CHAP. accurate form of the same proof. All that moves What is in space reposes Therefore is in space: what is moved reposes. consequently nothing at all is. 1 Sext. Math. x. 112. 2 Id. x. 143 and 119. Alexander, too, De Sensu, 125, b, mentions Diodorus, λόγος περὶ τῶν ἀμερῶν. Id. ix. 362; Pyrrh. iii. 32; Dionys. in Eus. Pr. Ev. xiv. 23, 4; Stob. Ekl i. 103; Pseudoclement, Recogn. viii. 15, all of which point to one common source. Simpl. Phys. 216, b; Schol. in Arist. 405, a, 21. Diodorus called these atoms àμεpî. 4 Even the first proof, according to Sext. Math. x. 85, was put in such a shape as to prove that every atom fully occupied its space; but this is unimportant here. 5 See p. 265. 6 Sext. Math. x. 113. * κίνησις κατ ̓ ἐπικράτειαν and κίνησις κατ' εἰλικρίνειαν. XII. its particles moved, before it can move as a whole; CHAP. that it should move with the majority is, however, not conceivable. For supposing a body to consist of three atoms, two of which move whilst the third is at rest, such a body must move, because the majority of its particles move. The same applies, when a fourth atom at rest is added: for the body being moved κατ' ἐπικράτειαν, the three atoms of which it consists are moved, consequently the fourth at rest is added to the three moving atoms. Why not equally when a fifth and a sixth atom is added? So that a body consisting of 10,000 particles must be moved, if only two of these first move. If this is, however, absurd, a movement of the majority of particles is therefore inconceivable, and therefore a movement of the whole body. That there is an inconclusiveness in this argument Sextus has already noticed.' Diodorus, however, appears to have considered it unanswerable, and hence, he concludes all his researches by saying that it never can be said of a thing, It is moving, but only, It has moved." He was, in other words, prepared to allow what the senses seemed to prove,3 that a body is now in one place and now in another, but he declared the transition from the one to the other to be impossible. This is indeed a contradiction, and as such it was 1 Sext. Math. x. 112, 118. A further argument, the first argument of Zeno's, is not attributed to Diodorus by Sext. Math. x. 47. He only says as to its result, that Diodorus agreed therein with the Elea- 2 Sext. Math. x. 48; 85; 91; 3 This reason is specially mentioned by Sext. Math. x. 86. СНАР. (b) On Destruction. (c) On the Possible. laid to his charge by the ancients, and by him very inadequately met. At the same time it is a deviation from the original teaching of his school. Euclid denied motion absolutely, and would just as little have allowed a completed motion as a transition in the present. With the third of these arguments agrees substantially the argument of Diodorus that nothing perishes. It is as follows. A Wall, he says, does not perish; so long as the stones keep together, it stands; but when the stones are separated it no longer exists. That it may however have perished, he appears to have likewise allowed. Closely related to the enquiry into motion, are his discussions on what is possible. In both cases the conceivability of change is the point raised, but in one case it is raised in reference to something, in the other abstractedly. In both cases, Diodorus stands on exactly the same footing with regard to his School. The older Megarians allowed as possible only what actually is, understanding by actual what was before them in the present. To this Diodorus added what might be in the future, by saying: Possible is what either is actual or what will be actual.4 1 See Sext. 91, 97. Diodorus here proves the assertion that anything predicated of the past may be true, whilst it is not true predicated of the