syllogism remain a heritage for all later logic, whether accepted in precisely Aristotle’s formula or no. It is because the intervening centuries had the Aristotelian basis to work on, sometimes in reduced quantity and corrupt form, but always in some quantity and some form, that the rest of our logical tradition is what it is. We stand upon his shoulders.

iii. Later Greek Logic.

After Aristotle we have, as regards logic, what the verdict of after times has rightly characterized as an age of Epigoni. So far as the Aristotelian framework is accepted we meet only minor corrections and extensions of a formal kind. If there is conscious and purposed divergence from Aristotle, inquiry moves, on the whole, within the circle of ideas where Aristotelianism had fought its fight and won its victory. Where new conceptions emerge, the imperfection of the instruments, mechanical and methodological, of the sciences renders them unfruitful, until their rediscovery in a later age. We have activity without advance, diversity without development. Attempts at comprehensiveness end in the compromises of eclecticism.

Illustrations are not far to seek. Theophrastus and in general the elder Peripatetics, before the rise of new schools with new lines of cleavage and new interests had led to new antagonisms and new alliances, do not break away from the Aristotelian metaphysic. Their interests, however, lie in the sublunary The Peripatetics. sciences in which the substantive achievement of the school was to be found. With Theophrastus, accordingly, in his botanical inquiries, for example, the alternatives of classification, the normal sequence of such and such a character upon such another, the conclusion of rational probability, are what counts. It is perhaps not wholly fanciful to connect with this attitude the fact that Aristotle’s pupils dealt with a surer hand than the master with the

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1. Metaphys. M. 1087a 10-12; Zeller loc. cit. 304 sqq.; McLeod Innes, The Universal and Particular in Aristotle’s Theory of Knowledge (1886).
2. Topics, 105a 13.
3. Metaphys. 995a 8.
4. E.g., Topics, 108b 10, “to induce” the universal.
5. Posterior Analytics, ii. 19, 100b 3, 4.
6. Topics, i. 18, 108b 10.
7. Prior Analytics, ii. 23.
8. Παράδειγμα, Prior Analytics, ii. 24.
9. Sigwart, Logik, Eng. trans. vol. ii. p. 292 and elsewhere.
10. Ueberweg, System, § 127, with a ref. to de Partibus Animalium, 667a.
11. See 67a 17 ἐξ ἁπάντων τῶν ἀτόμων.