Quadrivium

Liberal Arts, codified as the basis of intellectual education in the Middle Ages, brought together two groups of subjects for learning: the Quadrivium and the Trivium.  These became the basis of the Liberal Arts education.

The Trivium had to do with verbal proficiency: Logic, Grammar, and Rhetoric. Logic taught how to process ideas clearly. Grammar taught how to combine words precisely; Rhetoric taught how to communicate persuasively.  The Trivium was necessary for effective communication; these subjects taught how to talk well. They educate Sophists, as Plato said.  Significantly, trivium evolved the word trivia. The Swarthmore education excels in this, more talkers than thinkers.

The Trivium does not teach to cultivate the intellectual substance that makes communication worth the effort. This was the realm of the Quadrivium.

The Quadrivium consisted of arithmetic, geometry, astronomy, and music.  They all have to do with mathematics.  The names are misleading.  Arithmetic must be understood as the study of number, geometry of number in space, music of number in time, and astronomy of number in space and time.  The Quadrivium, in short, had to do with metaphysical thinking, and was thought to form the basis of philosophy.

Mathematical thinking is the core of the Liberal Arts Education and belongs more in the realm of humanities than in that of science.  We all know that but forget it too easily in the modern world, especially in modern college educatiion, in which verbal skill is overemphasized and too often mistaken for intellectual learning.