the art of Dialectic, which he also seeks to explain in actual thinking (1) to collect together into one form what appears scattered everywhere, in order to determine strictly each single one (Phaedr. p. 266, the mode of forming the notion by Abstraction and Definition), and in this way by the same manner to ascend further to higher notions, until the very highest is reached; (2) then to descend again from the higher notions to the lower, which are subordinate to it, to be able to distinguish how each individual has grown by means of the notions of the kinds' (Phaedrus, 1. i.—Division), and to examine what proceeds from the presuppositions laid down as a basis (Phaedon, 101-Deduction), in order to follow it out to the last consequences. Real essences correspond to the notions, rightly constructed, by which they are known, the ideas, and these separate into the graduated series which the notions have, from the lower up to the absolutely highest, the idea of the Good.2 Mathematics proceeds from postulates which are not the highest. Dialectic uses these said postulates as the basis on which to rear its ideal principles. Mathematics takes the opposite course, and derives from its postulates individuals and particulars. For this reason, mathematical knowledge takes a position between pure thought and sense-perception, and the objects of Mathematics are intermediate existences between ideas and sensible things. Since Plato distinguished in sense-knowledge between the trust in sense-perception and mere conjecture, and, in a corresponding way, in sensible objects between things perceived in sense and pictures or shadows, he arrives at the following division of ways of knowing:

Νόησις

ἐπιστήμη | διάνοια

Δόξα

πίστις

εἰκασία,

and at the following analogous division of the whole of exist

It is not only characteristic of Plato's method that he carries on together investigations into thinking and into what is thought about; it is also the peculiarity of the content of his doctrine that he transfers the whole relation of his forms of thought to the objects thought about. With him the logical and the metaphysical stand in a very close relation, and almost in immediate unity. (Yet he does not proceed to identify them.)

§ 15. Plato's followers in the Academy felt the need of a stricter systematic form for the purpose of a connected exposition of doctrines. Hence Speusippus was induced to divide the sciences in general, and Xenokrates the philosophical disciplines in particular. Xenokrates was the first to enunciate expressly the division of Philosophy into Physics, Ethics, and Dialectic. The second and third Academic Schools in the so-called Intermediate Academy, founded by Arkesilaus and Karneades, inclined to scepticism; the fourth and fifth, founded by Philo and Antiochus of Askalon, inclined to dogmatism and syncretism.

For Speusippus s. Diog. Laërt. iv. 2: ovтos πρŵτOS ÉV TOîs μαθήμασιν ἐθεάσατο τὸ κοινὸν καὶ συνῳκείωσε καθόσον ἦν δυνατὸν aλλýλois. For Xenokrates s. Sext. Empir. adv. Math. vii. 16: ὧν δυνάμει μὲν Πλάτων ἐστὶν ἀρχηγός, περὶ πολλῶν μὲν φυσικῶν, περὶ πολλῶν δὲ ἠθικῶν, οὐκ ὀλίγων δὲ λογικῶν διαλεχθείς ῥητότατα δὲ οἱ περὶ τὸν Ξενοκράτη καὶ οἱ ἀπὸ τοῦ Περιπάτου, ἔτι δὲ οἱ ἀπὸ τῆς Στοᾶς ἔχονται τῆσδε τῆς διαιρέσεως. For Karneades, who allowed no criterion of truth, but enunciated the doctrine of probability, s. Sext. Empir. adv. Math. vii. 159 sqq.; 166 sqq. For Philo Cic. Acad. pr. ii. 6: and for Antiochus, Cic. ib. ii. 6-18, 43.

§ 16. Aristotle (384-322 B.C.) established his theory of Logic, as he did every branch of his system, on

the foundation laid by Plato. But his peculiar service is: (a) his critical remodelling of Plato's logical doctrines; (b) their development; and (c) their systematic representation. The critical remodelling consists, in general, in this, that Aristotle sought to define more strictly the relation of the logical and metaphysical elements. The development belonged to every part of Logic; but, more especially, Aristotle created the theory of syllogism, which before him had scarcely been worked at. The systematic division extended equally to the representation of the whole, and of individual parts. Aristotle dedicated special treatises to the whole of the chief parts of Logic as the doctrine of thinking, and has given a strict scientific form to each one of them. For this service he has been rightly called the Father of Logic as a science. Aristotle collects together the most important part of his logical investigationsthe doctrine of inference and proof-under the title Analytic, because the logical structure of thought is here as it were analysed, i.e. separated and reduced to its elements. He does not give one common name to all the parts. His successors and commentators called his collected logical writings the Organon. Dialectic with Aristotle is the art of the critical raris of a thesis, or proceeding from propositions which are held to be true, but are doubtful, to derive conclusions, in order to get at some decision upon their truth or falsehood. The propositions it deals with are mainly probable (vòoža). Logical means with Aristotle the explanation of mere general notions (ayois), after the manner of Sokrates and Plato, in opposition to physical treatment, which

has to do with the specific and individual qualities. The science which is represented in the Organon was called Logic by the Stoics and by some of the commentators of Aristotle.