present by such irrelevant statements as that it can be said of Helen that she had three husbands (one after another), but never that she has three (cotempora neously). This example is 4 Cic. De Fato, 6, 12; 7, 13; 2 In proof of this statement he used an argument, which goes by the name of Kupiɛúwv, and is still admired after centuries,' as a masterpiece of subtle criticism. It is in the main as follows: From anything possible nothing impossible can result; but it is impossible that the past can be different from what it is; for had this been possible at a past moment, something impossible would have resulted from something possible. It was therefore never possible. And speaking generally it is impossible that anything should happen differently from what has happened.3 CHAP. XII. Philo. Far less exacting was Philo, a pupil of Diodorus, (5) That of when he declared everything to be possible, even should outward circumstances prevent it from being 9, 17; Ep. ad Fam. ix. 4; Plut. Sto. Rep. 46, p. 1055; Alex. Aph. in Anal. Pr. 59, b; Schol. in Arist. 163, b, 29; Simpl., ibid. 65, b, 7; Philip, ibid. 163, b, 19; Bocks, de Interpret. Op. ed. Basil, 364; Prantl, Gesch. d. Log. i. 19. The above sentence is expressed here thus: Possible is ὅπερ ἢ ἐστιν ἀληθὲς ἢ ἔσται. 1 Comp. Epict. Diss. ii. 18, 18 : we ought to be proud of moral actions, οὐκ ἐπὶ τῷ τὸν κυριεύοντα ἐρωτῆσαι, and just before: κομψὸν σοφισμάτιον ἔλυσας, πολὺ κομψότερον τοῦ κυριεύονTOS. He also mentions, ii. 19, 9, treatises of Cleanthes, Chrysippus, Antipater, and Archidemus on the κυριεύων. Chrysippus could only meet it (according to Alex. in Anal. Pr. 57, b, in Schol. in Arist. 163, a, 8), by asserting that possibly T the impossible might result 2 §ο ἀκολουθεῖν is rendered, 3 Epict. Diss. ii. 19, 1: 8 κυριεύων λόγος ἀπὸ τοιούτων τινῶν ἀφορμῶν ἠρωτῆσθαι φαίνεται· κοινῆς γὰρ οὔσης μάχης τοῖς τρισὶ τοῦτοῖς πρὸς ἄλληλα, τῷ πᾶν παρεληλυθὸς ἀληθὲς ἀναγκαῖον εἶναι, καὶ τῷ δυνατῷ ἀδύνατον μὴ ἀκολουθεῖν, καὶ τῷ δυνατὸν εἶναι ὁ OUT' čσT àλŋlès OŬT' ĔOTAL,' σvvidav THν μáxην Tαútny d Aióδωρος τῇ τῶν πρώτων δυοῖν πιθανότητι συνεχρήσετο πρὸς παράστασιν τοῦ μηδὲν εἶναι δυνατὸν ὃ οὔτ ̓ ἔστιν ἀληθὲς οὔτ ̓ ἔσται. Conf. Cic. De Fato, 6. (a) On the Possible. XII. therefor. СНАР. realised, provided a thing has only the capacity This was undeniably a departure from the Megarian teaching. (b) On hypothetical sentences. (c) On the meaning of words. In regard, too, to the truth of hypothetical sentences, Philo laid down criteria different from those of his teacher.2 Diodorus declared those conditional sentences to be true, in which the apodosis neither can be false, nor ever could be false if only the protasis be true. Philo says more vaguely, those are true in which there is not a true protasis and a false apodosis. The question here appears, however, to have been one of formal correctness in expressing logical rules.3 With Diodorus' view of the possible the assertion appears to be connected, that no words are meaningless or ambiguous, each one always meaning something, and everyone requiring to be understood according to this meaning: he will only allow that meaning of a word to be possible which is actually present to the speaker's mind. Respecting Diodorus, however, and the whole Megarian School, our infor 1 Alex.-Simpl. in Categ. Schol. in Arist. 65, a, 39, b, 6; Boeks, 1. c. Panthoides, according to Epict. Diss. ii. 19, 5, attempted by another turn to avoid Diodorus' argument, by disputing the sentence that every thing past must be of necessity. 2 See Sext. Pyrrh. ii. 110; The inferences by which Philo, do not affect his real In order to show that every word has a meaning, Diodorus, according to Ammon., gave the name ἀλλαμὴν το one of his slaves. |