Monday, November 17, 2014

The Trivium And The Quadrivium

The Seven Liberal Arts (and their aims)

At some point in the Middle Ages, through a slow process of growth and refinement, educators came to identify seven arts that were considered liberal.  The seven liberal arts were the arts practiced by people who were, or who would be, free.  (The Latin word liber can mean "a free man.")

The liberal arts were divided into two groups: the trivium and the quadrivium.  As the names suggest, the trivium included three arts, and the quadrivium included four.

The trivial arts sought to teach eloquentia, or eloquence, the proper use of words.  The quadrivial arts aimed at sapientia, or sapience, the proper use of numbers.

In each case there is a natural progression, beginning with the rudiments and building on those foundations to help the student master eloquence and sapience.

The Trivium and the Quadrivium (and how they are built)

The trivium proceeds like this:
  1. Grammar.  This is the study of words, and especially:
    • how definitions work, so that we can "come to terms" with one another; and
    • how words are assembled into meaningful sentences or propositions.
  2. Logic.  This is the study of the structure of arguments:
    • how to assemble propositions into arguments; and
    • how to draw proper conclusions from those propositions without error.
  3. Rhetoric.  This is the study of the proper use of arguments:
    • how to use arguments to persuade others; and
    • how and when to persuade without misleading people.
It begins with the basics of technique and ends with what we could consider the ethics of words.  Words are, after all, powerful things.  The old saw about "sticks and stones" is wrong.  Words can  hurt us, and they can do lasting damage.  They can also do lasting good in the mouth of a good leader,  in poems and songs, in well-crafted contracts, laws and policies.

The quadrivium proceeds like this:
  1. Arithmetic.  This is the study of number.
  2. Geometry.  This is the study of number in space.
  3. Music.  This is the study of number in time.
  4. Astronomy.  This is the study of number in space and time.
Once you've mastered the trivium, you have a proper understanding of eloquentia, and once you've mastered the quadrivium, you have sapientia.

But Is Any Of This Relevant?

It's not hard to see that a lot of this is outdated, especially in the quadrivium, which was like the STEM of the Middle Ages, focusing on mathematics, engineering, and natural sciences.  We no longer believe in the "music of the spheres" or that the motion of astronomical bodies is governed by harmony akin to music.  And our sciences and humanities have grown to include many other disciplines that (at least at first) don't seem to be included here.

It's also not hard to see that some of the way we educate today still has echoes of this structure.  For instance, until recently, we called children's schools "grammar schools," and this is why.We still consider it important to begin important enterprises with teaching the relevant vocabulary, grammar and logic: we often begin classes by introducing new vocabulary, and we begin contracts by defining terms.

And while we don't think of outer space as being a set of nested, harmonious spheres governed by intelligences who receive their direction from the Empyrean, we do think number is extremely important as a tool for discovering how nature works.  This may seem like the most obvious of points, but that is because the idea has pervaded our thinking.  It's a good idea, and it stuck.  Similarly, we have the hunch that inquiry into the nature of things will in fact be met with answers.  Again, this seems obvious, but not every culture has thought so.  The idea has stuck, and it has paid off.

Yes, But Only If You Care About Science And Freedom.

In my view, the trivial arts and their organization remain as relevant as they once were, for three reasons.

First, every free person needs to know how words are used.  If you don't learn to use them, and then practice with them, you will be easily misled. If you don't study persuasion, you are far less likely to know that you are being persuaded.

Second, and related to the first point, the sciences depend upon the trivial arts.  Students who cannot read and write cannot learn effectively.

Third, and perhaps most importantly, long study in the humanities leads one to consider both the way words are used for persuasion and the ethics of persuasion.  People who are trained in the conclusions of the sciences are not scientists, they are databanks.  People who are trained in some of the methods of the sciences are technicians.  Databanks and technicians are useful to other people.  But what we need are people trained in the scientific method, which, by the way, is not something we get from the sciences.  It is tested and approved by the sciences, but the natural sciences do not give it to us.  Which of the natural sciences could discover a scientific method, after all?  Scientific method is about the proper handling of data, the examination of claims and propositions, and the distribution of relevant conclusions.  Look back at the description of the trivium and the quadrivium and you'll see that this is the work of the former, not of the latter.

The Real Crisis In The Humanities

There is a lot of talk these days about the crisis in the humanities.  The money is all in the sciences, and smart students should go there to study, we are told.  College administrations look to humanities departments as service departments to bolster the offerings of the science departments, who do the real work of the university.

I actually don't dispute this view, even though I'm in the humanities.  It's quite obvious that much of the money is in the sciences, and I think that smart students should study the sciences.  That's because I think every student should study the sciences.

But I also think that smart students should engage in long study of the humanities.  The sciences depend upon the humanities, just as the quadrivium was legless without the trivium.  More importantly, people who want to be free -- that is, people who do not wish to be persuaded without their consent, people who wish to think for themselves, people who wish to wield tools and not just to be the tools of others -- these people need to study the humanities.

The crisis in the humanities is that even in the humanities we've allowed ourselves to forget how interrelated all the disciplines are. It's time to brush up our eloquence, for the sake of our students, and take this message to our schools.


Addendum: A friend wrote to me and pointed out that I called the second part of the Trivium "logic" when I should have named it "dialectic," which includes both logic and disputation.  I don't dispute his correction.

I've also since discovered  Dorothy Sayers' "The Lost Tools of Learning," an illuminating essay on the medieval liberal arts. I wrote this post hastily, after a meeting at my college where the question of what an education ought to do was under consideration.  I wanted to make a thumbnail sketch of the Trivium and Quadrivium for my colleagues, and this was the result of some quick typing in the last few minutes of the workday.  A fuller picture would have included C.S. Lewis' essay "Imagination and Thought in the Middle Ages," and at least some mention of Martianus Capella. Maybe another time I'll return to this topic and write that fuller essay.  For now, these references will have to suffice.

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