The talk above, on the Order of the Trivium and Quadrivium, was transcribed digitally by Otter.ai. It will be edited as time allows. To help with editing, please contact us.
A very common question that I receive regarding classical Catholic studies has to do with the order that exists within the Trivium and Quadrivium. I’m asked, Is there a certain order in which these subjects are to be studied? How do we know that order? How do we organize the study of the the Trivium? And the Quadrivium? Do we need to wait until the Trivium is completed before we start the Quadrivium? Do we need to wait until all of Grammar is completed before we start Reasoning? And is the same true before we start Rhetoric? Does all of Reasoning have to be finished first?, and so on.
So these questions about the order of the subjects and how the Trivium and Quadrivium are to be studied are very common. They’re necessary questions that have to get answered before we can organize a school or study program. So it’s obvious that good answers to these questions are necessary.
Now, having said that, we have to acknowledge that the reason people are asking this question is because they haven’t studied the Trivium and Quadrivium. That’s the reason why men and women are asking this question. They simply don’t know because they’re trying to organize something that they haven’t studied. Once one has studied the Trivium, and the Quadrivium, the order of them is very easy to understand. There’s no mystery to it, there’s no confusion about it. It’s very simple. And I like to say it’s natural; there’s a natural or logical order to our studies, and it’s very simple, nothing complicated.
I’d also like to say that, if you’re looking to study the Trivium, or the Quadrivium, I think the best place to do so, at this point in time is with me, in the Classical Liberal Arts Academy. The entire curriculum is already laid out and broken down into the courses, the texts are already prepared, the lessons are already prepared, and you can save yourself a lot of time and trouble by simply studying in the Classical Liberal Arts Academy. If you’re a school teacher, or school administrator, and you’re trying to bring classical Catholic education into your school, again, the best solution, I believe, is to simply work with me in the Classical Liberal Arts Academy, because the work’s already done, and you’re going to waste a lot of time and energy reinventing the wheel when you could pick up from where things are already at and focus on more important issues, which is what I’d recommend.
But anyway, I’d like to take some time to discuss this question of the order of studies in the Trivium and Quadrivium. This is not a prepared lecture, I don’t have notes or anything in front of me. So bear with me and listen patiently as I think and talk through the subject and try to provide the best answer that I can.
There is no question that there is an order in the Trivium and the Quadrivium. There’s no question about that. There is no question that Grammar comes before Logic and Logic before Rhetoric. There is no question that Arithmetic comes before Geometry, and that Geometry comes before Astronomy. There’s no question that Arithmetic comes before Music. No question that there is an order in the arts of the Trivium and the Quadrivium.
The problem is that the order in these arts is based on the order of ideas. It’s the order in which ideas can be understood, very simple. It’s not some complicated order. It’s certainly not an absolute order in the sense that one must be finished before another can be started. That’s not true at all. The order is simple and natural. It’s a common sense kind of order and I’ll explain what I mean by that.
But if we’re asking the question, let’s just take an example, let’s say we have a 10 year old student, and a parent wants to know, where his son should begin studying. He’s 10 years old. Where should he begin? Should he begin at the beginning in Grammar? And does he need to finish Grammar and Logic and Reasoning before he begins Classical Arithmetic?
The answer to that question is no. The student does not have to wait until entire arts are studied before another art can be started. We have to understand the order that we’re talking about when we discuss the Trivium and the Quadrivium. And again, I want to emphasize the reason why people are asking this question whether it’s a parent, or an adult student, or a school teacher, or administrator, is because those asking haven’t studied the classical liberal arts. So my advice to everyone is just study the classical liberal arts and these questions will take care of themselves. Focus on studying the arts yourself, whether you’re a parent or a teacher, or an administrator. You can’t put off these studies and expect to be able to lead students to mastery of them. You’re going to eventually have to address these studies directly yourself; and if you would do so, these questions would disappear.
I understand why people ask this question. I understand they’re trying to figure it out. They’re trying to organize and plan, consider whether changes can be made, etc. I understand the purpose of the question, but I just want to make sure it’s clear that you can only continue talking about classical education for so long. At some point, someone’s going to have to stop talking about it, and study it; do the actual studies. And when that person does the actual studies, these questions will go away. So do the actual studies.