The Aristotelian remodelling of the Platonic doctrines cannot be understood, although modern writers have often so misunderstood it, in the sense that Aristotle considered the form of thought without any reference to objective reality. The standpoint of the Aristotelian is by no means identical with that of the modern Subjective-formal Logic. This has been proved by Ritter,' Trendelenburg,2 Zeller,3 Bonitz, Brandis (although he accepts an essential relationship between the Aristotelian and the modern Formal Logic), and by Prantl. Aristotle finds the standard of truth, as Plato had, in the agreement of thought with what actually exists, which is the limit of science. The notion, rightly formed, corresponds, according to Aristotle, to the essence of the thing (ovoía or тò tí v ɛivai, cf. § 56); the judgment is an assertion about an existence or a non-existence; affirmation and negation correspond to union and separation in things; the different forms which the notions take in the judgment (or the kinds of denotation of existences, oxματα τῆς κατηγορίας τῶν ὄντων) determine themselves according to the forms of existence; the middle term in a syllogism correctly constructed corresponds to the cause in the connected series of real events; the principles of scientific knowledge correspond to what is actually the first in the nature of things. Aristotle gives to the whole of his logical investigations the

In his Geschichte der Philos. iii. 117 ff. 1831.

2 In his Logischen Untersuchungen, 1st ed. 18-21, 1840; 2nd and 3rd ed. 30-33, 1862, 1870; cf. Elem. log. Arist. 6th ed. 1868, ad § 63. 3 Philos. der Griechen, ii. 373 ff., 1846; 2nd ed. ii. 2, 131 ff., 1860. 4 Commentar zur Arist. Metaph. 187, 1849.

5 Gesch. der Gr.-R. Phil. ii. 2nd ed. 371 ff.; 432 ff., 1853.

6 Gesch. der Logik, i. 87 ff.; 104 ff.; 135, 1855.

7 Metaph. iv. 7; ix. 10; x. 6; cf. Categ. 12, 14 B. 21: Tậ yàp εἶναι τὸ πρᾶγμα ἢ μὴ ἀληθῆς ὁ λόγος ἢ ψευδὴς λέγεται.

name Analytic (τà ávaλutíká), i.e. the analysis of thought (not the doctrine of merely analytic thinking), and desires that every one will first make himself familiar with it before he proceeds to study the First Philosophy or Metaphysic.'

With regard to the single logical writings, the book De Categoriis, περὶ κατηγοριών (whose authenticity is not quite undoubted; perhaps caps. x.-xv. have been inserted by a stranger), treats of the forms of notions and of the corresponding forms of existence. The book De Interpretatione, Tepi Eρunveías (whose authenticity was doubted by Andronikus of Rhodes), treats of the proposition and judgment. The two books Analytica Priora, ávaλuTкà πρóтEрa, treat of inference. The two books Analytica Posteriora, αναλυτικὰ ὕστερα, treat of proof, definition and division, and the knowledge of principles. The eight books of the Topica, TожIKά, treat of dialectical or probable inferences. Lastly, the book De Elenchis Sophisticis, περὶ σοφιστικῶν ἐλέγχων, treats of the deceptive inferences of the Sophists and of their solution. The best new collected edition of these writings is Aristotelis Organon, ed. Theod. Waitz. Trendelenburg's Elementa Logices Aristoteleae is a very good help to the study of the chief doctrines of Aristotle's Organon. For a wider and more thorough-going acquaintance, the student may be referred to the well-known historical work of Prantl, Geschichte der Logik, and more especially to the representation of the Aristotelian philosophy given by Brandis in his Handbuch der Geschichte der Griech.-Röm. Philos. ii., 2nd pt., 1853. Biese (Die Philosophie des Arist. Logik und Metaphysik, 1835) may also be consulted. For the meaning of the expressions Analytic and Dialectic in Aristotle, sec Trendelenburg, Elem. Arist., Int. and § 33; and Charles Thurot, Études sur Aristote, Paris, 1860, p. 118 ff. For the meaning of Aoyikós, see Waitz ad Organon Arist. 82 B, 35 ; Schwegler ad Arist. Metaph. vii. 4; xi. 10; Prantl, Geschichte der Logik, i. 535 f. Aristotle refers the Aoyik@s

1 Metaph. iv. 3; vii. 12.

3

3 Berol. 1836, 5th ed. 1862.

Ꭰ .