Today is Thursday, December 5, 2024, and this is William Michael of the Classical Liberal Arts Academy. Today, I’d like to take some time to talk about the quadrivium because recently, I posted a talk on the trivium that was titled, What is the Trivium and Why Do We Need It? At the end of that talk, I said that I would devote another talk to the quadrivium. So this talk will be titled, “What is the Quadrivium, and Why Do We Need It Now?”.
With the trivium, many people who are involved in modern classical education or homeschooling circles will have heard of the trivium. This talk of the three stages of learning, which was talked about in almost complete obscurity by Dorothy Sayers back in the early 1900s, was latched onto by Protestant homeschool publishers in the late 1990s. It was used as a clever gimmick to rebrand modern education and give it an appearance of private schooling or homeschooling—a supposed restoration of the lost wisdom of the ancients.
This was led, as I said, by Protestants back in the 1990s when a Protestant pastor, who you may see on YouTube today, named Doug Wilson wrote a book titled Recovering the Lost Tools of Learning. There’s this message of recovery or rediscovery or restoration of something that had been lost. Recovering the Lost Tools of Learning is taken from that talk given by Dorothy Sayers in, I think, the early 1900s. The title of her talk was The Lost Tools of Learning.
Again, you can see how we’ve got this talk in modern times about how something has been lost. There’s this great mystery of what’s been lost, and we present ourselves as people recovering something that was once of great value and widespread use but has been lost. Dorothy Sayers used the title The Lost Tools of Learning to present nothing but a modern philosophy of education based on modern psychological ideas about child development.
All she did was comment in that talk about what psychologists have to say about children’s development and education. She observed that it seems to fall into three stages, and we can give a fancy name to each of these stages to make it appear to be something medieval. She took the elementary stage of learning and called that the “grammar stage.” Then, she took the middle school years and called them the “logic stage.” Finally, she took the high school years and called them the “rhetoric stage.” She said, “Oh, look how clever I am. I can call this the grammar stage, the logic stage, and the rhetoric stage, and we can call this the trivium of education.”
It’s really just nonsense about modern theories of psychological development. She stole these names from history, redefined them, and began using them with new definitions. Then, she pretended to restore something lost because the old names are now being reused.
Dorothy Sayers talked about The Lost Tools of Learning, and Protestants latched onto this idea. They started the so-called classical education movement among Protestant people, as crazy and irrational as that is. Protestants were the ones who rejected classical education in the first place. But the Protestants, in the 1990s, pretended they were recovering the lost tools of learning, which they blamed on modern, secular society. In reality, it was Protestant-led revolutions in education back in the 1500s and 1600s that caused this loss.
The Protestants claimed to be recovering The Lost Tools of Learning, and a whole movement started in the 1990s called the classical education movement. It began in Protestant circles and was latched onto—more embarrassingly—by Catholics. This movement was adopted by Catholics like Laura Berquist, who started Mother of Divine Grace School in 1995. At the same time, the classical education movement was starting among Protestants, and Berquist just took all of that Protestant material and brought it into Catholic circles.
She used the same language, even quoted Dorothy Sayers as the foundress of their entire educational system, and started the so-called Catholic classical education movement. The undiscerning Catholic people gobbled it all up, ran with it, and have now created a terribly embarrassing plan for education. They pretend it is some kind of restoration of the education of saints and wise men, but it’s now been demonstrated quite clearly to be a total scam.
They’ve thrown around these words—grammar, logic, rhetoric, the trivium, and so on—as gimmicky marketing terms to give the appearance of secret knowledge of the past that they are recovering and selling to modern Catholic families. It’s just a big, embarrassing scam among both Protestants and Catholics—this classical education movement—which I regularly refer to as the fake classical education movement because it’s just completely fake.
Because of the misuse of the term “trivium”—grammar, logic, and rhetoric as stages of development—and all this irrational nonsense, the term “trivium” might be familiar, but the quadrivium will be unfamiliar. It really has nothing to do with the fake classical education movement, even though it is central to real classical education. When we go back in history—real history, history that you can and should actually go back, check, and confirm—we find that during the Middle Ages, in the lives of men like St. Thomas Aquinas, St. Albert the Great, and St. Augustine, their understanding of education had, at its foundation, the study of seven core subjects.
These seven subjects were the core curriculum from ancient times through the Middle Ages until the Protestant schism and the scientific revolution in the 1600s. The seven subjects are known as the classical liberal arts. The first three were grammar, logic, and rhetoric—not stages of learning but arts, subjects to be studied and practiced. Grammar, reasoning, and rhetoric are the first three and are referred to as the trivium. I talked about those in a previous talk, as I mentioned.