I especially hope that this question is not being asked by people who are faking it, who are trying to appear to be some kind of teacher or school administrator, or some classical educator, acting as if they have some knowledge in front of other people that they don’t actually have. I hope that that’s not the motive behind this question, so that you can have an appearance of wisdom so that you can do business with that appearance. That’s what sophistry is. So I recommend that if, if that’s where you’re at, if you’re asking these questions, because you’re trying to make money and you’re trying to appear to have knowledge and education that you don’t actually have, so that you can impress people and possibly collect money as a tutor or a school administrator, I ask that you please, please not do that. That’s what sophistry is all about. Sophistry, as Aristotle explains, is, when a man gives an appearance of wisdom, he pretends to have wisdom, for the sake of moneymaking. That’s what sophistry is. If you want to understand these things, please take the time, do the work, and study the classical liberal arts for yourself. I invite you to join me in that study in the classical liberal arts academy, rather than fake it, rather than live behind appearances and try to always piece things together. When you don’t actually know what you’re talking about. My advice is, join me and study the classical liberal arts so that these questions and uncertainties can go away by actually studying.
But nevertheless, like I said, it’s a good question. And for those who simply want to understand or learn more about the classical liberal arts, I’m happy to get into this topic.
The Seven Liberal Arts
Let’s start by simply identifying the seven liberal arts and talking about what each of them is, because that’ll help us to understand the order. We have two divisions of the seven, classical liberal arts, two divisions. The first division consists of three arts that relate to language studies and reasoning and communication. And this is the Trivium, three arts of the trivium. Everyone knows the names, but few people actually study them. The names of the three arts of the Trivium are Grammar, Reasoning (I prefer to use Reasoning rather than logic, or dialectic.) and Rhetoric. Grammar, Reasoning, and Rhetoric. Those are the three arts of the Trivium.
And then the four arts that make up the Quadrivium have to do with the study of quantity. The mathematical arts, each of them focuses on a different species of quantity. If we take the subject of quantity, we can divide it into two different species, quantity divides into multitude, and magnitude. Multitude then divides into absolute (or discrete) multitude, and relative multitude. The study of absolute multitude is Arithmetic, classical Arithmetic; the study of relative multitude is Music. The other division of quantity, magnitude, divides into magnitude at rest, and magnitude in motion. The study of magnitude at rest is Geometry, and the study of magnitude in motion is Astronomy.
So we have these seven, classical liberal arts, three of them, like I said, relate to language, thinking and communicating, and the other four relate to mathematical studies, the study of quantity in the four different species of quantity. So make sure that you understand that. Take a minute, go back, and make sure that you can name the seven liberal arts, and you can explain what each of them is. That’s the first obstacle in understanding the order of the seven liberal arts.
Grammar
Now, if we go back to the first of the liberal arts, the first art of the Trivium, I should say, it was Grammar, and Grammar itself divides into four different parts. Grammar, the first art of the Trivium divides into four parts. Generally speaking, Grammar is the study of speaking and writing, rightly speaking and writing correctly. That’s what we study in the art of Grammar: how to speak and write correctly.
And what does it mean to speak or write correctly? Well, we start getting into philosophical issues. Right off the bat, Aristotle teaches that language is established by convention, language is not natural. Men established languages by agreeing on the details of a language. If you think of what a dictionary is, a dictionary is a book that contains lists of all of the words used in a language, and what those words are used to signify. It’s an explanation of the meaning of the words used in a language. That’s what a dictionary is. If you’re an English speaking person, you have one dictionary. If you live in a different country, and don’t speak English, let’s say you speak French or Spanish or Chinese or Russian, you’ll have a different dictionary. If an animal runs across the field, each person representing each of the different languages will refer to that thing by a different name. The name of that thing is not natural. The name of that thing is established by convention, and it differs from one language to another. And so in order to speak and write rightly, we have to study to basically learn what men have agreed upon. So that the language can be spoken and written in a way that can be understood by everyone else. That’s what it means to speak and write rightly. It means to speak and write according to the established usages and practices of those who speak a certain language. And that’s what we study in the art of Grammar, we learn the rules of a language, and Grammar needs to be studied separately for every language that we wish to learn. If we want to learn Latin, we have to study the Grammar of Latin. If we want to learn English, we have to study the Grammar of English. Greek, French, Spanish, Italian, Russian, Chinese, Hebrew, the same is true, we have to study the Grammar of each language because each language is spoken and written according to convention according to agreements made by men. And we have to learn how to speak and write the language as everyone else does, so that we can communicate. So