De Quadriformisratio

On The Quadrivium

Preface

"For what avails a golden key if it cannot give access to the object
which we wish to reach, and why find fault with a wooden key if it
serves our purpose?" (De Doctr. Christ., IV, 11, 26). - Augustine

This book is an extended argument for the utility, beauty, and subtle necessity of an ancient discipline and practice known as the Quadrivium. As we discuss the Quadrivium in detail in the following chapters, we will see that it is higher Number, as manifested by itself (Mathematics), in space (Geometry), in time (Music), and in Space plus Time (Cosmology). If the Trivium (grammar, logic, and rhetoric) is the means whereby the Egyptians are spoiled of their treasure, then the Quadrivium is the design for the tabernacle of the Lord, which was built with attention to mathematics, order, detail, and according to a design which was divinely inspired, according to the archetype of the true Jerusalem, which is from above and heavenly. The Trivium properly is the glory or the spirit of the Faith, but the Quadrivium properly represents the body or wisdom of the Faith, the matter of what is made known.

I say this as a generalization, since it is quite equally true to assert that the matter or content of the Quadrivium generates a style or form all of its own, just as the style and flair derived from the Trivium is capable of generating content or substance. Yet this, all the more, should inform us that the Trivium and the Quadrivium go properly together – they are indivisible at the highest level of human knowledge, and each is indispensable to the other.

In order to put this case at length, I will start in media res (in the middle of things) with the Trivium, its better known twin sister. All too often, both the Trivium and the Quadrivium have been allowed to rest in the hands of the enemies of the Faith, but lately, we have made progress in recovering one of them. It is a start, and a beginning. But there is more to the story, and much more to even that part of the story.

The 20th century witnessed the unexpected resurgence of something called the classical Christian school movement. Inspired by the famous 1947 Oxford essay by Dorothy Sayers, the movement took (as its hallmark) not only a return to God-centered education, but a focus on the ancient Trivium. In Sayers' words, she retrieved what she called a "modern Trivium – with modifications", from the dusty shelves of Oxford and the medieval period, and dusted it off to show it in a new light. Although she said her views were “neither orthodox nor enlightened", Sayers had the interesting and admittedly personal insight that there are roughly three stages of learning that you naturally see in the development of the human psyche, and that these three stages can roughly be correlated to the grammar, logic, and rhetoric of the old Trivium. She identified a poll-parrot stage elementary school stage, followed by a “difficult” stage of argument in the junior high years, and finally a rhetorical stage of expression in the late teen years, and beyond. This essay was republished in The Lost Tools of Learning, by Douglas Wilson, and became a set-piece for the classical Christian school movement.
Regardless of the possible critiques, objections, and second thoughts one may proffer to and about Sayers, her essay inspired the movers and shakers of the late 20th century in what may justly be called (along with homeschooling) a massive rebirth of Christian education. It is not too much to say that her essay was the efficient means of sparking a revival, of Christian education in America. Whether she was right or misguided, can be debated – those who began the movement were inspired by her essay, although it remains to be seen whether the revival will result in renaissance and restoration. Certainly, recovering the Trivium tradition was on the whole immensely important.

Dorothy Sayers, in her essay, asks if you've ever watched and wondered why it is that modern literate people cannot seem to define their terms, distinguish first principles, respond to arguments appropriately, or follow a highly complex chain of reasoning. She wishes us to see that it is the neglect of the Trivium disciplines which are indirectly responsible for the slobbish and retarded condition of our public discourse, & I for one am inclined to agree with her line of thought. It is certainly true that the medieval ancestors would have never tolerated such sloppy public discourse in their dialectic quod libetas or university debates. Whether Sayers was right or not in her theories of human learning and development, it is certainly true that restoring the Trivium to a central position would add lucidity to modern thought. Even her staunchest opponents would have to admit that it was a “happy blunder”, in that sense. It is not too much to expect, of a high school graduate, that they can define their terms (grammar), reason soundly and recognize confused reasoning (logic), and express themselves clearly (rhetoric).

Sayers, in her essay mentions the Quadrivium but skips over it for the time. She also concludes her essay with this striking paragraph:

“The combined folly of a civilization that has forgotten its own roots is forcing them to shore up the tottering weight of an educational structure that is built upon sand. They are doing for their pupils the work which the pupils themselves ought to do. For the sole true end of education is simply this: to teach men how to learn for themselves; and whatever instruction fails to do this is effort spent in vain.”

