Abstract
Plato was the first to apply the term ‘element’ to the basic constituents of all things. So Diels tells us in his interesting history, Elementum1. Element (στοιχεĩον) had been a common word in Greek to denote letters of the alphabet, corresponding to our ‘ABC’s’. But it was put to philosophic use first in the Theaete- tus (201e). Socrates says that he remembers in a dream having heard someone say that things were built up out of prior things, just as the alphabet arises from letters2. (See 203a f., Rep. 402a f.) One need not accept Diels at all points. For example, his statement is rather extreme that the theory of elements never belonged to the heart of Plato’s philosophy, but was a late, Pythagorean development. Nor need one accept his puzzling interpretation that the term ‘element’, applied first to geometrical figure, was used later by Plato to describe the one and infinite two. And the eventual demonological meaning of the term lies beyond the scope of the present study 3.
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References
H. Diels, Elementum (Leipzig, 1899).
Ibid., p. 58. Diels thinks that Plato got the usage from the Atomists; Taylor differs Taylor, A Commentary on Plato’s Timaeus (Oxford, 1928), p. 307.
Diels, op. cit., pp. 21-2, 57-8.
Ibid., pp. 58, 81-2.
As beginning: Prot. 318a, Phaedr. 237b, d, 262d, Parm. 137d, 153c, Rep. 2.377a, Laws 6.753e, 768d, 775e, 2.671a, 672c, Gorg. 466b, Tim. 48b. As leader, ruler: Prot. 344c. As non-material principle: Phaedr. 245cd, Phaedo lole, Rep. 6.510b, 511bc.
Taylor, op. cit., p. 393, cf. De Gen. et Corr. 325b28-9 and Tim. 53d.
Cf. his use of ἀρχή in the references listed in Bonitz, Index Aristotelicus (Berlin, 1870), 111a28-113b26.
Under no circumstances should the fire, earth, air, and water we know be confused with the kinds mentioned by Plato, for he identifies them by nature rather than by our experience of them. Cf. Cornford, Plato’s Cosmology (London, 1937), pp. 188-91 and Tim. 50b.
Cf. De Gen. et Corr. 330b34-33la3. Aristotle has the same intermediates.
With’ square’ numbers, only one mean is required in the proportion, but in’ solid’ or cubic numbers, two mean terms are required, as: x3: x2y::x2y: xy2:: xy2: y3. Cf. Heath, A History of Greek Mathematics (Oxford, 1921), I, 89, 297.
Zeller, Plato (London, 1888), pp. 372-3n Philolaos connected the fifth element with ether as did Xenocrates, who (apud Simpl. Phys. 205b Schol. in Aris. 427a) attributes this view to Plato. Zeller disagrees, but cites Martin, 111, 140 sq., as concurring. Burnet’s demonstration that the fragments of Philolaos are probably apocryphal makes dependence on them a risky business. (Plato, Timée-Critias (Paris, 1949), Vol. X of Budé ed., tr., ed., and intro. by A. Rivaud, pp. 24, 24n, 81-82, citing Burnet, Early Greek Philosophy, ed. 3, pp. 277, 284-303.) As is well known, Aristotle’s fifth element was ether (see Zeller, Aristotle (London, I897), pp. 476-7). Although one can speculate that the alacrity with which Plato’s followers accepted ‘ether’ as the fifth element might show that it arose in the Academy and was put forth before Plato’s death (Jaeger, Aristotle (Oxford, 1948), pp. 300-1 and 300n.), there is no real proof that this was Plato’s view. Rivaud (Timée-Critias, Budé, p. 84) thinks in contrast to the above that Plato’s followers considered ether a variety of fire.
Rivaud, Timée-Critias (Budé ed.), pp. 117, 81-2.
Sachs, Die fuenf platonischen Koerper (Berlin, 1917), pp. 186, 105. Cf. Burnet, op. cit. (ed. 4), pp. 283-4, 293, rejecting the hypothesis that the Pythagoreans introduced them.
Cf. Phaedo nob, where it is said that the true earth, if seen from above, is many-colored, like the balls made of twelve pieces of leather. Robin, Greek Thought (London, 1928), p. 227, suggests that the number of pentagonal surfaces in this element remind one of the twelve signs of the zodiac, which are like an adornment for the sky. It may, therefore, be the body in which the stars move, namely, the ether. (Cf. Rep. 7.529bc, Epi. 981c.) Rivaud, op. cit., p. 84, is inclined to take this position.