you can see right off the bat, if you want to learn multiple languages, you may be studying grammar when you’re eight years old to learn Latin. In school, you may be studying grammar, when you’re seven years old to learn the grammar of your own native language. But if you choose to go to college, or seminary, or even as an adult, take up a language, you’re going to be studying grammar at all different points of your life. Because grammar is simply an art. It’s an art of speaking and writing rightly, in a particular language. It’s not connected to any level of study, any level of or stage of learning, it’s not connected to any age. It’s an art that can be studied at any time and normally is studied at many different times in life depending on what we need to know and when we need to know it. So grammar comes first, because in grammar, we learn the rules of a particular language. That’s what we mean when we say that grammar is the first art of the trivium. We can’t talk about reasoning. Until we’ve studied grammar. We can’t talk about rhetoric, until we first learned the grammar of language. So grammar comes first, because we can’t think or communicate until we’ve learned to speak and write rightly, in a particular language. And I said before that grammar has four parts, there are four parts of grammar. And the four parts are orthography, etymology, syntax and prosody. orthography, etymology, syntax and prosody. Now, each of those parts, obviously focuses on a certain topic orthography the first part of grammar focuses on letters and the sounds of letters. It doesn’t necessarily focus on pronunciation because pronunciation is complicated, and also relates to what’s called prosody, which is the fourth part. Orthography is primarily concerned with simple phonics, learning the alphabet, the sounds of the letters, things like accents, breathing marks in a language like Greek diphthongs special combinations of letters that have unique pronunciations, those sorts of things how to read and write the language are the concern of orthography. It’s, it’s okay to think of orthography as, as handwriting and phonics. That’s basically what orthography is. So learning the Greek alphabet, would be Greek orthography. Learning the English alphabet or the Hebrew alphabet, that would be orthography. Learning the letters learning the sounds of the letters how to read the words of the language, simple phonics is orthography and also learning a little bit how to articulate all the sounds of a language. So that basic speaking can be understood. Like I said, pronunciation relates also to prosody, which is part four of grammar. The second part well, let me just say the first part we study the letters of a language, we study the letters, which are the parts of words, words are made of syllables, syllables are made of letters. orthography is the study of letters and syllables. Speed speech, however, speech is made of words. And the second part of grammar is called etymology. And in etymology, we study the parts of speech that is, we study the classes of words, used in a language. Classically, there are eight parts of speech eight different classes, into which words can be grouped. So though there are 1000s, and 1000s of words, there are only eight classes of words. And in etymology, we learn the classes of the words or the parts of speech. And we learn how words are formed in a language. So we learn declensions conjugations, all different forms and endings of words. Etymology is where we study the words of a language, the parts of speech. And the third part of grammar, we want to understand how to put words together in order to form speech in order to make sentences. And if you think about it, that that activity is called construction, we want to learn how to put the parts of speech together to construct sentences to make speech. In Latin, this is called construct to its construction. That’s what this third part is putting words together properly, to make sentences in a language. In Greek, it was called syntaxes. And that’s where we get the word syntax from. The idea of syntax is like cement, putting bricks together with cement to make a wall. That’s the idea of syntax, the rules of how sentences are constructed, putting the words together in order to express ideas. So the rules of construction, the rules of sentence making, is what’s studied in the third part of grammar syntax. Once we learn how to put sentences, or how to make sentences, then we want to learn about different kinds of sentences. We want to learn the details of, of other things that we can do with language like how we can use rhythm, how we can use meter, how the pronunciation can be varied to accomplish different effects, we want to get into the principles of poetry. That’s what’s studied in the fourth part of grammar, which is called prosody. We get into the the more beautiful or persuasive uses of language. We normally call that poetry, but it’s called porosity in the old grammar books, and we study that in the fourth part of grammar. So we go from the study of letters and syllables and Part One to the study of words in part two, the study of sentences in part three. And finally, more elaborate uses more rhetorical uses of language in part four. And remember, I said that Part four is more rhetorical uses of language now. Grammar comes first, because if we don’t know the letters and sounds and words of a language, how can we possibly study reasoning, or rhetoric we can’t. The knowledge of those arts assumes that we already know how to write and speak rightly in a language and so grammar comes first, but all four parts of grammar don’t have to come first. When we say grammar comes first, we need to be able to read and write the language we need to know orthography and etymology because we need to construct sentences. So let’s consider those first two parts of grammar orthography and etymology and now let’s look at the study of reasoning.