I would like to raise a question, at this point, one which she might (perhaps) have answered had she discussed the Quadrivium in more depth. Is there not a difference between Learning (on the one hand) and (Wisdom) on the other? The medieval idea (and the ancient one) was that education's goal was Wisdom, and not Learning per se at all, as much as it was cherished. The modern idea that education's purpose was the “shoring up of civilization” was only one aspect of their aims in instruction. Perhaps her choice of words was dictated by the audience she spoke to, and that is certainly the charitable point of view. Yet I would ask the reader to go with me a little deeper, into the Quadrivium, and the quest for Wisdom with a capital W, beyond the statistics of the US Dept. of Education, beyond the degrees and the dollars, beyond even the scholars, and certainly beyond what today is called “higher education”. To bring lucidity to modern thought is certainly desirable, but not if the assumptions of modern thought go unchallenged: it is certainly possible (for example) to hold a purely material view of the world, and defend it with grammar, logic, and rhetoric.

We may well go on to ask then (as she does not), why it may be that even were our collective discourse to become sharp and precise, it would still be lacking both elevation and sublimity. That is, having addressed the method of “how do we learn” and offered a strong correction, there still persists the question “what shall we learn about?”. What is the content and the form and the goal of Education? Originally the Trivium's whole point was to create a fortress and weapon of the Mind (in the service of Wisdom, and later, “the Faith”). Now along the way and incidentally, it certainly does manage a great deal of this, for in order to study the Trivium, students read a great deal in the classic humanities. It is hard to read Cicero and Virgil and Milton without acquiring some elevation and also some profound sublimity. Contact with the “classics” often imparted some of the tone and moral style in them to the mind of the student.

Nonetheless, reintroducing the Trivium will not formally or substantially solve the horrifying problem of the lack of substance, sublimity, and richness. By itself, the Trivium gives us comprehensiveness, efficiency and clarity, and style: but it can only borrow substance from the humanities which it uses to cut its teeth on - Greek and Roman history, literature, and philosophy. This is done indirectly, as the Trivium student works through the humanities. The humanities proper are to be considered as principle subjects, as opposed to the tool disciplines of the Liberal Arts (the Trivium + Quadrivium). Now it is true that Christian education addresses the issue of content directly through the confessions of Faith which over-arch the classical Christian movement. New Saint Andrews makes it clear that the context of the Faith defines the context which the Trivium works upon:

The Scriptures of the Old and New Testaments are our only infallible rule of faith and practice. The Lord Jesus Christ committed these inspired Scriptures to His Church (1 Tim. 3 :15). We therefore defer to the witness of the historic Christian Church as a genuine but fallible authority, subordinate to the Scriptures themselves, in discerning what the Scriptures teach. Because they faithfully witness what is taught in the Word of God, we receive the great creedal statements the Church has affirmed throughout the ages: The Apostles Creed, The Nicene Creed, and the Definition of Chalcedon. Moreover, we believe that the reformational confessions of the 16th and 17th centuries (including the Westminster Confession of Faith of 1646, the Heidelberg Catechism, the Belgic Confession, and the Canons of Dort), of all historic statements, most fully and accurately summarize the system of orthodox Christian doctrine revealed in Scripture. Therefore, the specific headings below do not exhaust our doctrinal understanding, but rather identify those doctrines that merit greater attention today.

NSA (New St. Andrews is the college which Douglas Wilson started and an intellectual headquarters of the movement in Moscow, Idaho) mentions the Quadrivium as something people can “go on to study” as part of more “advanced study”. So hasn't this settled the issue? Isn't this the way to “enhance the Trivium”? To do more than just impart lucidity to the conditions of modern thought, but to begin to challenge its core assumptions as well?

Their argument might run as follows - Christ Himself is the Substance of what the Trivium studies, and provides the treasure which the well trained classical Mind defends by attacking every thought hostile to Christ and taking it captive. So why cannot we say that the Faith, or Christ Himself, is the beauty, truth, and goodness which we seek? The “more” which the Trivium helps us to learn how to learn about? Can't we just weave the Greco-Roman (Hellenistic) world into a narrative which dovetails with the narrative of God's redemption in His people? And content ourselves with the history, literature, art, and philosophy of the classical era, spoiling its riches (to use Augustine's phrase) to adorn the tabernacle of the Faith of God? Can't we just develop a grammar, logic, and rhetoric of Truth, Beauty, and Goodness, as summed up in Jesus Christ? Why would we have to make things more difficult by adding canonical subjects which can handled electively? For that matter, why is music or geometry anymore important than pre-medical studies or foreign languages for high school students, or anthropology or nano-technology for our collegiates? In short, aren't we hunting snipes here? Or maybe just cow-tipping? Finally, doesn't the Quadrivium have a funny name? Just what is the Quadrivium, anyway? Doesn't it have something to do with mathematics?

