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"I think that one of the most important goals of ontology is to determine what the ultimate nature of the worldactually is, and Plato's contribution toward that end cannot be gainsaid. His attempts would be instructive evenif they were merely erroneous historical curiosities, but these attempts are not merely curiosities. Plato'schemistry and ontology does in fact appear to have a certain tenability. To that end I must also cite the work of

Francis Cornford (1937) in the area of the chemistry of the Timaeus as very influential. Cornford showed howthe triangle has the utmost importance in Plato's chemistry, and he showed how Plato's chemistry, with itsreliance on triangles, can be considered as a great speculative chemical system. In this essay, I will examine whythe ultimate building blocks in this system - the triangles - are not given any definite size by Plato. AlthoughCornford insists that Plato must hold that there must be a smallest triangle, which would stand as the ultimate inPlato's chemistry, I will argue that Plato need not have such a smallest triangle. I will instead make a case thatall the triangles that exist as the faces of the regular solids can be divisible in principle, and, therefore, we couldhave ever smaller triangles in principle. In other words, I will show how Plato's chemistry need not have asmallest elemental triangle. Let us begin with what Plato states of the chemistry in the Timaeus. We are told thatthere are four and only four solids which comprise the objects of the universe (Fig. 1). First, there is fire. Thiselement has the form of the tetrahedron. Then air, which takes the form of the octahedron. Third is water, whichtakes the form of the icosahedron. Finally, there is earth, which has as its form the cube. Plato's regular solids:tetrahedron (fire), octahedron (air), icosahedron (water), cube (earth). The perfect solid 'dodecahedron' iseliminated from Plato's chemistry. Why does it have no place here? Well, for one thing, there is only fire, air,

water, and earth in Plato's Timaeus, and the dodecahedron is left out simply because it would correspond to anon-existent fifth kind. Furthermore, Plato inherited (from the Pythagoreans) a view that the dodecahedronpossessed a peculiarly ethereal nature. We could say that the dodecahedron simply has no place in the mundanerealm of fire, air, water, and earth. However, it will become clear shortly why the dodecahedron, with its twelvefaces of regular pentagons, will be impossible to incorporate into the Platonic chemistry." /John Visitainer, A Potential Infinity of Triangle Types On theChemistry of Plato's Timaeus/ ' ( -(# * ) ", * # ) "#+ ' #, * +(# ( , (# --+ ' ) (#(+, ) ## # -. # ($#, *, 1997., . 83-87; 98-111).


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##,(: If we look at the text of theTimaeus, we shall see that at any rate Plato does not mean to say that there ever was a time before Godconstructed the world, since he tells us, as Aristotle allows /Ar. Phys.251b17;Metaphys. 1072a1/ that time andthe world `began`together, God, in fact, making both of themAgain, as will be clearer from what we shallhave to say later on about the use of the notion of `necessity`, it seems plain that the Timaeus knows of noexternal limitation imposed on God`s will by conditions independent of God himself. The `maker`s` goodness isthe whole and complete explanation of the very existence of the natural world. This should justify us in sayingthat the `Demiurge` really is thought of as a Creator in the full sence of the wordin the Platonic conception theworld is always `in evolution`, even if the evolution never began and will never come to an end. This is why theworld, unlike God, has a history. It is always getting itself made, there is never a point at which it is full-made

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