Reasoning
The second art of the trivium Our source for the study of the art of reasoning is not some modern logic textbook or anything like that. The source of the art of reasoning is Aristotle’s Organon. And that’s a collection of books. And in each book, Aristotle teaches the science of one part of reasoning. Just like we talked about four parts of grammar. Aristotle teaches the parts of reasoning. The first book of the Organon is called the categories. And in that first book, we study the relationship between ideas and words, just like the beginning of grammar. We talked about the importance of words and their effect in reasoning. We learn Aristotle’s 10 categories, which I’m not going to talk about now, because that’s a complex subject that you learn to learn by studying in reasoning. We learned about Aristotle’s 10 categories, we learned about how words are used in reasoning, and what role they play in the activity of reasoning. That’s Aristotle’s categories. The first part of reasoning. In the second part of reasoning, we study Aristotle’s book on interpretation. And in the book on interpretation, we learn how propositions are formed. This is comparable to syntax. In grammar, we learn how sentences are formed, but only one particular kind of sentence. This is what’s important. In grammar, we learned that there are a number of different kinds of sentences that can be constructed. We can construct indicative statements, we can construct imperative statements or commands, we can construct. Or I should say, we can use moods of verbs that are subjunctive, or Optative, or potential. When we express something that’s not necessarily true or factual, maybe a wish, or a prayer, or a conditional statement. That’s not indicative. Its Optative, or potential. So there are different kinds of sentences that we can form. And we learn about these in grammar and syntax. But when we come to reasoning, in in reasoning, there’s only one kind of sentence that we can use. And it’s the Indicative statement, or Aristotle refers to it as the enunciative statement. An indicative statement is a proposition that is either true or false. We can only use these indicative statements in reasoning. So if I were to say, I hope it rains tomorrow, that’s not a statement that can be used in reasoning. Or if I were to pray and say, may God grant me health, that’s not an indicative statement. It’s not true or false. If I give a command and I say, sit down, that’s not true or false. The only statement that can be true or false is a simple indicative statement with a subject and a predicate. If I say it’s raining outside, that’s an indicative statement. That’s either true or false. If I say all men are rational animals, that’s an indicative statement. So in Aristotle’s book on interpretation, we learn about what kind of proposition is acceptable in reasoning. And like I said, indicative statements are the only acceptable type of sentence for the art of reasoning. So going back to grammar, when you learn about the different moods of verbs and different kinds of sentences that can be made, you can see you don’t need to understand that in reasoning. In reasoning, all you need to understand are indicative statements, which are the simplest kind of statements. So to go on past indicative sentences and get into questions and commands and wishes and prayers and other kinds of expressions. That doesn’t have to do with reasoning that has to do with rhetoric, as we’ll see in a bit. And so grammar gets into topics that are not necessary for the study of reasoning. Grammar gets into topics that are necessary for reasoning, which is the next art in the trivium. So You don’t have to study all of grammar, all four parts of grammar before you can begin the study of reasoning because reasoning doesn’t use everything that grammar teaches us about. You don’t need to learn the principles of poetry. You don’t need to learn all of the different moods of verbs and all the different types of expressions that can be made. Reasoning focuses on simple, indicative statements that are true or false. These are the simplest kind of sentences there are. We learn these right in the beginning of syntax. And so that’s what I’d like you to see that reasoning doesn’t follow the whole art of grammar. It only requires some of the art of grammar. It follows grammar, because without grammar, you cannot study reasoning. But you do not need to study the whole art of reasoning before you begin the study of the art of reasoning. So the second book of Aristotle’s work on reasoning deals with indicative statements that’s on interpretation. Now, we put words together to form propositions. That’s what we study in on interpretation. That’s what we study in syntax and grammar. But what happens when we begin to put propositions together? When we begin to put propositions together, then we learn that when we combine some propositions, something happens when we combine certain propositions, new propositions necessarily arise from them. And this is the process of reasoning. This is what reasoning is. The mind because it’s been gifted with this power of reasoning, acts upon propositions when propositions of a certain kind are presented to the mind, reasoning, joins them together, and produces new propositions. Reason creates knowledge by joining together, propositions to produce new, necessary conclusions that result from those other propositions. Aristotle in his work prior analytics, prior analytics explains the structure of an argument or a syllogism in reasoning. And a syllogism is a certain combination of propositions of two propositions. That leads to a third proposition necessarily, this is what reasoning is. This structure of a rational argument is what Aristotle explains, in prior analytics, the general idea of a syllogism, the general idea of what we’d call a logical argument, is taught in prior analytic, so see how it develops in grammar, we had letters, then words, then sentences, and then more elaborate forms of speech in prosody. In reasoning, we start again with words, and then propositions. And then in the third part, we move on to combinations of propositions to form syllogisms, or arguments. That’s the third part of reasoning. The fourth part of reasoning, Aristotle takes that doctrine of syllogisms, which is established in prior analytics. And he explains how it’s used with premises that are universal and self evident, that are absolutely true. So when we have a certain kind of first premise, and we apply the doctrine of the syllogism to that type of first premise, a self evident, universal truth, it produces a certain kind of reasoning that produces a certain kind of conclusion. And this is called demonstrative reasoning. So the next part of the art of reasoning is