Trivium & Quadrivium

The trivium and quadrivium together represent the most important and integral principles of a classical curriculum. The word “trivium” literally means “three roads” or “three ways,” and these are grammar, logic, and rhetoric. The word “quadrivium” means “four roads” or “four ways”—arithmetic, geometry, music, and astronomy. Together these seven liberal arts have been the backbone of Western education for more than two millennia.


People often talk about the trivium or the quadrivium as “stages,” but this is misleading and in some ways incorrect. While it is true that every subject “has a grammar,” grammar is itself a subject, and so too is logic, and so on with all the liberal arts. At Holy Family Cathedral School we teach each of the seven liberal arts as subjects, seeing each as a content-area and not merely as a metaphor.


The most ancient theory of liberal arts education, now more than 2,500 years old, holds that being persuasive (rhetoric) depends first on being able to reason well (logic). Cogent reasoning and the ability to persuade both require competency in grammar. This is why grammar, logic, and rhetoric form an integral sequence in classical education.


Similarly, it is not possible to do math in time and space (to do vector calculus, for example) until each of these can be done in isolation. Understanding number in itself (arithmetic) is a precondition for using number in either space (geometry) or time (music) or both (astronomy). In mathematics, therefore, arithmetic leads to geometry, geometry to music, and music to astronomy.


The sequences which constitute the seven liberal arts are recursive. Once a given sequence is “completed” for the first time, that “course” is “run” over and over again. Just as an athlete runs the course again and again in order to train to a standard of performance, so too does the student of the liberal arts “run the courses” of learning again and again in order to achieve excellence. In this analogy of “course-work” these sequences are also “spiraling,” meaning that no subject really ever gets left behind and that all subjects are continually coming up in different ways.


The timeline of history represents another important recursive and spiraling element of a classical education. It is not enough to know the seven liberal arts in the abstract; these must be made concrete, and this is done by anchoring each to history—to the history of art, architecture, proportion, perspective, engineering, music, composition, literature, and especially cosmology, how different people in different times and places have understood humanity’s relationship to the heavens. To explain the order of the universe, one of the most ancient metaphors in the liberal arts tradition is music. The “music of the heavenly spheres” describes for the ancients the harmony of the planets’ orbital vectors, leading naturally to questions which can be solved only by philosophy and theology.


History’s most impressive philosophers, Socrates, Plato, and Aristotle, went against their culture of polytheism and proposed instead belief in monotheism, that there is only one god. Aristotle, on the basis of reason alone, posits that the one true god is the originator of all else that is, that he is the “Prime Mover.” Implicit in Aristotle’s view of the cosmos is the notion of intelligent design: the idea that the order of the world can be discovered because that order was written into the nature of all that is by its creator, God. To return to the metaphor of music, God our Creator is the “composer” and the movements of the heavenly spheres are His “music.”


Classical Catholic education therefore sees all science in the light of faith. We especially seek to understand how and why the laws of God bring into harmony all the laws of the universe, so that the Ten Commandments and The Beatitudes are no less a law of human happiness than the laws of chemistry which govern the behavior of gases which have eight valence electrons and are therefore called “happy” by chemists.


The questions raised by classical education clearly show the need for something more, and here at Holy Family Cathedral School that “something more” is our treasured, cherished, and beloved Catholic Faith. The Catholic tradition in education and culture anchors our curriculum to a firm belief in Jesus Christ and his mission of salvation, which is God the Father’s will and desire for all people in all times and places. For our faculty and staff, this is both a set of truths and a great love to be shared in a spirit of charity and with a feeling of great joy.

2020 – 2021 Enrollment

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