During the medieval period, the seven liberal arts were divided into three verbal arts, or trivium, and four mathematical arts, called the quadrivium. The trivium is comprised of grammar, rhetoric, and dialectic, and the quadrivium consists of arithmetic, music, geometry, and astronomy. The trivium and quadrivium represent the historic evolution of the classical education of ancient Greece and Rome, as well as laying the groundwork for the birth of academe. Traditionally, a mnemonic has been used to introduce the subjects of the trivium and quadrivium: Grammar speaks, dialectic teaches truth, rhetoric adorns words, music sings, arithmetic counts, geometry measures, and astronomy studies stars.
The quadrivium has roots in ancient Greece among the Pythagoreans, whose belief that number is an ordering principle of the universe led them to seek out mathematical harmonies through systematic, philosophical analysis. Thus, arithmetic is the philosophy of number rather than the computational subject that later assumed the name. Addition, subtraction, multiplication, and division would, by the medieval period, be called algorism, whereas the problems of unity, equality, ratio, and proportion were regarded as the proper objects of arithmetical study. Similarly, the study of music engaged questions about the relation of number to sound and sound to harmony. Boethius’s laconic remark that geometry is the study of immobile magnitude and of forms circumscribes that topic well. Finally, astronomy is the study of the movement of heavenly bodies.
The trivium began in earnest with the rhetorical tradition of ancient Greece, although the systematic study of rhetoric was an invention of Plato’s in response to the rhetorical philosophy of the sophists. Rhetoric began as the practical study of oratory, intended to prepare Athenian citizens to take part in assemblies or to litigate at court. By the thirteenth century, rhetoric had turned to the art of embellishment. Circumlocution and amplification—the practice of superfluous speech or writing—took on such importance as to mark virtually all of the poetry of the period with endless digressions and distracting linguistic ornamentation. Grammar was considered the foundational discipline upon which all other disciplines were built. Grammar, the study of language and meaning, was the student’s first contact with the word, which is the principle of the trivium much as unity is the principle of the quadrivium. The student of grammar learned spelling, reading, and writing in his early years, and introduction to philosophical topics comprised the study of grammar for young men. The third subject of the trivium, dialectic, is the study of reasoning. Dialectical argument takes as premises answers put forward by one party in response to probative questions of another. The questioner then reasons from the given premises to a conclusion. The difficulty of dialectical argument lies in the fact that the answerers must accept the premises that the questioners form out of their responses. If no agreement can be established, dialectical argument cannot proceed.
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