The latter four were arithmetic, music, geometry, and astronomy. These four mathematical arts were referred to together as the quadrivium, or the four ways. So, we have the trivium referring to what we might consider the language arts or rational philosophy, and the four mathematical arts in the quadrivium. These seven arts—these seven subjects of study—were the core curriculum from ancient times through the Middle Ages until the Protestant schism and the scientific revolution, both of which rejected scholasticism.
Scholasticism is the philosophy of the Catholic Church, rooted in Aristotelian philosophy, which was embraced and demonstrated to be in harmony with Catholic theology by St. Thomas Aquinas. Protestantism and the scientific revolution rejected Aristotelian philosophy. This rejection disconnected education from the classical tradition and medieval education. This disconnection by the Protestants and the leaders of the scientific revolution began the decline of education, which we now see all around us.
When I talk about classical Catholic education in the Classical Liberal Arts Academy, I’m talking about going back in time before the Protestant schism and the scientific revolution and getting back on track—where Catholic education left off, where everything ran off the rails. I’m talking about going back to scholastic education and simply picking up where Catholics left off in the 1600s.
Now, some may say, “Well, maybe St. Thomas Aquinas, who lived way back in the 12th and 13th centuries, had a form of education that isn’t appropriate for modern society.” If that’s the case, I’d like for Catholics to explain why St. Ignatius of Loyola and the Jesuits in the late 1500s and 1600s worked to restore scholastic education. Why were they teaching Aristotle? Why were they teaching according to the teachings of Thomas Aquinas? Why were they having students read Cicero in class? It’s because it was very clear to the saints in the 16th century that the education of the 12th and 13th centuries remained true Christian education.
They were fighting against the Protestant reformers and the leaders of the scientific revolution by starting new schools that preserved real classical Catholic education. We can read this in the Ratio Studiorum. Moreover, when we go to the 19th century—the 1800s—we find Pope Leo XIII urging Christian people to restore Christian philosophy. When he said “Christian philosophy,” he meant the philosophy taught by scholastic tradition in the Catholic Church. He called for the restoration of Christian philosophy in the 1800s.
It doesn’t matter that this philosophy was promoted in the 12th century. It was also promoted in the 16th century by saints, in the 19th century by a saintly pope, and even into the 20th century by Pope Pius X. In his encyclical against modernists, Pius X argued that the teachings of St. Thomas Aquinas must remain the foundation of Catholic education.
That’s the 20th century. So, any talk dismissing scholasticism or classical education as something from the Middle Ages or the 12th century simply ignores the history of Catholic education.
In the Classical Liberal Arts Academy, we work to research, restore, publish, and teach the classical liberal arts—the real classical curriculum and real classical education. This consists of grammar, reasoning, rhetoric, arithmetic, music, geometry, and astronomy—the seven classical liberal arts.
I encourage you to go online. When the kids go to bed one night, hop on Google and search “seven liberal arts.” Don’t go through the articles or website results—you’ll get lost in fake classical education garbage. Go to the images instead. Look at the history of paintings, engravings, and statues of these seven liberal arts. You’ll find that they were the curriculum of Christian education throughout history. There’s a great artistic tradition of personifying and illustrating the seven liberal arts. That’s true classical education—classical Catholic education—the only kind of education there ever was in Catholic history.
When we talk about the trivium, we mean the arts of grammar, reasoning, and rhetoric—speaking, reading, and writing rightly; developing and ordering our thoughts according to the science and true understanding of reason; and then communicating reason to others to help them order their thoughts. These three arts are the trivium.
When we talk about the quadrivium, we’re brought to the four mathematical arts. The real proof of the falsehood of the fake classical education movement is its complete avoidance of the topic of the quadrivium or the four mathematical arts. They talk about classical education as if it were three stages of learning rather than seven arts—a total fabrication.
The quadrivium consists of the mathematical arts of arithmetic, music, geometry, and astronomy. These four arts are not even mentioned in the fake classical education movement because they can’t figure out how to fit them into their nonsensical system of three stages. So, they just ignore them. If you listen to one of these promoters like Martin Cothran from Memoria Press, he’ll claim that modern mathematics like algebra and calculus replace the quadrivium—just clueless nonsense.
Modern mathematical sciences like algebra and calculus are practical. They’re useful for modern natural sciences, like chemistry and physics. But they are not the same as the quadrivium. They belong to different systems of education. The quadrivium is for those seeking wisdom and philosophy, while modern mathematical sciences serve modern educational goals like high school diplomas and college admissions.
