Three points obviously need development, the nature of defini tion, its connection with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.
Definition is either of the subject-kind or of the property that is grounded in it. Of the self-subsistent, definition is by exposition of genus and differentia. It is indemonstrable. It presumes the reality of its subject in a postulate of existence. It belongs to the principles of demonstration. Highest genera and groups below lowest species are indefinable. The former are susceptible of elucidation by indication of what falls under them. The latter are only describable by their accidents. There can here be no true differentia. The artificiality of the limit to the articulation of species was one of the points to which the downfall of Aris totle's influence was largely due. Of a non-self-subsistent or attributive conception definition in its highest attainable form is a recasting of the syllogism, in which it was shown that the attri bute was grounded in the substance of the self-subsistent subject of which it is predicated. Eclipse of the moon, e.g., is a privation of light from the moon by the interposition of the earth between it and the sun. In the scientific syllogism the interposition of the earth is the middle term, the cause or "because"; the residue of the definition is conclusion. The difference, then, is in verbal expression, way of putting, inflexion. If we pluck the fruit of the conclusion, severing its nexus with the stock from which it springs, we have an imperfect form of definition, while, if further we abandon all idea of making it adequate by exhibition of it: ground, we have, with still the same form of words, a definition merely nominal or lexicographical.
The rest is a consideration of scientific inquiry as converging in the investigation of the link or "because" as ground in the nature of things. Real ground and thought-link fall together. The advance from syllogism as formal implication is a notable one. It is not enough to have for middle term a causa cognoscendi merely. We must have a causa essendi. The planets are near, and we know it by their not twinkling, but science must conceive their nearness as the cause of their not twinkling and make the Arius in the real order of the middle term of its syllogism. In this irreversible catena proceeding from ground to consequent, we have left far behind such things as the formal parity of genus and differentia considered as falling under the same predicable, and hence justified in part Porphyry's divergence from the scheme of predicables. We need devices, indeed, to determine priority or superior claim to be "better known absolutely or in the order of nature," but on the whole the problem is fairly faced.
Of science Aristotle takes for his examples sometimes celestial physics, more often geometry or arithmetic, sometimes a con crete science, e.g., botany. In the field of pure form, free from the disconcerting surprises of sensible matter and so a field of absolute necessity, no difficulty arises as to the deducibility of the whole body of a science from its first principles. In the sphere of abstract form, mathematics, the like may be allowed, abstraction being treated as an elimination of matter from the oi)voXoy by one act. When we take into account relative matter, however, and traces of a conception of abstraction as admitting of de gree, the question is not free from difficulty. In the sphere of the concrete sciences where law obtains only cis E7ri To roXi, this ideal of science can clearly find only a relative satisfaction with large reserves. In any case, however, the problem as to first principles remains fundamental.
