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to the current mode of thought, the greater became the necessity of fortifying their own position against assault. Here again they had only to follow the example of the Eleatics. To prove the soundness of their position directly, as Parmenides had done, was no easy matter. More important results might be expected, if their opponents' ground was assailed by the criticism of Zeno and Gorgias. From Zeno the founder of the School had appropriated the Eleatic doctrine precisely in this its critical function, Zeno and the Sophists being the principal persons who drew attention hereto in central Greece. This path of criticism the Megarians now struck out with such preference, that the whole school herefrom derived its name.1 We are assured by Diogenes,2 that it was the practice even of Euclid, to attack conclusions and not premises-in other words, to refute by a

1 See p. 250, 3.

2 ii. 107 : ταῖς τε ἀποδείξεσιν ἐνίστατο οὐ κατὰ λήμματα ἀλλὰ κατ ̓ ἐπιφοράν. Since in Stoical terminology-which we are of course not justified in ascribing to Euclid on the strength of this passage-λῆμμα means the major premiss, or more often both premises, and ἐπιφορὰ the conclusion (Deycks, 34; Prantl,

reductio ad absurdum. It is also said that Euclid3 (1) That rejected explanations by analogies—a form much of Euclid. used by Socrates-because a similar thing when cited makes nothing clearer, and a dissimilar thing is irrelevant. The most telling description of Euclid's method will probably be found in Plato, who, speak

470), it is most probable that
the meaning given above is the
real meaning of these words.

3 Ibid. καὶ τὸν διὰ παραβολῆς
λόγον ἀνῄρει, λέγων ἤτοι ἐξ ὁμοίων
αὐτὸν ἢ ἐξ ἀνομοίων συνίστασθαι·
καὶ εἰ μὲν ἐξ ὁμοίων, περὶ αὐτὰ
δεῖν μᾶλλον ἢ οἷς ὁμοιά ἐστιν
ἀναστρέφεσθαι· εἰ δ ̓ ἐξ ἀνομοίων,
παρέλκειν τὴν παράθεσιν.

CHAP.
XII.

CHAP.
XII.

1

ing in the Sophistes of the philosophers of conceptions, says that in their discourses they destroy matter piecemeal, in order to prove that it has no real being but is subject to flux and change. This is exactly the line which Zeno adopted, in order to prove the uncertainty of the perceptions of the senses; and which we notice also in the Sorites of the later Megarians: the apparently substantial bodily mass is divided into its component parts, and there being no limit to the division, and no ultimate atom on which contemplation can rest, it is argued that matter must be itself unreal, and a mere passing phenomenon. Euclid is accordingly rightly regarded as the founder of the Megarian criticism. Still, with him criticism does not seem to have attained the character of formal captiousness, although objection may be taken to his controversial tone :3 it would appear that, like Zeno before him, he was primarily anxious to maintain his positive principles, and that he only used the subtleties of argument as a means to this end. Nothing, at least, is known of him which would lead to an opposite conclusion, nor is any one of the quibbling fallacies laid to his charge, for which the Megarian school was afterwards notorious.

1 See p. 256, 1; 259, 2.
2 See Zeller, G. d. Griech. Part
I., 496.

According to Diog. ii. 30, Socrates had already observed, that because of his captiousness, he might associate possibly with Sophists, but not with human beings. But this

statement proves but little, since it uses the term Sophist in a way peculiar to post-Socratic times. It is more worthy of belief (Diog. ii. 107) that Timon called him a quarrelsome person, who introduced amongst the Megarians a rage for disputes.

Among the immediate successors of Euclid, however, the element of captiousness prevailed over positive teaching. Such teaching as they had was too scanty to command attention for long, and too abstract to admit of further development. On the other hand a polemic against prevailing opinions presented to the sharp-witted, to the contentious, and to those ambitious of intellectual distinction, an unexplored field, over which the Megarians eagerly ranged. Not seldom their metaphysical assumptions served only as occasions for hard-fighting with words. Among the fallacies which are attributed to Eubulides, though they probably belong to an earlier

1 The ordinary form of these captious proofs is that of asking questions. Hence the regular expression: λóyov pwTây (to raise a point) in Diog. ii. 108; 116; Sext. Math. x. 87; and the Μεγαρικὰ ἐρωτήματα in the fragment of Chrysippus; in Plut. Sto. Rep. 10, 9, p. 1036. Conf. Arist. Phys. viii. 8; 263, a, 4, 7; Anal. Pr. ii. 19, 66, a, 26; 36; i. 32, 47, a, 21. But like the Sophists, they refused every answer but Yes or No. Diog. ii. 135.

