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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 as supplying a principle of nexus or organization to an indefinite multiplicity of particulars. But if Antisthenes is to be answered, a further step must be taken. The principle of difference must be carried The one in the many. 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 Sophistes 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 privative 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 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 Division. 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 Parmenides. It is its use, however, not the theory of it, that precedes. The latter is expounded in the Politicus (260 sqq.) and Philebus (16c sqq.). The ideal is progressively to determine a universe of discourse till true infimae 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 μέσα of Philebus 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 exclusiva. 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.^[1] 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 Epicrates gives a picture of it at work.^[2] 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 rôle in inference 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 examples, Plato represents it as the bringing of one and the same element seen in diverse settings to Combination. 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, ἐπάγειν, is to refer back, ἀνάγειν,^[3] 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 interconnexion of ideas, but that of their epistemological presuppositions. Mental synthesis. 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 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 κοινὰ, 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.^[4] 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^[5] 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 συλλογισμός^[6] in which knowledge consists. But as ideas,^[7] though of a type quite apart,^[8] 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 “categories” of the Theaetetus. In his doctrine as to ἕν τὸ ποιοῦν or κρῖνον, as generally in that of the activity of the νοῦς ἀπαθής, Aristotle in the de Anima^[9] is in the main but echoing the teaching of Plato.^[10]

1. Aristotle, An. Pr. i. 31, 46a 32 sqq.; cf. 91b 12 sqq.
2. Athenaeus ii. 59c. See Usener, Organisation der wissenschaftl. Arbeit (1884; reprinted in his Vorträge und Aufsätze, 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.
5. Timaeus, 37a, b (quoted in H. F. Carlill’s translation of the Theaetetus, p. 60).
6. Theaetetus, 186d.
7. Sophistes, 253d.
8. Ib. id.; cf. Theaetetus, 197d.
9. Aristotle, de An. 430b 5, and generally iii. 2, iii. 5.
10. For Plato’s Logic, the controversies as to the genuineness of the dialogues may be treated summarily. The Theaetetus labours under no suspicion. The Sophistes 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 Politicus and Philebus are guaranteed by the use made of them in Aristotle’s Ethics. The rejection of the Parmenides would involve the paradox of a nameless contemporary of Plato and Aristotle who was inferior as a metaphysician to neither. No other dialogue adds anything to the logical content of these. Granted their genuineness, the relative dating of three of them is given, viz. Theaetetus, Sophistes and Politicus in the order named. The Philebus seems to presuppose Politicus, 283-284, but if this be an error, it will affect the logical theory not at all. There remains the Parmenides. It can scarcely be later than the Sophistes. The antinomies with which it concludes are more naturally taken as a prelude to the discussion of the Sophistes than as an unnecessary retreatment of the doctrine of the one and the many in a more negative form. It may well be earlier than the Theaetetus in its present form. The stylistic argument shows the Theaetetus relatively early. The maturity of its philosophic outlook tends to give it a place relatively advanced in the Platonic canon. To meet the problem here raised, the theory has been devised of an earlier and a later version. The first may have linked on to the series of Plato’s dialogues of search, and to put the Parmenides before it is impossible. The second, though it might still have preceded the Parmenides might equally well have followed the negative criticism of that dialogue, as the beginning of reconstruction. For Plato’s logic this question only has interest on account of the introduction of an Ἀριστοτέλης in a non-speaking part in the Parmenides. If this be pressed as suggesting that the philosopher Aristotle was already in full activity at the date of writing, it is of importance to know what Platonic dialogues were later than the début of his critical pupil. On the stylistic argument as applied to Platonic controversies Janell’s Quaestiones Platonicae (1901) is important. On the whole question of genuineness and dates of the dialogues, H. Raeder, Platons philosophische Entwickelung (1905), gives an excellent conspectus of the views held and the grounds alleged. See also Plato.