Just as we define our method in the Trivium, a method for the mind, so we can call Christ our goal and content, the treasure chest of Beauty, Truth, and Goodness. So we seem to already have an answer of sorts, ready made, within the classical Christian movement – the sovereignty and majesty of the King becomes the material which the mind exercises itself upon. The Faith is the body of knowledge and belief which the Trivium uses and meditates upon, and even as students read about the wars of Caesar or savor the poetry of Homer, they are being taught to look through the lens of that earthly beauty, toward something “more”. By faith, we know what that “more” is. It is a sound argument, both cogent and well constructed, and the conclusions follow from the given premises; it can be beautifully expressed, and often is; it is capable of defining its terms, and it is an improvement on just adding Bible class to a public school education. This much, this far, is very sound.

The corollary to the above is that we really don't need the “Quadrivium”; not as Tradition defines it, or at least not the Quadrivium per se. Students can supplement the Trivium training, the theology and the philosophy of the Faith, and the exercises in the humanities, with courses in practical art, music, perhaps a foreign language other than Latin, maybe some athletics. We have our method, and we have our standard, goal, and our motive, which points us to the great body of truth - Christ. We seem to have it all, here. All that remains is the carrying it out. Go forth, we tell our young students, and take every thought captive to Christ! The Quadrivium is optional, but certainly not necessary or even extremely useful. At the very least, it is the mysterious younger sister of the pair, and by far the least important.

Now while the recovery of principal subjects (under the eye of the confessions of the Faith) does constitute a direct address to the problem of content, it still remains true that it fails to address the issue of the innate form of the content, by neglecting the tool disciplines of the Quadrivium, which impart a certain form or structure (a discipline) to the content indirectly preserved in the principle subjects and indirectly recovered through texts encountered in work with the Trivium. This includes, but goes beyond, mathematical Form in general, just as the Trivium includes, but goes beyond, linguistic Form in general.

If the Faith points us towards God, and the Trivium helps us sharpen our Mind, then the Quadrivium tells us something about the body and scope of Nature, considered in and of itself. Faith reaches the summit of the Divine (Super-Nature or the Lord God), and the Trivium teaches the Mind to reach its own summit in lucid self-reflection. But the Quadrivium investigates that which is Logos – that is, the specific and real union between God & Man. All three (confessional, linguistic, and mathematical) forms have a proper center of gravity, but all three include (or touch) each other. Remove one of the legs, and it weakens the structure of the whole, a structure which we express in the principal subjects like History, Literature, and even Philosophy and Theology.

We might go even further to illustrate this hunch. If the Trivium helps us "learn how to learn" (in Sayers arresting and concluding turn of phrase), the Quadrivium helps teach us what to teach, and how to teach it. The Quadrivium demonstrates intuitively how the Logos knits together the world of all that is, including God Himself. The Quadrivium tells us about the actual pattern God uses to draw Nature up into Super-Nature, transforming it and sublimating, making it One with Him. It teaches us to discern the method whereby God incorporates Nature (or the world) into Himself. It is a bridge between the Trivium and the Faith, just as it is a bridge between the Mind and Super-Nature. It considers all things as part of a whole, which is God.

Perhaps this is why the Quadrivium is not more discussed – it involves very old and deep theological realities which have been forgotten or distorted. We follow CS Lewis on this point – God is that which is most Real. In The Great Divorce, Lewis makes the case that the reality of God is the source of “reality”, and is therefore, more “real” than mundane reality. We become real by restoring His image and being transformed into His likeness. God created the world by an act of Love, withdrawing or “wounding” Himself, and then speaking the Creation into existence with the power of His word, out of the “Void” or “Nothing” which was created by His wounding. We do not live in a world of dead matter and empty space, but a world that is groaning and trembling as it works through the process of Redemption. Now, each of the theological confessions of the Church differ as to the details of how this works, but they all agree (at least in principle) that the end reality is that God will be “All in All”. Against the modern worldview of “atoms in motion” in a permanently cold and lifeless space, the Christian confesses that the world is being born again (however slowly this may happen). Indeed, the Christian confesses that God is already “all in all”, and that we work with Him (however slowly) to manifest this in time and space, which is not empty or dead.

