The bond of the cosmos: a significant metaphor

has (ea) Mort LEY, RA): \ aba Mont boy | — The bond of the cosmos. A ‘significant metaphor. (Tim. 31c MT): Hermes XCVII 1969 372-373. | La'proportion, ¿vaAoyix, qui régit les quatre éléments, 2 Miszellen 373 est employée par. Platon dans’ le: même. que ola. chez Empédocle, c'est-à-dire comme. une force motrice et un lien, ôeou6c, métaphysique du „etaphor if the proportion is regarded as merely descriptive. Yet this is not cosmos. ere -. y the case: the proportion is equally much a force as Empedocles’ ix. There are three reasons: firstly the xécyo¢ is said to be ¿Duros because of the proportion, which implies that the latter has some integrating force; secondly, as my title suggests, the proportion is referred to as a 526265 or bond throughout MISZELLEN the passage. Thirdly Plato's concept of number was metaphysical: as a logical realist he would commit himself to the proposition that numbers are abstract realities*, The numbers that could be used in a proportion such as this would not represent relations between clements, but cosmic forces existing as Forms and affecting the sensible world in the same way as other Forms, THE BOND OF THE COSMOS: A SIGNIFICANT METAPHOR (TIM. 31c ff.) There has been much recent discussion? of the mathematics of this passage and of the actual proportion (dvaeyla) in which fire, air, water and earth are involved. Apart from such questions of mathematical detail, and the problematic question of the relation of this passage to 53dff., there remains the problem of the role which Plato assigned to the proportion. In other words, what is the function of this proportion in the life of the Cosmos? It is usually thought that this proportion is a simple statement of the relation between the four elements; that each of them stands in a certain proportion to the others, like ingredients in a pudding. Yet this interpretation, clear though it is, betrays a modern non-metaphysical view of mathematics, The proportion therefore does not belong simply to the theory of the observer, but is an actual reality present in the world itself, existing independently of the observer. (We may perhaps go even further if we accept secondary evidence and say that even Forms owe their existence to numbers!) CROMRE alleges® a general ambiguity in the status of Platonic mathematics corresponding roughly to the alternatives 1 have been discussing: it seems to me that this is one point at least where there is no ambiguity. In conclusion then: Plato deliberately echoes Empedocles by naming his proportion pula; secondly this metaphor is not carelessly employed—rather it reveals the true role of numbers in Plato’s thought. Monash University Raour Melbourne, Australia ? J. MORTLEY | in which the Platonic proportion would stand as nothing but a description of the ratio of quantities of the elements to cach other, In this case the proportion has no function, strictly speaking, in the scheme of things. Thus the whole question of the status of Plato's mathematics is raised; are we to take the mathematical theory of the Timaeus as an instrumentalist hypothesis—a ZU ANTH. PAL, 5, 162 (ASKLEPIADES) key that may be useful in interpreting the code of the physical world, a kind of programme for exploration, or alternatively as a description of actual 'H Aauupn je Expmce Dodaluoy, el dì 1ò tpabpa un capés, GAA’ 6 nôvos Seras sic Svvya. olyou’, "Epwress, bwha, Srotyopat, ele yao Eyıövav reality? What is the proportion ? The instrumentalist interpretation of the proportion is contradicted later in the passage where Plato makes some general observations about it (32b 8ff.). It is said to guarantee pula to the xdopec, and consequently the latter is indestructible (Zuz0¢): what does Plato mean by this?? Just as he chose the four roots of Empedocles as his starting-point, and later went on to refine this point of view by the introduction of his atomic theory, so he uses and interprets Empedocles’ guix in his own terms. For Empedocles pula is the integrating force in the physical world, uniting dissimilars. It is recognised as a motive force or power?; so much so that it has a name-Aphrodite. It is this force that Plato uses to characterise his proportion and it is a very uneasy 1 F.g, Ch, Muczur (REG 66, 1953, 56—87; and Physique de Platon, ch. 1); A. Ravaup, Bude Edn., p. 7241. 2 The terms are slightly obscure here: puta is said Lu originate ty tobtey. +09T0V may (see be a general term referring to the whole discussion on the dvz)ola and the elements elements Bury’s translation, Loeb Edn. p. 61) or else it may refer specifically to the foursame thing designated already as to97@v in the same sentence. In any casc it amounts to the since the unity, the quie of the cosmos results from the action of the &vadoytz on the elements. It is of course the Snuougyés who unifies the elements by means of the proportion. 2 Durs, Fr. Vors. 31 B 17, 27%. wortalay Entry 145" Edtyov 7’ alba. 3 Epdvav WALTZ: Etaipav C 4 78 ¿Diyov =’ dida A. a. corr.: 53 ¿Diyov +’ dida: C Gow bemerkt zum letzten Halbvers dieses Gedichts (845 G.-P.): »The end of the line seems clearly to mean ‘and am nearly dead in consequence’ fe. 1 31¢ 1, c2: cuvdéro; 32b 1, b7, 3204. - The Timacus involves both arithmetic and geometry and closely relates them. Plato's conception of number is parallel to his conception of geometrical shape. They are both sets of abstract realities-Forms (cf. Anders WEDBERG, Plato's Philosophy of Mathematics, p. G4 ff.). 3 See Phaedo 101b 4—¢ 7, where the existence of Ideal numbers is recognised, and where they are aligned with other Forms in respect of their relationship to the sensible world. Similarly in Tim. 53d 8, the principles still higher than the triangles are probably numbers; and we may relate this to the paradcigmatism affirmed in 28ff, | * E.g. Arist. Metaph. A 6. 087a 2011, È = Re Or ES di Doctrines, Vol. IL, p. 245. e Greck An gy, Cambridge 1965, Bd. IL te. Hellenistic Epigrams, edited by A. S. F, sir EI See ae