demonstrative reasoning, which is studied in posterior analytics. We learn what happens when we combine In certain kinds of propositions, so that the first proposition is universal and self evident or previously demonstrated. And when we combine the propositions it produces a conclusion of a certain quality. And that’s demonstrative reasoning. demonstrative reasoning is the reasoning that’s used to establish and teach philosophical sciences. demonstrative reasoning, which is taught in posterior analytics is the science or art, of philosophical demonstration. That study in posterior analytics is what is unique to the work of Aristotle, that’s his most important contribution to philosophy and the pursuit of wisdom in world history was the establishment of the art of demonstrative reasoning in posterior analytics. So let’s move on the next book, in the art of reasoning is titled The topics, the topics. And what we look at, in this next book, or this next part of reasoning is what happens when we take the doctrine of the syllogism. But we start with a different kind of first premise, instead of a universal premise, that’s self evident. What if we start with something that’s not necessarily self evident, but is simply probable? Or maybe it’s a statement that someone else grants as true? And we’re going to use the first premise. Or we’re going to use for the first premise, something that someone has granted. And where you see this kind of reasoning is in the dialogues of Plato. When Socrates asks a question, and the person with whom Socrates is speaking, answers the question, Socrates then takes that answer begins with that answer and reasons from it to a conclusion. Now, that is not the kind of reasoning that we learn in demonstrative reasoning. That’s not what we learned in prior analytics. It’s a different kind of reasoning. It doesn’t lead us to certain truth, like demonstrative reasoning, because we don’t start with self evident truths, or previously demonstrated truths. We’re starting simply with a statement that someone says is true. And we’re simply reasoning from what they concede. We present them with a question that proposes a choice between two opposites. For example, whether a person must study in order to know something, yes or no,
there are only two options. You can either say, a person must study to know something, or you can say a person does not need to study to know something, there’s only two options. And however you answer that question, we’re going to start with that as our first premise. And then reason using the doctrine of syllogism to a conclusion. But that conclusion is not going to be of the same kind as the conclusion that we saw in demonstrative reasoning. This is what’s called dialectical reasoning. It’s the Socratic method, dialectical reasoning. This is what Aristotle teaches the art of this kind of reasoning. He teaches in his work titled The topics. There’s one last book one final part in the art of reasoning. The title of the book is sophistical, refutations, sophistical refutations. And in this final part, after having established the whole art and science of reasoning, in these other books, having taught about the role of words in reasoning and ideas in in the categories, having taught how propositions are made in on interpretation, having taught how the syllogism is made in prior analytics, having taught how we reason from self evident, self evident universal truths to conclusions that are certain in demonstrative reasoning, and then how we reasoned from one of two possible contradictions to come to probable or possible conclusions or contradictions you In conclusion, we learned about that in the topics on dialectical reasoning. Having established all of that doctrine, all of that art of reasoning. Aristotle, at the end examines false arguments that are used by sophists to mislead people, because they have an appearance of being reasonable. But when we understand the art of reasoning, we can see what about them is actually false, but appears to be true. And these are what we call the fallacies if you hear the term logical fallacies. These are taught in the last book of Aristotle’s Organon called sophistical refutations. So, you see reasoning has a series of parts just like grammar. All of grammar does not need to be studied before one can begin the art of reasoning. But some of grammar must be studied before reasoning can be started. If you take up the first lesson in the first course in classical reasoning, in the classical liberal arts academy, you’re going to learn very quickly whether your language skills are sufficient to allow you to read and understand the lesson. That’s how much grammar you need to start reasoning. You need to be able to read and understand the teaching on the art of reasoning. If your language skills are sufficient to be able to read and comprehend accurately, then you have enough grammar to begin the study of reasoning. And you’ll continue to study the rest of the art of grammar as you begin the art of reasoning.
Rhetoric
Now, the next art of the trivium is rhetoric. And so the question is, what do we have to know? In order to study the art of rhetoric? What do we need to know to study rhetoric? Well, if you open the source text for the art of rhetoric, which is Aristotle’s book titled, The Art of rhetoric, you’ll see he begins his book on rhetoric with a discussion about dialectic, or dialectical reasoning. Now, if you don’t know what dialectical reasoning is, because you haven’t studied Aristotle’s topics, you’re in trouble right from the start. Aristotle explains that whether we’re working in logic and philosophy, or in rhetoric, we have to use the syllogism. We have to understand prior analytics, we also have to understand the difference between demonstrative reasoning, which usually is not the concern of rhetoric, and dialectical reasoning, because dialectical reasoning is what’s usually what we’re concerned with in rhetoric. So you can see, you don’t need to know the entire art of reasoning to get started in rhetoric, but you have to understand enough of it to know what Aristotle is talking about when he begins talking right off the bat, about enthymeme and syllogisms. If you don’t know what those things are, and you can’t understand his explanation, that proves that you haven’t studied enough of the art of reasoning. So there’s just a natural order to these arts, you do not need to finish one before starting the other. But your attempt to begin, the higher art will reveal whether or not you’ve studied enough of the lower art, to be able to continue in the hierarchy. And as you can, as you get started in the hierarchy, you will continue to work through the rest of the lower art. And that’s why I say if you would simply study