If we reject the infinite regress and the circle in proof (circulus in probando) which resolves itself ultimately into proving A by B and B by A, we are confronted by the need for principles of two kinds, those which condition all search for truth and those which are the peculiar or proper principles of special sciences, their "positions," viz., the definitions of their subjects and the postulates of the existence of these. All are indemonstrable and cannot be less sure than the body of doctrine that flows from them. They must indeed be recognized as true, primary, causative and the like. But they are not congenitally present in the indi vidual in a determinate shape. The doctrine of latency is mys tical and savours of Plato's reminiscence. Yet they must have something to develop from, and thereupon Aristotle gives an account of a process in the psychological mechanism which he illustrates by comparative psychology, wherein a X6-yos or mean ing emerges, a "first" universal recognized by induction. Yet PoOs, intelligence, is the principle of first principles. It is infallible, while, whatever the case with perception of the special sensibles, the process which combines particulars is not. On the side of induction we find that experience is said to give the specific prin ciples, "the phenomena being apprehended in sufficiency." On the side of intuition, self-evidence of scientific principles is spoken of. Yet dialectic is auxiliary and of methodological im portance in their establishment. Mutually limiting statements occur almost or quite side by side. We cannot take first principles "as the bare precipitate of a progressively refined analysis" nor on the other as constitutive a priori forms. The solution seems to lie in the conception of a process that has a double aspect. On the one hand we have confrontation with fact, in which, in virtue of the rational principle which is the final cause of the phenomenal order, intelligence will find satisfaction. On the other, we have a stage at which the rational but as yet not reasoned concepts developed in the medium of the psychological mechanism are subject to processes of reflective comparison and analysis, and, with some modification, maintained against chal lenge, till at length the ultimate universals emerge, which rational insight can posit as certain, and the whole hierarchy of concepts from the "first" universals to ra are intuited in a co herent system. Aristotle's terminology is highly technical, but, as has often been observed, not therefore clear. Here two words at least are ambiguous, "principle" and "induction." By the first he means any starting-point, "that from which the matter in question is primarily to be known," particular facts, therefore, premises and what not. What, then, is meant by principles when we ask in the closing chapter of his logic how they become known? The data of sense are clearly not the principles in question here. The premises of scientific syllogisms may equally
be dismissed. Where they are not derivative they clearly are definitions or immediate transcripts from definitions. There re main, then, primary definitions and the postulates of their real ization, and the axioms or common principles "which he must needs have who is to reach any knowledge." In the case of the former, special each to its own science, Aristotle may be thought to hold that they are the product of the psychological mechanism, but are ascertained only when they have faced the fire of a critical dialectic and have been accepted from the point of view of the integral rationality of the system of concepts. Axioms, on the other hand, in which the sciences inter-connect through the employment of them in a parity of relation, seem to be implicit indeed in the psychological mechanism, but to come to a kind of explicitness in the first reflective reaction upon it, and without reference to any particular content of it. They are not to be used as premises but as immanent laws of thought, save only when an inference from true or admitted premises and correct in form is challenged. The challenge must be countered in a re ductio ad impossibile in which the dilemma is put. Either this conclusion or the denial of rationality. Even these principles, however, may get a greater explicitness by dialectical treatment. The relation, then, of the two orders of principle to the psycho logical mechanism is different. The kind of warrant that intelli gence can give to specific principles falls short of infallibility. Celestial physics, with its pure forms and void of all matter save extension, is not such an exemplary science after all. Rationality is continuous throughout. A Xbyos emerges with some beings in direct sequence upon the persistence of impressions. Sense is of the "first" universal, the form, though not of the ultimate universal. The rally from the rout in Aristotle's famous metaphor is of units that already belong together, that are of the same regiment or order. On the other hand, rationality has two stages. In the one it is relatively immersed in sense, in the other rela tively free. The same break is to be found in the conception of the relation of receptive to active mind in the treatise Of the Soul. The one is impressed by things and receives their form without their matter. The other is free from impression. It thinks its system of concepts freely on the occasion of the affections of the receptivity. Aristotle is fond of declaring that knowledge is of the universal, while existence or reality is indi vidual. It seems to follow that the cleavage between knowledge and reality is not bridged by the function of thought in relation to "induction." What is known is not real, and what is real is not known. It is in induction, which claims to start from par ticulars and end in universals, 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 the Platonic sense of the corresponding verb, viz., to lead forward to the as yet unknown, and his substitute is not quite clear. Perhaps con frontation 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. 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" whose liability to rebuttal by an exception has been already noted in connection 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 syl logism, a syllogism in the third figure concluding universally, and yet valid because the copula expresses equivalence, and in analogy in which instances are weighed and not counted. In the former Aristotle's illustration does not combine particular facts into a lowest concept, but specific concepts into a generic concept, and 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 interpreta tion that dialectical induction struggling with instances is f or mally justified only at the limit, and this, where we have ex hausted 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 van 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. He laid down the programme which the after history of logic was to carry out.
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 inter vening centuries had the Aristotelian basis to work on, that the rest of our logical tradition is what it is. We stand upon his shoulders.