Proportion and Mathematics in Plato's Timaeus


Abstract


Most discussions of mathematics in Plato's Timaeus focus on the actual numbers Plato employs and their significance. Cornford for example examines the proportions of the world soul in detail to show that Plato's division is not derived exclusively from the proportions describing musical intervals,1 while Brisson provides an extensive analysis of the proportions used in the creation of the elements.2 The focus of this paper is different, for it takes John Cleary's approach to the investigation of mathematics in the work of a philosopher. Cleary did not believe that the most critical thing to explain about a philosopher's use of mathematics is the detail of the numbers used or even the place of that work in the history or philosophy of mathematics. Instead, what Cleary believed to be most important when one examined the use of mathematics in a philosopher's work is 'to situate his philosophy of mathematics within the broader context of his whole project'.3 In 'Proclus' Philosophy of Mathematics', for instance, Cleary's chief concern was to explain how Proclus' ideas about mathematics are related to his understanding of the role of mathematics in the education of the rulers in Plato's Republic .4 I intend to follow Cleary's lead in this paper by looking at how the use of proportion in Plato's Timaeus relates to larger concerns in the dialogue as a whole.

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