(ǎxpira pûra) who hold Being and Not-Being to be identical, and at the same time not identical, and change every thing into its opposite : οἷς τὸ πέλειν τε καὶ οὐκ εἶναι τωὐτὸν νενόμισται κοὐ τωὐτὸν, πάντων τε παλίντροπος ἐστι κέλευθος. Parmenides in these verses' refers most probably to Heraklitus, for it is Heraklitus who has enunciated this doctrine: Tauró τ' ἔνι (leg. ταὐτόν ἐστι) ζῶν καὶ τεθνηκός, κ.τ.λ., πάντα εἶναι καὶ μὴ εἶναι,—παλίντονος (παλίντροπος) ἁρμονία κόσμου, ὅκωσπερ Xúpηs Kai Tóğov. He does not, however, refer to Heraklitus as a solitary thinker, but as a representative of the uncritical many,' who, trusting to the senses, get involved in that mode of viewing things, full of contradictions, to which Heraklitus has given a philosophical form.5 Since Heraklitus called the synthetic unity of opposites, their identity, and their existence in combination, a oneness of existence, he provoked that strong thinker, Parmenides, to the counter-assertion, and to seize on the opposite extreme. Parmenides denied that true existence could have any multiplicity or any change. (This is the very opposition of fundamental philosophical conception which appears in the Hegelian and Herbartian systems. The difference is that the perception of Heraklitus has been absorbed in the dialectic method of Hegel, and that Herbart believes that the multiplicity and change of the qualities 1 Parm. Fragm. ed. Mullach, vv. 35, 43–51. 2 To which Steinhart in the Hall. Allg. Litteraturz, 1845, p. 892 f., and Bernays in the Rhein. Museum, vii. 114 f., have paid careful attention. 3 Plut. Consol. c. 10; Arist. Metaph. iv. 7, cf. iv. 3.* 4 Plutarch, De Is. et Os. c. 45; De An. Procr. 27, 2. 5 So also Aristotle, De An. i. 2 : ἐν κινήσει δ' εἶναι τὰ ὄντα κἀκεῖνος WETO Kai oi Toλλoi, cf. Plat. Theaet. p. 179. In a wholly analogous way Herbart accuses Hegel of empiricism. * Metaph. iv. 3, § 14, perhaps καθάπερ τινὲς οἴονται Ηράκλειτον should be read, and voλaußártir, not Meyer, understood; for Heraklitus actually said that the same was and also was not (cf. eiμer kai ov eiμer, Her. Alleg. Hom. c. 24), but could not accept it or think it because it was not at all possible. of one thing are contradictory, but grants the multiplicity of individual real essences. Herbart also attempts the problem, not considered by Parmenides, to derive philosophically the illusion of the changeable from the being of the changeless.) Parmenides further teaches that thought belongs to the One, to the truly existing, which is thought of and is identical with it. What exists, is itself thinking, the voûs. Parm. Frag. vv. 94-97: τωὐτὸν δ ̓ ἐστὶ νοεῖν τε καὶ οὕνεκέν ἐστι νόημα· The deceiving senses do not judge of truth, the reason does. Parm. Frag. vv. 54-57: μηδέ σ ̓ ἔθος πολύπειρον ὁδὸν κατὰ τήνδε βιάσθω, καὶ γλῶσσαν· κρῖναι δὲ λόγῳ πολύδηριν ἔλεγχον 1 Of Zeno the Eleatic, Diogenes Laertius informs us (ix. 25): φησὶ δὲ Ἀριστοτέλης ἐν τῷ Σοφιστῇ, εὑρετὴν αὐτὸν γενέσθαι διαλεκTIKĤs. Zeno's dialectic art consisted essentially in this, that by reasoning against the existence of the many and of motion 2 he undertook to bring forward indirect proof for the truth of Parmenides' doctrine of the One, which was genuine.3 His dialogues appear, according to (Plato's ?) Parmenides, p. 127, to have contained regular courses of reasoning (Móyous). § 12. The Sophists elaborated the dialectic art, but often misapplied it to the purposes of subjective caprice. Sokrates (470-399 B.C.), who was animated by the idea of science, made it serve to aid the striving after that objectively valid knowledge, which may be recognised by every thinking subject to be true in the same way, and 2 Arist. Phys. vi. 9. 3 Cf. (Plato's?) Parmen. p. 128. 1 Simplic. in Phys. fol. 30 B. necessarily. He sought by collecting and testing instances to recognise the general from the basis of individuals. When he had discovered the universal, he endeavoured to describe it by means of the definition of the notion. He is therefore the founder of Induction and Definition, but only in their application to ethical problems, and apart from any logical theory. Protagoras ap. Diog. 1. 9. 