[G.E.R. Lloyd] Early Greek Science-Thales to Aristotle by Unknown

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PLATO pushes a. Third, and most important, whereas the atomists apparently postulated an indefinite variety of atomic shapes and sizes and described the interactions between them in only the most general terms, Plato attempted a definite and specific account both of the shapes of the primary bodies and of the transformations that take place between them. At 56d ff he makes a number of specific suggestions about, for example, how water may be decomposed into fire and air. Thus the icosahedron of water may become two octahedra of air and one tetrahedron of fire, the original solid of twenty faces being broken down into two solids of eight faces each and one of four. Many details of Plato’s theory remain obscure. How can the primary bodies disintegrate and recombine to form other figures? How indeed can the primary solids be described as bodies at all, when they are geometrical entities constructed from plane surfaces? There are, too, many fanciful and arbitrary elements in Plato’s doctrine. Thus having assigned four of the five regular solids to the four simple bodies, and not finding any other task for the fifth, the dodecahedron, he identified it with the twelve signs of the zodiac. Again when we find that earth is excluded from the transformations that affect the other primary solids, the reason for this does not lie in any real or supposed empirical data, but it is a direct consequence of the geometry of the theory, once earth had been identified with the cube. Yet what Plato did, that the atomists themselves never attempted, was to propose a precise geometrical account of the shapes of the primary bodies and to reduce the changes that take place between them to mathematical formulae. Many of his ideas, like those of Leucippus and Democritus, are still based on crude physical analogies — as for example the identification of fire with the tetrahedron and earth with the cube — but he attempted to carry the geometrisation of atomism much further than the original atomists themselves did. The Timaeus contains a wealth of detailed physical 77

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