the classical liberal arts instead of standing on the outside, trying to guess what’s on the inside and how it’s organized, you would see that the answer to this question about the order of the trivium and quadrivium is just common sense. If you try to read Aristotle’s works on reasoning, and you can’t read them because your language skills are not good enough. Let’s say you’re an eight year old student, and you can’t even comprehend what the chapter says as as you begin classical reasoning. You need to focus on grammar and improve your language skills until you can handle the language of the classical reasoning course. The same thing is true of rhetoric. If you You start to read rhetoric and have no idea what he’s talking about because Aristotle’s making references to things explained in reasoning. Well, that determines whether or not you can get started. In rhetoric. It’s very simple. There’s a simple, natural, necessary order just based on comprehension. Now, when we look back at old classical schools, we find that in the early years, when students got started, they immersed the kids in grammar studies, they didn’t study reasoning, they didn’t study rhetoric, they immerse them in grammar. Why? Because everything depends on grammar. Your ability to study any subject depends on your ability to read and write and speak the language and so they immersed children, and focused entirely on grammatical studies, because grammar ultimately sets the limit for what you can study. Emphasis was always placed on grammar to a certain level. And I don’t have enough time to get into all of these details. But even the old grammar books were divided so that students could understand where different levels or cut offs were in the study of grammar before they moved to a higher class and got into more advanced studies. If you think about medieval Education, University of Paris, said that no one was allowed to lecture at the university unless he was 20 years old. And he already had been in attendance at the University for six years. So that tells us that the idea of the university in medieval Europe started at age 14. So students went to grammar school where they were immersed in the study of language itself by grammarians so that they could be made fluent in one or more languages that were necessary. And then as soon as they became fluent, as soon as they became independent readers and students, they were then ready to to move on to the university, where their studies intensified, and they moved up into higher arts.
So you can see that there’s an order in the trivium. It’s not some kind of ridiculous, rigid mechanical order where one art comes before the other art and that’s why this Dorothy Sayers stuff that’s popular, we’ll be talking about stages of learning, it doesn’t even make any sense. If you’ve actually studied the arts of grammar, reasoning, and rhetoric, it’s, it’s for ignorant people who have no idea what the classical liberal arts are no idea what the arts contain. And it’s just something that’s used to explain an approach to education. That’s, that’s nothing but public schooling, rebranded with new words, instead of saying elementary school, middle school, high school, we want to appear to be some kind of fancy school or fancy teachers. So we say, oh, instead of elementary school, we’re going to use the term grammar stage. And instead of middle school, we’re going to say, logic stage. And instead of high school, we’re going to say rhetoric, it’s like, it’s like the scheme that Starbucks used to change the way we talk about sizes of coffee. It’s just a marketing scheme. It’s a gimmick. It’s not it’s not reality has nothing to do with the actual classical liberal arts. Like I said, you may study the grammar of Hebrew, when you’re 22 years old, and a university student, it has nothing to do with your age or your level of study, or it’s simply an art. And in order to begin studying in a new language, you have to start with the first art which is grammar. And when you get to a certain point, you can begin to read in that language and study other books in that language while you continue to study the grammar of that language. Simple, natural, logical, none of this goofy, fake classical education stuff. No, Dorothy Sayers, no stages of learning. Anyone who actually studies the classical liberal arts, notice that all of that talk is meaningless. This is very simple. The books of the Masters works are arranged to show us this order. And anyone who undertakes the actual work of studying them will understand how the order works, because you simply won’t be able to understand a certain book if you haven’t studied enough of the inferior arts and that’s How the order work. So that’s how the trivium works. Okay? I’d like to stop talking about that. So I can also devote some time to the quadrivium.
The Quadrivium
When we get to the Quadrivium, we see four mathematical arts, and I explained before where these arts come from. Quantity, which is the subject of mathematics, divides into two different kinds are species, multitude and magnitude. Multitude divides into two species, absolute multitude and relative multitude. Magnitude divides into two species, magnitude at rest, and magnitude in motion.
Now, philosophically, absolute multitude comes before relative multitude; logically, absolute multitude, comes before relative multitude. This is very simple to understand. What comes first, a number, or a ratio? Obviously a number, because a ratio is a comparison of two different numbers. A ratio, which is a relative multitude is more complex than a number (even though a number is a ratio–but that’s another topic). A number is simple, a ratio is compound. And so, since Arithmetic is the study of number, and Music is the study of ratio, Arithmetic is simpler than Music, and therefore must come first. The ideas that are studied in arithmetic understanding the principles the nature of number, the number, the nature of absolute multitude is necessary. Just like the study of the alphabet, the sounds of the letters, the forms of the words, was necessary in grammar. Before we can move on to reasoning, we have to understand the principles of number. Before we can study music. Before we can study geometry before we can study astronomy, so of the four arts of the quadrivium arithmetic comes first, because we have to learn the doctrine of number we have to learn about absolute multitude because that comes first. Once we’ve and again, we don’t have to study the entire art of arithmetic because it gets pretty complicated, it gets pretty deep in terms of how far we go into this doctrine of numbers. But we have to learn the basics, the essential principles of number, so that we can understand what’s necessary to begin music and geometry.
