concepts of natural groups objectively regarded, to categories, to aesthetic and ethical ideals, to the concrete aims of the craftsman as well as to scientific laws-that have obscured his doctrine, viz. that wherever there is law, there is an idea. (b) The paradox of the one in the many is none, if the idea may be regarded assupplyingaprinciple of nexus or organization to an indefinite multiplicity of particulars. But if The oneln . .

me may Antisthenes IS to be answered, a further step must be taken. The principle of difference must be carried into the field of the ideas. Not only sense is a principle of difference. The ideas are many. 'The multiplicity in unity must be established within thought itself. .Otherwise the objection stands: man is man and good is good, but to say that man is good is clearly to say the thing that is not. Plato replies with the doctrine of the interpenetration of ideas, obviously not of all with all, but of some with some, the formula of identity in difference within thought itself. Nor can the opponent fairly refuse to admit it, if he affirms the participation of the identical with being, and denies the participation of difference with being, or affirms it with not-being. The Sap/:isles shows among other things that an identity-philosophy breaks down into a dualism of thought and expression, when it applies the predicate of unity to the real, just as the absolute pluralism on the other hand collapses into unity if it affirms or admits any form of relation whatsoever. Identity and difference are all-pervasive categories, and the speech-form and the corresponding thought-form involve both. For proposition and judgment involve subject and predicate and exhibit what a modern writer calls “identity of reference with diversity of characterization.” Plato proceeds to explain by his principle of difference both privatise and negative predicates, and also the possibility of false predication. It is obvious that without the principle of difference error is inexplicable. Even Plato, however, perhaps scarcely shows that with it, and nothing else but it, error is explained. (c) Plato's Division, or the articulation- of a relatively indeterminate and generic concept into species and sub-species with DMS, ” 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 development of that formula, though not, save very vaguely, the exhibition of it, negatively, in the antinomies of the one and the many in the Parmenidcs. It is its use, however, not the theory of it, that precedes. The latter is expounded in the Polificus (260 sqq.) and Philebus (160 sqq.). The ideal is progressively to determine a universe of discourse till true injimae 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. T he 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, notparts. The later examples of the Politicus show that the permission of three 'or more coordinate species is not nugatory, and that the precept of dichotomy is merely in order to secure as little of a sallus as possible; to avoid eg. the division of the animal world into men and brutes. It is the middle range of the /.iéaa of P/zilvbus 17a that appeals to Bacon, not only this but their mediating quality that appeals to Aristotle. The media axiomata of the one and the middle term of the other lie in the phrase. Plato's division is 'nevertheless neither syllogism nor exclusive. 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 concession for what it should prove.' Nor is it Bacon's method of exclusions, which escapes the imputation of being dialectical, if not that of being unduly cumbrous, 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

• Aristotle, An. Pr. i. 31, 46a 32 sqq.; cf. 9112 12 sqq.

Epicrates gives a picture of it at work.” And the movement of disjunction 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 inference has been made by so notable a modern logician as Lotze.

(d) T he 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 C bl use of examples, Plato represents it as the bringing HZ: M 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 compared 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, évrévyew, is to refer back, dvétq/env, ” 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 scattered 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) Back of Plato's illustration and explanation of predication and dialectical inference there lies not only the question of their metaphysical grounding in the iuterconnexion of ideas, but that of their epistemological presuppositions. g, :;j, fs, s This is dealt with in the Theaetetus (184b sqq.). The manifold affections of sense 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 instruments. It is this unity of apperception which enables us to combine the data of more than one sense, to afnrm 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 Kon/d, and describes them as developed by the soul in virtue of its own activity. They are objects of its reflection 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 mind5 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 or av})o'ytap6s6 in which knowledge consists. But as ideas,7 though of a type quite apartf 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 Sophisles, only motion and rest, the ultimate “kinds ” in the physical world, have no counterparts in the “categories ” of the T/zeaelelus. In his doctrine as to ev To vrotoiiv or Kp'€1/ov, as generally in that of the activity of the I/089 6:/ra0f]s, Aristotle in the de Animag is in the main but echoing the teaching of Plato.” Athenaeus ii. 596. See Usener, Organisation der wissenschaftl. Arbeit (1884; reprinted in his Vortrdge und Aufsdtze, 1907). 3 Socrates' reference of a discussion to its presuppositions (Xenophon, Mem. iv. 6, 13) is not relevant for the history of the terminology of induction.

4 Theaetetus, 186c.

Timaeus, 37a, b (quoted in H. F. Carlill's translation of the Theaetetus, p. 60).

5 T heaetetus, 186d. 7 Sophisles, 253d.-3

Ib. id.; cf. Theaetetus, 197d.

9 Aristotle, de An. 430b 5, and generally iii. 2, iii. 5. 1° For Plato's Logic, the controversies as to the genuineness of the dialogues may be treated summarily. The Theaetetus labours under no suspicion. The Sophisles is apparently matter for animadversion by Aristotle in the Metaphysics and elsewhere, but derives stronger support from the testimonies to the Politicus which presumes it. The Polilicus and Philebux are guaranteed by the use made of them in Aristotle's Ethics. The rejection of the Parmenides

'.'Ulllfl involve the paradox of a nameless contemporary of Plato