§ 9. The History of Logic has worth and meaning in a double relation: (a) for its own sake, inasmuch as it brings clearly before us the ever-ongoing struggle of the human mind to obtain an understanding of the laws of its thinking and knowing; (b.) as a mean to understand the present position of Logic, since it informs us of the genesis both of the parts scientifically certain, and of the diverse opinions prevailing at present. Of the works which treat of the general history of Logic, the most complete and thoroughgoing is the Geschichte der Logik im Abendlande, by C. Prantl, 1st vol. (containing the development of Logic among the ancients), Leipzig, 1855, 2nd vol. (referring to the first half of the Middle Ages), do., 1861, 3rd vol., do., 1867, and 4th vol., do., 1870 (referring to the latter half of the Middle Ages). § 10. The foundation of Logic as a science is a work of the Greek mind, which, equally removed from the hardness of the Northern and the softness of the Oriental, harmoniously united power and impressibility. : For its general characteristic, cf. Plato, De Republ. iv. 435 E (ed. Steph.), and Arist. Polit. vii. 7. The impressible fancy of the Oriental has not the measure nor grip of strong thinking it wants the mental power of the genuinely scientific mind. In its attempts to philosophise it is not ruled by the tendency to strict demonstration and to representation in a scientific form; and where the art of strictly scientific thinking is absent, the theory can still less develope itself. Yet some true, deep fundamental thoughts appeared which, if they had been consistently followed out, would have served very well to be a foundation of a system of Logic. Thus the Chinese Meng-tse, a disciple of Kon-fu-tse, says, 'The human mind has in itself the possibility of knowing all things; it must therefore look to its own nature and essence, otherwise it errs. Only the virtuous can fathom his own essence: he who has fathomed his own nature can also know that of other men, he can fathom the essence of things.' According to this writer the general original power of reason shows itself in man as the law of duty.' Among the Hindoos we find, in the philosophies of the Sankhya and the Nyaya, an enumeration of the kinds and objects of knowledge. The three ways of obtaining knowledge, according to the Sankhya doctrine, are, (1) Perception; (2) Conclusion (from the cause to the effect and from the effect to the cause, and also by analogy); and (3) Tradition (by human testimony and Divine revelation): the Nyaya adds Comparison. The Nyaya, which perhaps first arose under Greek influence, recognises the syllogism Nyaya (from which the system takes its name) in the form of five propositions, which arise out of the three propositions by the repetition of the minor premise and conclusion, according to the following scheme:— Thesis-The hill is fiery. Proof-What smokes is fiery. Reason-For it smokes. Application-The hill smokes. Conclusion-It is fiery." It is very doubtful whether the Egyptians constructed a logical theory. Plato praises the antiquity of their knowledge, but by no means the elevation of their philosophy. The Greek thinkers, even if acquainted with Egyptian wisdom, had to find out for themselves both the fundamental doctrines of Logic and the proofs of the elementary propositions in Geometry. The Greeks have undoubtedly learned much of the material of their knowledge from the Egyptians, and from the Orientals generally. The Greek mind may have needed an impulse from without for its development, but it owes to its own inborn independent power, not to foreigners, what is the more essential, its scientific and artistic form, however actively impressible it may have made their treasures its own. Cf. Hegel,3 From 1 Cf. Wuttke, Das Heidenthum (Breslau, 1853), ii. 102. 2 [Cf. Colebrooke's Misc. Essays, i. 8, and the Aphorisms of the Nyúga Philos., by Gautama, Allahabad, 1850.] 3 Philos. der Geschichte, 1837, p. 216. what they have naturally received the Greeks have created the spiritual.' The assertion of Lepsius agrees also with this:' The Greeks of this great period (Thales, Pythagoras, &c.) collected the learning of the barbarians of all regions as ripe corn to the threshing-floor, to be new seed for their own fertile soil.' § 11. The speculation of the older Ionic natural philosophers (in the sixth century B.C.)