If your aim is wisdom, study the quadrivium. If your aim is a diploma or degree, study algebra and calculus. The two are not in competition—they’re just different pursuits for different ends.
The classical liberal arts belong to the pursuit of wisdom through philosophy. Modern mathematical sciences belong to vocational or academic qualifications. Real students—those who seek wisdom—are devoted to lifelong study, not just schooling for a diploma or degree.
So, if you want to pursue wisdom, study the quadrivium: arithmetic, music, geometry, and astronomy. These are the four arts of the quadrivium. This is what the Classical Liberal Arts Academy offers—courses in classical arithmetic, classical music, classical geometry, and classical astronomy. These are the real arts of the quadrivium.
The reason why we call them classical arithmetic, classical music, classical geometry, and classical astronomy is to distinguish them from the use of these words in modern circles where they have other meanings. But that’s what those four courses are for in the Academy. Those are the four arts of the quadrivium.
Again, if you look at the fake classical education movement, you won’t even find them mentioned because they can’t even figure out how to squeeze the quadrivium into their three stages of learning. It doesn’t even make any sense, so they just ignore it. They just ignore it.
And if you listen to one of these fakers, like Martin Cothran, who works with Memoria Press, he’ll just talk about how modern mathematics, like algebra and calculus, replaces the quadrivium. It’s just clueless nonsense. There’s a distinction between modern mathematical sciences like algebra and calculus and the mathematical arts of the quadrivium.
Modern mathematical sciences are useful, just as modern natural sciences are useful. If you want to study modern chemistry or modern physics, it’s very helpful—and even necessary—to study algebra and calculus. These modern mathematical sciences are used for calculation in modern natural sciences. They’re useful, but they have nothing to do with quantity in a philosophical sense. They are practical mathematical sciences used in modern natural science, going back to Isaac Newton, who argued that natural philosophy should be pursued through mathematics. In fact, he was one of the founders of calculus for that reason.
So this isn’t an either/or. These different sets of mathematical studies belong to two different kinds of education. The quadrivium consists of the mathematical arts for those seeking philosophy, timeless ancient philosophy. We pursue philosophy through the arts of the quadrivium because these four arts are the study of the four subjects of quantity. And quantity is the second category of being in philosophy.
If you’re asking, “Does my son need to study algebra?” I would say, “Yes, probably.” First, because it’s considered a normal high school requirement in our generation, so I would study it for the sake of a high school diploma. Second, it’s important for college admission, which is part of how our economic educational system works. So if you want to apply for admission to a selective college, you’ll need to show you’ve studied modern algebra. Yes, you should study it, but that’s the reason why you study it.
You don’t study algebra for the sake of philosophy, and you don’t study classical arithmetic or classical geometry for the sake of college admission or a high school diploma. These are two completely different systems, two different worlds in education. It’s not about choosing one or the other but understanding that in different spheres of life, we have obligations to both.
I would argue that algebra and calculus are more important when you’re a school-age student trying to get a high school diploma for college admission. At that stage of life, algebra and calculus are more valuable because you need them for immediate concerns, like your diploma and college admission. But in the long term, if you’re going to pursue wisdom and study philosophy, which very few do, you’ll need to study the four mathematical arts of the quadrivium. That’s what they are.
The quadrivium is not to be confused with a high school curriculum. It has nothing to do with high school diplomas or high school education. Real students—students seeking wisdom—don’t stop talking about education when they graduate or get their degree. Their whole life is devoted to the pursuit of wisdom. Real students are seeking wisdom throughout their entire life, not just while in school.
So don’t get these things confused. Don’t try to mix them into a school program to make money off of anxious parents worried about their kids getting diplomas or into college. Don’t drag these words into a K-12 school where teachers who only serve high school diplomas are pretending to be philosophers restoring ancient education. Ancient education didn’t have high school diplomas or grade levels.
This fake classical education movement is just confusing these things for the appearance of wisdom to make money—which is what sophists do. But if we’re interested in real philosophy and wisdom, then we can talk about the four arts of the quadrivium. This is why the modern, fake classical education movement has nothing to do with the quadrivium. It also has nothing to do with the trivium; it just uses those words as marketing gimmicks to persuade parents to give money to unqualified teachers.
The seven liberal arts—grammar, reasoning, rhetoric, arithmetic, music, geometry, and astronomy—belong to the pursuit of wisdom, which has nothing to do with modern compulsory schooling. Keep these things separate.
This still isn’t the entire transcript. I will now finish the rest in the same format.
So, that’s what the quadrivium is. Let’s talk briefly about why it matters.
