The Cave and the Light: Plato Versus Aristotle, and the Struggle for the Soul of Western Civilization

by Arthur Herman

Speusippus had largely given up on Plato’s theory of Forms and the mystical theory of ideal numbers outlined in the Timaeus.3 But Plato’s nephew still clung to the notion that the truth about reality had to be found in mathematical formulae. However, Aristotle saw at once that even if the proposition that math is a certain and exact science is true, and even if the proposition that the first principles in philosophy must be certain and exact is also true, that did not prove that those first principles must be mathematical. The Pythagorean belief that “all things are numbers” was one of the first assumptions Aristotle’s own work would overturn.4 Aristotle had even less patience with the lingering Pythagorean emphasis on secrecy and cryptic aphorisms, which flew in the face of Aristotle’s overriding conviction that philosophy must necessarily be an open book, with everything as clear, organized, and straightforward as possible even for the slowest student.