(c) Plato's Division, or the articulation of a relatively indeter minate and generic concept into species and sub-species with resultant determinate judgments, presumes of course the doctrine of the interpenetration of ideas laid down in the Sophistes, as the basis of predication, but its use precedes the positive develop ment of that formula, though not, save very vaguely, the exhibi tion of it, negatively, in the antinomies of the one and the many in the Parmenides. It is its use, however, not the theory of it that precedes. The latter is expounded in the Politicus (26o sqq.) and Philebus (16c sqq.). The ideal is progressively to determine a universe of discourse till true lowest species are reached when no further distinction in the determinate many is possible, though there is still the numerical difference of the indefinite plurality of particulars. The process is to take as far as possible the form of a continuous disjunction of contraries. We must bisect as far as may be, but the division is after all to be into limbs, not parts. The later examples of the Politicus show that the permission of three or more co-ordinate species is not nugatory, and that the precept of dichotomy is merely in order to secure as little of a saltus as possible ; to avoid, e.g., the division of the animal world into men and brutes. It is the middle range of the *a of Philebus, I 7a that appeals to Bacon, not only this but their medi ating quality that appeals to Aristotle. The mediate axioms of the one and the middle term of the other lie in the phrase. Plato's division is nevertheless neither syllogism nor method of exclu sions. It is not syllogism because it is based on the disjunctive, not on the hypothetical relation, and so extends horizontally where syllogism strikes vertically downward. Again it is not syllogism because it is necessarily and finally dialectical. It brings in the choice of an interlocutor at each stage, and so depends on a con cession for what it should prove. Nor is it Bacon's method of ex clusions which escapes the imputation of being dialectical, if not that of being unduly combrous, in virtue of the cogency of the negative instance. The Platonic division was, however, offered as the scientific method of the school. A fragment of the comic poet Epicrates gives a picture of it at work. And the movement of dis junction as truly has a place in the scientific specification of a concept in all its differences as the linking of lower to higher in syllogism. The two are complementary, and the reinstatement of the disjunctive judgment to the more honourable role in infer ence has been made by so notable a modern logician as Lotze.
(d) The correlative process of Combination is less elaborately sketched, but in a luminous passage in the Politicus (§ 278), in explaining by means of an example the nature and use of ex amples, Plato represents it as the bringing of one and the same element seen in diverse settings to conscious realization, with the result that it is viewed as a single truth of which the terms com pared are now accepted as the differences. The learner is to be led forward to the unknown by being made to hark back to more familiar groupings of the alphabet of nature which he is coming to recognize with some certainty. To lead on, 7r-evyctv, is to refer back, avo.yety to what has been correctly divined of the same elements in clearer cases. Introduction to unfamiliar collocations follows upon this, and only so is it possible finally to gather scat tered examples into a conspectus as instances of one idea or law. This is not only of importance in the history of the terminology of logic, but supplies a philosophy of induction.
(e) Behind Plato's illustration and explanation of predication and dialectical inference there lies not only the question of their metaphysical grounding in the interconnection of ideas, but that of their epistemological presuppositions. This is dealt with in the
Theaetetus (184b sqq.). The manifold affections of senses are not simply aggregated in the individual, like the heroes in the Trojan horse. There must be convergence in a unitary principle, soul or consciousness, which is that which really functions in perception, the senses and their organs being merely its instru ments. It is this unity of apperception which enables us to corn bine the data of more than one sense, to affirm reality, unreality, identity, difference, unity, plurality and so forth, as also the good, the beautiful and their contraries. Plato calls these pervasive factors in knowledge Kot.v6, and describes them as developed by the soul in virtue of its own activity. They are objects of its reflec tion and made explicit in the few with pains and gradually. That they are not, however, psychological or acquired categories, due to "the workmanship of the mind" as conceived by Locke, is obvious from their attribution to the structure of mind and from their correlation with immanent principles of the objective order. Considered from the epistemological point of view, they are the implicit presuppositions of the construction in which knowledge consists. But as ideas, though of a type quite apart, they have also a constitutive application to reality. Accordingly, of the selected "kinds" by means of which the interpenetration of ideas is expounded in the Sophistes, only motion and rest, the ultimate "kinds" in the physical world, have no counterparts in the "cate gories" of the Theaetetus.
(I) The Categories, on names signifying things which can become predicates; (2) De Interpratione, on the enumeration of concep tions and their combinations by names and propositions; (3) The Prior Analytics, on syllogism; (4) The Posterior Analytics, on demonstrative syllogism; (5) The Topics, on dialectical syllogism, or argument ; (6) The Sophistical Elenchi, on sophistical or con tentious syllogism, or sophistical fallacies. Aristotle does not appear to have had any one name for all these investigations. But his followers called this collection of treatises the Organon (The Instrument, that is, of Knowledge), and from it there emerged gradually a system of Logic. Their production as rela tively self-contained treatises accounts for the absence of a precise definition of their field of enquiry. And this original lack of precision in the delimitation of the scope of Logic haunts the sub ject to this day. Aristotle gave no clear intimation as to the rela tion in which he supposed this field of enquiry to stand to other disciplines. In his definite classification of the sciences, into First Philosophy, Mathematics and Physics, it has no place. Its axioms, such as the law of contradiction, belong to first philosophy, but the doctrine as a whole falls neither under this head nor yet, though the thought has been entertained, under that of mathe matics, since logic orders mathematical reasoning as well as all other. The speculative sciences, indeed, are classified according to their relation to form, pure, abstract or concrete, i.e., according to their object. The logical enquiry seems to be conceived as dealing with the thought of which the objects are objects. It is to be regarded as a propaedeutic, which although it is in contact with reality in and through the metaphysical import of the axioms or again in the fact that the categories, though primarily taken as forms of predication, must also be regarded as kinds of being, is not directly concerned with object-reality, but with the determination for the thinking subject of what constitutes the knowledge correlative to being. Logic, therefore, is not classed as one, still less a branch of one, among the 'ologies, ontology not excepted.