Why should we care about the quadrivium? Well, I can speak to the most purely philosophical listener and say this: the reason why you need to study the quadrivium is that it is the means of pursuing wisdom. Quantity is the second category of being. The right way of philosophizing, as the ancient philosophers said, is to go through the quadrivium to pursue the study and understanding of this second category of being—quantity.
But again, the question is, why? Why is quantity in philosophy so important? That’s the key question we have to answer. Why is quantity important? Why did philosophers like Pythagoras make quantity the most important study in the pursuit of wisdom? Why did Plato consider quantity so central to the pursuit of wisdom? Why this obsession with mathematical pursuits in ancient philosophy? This relates to theology and natural philosophy.
When we look at the natural world, remember that the goal of philosophy is to know God and His works. As the Book of Wisdom says, philosophy is the pursuit of the knowledge of God and His works. That’s what philosophy really is. That’s what wisdom really is.
Ancient philosophers, outside of Israel and divine revelation, sought to know God through philosophy. We find Aristotle teaching true things about God in his writings. They did this philosophically, through reasoning. They also sought to understand natural philosophy—the order in nature that God used in the design of the world. As the philosophers studied the order in nature, they asked: What is the ordering principle of this world? How can we figure out the design of this world?
And here’s what they were trying to discover: If there is a God, if there is a divine, infinite being, did He have a plan in creation? Was there a design, a form, or a pattern? Was there an end by which and for which He made everything that exists? The philosophers studied and observed the natural world, and thinkers like Pythagoras concluded that the principle of order in the world relates to quantity. It seems that God is a mathematical designer, designing things according to quantity.
For instance, look at the moon. God could have made it a flat triangle, a square, a cube, or a pyramid. He chose to make it a sphere. Look at Jupiter—sphere. Look at the Earth—sphere. Not only are the celestial bodies spherical in shape, but their motion is circular. They’re not moving chaotically but in discernible, orderly patterns.
This principle of order is why quantity is significant. The natural world is not chaotic. God, the Creator, is a mathematical intelligence. To know God and understand His works requires us to understand quantity. This is why the study of quantity was central to ancient philosophy and why the ancients said the only way to philosophize rightly is through the quadrivium. The whole world is ordered by the quadrivium.
This is why the quadrivium is so important for the study of philosophy and the pursuit of true wisdom. But it goes even deeper. Christians may find this surprising: When God chose to reveal Himself to men through divine revelation, He revealed Himself primarily through quantity. The fundamental doctrine of Christianity is mathematical.
What is the first concept to be learned about the essence of God? The fundamental characteristic of God is His number. Christians profess that God is a Trinity—one divine being in three persons. This is a doctrine of quantity. God is three in one. The fundamental doctrine of the Christian faith is mathematical in this ancient sense.
The ancient Jews professed, “The Lord our God is one.” Christianity builds on this, revealing that God is more mysterious—He is one God in three persons. This doctrine of the Trinity is central to divine revelation. The Apostles’ Creed and Nicene Creed draw our attention to this doctrine, which begins with God’s quantity.
This shows us that the study of classical philosophy, including the mathematical philosophy of the quadrivium, is not just some obscure intellectual hobby. It’s central to the Christian faith. Abandoning classical studies leads to a neglect of this fundamental aspect of our theology. Many modern churches no longer talk about the Trinity because, in the modern mind, it seems irrelevant. Yet divine revelation begins with quantity.
The ancient philosophers understood the significance of quantity. Aristotle, for example, uses mathematical reasoning in his arguments about the soul and other philosophical topics. Understanding the quadrivium allows us to contemplate and understand both natural and divine truths more deeply.
Of course, most people aren’t interested in wisdom. Aristotle identified three types of people: those who live like cattle, seeking only to avoid pain and enjoy pleasure; those who seek honor, fame, and recognition; and those who seek wisdom. The study of the quadrivium is for the last group—those who desire to know God and His works.
This pursuit is not going to be popular. It’s not something you’ll discuss at the dinner table or in casual conversation. It’s for private contemplation. As you grow in understanding, you may inspire others to join the pursuit of wisdom. But don’t expect it to be a mainstream interest.
The quadrivium matters because it allows us to know God and understand His works. It leads to wisdom. The seven liberal arts—grammar, reasoning, rhetoric, arithmetic, music, geometry, and astronomy—are the steps to wisdom. Understand what they are, and most importantly, study them. It’s not enough to know about them or talk about them; we must master these arts to enjoy their fruits.
That’s what the quadrivium is and why it matters. If you have any questions or would like to explore related topics, feel free to comment or email me. Most importantly, join us in the Classical Liberal Arts Academy and study these things. That’s the only way to become wise.
God bless you.
