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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 its ground, we have, with still the same form of words, a definition merely nominal or lexicographical. In the aporematic treatment of the relation of definition and syllogism identical as to one form and in one view, distinct as to another form and in another view, much of Aristotle’s discussion consists. The middle term. The rest is a consideration of scientific inquiry as converging in μέσου ζήτησις, the investigation of the link or “because” as ground in the nature of things. Τὸ μὲν γὰρ αἴτιον τὸ μέσον^[1] 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,^[2] but science must conceive their nearness as the cause of their not twinkling and make the prius in the real order 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,^[3] 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.^[4]

Of science Aristotle takes for his examples sometimes celestial physics, more often geometry or arithmetic, sometimes a concrete science, e.g. botany.^[5] In the field of pure form, free from the disconcerting surprises of sensible matter and so 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 σύνολον by one act. When we take into account relative matter, however, and traces of a conception of abstraction as admitting of degree,^[6] the question is not free from difficulty. In the sphere of the concrete sciences where law obtains only ὡς ἐπὶ τὸ πολὺ 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,^[7] 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 Formal and scientific principles. 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^[8] they are not congenitally present in the individual in a determinate shape. The doctrine of latency is mystical and savours of Plato’s reminiscence (anamnesis). 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 λόγος or meaning emerges, Induction and dialectic. a “first” universal recognized by induction. Yet νοῦς, intelligence, is the principle of first principles. It is infallible, while, whatever the case with perception of the special sensibles,^[9] the process which combines particulars is not. On the side of induction we find that experience is said to give the specific principles,^[10] “the phenomena being apprehended in sufficiency.” On the side of intuition, self-evidence of scientific principles is spoken of.^[11] Yet dialectic is auxiliary and of methodological importance in their establishment.^[12] Mutually limiting statements occur almost or quite side by side. We cannot take first principles “as the bare precipitate of a progressively refined analysis”^[13] 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 subjected to processes of reflective comparison and analysis, and, with some modification, maintained against challenge, 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 τὰ ἀμερῆ are intuited in a coherent 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,”^[14] 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 remain, then, primary definitions and the postulates of their realization, and the axioms or common principles, “which he must needs have who is to reach any knowledge.”^[15] 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 interconnect^[16] 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 reductio 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.^[17] The relation, then, of the two orders of principle to the psychological mechanism is different. The kind of warrant that intelligence 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 λόγος emerges with some beings in direct sequence upon the persistence of impressions.^[18] 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 relatively 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.^[19] 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 individual. It seems to follow that the cleavage between knowledge and reality

1. 90a 6. Cf. Ueberweg, System der Logik, § 101.
2. 78a 30 sqq.
3. Topics, 101b 18, 19.
4. Posterior Analytics, ii. 13.
5. Posterior Analytics, ii. 16.
6. Posterior Analytics, i. 13 ad. fin., and i. 27. The form which a mathematical science treats as relatively self-subsistent is certainly not the constitutive idea.
7. Posterior Analytics, i. 3.
8. Posterior Analytics, ii. 19.
9. De Anima, 428b 18, 19.
10. Prior Analytics, i. 30, 46a 18.
11. Topics, 100b 20, 21.
12. Topics, 101a 25, 36-37, b1-4, &c.
13. Zeller (loc. cit. p. 194), who puts this formula in order to reject it.
14. Metaphys. Δ 1, 1013a 14.
15. Posterior Analytics, 72a 16 seq.
16. Posterior Analytics, 77a 26, 76a 37 sqq.
17. Metaphys. Γ.
18. Posterior Analytics, ii. 19.
19. de Anima, iii. 4-6.