Those who are bringing back classical education as an alternative to the deadends evident in John Dewey’s progressive education are familiar with the trivium: grammar, logic, and rhetoric, the three liberal arts that lead to a mastery of language. The other four liberal arts, the quadrivium, though, gets short shrift: arithmetic, geometry, music, and astronomy.
Many people think that the liberal arts is just another word for the humanities, forgetting the quadrivium completely. Dorothy L. Sayers, whose essay “On the Lost Tools of Learning” was a major catalyst for the revival of classical education, thought that the quadrivium represented “subjects” that would be learned after the trivium provided the tools for doing so. In this she was just wrong. The quadrivium are “arts”; that is, powers of the human mind. They are essentially mathematical, even in the way music was approached. Thus, classical education embraces the two spheres that educators recognize are necessary for education: language and mathematics.