The Chemistry of Platonic Triangles: Problems in the Interpretation of the Timaeus

D. Robert Lloyd

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HYLE – International Journal for Philosophy of Chemistry, Vol. 13 (2007), No. 2, 99-118.

Abstract: Plato’s geometrical theory of what we now call chemistry, set out in the Timaeus, uses triangles, his stoicheia, as the fundamental units with which he constructs his four elements. A paper claiming that these triangles can be divided indefinitely is criticized; the claim of an error here in the commentary by F.M. Cornford is unfounded. Plato’s constructions of the elements are analyzed using simple point group theory. His procedure generates fully symmetric polyhedra, but Cornford’s ‘simpler’ alternatives generate polyhedra with low symmetries and multiple isomeric forms. However, Cornford’s principle of constructing larger triangles by assembling smaller ones is still valid.
Introduction
The Timaeus1 has been the object of study and commentary ever since its appearance,2 and was long regarded as the most significant work of Plato. As an indication of this importance through the late middle ages and beyond, Raphael (1483-1520), in his fresco ‘The School of Athens’, characterizes Plato by showing him holding this work in his hand (apparently written in
Italian!). In his extraordinary work, Plato sets out to provide a “reasonable account” (eikos logos) of the whole of Creation by the ‘Demiurge’, both at the cosmic scale and also at the microscopic level. It is important to appreciate, given the intervening Christian centuries, that neither is this is a creatio ex nihilo, nor is the Demiurge omnipotent. Some versions in English give him the literally translated name of ‘The Craftsman’; he works with the preexisting materials available to him, and I will return to this point.
In the context of this Journal, Plato’s account of the nature of the four elements is his most significant contribution. In the second part of the Timaeus, Plato sets out a scheme for what we now call chemistry, biochemistry,…

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