ACCS conference notes, part 4 (of 5)
You aren't actually teaching the quadrivium, instilling virtue preserves justice when the legal system falls apart
Now coming to you from way in the back.
Here we go.
Timothy and Stephanie Slater, Reinvigorating the Contemporary Quadrivium
I appreciated the honesty of this talk, and the fact that you can usually trust scientists to say what they think, even if it gets them into tremendous trouble. In this case, classical schools often like to fancy that they teach the quadrivium: arithmetic, geometry, music, astronomy, those four liberal arts. But, they said, we don’t, in part because we now mean something substantially different by all four of those words, than what the ancients meant. But that’s OK. Christian schools, our goal is to bring students closer to God. The quadrivium isn’t sacred. If it helps us do that, keep it. If it gets in the way, jettison it. Our duty is toward the truth.
By the end of their talk, they “kept” arithmetic and geometry, but defined those terms in ways that would make good sense to moderns. Music and astronomy they kicked out - they still teach those subjects, but they aren’t really mathematical liberal arts as they were to the ancients. And they added in “natural philosophy”, so the final quadrivium that they teach is actually three subjects.
And now some notes.
The quadrivium is merely a tool to serve God, we are not a slave to it. So we began a project to think about if and how we should teach it today. Great projects are worthwhile (they do good, the results are beautiful, they offer a good return on investment) and truthful (the foundations are strong, we don’t hold our preconceptions as sacred, definitions are correct and honored).
The trivium is pretty well settled in classical schools, but the quadrivium is not. How it is different?
In the classical period, math and linguistics were taught at different stages of development. Now we teach them simultaneously.
The sciences are much different now than they used to be. Ptolemy, today, would not teach Ptolemy, he would say that’s wrong.
Math is unchanging, but the mathematical arts are supposed to change.
The quadrivium has been connected to occult practices.
Definitions change over time (what is number, for example?)
We asked ourselves the following questions to help guide our work:
How truthful are we? Is what we tell parents we are teaching, what we are actually teaching? (Is music actually a mathematical art, for example? Not the way almost all of us are teaching it now, no.)
What texts are we building upon? Are they appropriate?
What preconceived notions are we wedded to? (Do we think we have to keep teaching Ptolemy just because we’ve always taught Ptolemy?)
How fuzzy are our definitions?
What is a liberal art, anyway? There are a lot of classical definitions. Sometimes they are the seven unique skills, used to create and justify scientia. (And by the way, why seven? The people who thought there had to be seven were into numerology. We aren’t into numerology.) Sometimes they are defined as the tools by which all knowledge is justified.
Their school decided on the definition, “a liberal art is a fundamental subject that provides knowledge and skills to be used in other subjects”.
Again, we should not be scared about disqualifying historical liberal arts. The goal is always to direct attention to God.
What is the quadrivium? Historically, arithmetic, geometry, astronomy, and music. But smart people have disagreed, so we have the right to disagree too.
We defined the quadrivium as a collection of mathematical liberal arts. They allow students to explore and understand harmony in God’s creation. They develop abstract reasoning employed in other subjects. And they help students be better equipped to serve God through mathematical reasoning.
OK, now, what is arithmetic? Well, the famous Clark and Jain book says it is perceiving and relating discrete number, but that’s rather vague. A lot of schools like Nicomachus’s ancient book of arithmetic, but he clearly understood number very differently from the way we do. We don’t care, at all, about perceiving the mystical and powerful parts of a number. The ancients did. Some of what Nichomachus discusses (multitudes v. magnitudes) is really an artifact of the Pythagorean cult which, again, we don’t care about. To a significant extent, Nichomachus was an arithmologist, he was practicing numerology. We don’t need that in a modern Christian school. There are better foundations.
So we defined arithmetic as the study of quantity. We continue to study quantities all the way through Calculus.
What about the rest of the quadrivium? Well we asked, one, does it teach its own mathematical art? The sciences and their content are not arts, they are scientia. And, do they direct students to God?
Geometry we defined as the study of space and shape. Euclid is still good on this, still a valuable resource for moderns.
Music… the ancients cared about music for a lot of reasons we don’t care about it. Pythagoras thought the perfection of the human soul involved a sort of assimilation with the resonances of the cosmos. They taught about the resonances of the human body. We aren’t teaching any of that stuff. We don’t teach music as a mathematical liberal art. You don’t generally use the math you learn in music for other classes. We do teach music at our school, we love it. But it’s not a liberal art, so we boot it out of the quadrivium.
Astronomy, as taught today, also does not teach a separate mathematical skill. It is not seen as the basis for another subject unless you want to use it for divination or something. So it also is not a liberal art, we kick it out of the quadrivium.
But we added in natural philosophy, which we define as the study of quantity, space, and shape of the natural world. It includes having students describe: attributes, physical and chemical characteristics, functional characteristics, counting stuff by color and size and shape, measuring stuff, making lots of maps, and eventually creating research questions and generally exploring the big ideas via mathematical arts.
Louis Markos: Homer on Justice
The Iliad takes place in a pre-law society, a society with no criminal justice system. How do you keep order in that kind of society? You instill virtue in aristocratic leaders.
Our democracy, today, is falling apart because its citizens lack virtue.
If you want your kids to be healthy, you can either put a padlock on the fridge (which ceases to work when they go away to college), or instill in them a respect for their bodies.
In the US, the South still instills virtue in people in a way that doesn’t happen in the North. People learn courteous ways of interacting with the world. There are phrases like “don’t be ugly” that is really a warning against being ugly on the inside.
One very important way to get people (fictional or real) to internalize justice is via the concept of shame. You instill in your children not to do anything that would shame them or your family name. To the Greeks, “nemesis” is what shoots you down when you do something shameful.
The self-esteem movement is the worst thing that ever happened to education.
Shame is how the cowards are called to order in the Iliad. You internalize justice by avoiding doing that which is shameful. Shame does for our souls what pain does for our body. Shame is a signal that we’re doing something that hurts our soul.
“The best shame and blame culture is the Klingons.”
Another word the Greeks like is themis, which means justice, as in the right order of doing things, the right conduct.
And finally, xenia, which is the rules of hospitality between guests and host, or between the stronger party and the weaker party. In the Odyssey, you can identify who is good (Telemachus) and who is bad (the guests) by who honors xenia. A host is supposed to take a stranger into his house, feed him, clothe him, and only then ask his name. Guests reciprocate by not intruding on that kindness, eating too much, staying too long, etc.
THE END
Is it a good idea to keep the concept of a trivium and a quadrivium?
Also, I don't mean to dispute with Louis Markos third-hand, but societies that operate without stable courts tend to rely on violence, either constantly or as a last resort. Let's not overlook the Iliad being a depiction of war, a poem in which men are seeking and gaining status based on their ability to kill other men.