Plato and Mathematics
In 1987 Myles Burnyeat, who was Professor of Ancient Philosophy at the University of Cambridge, appeared on a BBC television programme in which he was interviewed about Plato. We give below a couple of the questions he was asked, relating to Plato and mathematics, and give his responses:
The 'Timaeus' stands aside from his other works, partly because it contains more cosmology and science than philosophy, but mostly because it contains a wonderful poetic creation myth - not all that dissimilar to the one in the 'Book of Genesis'. Why did Plato produce such a thing? Do you think he believed in his creation story literally, in the way one must assume that ancient Hebrews believed in the 'Book of Genesis'?
I myself think that he did not believe it literally. The question was controversial in ancient times, but Plato's closest associates took the view that Timaeus's narrative of the divine craftsman imposing order on chaos is a vivid way of presenting an analysis of what Plato took to be the fundamental structure of the whole universe. He wanted to see the entire universe as the product of order imposed in disorder, and by order he meant above all mathematical order. This, of course, is very different from the 'Book of Genesis'. Plato's divine craftsman is mathematical intelligence at work in the world.
So it is really a poetic way of explaining the intelligibility of the world, which has been a mystery for reflective human beings from the earliest times until now?
Yes. And of course such a very general proposition as the proposition that the whole universe is the product of imposing order on disorder is not something you can prove either in general or in all its detailed ramifications. Plato is well aware of this; it is a further reason for his clothing the proposition in a myth. All the same, the myth served as the guiding inspiration for something that Plato was very serious about indeed: a research programme for which he enlisted at the Academy the leading mathematicians of his day. Every advance in geometry, in mathematical astronomy, in mathematical harmonics, even a medical theory which exhibits disease and health as resulting from the propositions between constituent elements of the body - each such step forward is further proof of something Plato cared deeply about, the idea that mathematical regularities and harmonics and proportions are what explains things. And since these mathematical harmonies and proportions are for Plato the prime examples of goodness and beauty, this is a scientific research programme which is designed to show that goodness and beauty are the fundamental explanatory factors in the world at large. ... in the 'Republic' is the sketch of a programme for a scientific, above all a mathematically scientific, understanding of the world. In the 'Timaeus' Plato begins to carry it out, do his share of the work. ... the research programme, as I called the 'Republic's recommendations for progress in the mathematical sciences - this programme was actually carried out by the leading mathematicians whom Plato had gathered in the Academy to demonstrate the power and scope of mathematical order. From their efforts stem many of the greatest achievements of Greek mathematical science down to Ptolemy. Ptolemy's astronomy is the ultimate descendant of the astronomy done in the Academy with the backing of Plato's recommendations for the sciences. And since mathematical order is the expression for Plato of goodness and beauty, these sciences which show us the world as mathematically intelligible are simultaneously sciences of value.