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accurate form of the same proof. All that moves is in space: What is in space reposes :
Therefore what is moved reposes. A third proof? is based on the assumption of infinitesimal atoms and particles. It is generally attributed to Diodorus. Probably he only used it hypothetically, as Zeno did his argument, to refute ordinary notions. It is this : As long as the particle a is in the corresponding space a, it does not move, because it completely fills it. little does it move when it is in the next following space, B; for no sooner is it there than its motion has ceased. Accordingly it does not move at all. In this conclusion one cannot fail to discover the note of Zeno's inferences, and of that critical process which had been already described by Plato. The fourth proof, besides assuming the existence of atoms, distinguishes between partial and complete motion." Every moving body must first have the majority of
consequently nothing at all is. * Id. ix. 362; Pyrrh. iii. 32; It is possible that this argu- Dionys. in Eus. Pr. Ev. xiv. 23, ment also belongs to Diodorus. 4; Stob. Ekl i. 103; PseudoBut Steinhart is wrong in at- clement, Recogn. viii. 15, all of tributing to him (Allg. Encykl which point to one common Sect. i. vol. XXV. p. 288) the
Simpl. Phys. 216, b; distinction between space in Schol. in Arist. 405, a, 21. the wider and in the narrower Diodorus called these atoms sense, which is found in Sext. åpepû. Pyrrh. iii. 75; Math. x. 95, 4 Even the first proof, accor. since it would appear from ding to Sext. Math. x. 85, was these passages that the dis- put in such a shape as to prove tinction was made with a view that every atom fully occupied to meet Diodorus' objections. its space; but this is unim. 1 Sext. Math. X. 112.
portant here. 2 Id. x. 143 and 119. Alex- 5 See p. 265. ander, too, De Sensu, 125, b, 6 Sext. Math. X. 113. mentions Diodorus, λόγος περί 1 κίνησις κατ' επικράτειαν and των αμερών.
κίνησις κατ' ειλικρίνειαν.
its particles moved, before it can move as a whole ; 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' επικράτειαν, 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, 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 agreed therein with the Eleafurther argument, the first tics. argument of Zeno's, is not at- 2 Sext. Math. x. 48; 85; 91 ; tributed to Diodorus by Sext. 97-102. Math. X. 47. He only says as
3 This reason is specially to its result, that Diodorus mentioned by Sext. Math. x. 86.
(6) On Destruction.
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
(c) On the Possible.
1 See Sext. 91, 97. Diodorus neously). This example is here proves the assertion that sufficient to show how erroneous anything predicated of the past Grote's view (Plato iii. 501) is, may be true, whilst it is not
that Diodorus only intended to true predicated of the present assert that present motion is by such irrelevant statements only the transition point beas that it can be said of Helen tween the past and the present. that she had three husbands 2 Sext. Math. x. 347. (one after another), but never 3 See p. 261. that she has three (cotempora
4 Cic. De Fato, 6, 12; 7, 13;
In proof of this statement he used an argument, which goes by the name of kupcevwv, 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. Far less exacting was Philo, a pupil of Diodorus, (6) Thut of
Philo. when he declared everything to be possible, even (a) On the should outward circumstances prevent it from being Possible.
9, 17; Ep. ad Fam. ix. 4; Plut. the impossible might result
1 Comp. Epict. Diss. ii. 18, Kuple'wv nóros ånd TOLOÚTWv Tlv@v 18 : we ought to be proud of αφορμών ήρωτήσθαι φαίνεται κοιmoral actions, ουκ επί τω τον νης γαρ ούσης μάχης τοϊς τρισι κυριεύοντα ερωτησαι, and just τούτοις προς άλληλα, το παν παbefore: κομψον σοφισμάτιων έλυ- ρεληλυθός αληθές αναγκαίον είναι, σας, πολύ κομψότερον του κυριεύον- και τη δυνατώ αδύνατον μη ακο
He also mentions, ii. 19, λουθείν, και το δυνατόν είναι και 9, treatises of Cleanthes, Chry- otr' ČOTI åandès oớt' čoral, sippus, Antipater, and Archi- ouviddu Thu Máxnv taútnu o A1bdemus on the κυριεύων. . Chry- δωρος τη των πρώτων δυοϊν πιθαsippus could only meet it (ac- νότητι συνεχρήσετο προς παράcording to Alex. in Anal. Pr. στασιν του μηδέν είναι δυνατόν 57, b, in Schol. in Arist. 163, a, και ούτ' έστιν αληθές ούτ' έσται. 8), by asserting that possibly Conf. Cic. De Fato, 6.
realised,' provided a thing has only the capacity therefor. This was undeniably a departure from
the Megarian teaching. (6) On hy- In regard, too, to the truth of hypothetical senpothetical sentences. tences, Philo laid down criteria different from those
of his teacher. 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. (c) On the
With Diodorus' view of the possible the assertion meaning of nords.
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 : 4 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. Philo, do not affect his real Schol. in Arist. 65, a, 39, b, 6; meaning at all, however much Boeks, l. c. Panthoides, accor- they may follow from the words ding to Epict. Diss. ii. 19, 5, of his definition. Hence Prantl, attempted by another turn to p. 454, can hardly have quite avoid Diodorus' argument, by grasped the meaning of Philo. disputing the sentence that 4 Gell. xi. 12; Ammon., De every thing past must be of Interpret. 32, a; Schol. in Arist. necessity.
1103, b, 15; Simpl. Categ. f. 6, 2 See Sext. Pyrrh. ii. 110; h. In order to show that every Math. viii. 113; i. 309; Cic. word has a meaning, Diodorus, Acad. iv. 47, 143.
according to Ammon., gave the : The inferences by which name άλλαμήν to one of his Sextus, M. viii. 115, refutes slaves.