Euclid gives details regarding the construction of the five basic solids in his Elements, XIII, 13-18 and addendum. Cf. Heath, op. cit., I, 415-9.
As may be confirmed by reasons already given as well as by the apology with which he prefaces the passage cited. His method, Plato says, is ‘technical’ and ‘most unusual’ (53bc).
Some think this the starting point of Plato’s later theory of the derivation of the world from square and cubic numbers. E.g., Stenzel, Zahl und Gestalt bei Platon und Aristoteles (Leipzig, 1933), pp. 88-9, 70-1.
Aristotle even follows Plato in the use of ἐπίπεδος in this passage.
πέρας or ὅρος. The word ὅρος, which occurs frequently in the Prior Analytics, is found more rarely in the Posterior Analytics. This was taken by Solmsen to be the last link in Aristotle’s gradual development from a Platonic view of form to something purely logical in implication. (Ross, Aristotle’s Prior and Posterior Analytics (Oxford, 1949), p. 16). This conforms to the chronological view adopted in this study.
Shorey, in American Journal of Philology, IX, 4; 416.
See arrangement in Oxford tr., Physics, 212b32 n., as listed by R. P. Hardie.
Rep. 7, esp. 524b-531c. Cf. Heath, op. cit., I, 284-7, Burnet, Greek Philosophy, Part I (London, 1924), pp. 224-8.
Mansion, Introduction a la Physique Aristotélicienne (Louvain, 1946), p. 225, citing 299a11-7.
Ross, op. cit., p. 14. The doctrine applies to his whole work, not just to an early ‘Platonic period’. Cf. the chronology in Chapter One, supra, and Mansion, op. cit., pp. 192-3.
Called ‘metaphysics’ by later gneraetions.
Plato in 56ab makes the pyramids cut, but he does not mean by virtue of their geometrical nature only (Cornford, op. cit., p. 222).
E.g., ‘sandpaper scratches because it is rough’.
Joachim in his edition of Aristotle On Coming-to-be and Passing-away (Oxford, 1922), p. 76, referring to his notes in Oxford tr. to 968a9-12. Aristotle is probably not the genuine author of De Lineis Insecabilibus. Ross, Aristotle (London, 1945), P 13, finds it primarily directed against Xenocrates, and to resemble in its doctrine Theophrastus, to whom Simplicius ascribed it; Strato has also been suggested as its author. W.S. Hett in Aristotle Minor Works (Loeb ed.), p. 415, says only that this ‘most interesting” and ‘extremely difficult’ work was written by some author of the Peripatetic School. At any rate, it is in conformity with Aristotle’s position in his recognized works.
Burnet, Early Greek Philosophy (ed. 4; London, 1948), pp. 290-1. He notes that Zeller differs. Cf. Meta. M, 6, 1080b18 f. and De Caelo, 3ooa16.
Milhaud, Les Philosophes-Géomètres de la Grèce (Paris, 1900), p. 341. Cf. Meta., Delta.
Cherniss, op. cit., I, pp. 131-2. See Meta. 1091b30-5, 1028021-4, and 1085b27-34. Cf. Ross, Aristotle’s Metaphysics (Oxford, 1924), II, p. 457 n. 32.
1016b1-6, 23;1034a8 fin.; 104434-9; 1045b23;1052329-36; 1088b14-16, 25-8. Also, De Anima, 412b6-9, 430b14-20, 27-31. This does not affect, of course, his general attack on the divisibility of solids, to be found in De Gen. et Corr., 325b25-326b7.
Vs. Cherniss, op. cit., I, 150.
As Martin did, cf. Cornford, op. cit., p. 229.
There is a striking parallel between the rigid field convention of modern quantum physics and the Receptacle of Plato. Both are delimited in order for solid bodies to appear. Solid bodies of any type can appear anywhere, subject only to the delimiting factors involved (object-particles in the case of modern physics, planes in the case of Plato) and other bodies in the field. Both are ‘nothing ‘until delimited, but potentially everything. This was first brought to the writer’s attention by Dr. Nels Lindenblad of Princeton, N.J. Cf. Eddington, Fundamental Theory (Cambridge, 1946), pp. 22-5.
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© 1954 Martinus Nijhoff, The Hague, Netherlands
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Claghorn, G.S. (1954). Aristotle’s Criticism of the Simple Bodies. In: Aristotle’s Criticism of Plato’s ‘Timaeus’. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-8839-5_3
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