Overview

Above the gateway to Plato's Academy appeared the following inscription: "Let no one who is ignorant of geometry enter here." Plato (427?-347 B.C.)—an ancient Greek philosopher thought by many to be the most influential of all philosophers—regarded an understanding of the principles of geometry essential to the training of philosophers. Philosophers had begun to recognize a relationship between mathematical proofs, such as those exemplified through the study of geometry, and logic, the science of identifying the formal principles of reasoning. It was not until Aristotle (384-322 B.C.), a student of Plato's, however, that logic was systematized into a form that remains, for the most part, intact today.

Background

The need for definitive proof in philosophy became apparent early in history, especially in those instances where philosophical positions contradicted each other. Perhaps...