51: πάντων χρημάτων μέτρον ἄνθρωπος, τῶν μὲν ὄντων ὡς ἔστι, τῶν δὲ οὐκ ὄντων ὡς οὐκ ἔστιν. Ibidem: πρῶτος ἔφη δύο λόγους εἶναι περὶ παντὸς πράγματος ἀντικειμένους ἀλλήλοις. Arist.?) de Melisso, Xenophane, Gorgia, c. 5 : (ὁ Γοργίας) οὐκ εἶναί φησιν οὐδέν· εἰ δὲ ἔστιν, ἄγιωστον εἶναι· εἰ δὲ καὶ ἔστι καὶ γνωστὸν, ἀλλ' οὐ δηλωτὸν ἄλλοις. Arist. Metaph. xiii. 4 : δύο γάρ ἐστιν ἅ τις ἂν ἀποδοίη Σωκράτει δικαίως, τούς τ ̓ ἐπακτικοὺς λόγους καὶ τὸ ὁρίζεσθαι καθόλου· ταῦτα γάρ ἐστιν ἄμφω περὶ ἀρχὴν ἐπιστήμης. Arist. Metaph. i. 6: Σωκράτους δὲ περὶ μὲν τὰ ἠθικὰ πραγματευομένου, περὶ δὲ τῆς ὅλης φύσεως οὐθέν, ἐν μέντοι τούτοις τὸ καθόλου ζητοῦντος καὶ περὶ ὁρισμῶν ἐπιστήσαντος πρώτου τὴν διάνοιαν. 13. Of the one-sided Sokratie Schools, the Cynic of Antisthenes, and the Cyrenaic or Hedonist of Aristippus, treat of ethical problems chiefly. Their contributions to Logic rest on their negative polemic against contemporary systems. The Megaric School of Euklid, and Eretric School of Phaedo and Menedemus allied to it, mix together the principles of Sokrates and the doctrines of Parmenides. Since the Megarics, in order to defend the unity of existence, deny the truth of sensephenomena, their dialectic became gradually more and more a mere Eristic, which takes special delight to find out numerous captious and sophistical arguments. 1 Cf. Xenoph. Memorab. iv. 5, 12; iv. 6, 1. Antisthenes objected to the Platonic doctrine of ideas:-It could easily be said to what things were similar, but not what things were. Definitions of simple notions were a useless waste of words (μaxpòs λóyos).' The Cyrenaics restricted science to the consciousness of the sense-affections as such; what the real object was which excited these, and whether it was in itself white or sweet, &c. could not be known.2 Euklid of Megara identified the One, the true existence of the Eleatics, with the Good of Sokrates. He vindicated his doctrine, as Zeno did, by indirect argument, and sought to show the absurd consequences which flow from the opposite view, which ascribes plurality and change to reality. For this purpose his followers, Eubulides, Diodorus Kronus, and Alexinus, invented a number of captious arguments; e.g. 'The Liar,' 'The Veiled,' 'The Horned,' 'The Heap,' and 'The Baldhead.' The doctrine that no subject can be joined to a predicate which can be separated from it (e.g. man is wise), but that each must be predicated of itself only (e.g. man is man), is to be ascribed partly to the Megarics in general, but more especially to Stilpo, who mixed up their doctrines with those of the Cynics, and also to Menedemus the Eretrian. It is an immediate consequence from the doctrine of the oneness and unchangeableness of true existence. 5 6 § 14. Proceeding from the Sokratic method of Induction and Definition, Plato (427-347 B.C.) developed the art of Logic in many ways (a) He enriched it with the methods of Division and Deduction. 1 Simplic. in Arist. Categ. fol. 54 B.; Arist. Metaph. viii. 3, cf. Plat. Theaet. 201, Soph. 251. 2 Sext. Emp. adv. Math. vii. 191. 3 Diog. Laert. ii. 106; Cic. Acad. pr. ii. 42. 4 Diog. Laert. ii. 107. 6 Simplic. in Phys. 20 A. 5 Plut. adv. Col. 23. (b) He removed its limitation to ethical inquiry, and extended it to the whole sphere of philosophical thought. (c) He used it with ingenious sagacity, scientific exactness, care, and depth; and still more increased the value of these advantages by his masterly artistic representation. Plato also developed the theory of thinking in relations many (a) He surveyed the art of philosophical thinking in the general, and comprehended it under a general notion (the notion of Dialectic). (b) He strictly distinguished philosophical thinking, not only from sense-perception, as his predecessors had done, but from mathematical thinking. (c) He brought under observation also, and undertook to give an account of, the main operations of thought, more especially the formation of notions, Definition, Division, and partly also Deduction. But Plato's logical theorems, showing throughout the traces of their origin from reflection upon ideological thinking, want both a strict separation of the logical from the metaphysical elements, a scientific completeness, and representation in a systematic form. If Plato's lofty art of thinking and of representation rightly excites our admiration, his developments of logical theory have no less significance for the history of our science. Plato finds in existence the measure of thinking: Rep. v. 477 (cf. Cratyl. p. 385 Β): λόγος, ὃς ἂν τὰ ὄντα λέγῃ ὡς ἔστιν, ἀληθής, ὃς δ ̓ ἂν, ὡς οὐκ ἔστι, ψευδής, Soph. p. 263 Β ; λέγει δὲ ὁ μὲν ἀληθὴς λόγος τὰ ὄντα ὡς ἔστιν, ὁ δὲ ψευδὴς ἕτερα τῶν ὄντων, τὰ μὴ ὄντα ἄρα ὡς Övтa λéye). Plato theoretically assigns this double problem to |