Music and Geometry, however, belong to two separate divisions. Music is a study of multitude, Geometry, is a study of magnitude. Therefore, there’s no order between Music and Geometry, they belong to two different species of quantity. Arithmetic is the first of the arts. Once we’ve progressed in Arithmetic, we can then begin the study of both Music and Geometry. One doesn’t come before the other Music and Geometry both depend on the knowledge of the basics of Arithmetic. But once we’ve gotten those basics under our belt, we can begin both Music and Geometry, we can’t begin Astronomy, because Astronomy depends on a thorough knowledge of Geometry. So what we really have is four arts in the Quadrivium, and three different levels as it were. We have Arithmetic, which is first; then we have Music and Geometry, which are like 2A and 2B. Then, after them, we have Astronomy, and Astronomy has to come last, because we have to wait until we’ve learned Geometry. That’s the order of the Quadrivium.
Now just think about the simplicity of this. If you open Euclidean Geometry to the first lesson, what do you find there? Euclidean geometry begins with a list of definitions that have to be memorized. It’s simple grammar. We’re simply learning the definitions of words. To begin the study of Geometry, we have to learn the ideas of Geometry and their names. We have to learn the definitions. Then, we have to learn a set of postulates and then we have to learn a set of axioms. What are axioms? Axioms are self-evident truths. Where have we heard that before? Oh, yeah, we talked about self-evident truths when we talked about demonstrative reasoning in the art of Reasoning in Aristotle’s Posterior Analytics. That’s where we talked about self-evident truths. And so what do we find in Geometry? In Geometry, we find an example of demonstrative reasoning. We find Aristotle’s art of demonstrative reasoning applied to magnitude at rest. And we see Aristotle’s demonstrative method being the instrument that we use to investigate magnitude at rest, which is the study of Geometry. So, the study of Geometry assumes that we know something about the art of Reasoning, and therefore, it’s related to the Trivium. It’s not independent, it’s certainly not independent of Grammar, since we can’t even read the lessons unless we’ve studied Grammar. We can’t read Arithmetic lessons unless we’ve studied Grammar and are comfortable with the language. So in order to study Arithmetic, we have to know Grammar. How much Grammar? Obviously, we don’t need to know Prosody. In order to study Arithmetic, we need to be able to read and understand the language so that we can study a book about Arithmetic. Arithmetic follows Grammar. But just as regards comprehension, Geometry also follows Grammar, because of comprehension. But Geometry also follows Reasoning, because we use the demonstrative method in order to prove every proposition from self-evident truths.
And then that study of Geometry simply continues into the more complex subject of magnitudes in motion, because, as Aristotle explains, an object that is in motion is in a state that is more complex than an object that is at rest, because motion implies a change in place. Therefore, an object in place is simple, and an object in motion where it changes place is more complex. Therefore, Geometry, or magnitudes at rest, come before magnitudes in motion.
So that’s the order of the Trivium and the Quadrivium. It’s not this nice, nice, neat, black and white set of steps that you can install, in a study program or a school. It’s this living, organic, logical order of ideas, and studies that relate to one another and depend on one another in a certain way, as regards comprehension–our ability to comprehend the lessons of each of the arts.