2 Diog. ii. 108, enumerates 7: that called Yevdóμevos, that called diaλavbávwv, the Electra, the ἐγκεκαλυμμένος, the σωρίτης, the κερατίνης, the φαλακρός. The first of them is given as follows in Arist. Soph. El. 25, 180, a, 34, b, 2; Alex. ad loc. Cic. Acad. ii. 29, 95: If a man says he is at the moment telling a lie, is he telling a lie, or is he speaking truth? The diuλaved

vwv,

the ἐγκεκαλυμμένος, and the Electra are only different forms of the same fallacy. Do you know who is concealed? Do you know who is behind the veil? Did Electra know her brother before he announced himself to her? and the solution of them all consists in the fact, that he who was concealed, or behind the veil, or had not yet announced himself respectively, was known to, but not immediately recognised by, the lookers on. See Arist. S. El. c. 24, 179, a, 33; Alex. in loc. and 49; Lucian, Vit. Auct. 22, and Prantl. The κερατίνης is as follows: Have you lost your horns? If you say Yes, you allow that you had horns. If you say No, you allow that you have them still. Diog. vii. 187; vi. 38; Seneca, Ep. 45, 8; Gell. xvi. 2, 9; Prantl, p. 53. The Sorites consists in the question: How

CHAP.
XII.

of Eubu

lides.

time,' only one, the Sorites, has any intelligible relation to their metaphysics. By means of this form of (2) Eristic argument it could be proved that no enduring being belongs to objects of sense, but that every such object passes into its opposite, and represents what is changing, and not what is real and unchangeable.2 The rest appear to be simple sophisms, having no other object than to involve opponents in difficulties,3 critical works of art, which made indeed the need felt of an accurate investigation into the laws of thought, but in the pursuit of which the desire of conducing to a right intellectual method by pointing out difficulties and refuting untenable opinions falls altogether into the background.

The powers of Alexinus in argument seem to

CHAP.
XII.

(3) That of Alexinus.

many grains make a heap? or
more generally: With what
number does Many begin? Of
course it is impossible to assign
a number. See Cic. Acad. ii. 28,
92; 16, 49; Diog. vii. 82; Pers.
Sat. vi. 78; Prantl, p. 54. The
palakpòs is another form of the
same: How many hairs must
you lose to become a bald-head?
See Hor. Ep. ii. 1, 45; Prantl,
1. c.; Deycks, 51.

There are, for instance, in-
dications of the Sorites in
Zeno and Euclid. In general
it is difficult to say who are
the discoverers of quibbles,
which are taken seriously at
the time they are produced,
but are after all only bad jokes.
Seneca, Ep. 45, 10, says that
many books had been written
on the evoóuevos, among which
those of Theophrastus and

Chrysippus are known to us from Diog. vii. 196; v. 49. Chrysippus, according to Diog. vii. 198, 192, also wrote on the diaλavbávwv, the ¿ykekaλvμμévos, and the owpirns. Philetus of Cos is said to have worked himself to death in writing about the evdóuevos, Athen. ix. 401, e. The κερατίνης and ¿ykekaλvμμévos were also attributed to Diodorus (Diog. ii. 111), and the former (Diog. vii. 187) as also the Sorites (Diog. vii. 82) to Chrysippus, certainly without reason to Chrysippus.

2 Compare what will be later said about Diodorus' proofs in denying motion.

The motive which Prantl, p. 52, sees in the ¿ykeкaλνμμévos is not so patent, and the assumptions of Brandis, p. 122, do not seem accurate.

XII.

2

have been of a similar kind. He, at least, is only CHAP. known to us as a captious disputant. Nothing further is known of him beyond an argument in which he vainly attempted to entangle Menedemus in what is called the horned' fallacy, and a refutation of Xenophon's proofs of the reasonable arrangement of the world, which was subsequently repeated by the Academicians. In close connection with the Megarian doctrines may be placed the discussions of Diodorus on motion and destruction, on the possible, and on hypothetical sentences.

Tradition has preserved four arguments, by which (4) That of Diodorus. Diodorus attempted to support the fundamental (a) On teaching of his school on the impossibility of motion. Motion. The first, which in the main is the same as that of Zeno, is as follows. Supposing anything to move, it must either move in the space in which it is, or in the space in which it is not. In the former it has not room to move, because it entirely fills it; in the latter it can neither act nor be acted upon; hence motion is inconceivable." The second is a less

1 See p. 254, 1.
2 In Diog. ii. 135.

3 Sext. Math. ix. 107: Zeno had concluded, because the world is the best possible, and reason is higher than the absence of reason, that the world must have reason. See Cic. De N. D. ii. 8, 21; iii. 9, 22. To this Alexinus replied: To ποιητικὸν τοῦ μὴ ποιητικοῦ καὶ τὸ γραμματικὸν τοῦ μὴ γραμματικοῦ κρεῖττόν ἐστι· καὶ τὸ κατὰ τὰς ἄλλας τέχνας θεωρούμενον κρεῖττόν ἐστι τοῦ μὴ τοιούτου. οὐδὲ

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