What are the Seven Liberal Arts? : The Quadrivium and the Shortcomings of the Trivium

This is part of a  series devoted to classical education. 

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What is the Quadrivium?

The Quadrivium is the art of mathematics. It includes arithmetic, that is number; Music Theory, that is number in time; Geometry, that is number in space; and Astronomy, that is number in space and time.

As many parents who are trying to learn about classical education as adults who were educated in progressive schools, I struggle with defining the quadrivium any more so than I did above. As described below, I see how the Quadrivium, much like the Trivium, has its shortcomings. While traditionally the Quadrivium is meant to follow the Trivium, in today's society at least, we see that Quadrivium needs to intermingle with the Trivium as a student learns mathematics at a very young age and continues learning as he grows.

What are the shortcomings of the Trivium?

We took the method of the Trivium, that subjects can be conquered using Grammar, Logic, Rhetoric, and applied it to all subjects. This is very helpful when describing the pitfalls of Progressive Education. It is also very helpful in learning almost every subject. However, just because the Trivium is so helpful to learning, does not mean that it does not come with its own shortcomings. There are some subjects that did not fit into the ancient Greek's Liberal Arts. Terrence O. Moore writes in his essay entitled The Limits of  the Trivium, 

What do we not find in the trivium and the quadrivium?  History, government, 

economics (which had not even been invented yet), and ethics: the very disciplines 

that are central to the ancient and, later, the Enlightenment efforts to live a good and 

happy life in civil society.  We do not find poetry and art, either, though music 

is there.  That is a lot to leave out. 

In addition to these subjects that are missing in the Trivium, Moore discusses how a strict adherence to the Trivium can cause much frustration as Grammar level students are expected to spout facts and have no discussion (Logic/Rhetoric) and we find that Rhetoric students are still memorizing facts. Thus, we discover that these stages are not strict but yet should intermingle.

When we look at the modern classical education movement, we see that as we address these shortcomings of the Trivium, we indeed are teaching our children the Good, Beautiful, and True. We find that we are adhering to the definition of Liberal Arts; that we are forming the minds of the citizen - the free man.