Now, like I said before, you can save yourself a lot of time and energy and simply join us and study the classical liberal arts in the Classical Liberal Arts Academy, where all of this work has already been done, the organization of the studies, the restoration of the master texts has already been done. So spending all of this time pretending that you’re about to solve the mystery of the order of the seven liberal arts when it’s already been finished and restored in the classical liberal arts academy is a bad use of time unless you’re trying to pretend that you’re the, you know, the solver of the world’s problems, and they’re already solved. If you want to understand the order, like I said, the only way that you can even understand what I’m talking about is to actually study the master texts and learn the classical liberal arts. You can’t you can’t stand on the outside just talking about it forever. Eventually, you’re going to have to roll up your sleeves and actually do the work of studying the classical liberal arts and then you’ll see that everything I explain here is is very obvious and simple. There’s simply an order that determines what can be comprehended when based on the relationship that exists between the different arts. If you study them, you’ll see that you’ll see that you get to a chapter and you say, I can’t understand this. Chapter because it assumes a knowledge of ideas that I haven’t studied yet, which are taught in the lower art that I haven’t studied yet. It’s just a simple, logical order to the studies. So the first of all of the liberal arts is obviously grammar, we have to learn language. And that’s why classical schools almost exclusively focused on grammar. That’s why students began at schools that were called grammar schools, because they studied grammar, literally, they studied grammar in the grammar school, because that was what was called the gateway of the arts. If you could learn grammar, you could learn everything. If you don’t learn grammar, you can’t learn anything. And that’s true today. If your language skills are weak, you won’t be able to read the writings of philosophers or theologians, you won’t be able to understand the writings of poets because you simply don’t have the language skills. That’s the purpose of the study of grammar. But in order to study logic or reasoning, I should say, in order to study reasoning, you don’t have to know prosody. You don’t have to know how to use all of the different moods of verbs. All you need to understand are indicative sentences. And so by studying Aristotle’s Organon, we begin with the categories and simple disconnected words and ideas, then, the formation of propositions, then the formation of syllogisms. And then two different applications of syllogisms and then the sophistical refutations. And then to study rhetoric, you need to understand the syllogism because we use it in rhetoric. But you also need to to understand the more advanced studies in grammar, you do need to understand the different kinds of sentences, you do need to understand the uses of different moods of verbs. In rhetoric, you do need to study prosody for the sake of oratory and public speaking and communication, you do need to understand how words are correctly pronounced with accent and breathing and so on. And so, in order to actually master the art of rhetoric, you have to master the art of grammar, either before you study rhetoric, or simultaneously as you work through rhetoric going back and forth. We’ll also learn that rhetoric depends on a knowledge of, of the human soul, because we get into issues of emotional appeals and what it is that affects the soul of men. And Aristotle will teach us that the study of rhetoric depends on the study of moral philosophy. So there’s more than just the seven liberal arts, it’s the whole curriculum Taken as a whole that needs to be in place, or else, you can’t progress through any of the arts as you’ll need to, in order to become a master of them. So I hope that’s a helpful overview of the order of the arts. If you think that that’s complicated, if you think that that requires further explanation, I’d like to remind you that the problem you’re having is not my explanation of it. Because it can’t get much simpler than what I’ve explained. The problem is you’re continuing to stand outside the classical liberal arts, like a person looking at a cave entrance, but not willing to go in trying to understand what’s inside. And what I’m telling you is if you’ll just go inside, and do the studies, all of this will be simple and clear for you. The cause of your confusion is that you’re not doing the studies. And you’re trying to pretend that you’re going to understand something that you don’t, in fact, study and that’s the actual problem. The order of the seven liberal arts is very simple to those who study them. And my advice for you is, study them, start studying them. So I hope that’s helpful. If you have any further questions or would like to get into this in any more details or talk about the source materials and texts that I mentioned, I didn’t talk much about the the sources for the quadrivium I’m just to throw that out real quick. For arithmetic. We have the introduction to arithmetic by Nico Marcus or Nicole MCUs depending on how you pronounce it. We We also have de artist Nitika by by booth theists, Christian writer. But all the way theists really does summarize the other works. So he doesn’t offer anything, anything. He’s not a master of mathematics. He’s simply a translator. In geometry, it’s simply Euclid, and Euclid elements. And then in music, we do have a treatise on music by booth theists. There’s another by St. Augustine. I’m not sure whether that’s actually truly St. Augustine or just rumored to be by St. Augustine, but I know that there is a book that floats around de moussaka by St. Augustine, but we study but we theists is work on music. And then for astronomy, which opens up a new can of worms, you have the classical astronomy, of Aristotle and Ptolemy, which is the actual content of classical astronomy, not the modern Copernican model and all that it’s it’s the classical Aristotelian astronomy that was taught, or demonstrated, I should say, through Ptolemies work the all majeste the ALMA jest by Ptolemy is the master text on the mathematical art of astronomy. So read a an hour in five minutes or so I’d like to cut off this video. I hope that’s helpful. I hope that gets you thinking and starts to make sense out of things for you. But like I said, just study, get wisdom. Be a real student of the classical liberal arts stop standing on the outside, talking about classical studies, pretending to be a classical educator, get into the studies yourself, and you’ll see it’s not that complicated. You just need to do some work.
Mr. William C. Michael, Headmaster
Classical Liberal Arts Academy
Phone: (909) 281-7025
mail@classicalliberalarts.com
This article was composed by ChatGPT with directions and editing from William C. Michael.
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The Classical Liberal Arts Academy works to research, restore, publish and teach the classical Catholic curriculum that has been enjoyed by wise men and saints through history. We invite you to study in our self-paced online courses and enjoy the benefits of online quizzes, written assignments, progress records and more. Get started with a free 30-day trial.
Not enrolled? Get started today for free!
The Classical Liberal Arts Academy works to research, restore, publish and teach the classical Catholic curriculum that has been enjoyed by wise men and saints through history. We invite you to study in our self-paced online courses and enjoy the benefits of online quizzes, written assignments, progress records and more. Get started with a free 30-day trial.