-of Thales, Anaximander, Anaximenes-was immediately directed to things only, not to the human knowledge of things. The later natural philosophers (in the fifth century B.C.) -Heraklitus, Anaxagoras, Leukippus, and Demokritusshowed that sense-perception as such was not trustworthy. It is the reason mingled with it, and going all through it, which decides what truth is. Empedocles taught that things and man came from the same material and ideal elements, and that like is known by like. The Pythagoreans held that the elements of number, limit and the limitless, are the elements of all objects. They seek therefore, by means of mathematical investigation and speculation on numbers, to get at all knowledge. Xenophanes of Colophon, the founder of the Eleatic philosophy, led on by his theological speculation, distinguished certain knowledge from accidentally correct opinion. His immediate follower, Parmenides, the most developed of the Eleatic philosophers, in his polemic against the Heraklitic doctrine of the universal flow of all things, and of the identity of contradictories, first reaches the theoretic consciousness of the axioms of identity and contradiction, although as yet in an incomplete form. Similarly, Parmenides taught the identity of thought with the exist 1 Chronologie der Aegypter, i. 55. ence which is thought. He set in strict opposition to opinion about the multiplicity and change of what exists, resting on the deception of the senses, the knowledge of the One, which is truth, able to produce conviction, and attained by means of thinking. His young contemporary, Zeno the Eleatic, was the first to use in its strict form the art of managing philosophical dialogue, especially the art of indirect proof. Hence Aristotle calls him the founder of Dialectic. Heraklitus in Sext. Empir. adv. Math. vii. 126: Kakoi μάρτυρες ἀνθρώποισιν ὀφθαλμοὶ καὶ ὦτα, βορβόρου ψυχὰς EXOVTOS (according to the conjecture of Jac. Bernays; commonly: Bapßápovs ↓vxàs ¿xóvτwv). In Diog. Laert. ix. 1: Πολυμαθίη νόον οὐ διδάσκει. . ἓν τὸ σοφόν· ἐπίστασθαι γνώμην, ἥτε οἰακίζει (according to the conjecture of Bernays; commonly: ἦτε οἱ ἐγκυβερνήσει, Schleiem. ἥτε οἴη κυβερνήσει) πάντα διὰ πάντων. Yet the thinking through which wisdom is attained is, according to the view of Heraklitus, not so much an activity of the mind separable from sense-perception, and opposed to it, but rather the sense lying open and submitting itself to the universal all-ruling reason, while its isolation produces error.' Anaxagoras in Sext. Emp. adv. Math. vii. 90: vπò àþаνρότητος αὐτῶν (τῶν αἰσθήσεων) οὐ δυνατοί ἐσμεν κρίνειν τἀληθές. According to Anaxagoras, the divine reason knows all things, and the human is homogeneous with it: πάντα ἔγνω νόος-νέος δὲ πᾶς ὁμοῖος ἐστι καὶ ὁ μείζων καὶ ὁ ἐλάσσων. Demokritus, Sext. Emp. adv. Math. p. 138, informs us, divided knowledge into what is attained through sense-perception, and what through the understanding. The former he calls the dark (Korin), the latter the genuine (noin). Demokritus says (p. 140) that the work of the avvola is Zýτnois, the investigation of the unknown upon the ground of the sense-phe1 Cf. Sext. Emp. adv. Math. vii. 129. 2 In Simplic. in Arist. Phys. fol. 39 sqq. nomena. Yet this thinking warrants only relatively a higher certainty. Man has no science in the strict sense of the word. Demokritus in Diog. Laërt. ix. 72: ἐτεῇ δὲ οὐδὲν ἴδμεν· ἐν βυθῷ γὰρ ἡ ἀλήθεια.—Empedokles in Aristot. de Anima, i. 2: γαίῃ μὲν γὰρ γαῖαν ἐπώπαμεν, ὕδατι δ ̓ ὕδωρ, αἰθέρι δ' αἰθέρα δῖον, ἀτὰρ πυρὶ πῦρ ἀΐδηλον, στοργῇ δὲ στοργήν, νεῖκος δέ τε νείκεϊ λυγρῷ. The doctrines of the early Pythagoreans are not accessible to us as they themselves represented them, since the writing ascribed to Philolaus,' which gave us access to many fragments, cannot be held to be genuine according to the investigations of Schaarschmidt.2 We can only trust to a sketch given by Aristotle. Quotations such as the following are valuable only as bearing witness to the tendency of the later Pythagorean philosophy:-Pseudo-Philolaus in Stob. Εclog. i. 2, 3:4 οὐ γὰρ ἦς δῆλον οὐθενὶ οὐθὲν τῶν πραγμάτων, οὔτε αὐτῶν ποθ' (πρὸς) αὑτὰ οὔτε ἄλλω ποτ ̓ ἄλλο, εἰ μὴ ἧς ἀριθμὸς καὶ ἡ τούτω ἐσσία. Νῦν δὲ οὗτος κατὰ τὴν ψυχὴν ἁρμόζων αἰσθήσει πάντα γνωστὰ καὶ ποτάγορα (i.e. προσήγορα, corresponding to and connected by friendship) ἀλλάλοις ἀπεργάζεται. In Sext. Emp. adv. Math. vii. 92:5 ὑπὸ τοῦ ὁμοίου τὸ ὅμοιον καταλαμβάνεσθαι πέφυκεν. Xenophanes in Sext. Emp. adv. Math. vii. 49; 110; viii. 326 : καὶ τὸ μὲν οὖν σαφὲς οὔτις ἀνὴρ ἴδεν οὐδέ τις ἔσται Parmenides enunciates the axiom of Identity, in the metaphysical sense, in the words: ἔστιν or ἔστι γὰρ εἶναι, and the axiom of Contradiction in the words: οὐκ ἔστι μὴ εἶναι οι μηδὲν δ' (ἐστὶν) οὐκ εἶναι. He explains to be false the opinion of erring two-headed (δίκρανοι) mortals, of the uncritical tribes 1 Edited and commented on by Boeckh, Berlin, 1819. 2 Die angebliche Schriftstellerei des Philolaus und die Bruchstücke der ihm zugeschriebenen Bücher, Bonn, 1864. 3 Metaph. i. 5. 4 See Boeckh, Philol. 141. 5 Ibid. 191, 192. |