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

by Arthur Herman

The subtext of the Elements is also the principle Euclid may have absorbed from his teachers at the Academy: that mathematics and geometry are reason’s direct insight into the mind of the “supreme geometer,” God Himself. Indeed, Euclid’s principal works could almost have served as textbooks for Plato’s Rulers in the Republic. They were the Elements for arithmetic and geometry; the Conic Sections for the study of proportion and harmony; and his Phaenomena as a guide to astronomy, since it focuses on the theory of uniformly rotating spheres.13 Still, as a work the Elements is pure Aristotle: one reason Raphael set Euclid firmly in Aristotle’s camp in his School of Athens. The book’s layout, with definitions, postulates (for instance, “All right angles are equal” and “Any line segments can be extended indefinitely in either direction”), and axioms, follows precisely the guidelines of Aristotle’s logic of science in the Prior Analytics.14 Euclid’s aim was also the same as Aristotle’s for all science, and for all good pedagogy.

Plato's god