The Quadrivium is important because it gives us very vivid and detailed hints and clues (often in mathematical form) how that “all in all” began, and towards what it is tending. While the Trivium may anticipate the final destination, showing us the foundations of grammar-Logos in the “Word”, giving us a peak at the inter-relations of the Logos between various entities and in certain processes, and revealing the beauty of the Logos through the highest flights the human mind and imagination is capable of, it is the Quadrivium which deals with the very concrete details of Creation and Redemption. As we shall see later on, the last of the Quadrivial sciences is cosmology, and this science actually unifies the Trivium with the Quadrivium, as well as linking it with the principal subjects and with the religion and reality of the Christian Faith.

If the Trivium is the energy which saturates knowledge and makes it lucid, allowing the mind and the subject to become one in order to “hit the mark”, the Quadrivium is the technique of the archer as he aims the arrow at the goal. The goal or aim is the Logos, that through which the worlds were spoken, and that towards which the worlds return. The Logos is the re-unified world restored to its original state and then glorified, as seen in the Logos-Incarnate, the first fruit of this redemption. Christian education (then) is not merely becoming useful or skilled in manipulating data or objects in a plastic, passive, dead Nature. Nature is not a supine and mechanical Artifice that can be assigned a “spiritual” direction, arbitrarily. This Nature is something which, eventually, will become the body of God, when the marriage of Heaven and Earth takes place, just as man and woman become One on their wedding night.

When this is clearly understood (and it is often not understood at all), the ancient Quadrivium appears in an entirely different light. Rather than being the “weak sister” of the Trivium, it is the disciplined inquiry into the Pattern of Patterns, the supra-rational Order which has order (Number), structure (Geometry), harmony (Music), and is becoming a Body (Cosmology) – the four paths of the Quadrivium. The medievals and the ancients, however imperfectly, had gotten this far, and in this respect, were far more advanced than we are today.

The Quadrivium is the science of the Logos, understood in its relationship to Nature. Nature is here used as a term to encompass what is both human and Divine. Since the worlds were created through the second person of the Trinity, and since Christ is fully man, and totally God, Nature itself partakes of this totality in a derivative manner. When this is applied to history, it readily and explicitly shows us how the Hellenistic world was part of the “fullness of times” mentioned in Galatians:

So also we, while we were children, were held in bondage under the elemental things of the world. 4But when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law, 5so that He might redeem those who were under the Law, that we might receive the adoption as sons.…

God was using the Mediterranean basin (the cradle of Western civilization) to incubate a culture which dared to give full scope to man's rational powers (weak though they were) in the context of aiming for something “more” (Beauty, Truth, Goodness). It is for this reason that the Gospel of John opens with the words, “In the beginning was the Logos.” This is why the New Testament was written in koine Greek. It is why Paul quotes Aratus and Epimenides. It is why Christ refused to take up the mantle of the Messiah made in the image of Jewish nationalism. He was the “light of the World”. It is why Caesar came across the Rubicon with his soldiers to save a dying Rome. It is why Alexander was born to conquer the world. All of this was foreseen in the vision of Daniel, in which the dying Empires which prepared the way and inevitably fell short of the mark are replaced by an enormous boulder which covers the Earth and becomes the Holy Mountain. In Acts, Paul addresses the king:

"I am not out of my mind, most excellent Festus, but I utter words of sober truth. 26"For the king knows about these matters, and I speak to him also with confidence, since I am persuaded that none of these things escape his notice; for this has not been done in a corner.

The mighty acts of God were both grounded in Creation from the beginning, and yet were culminating in a holy purpose. While the Trivium may analyze the contents of Revelation in the Scripture (as well as the natural revelation in the spiritual and humane writings of the most noble and notable humans of the ancient world), it is the Quadrivium which shows us the full extent to which Creation remained faithful to the patterns of God, and how those patterns were achieving a subtle and wise purpose through God's Providence.

The Quadrivium is the missing arch in the classical Christian movement. It is the link between the Faith and the Trivium, a link which so many have questioned, impugning its integrity, sincerity, and holiness. It has the potential to energize the movement with a fullness of purpose that is impossible without its moorings and underpinnings. If the Trivium is a flying buttress of a Gothic cathedral, transferring the soaring weight of the vaulted roof safely to the ground, then the Quadrivium is the stained glass of the Rose window, which admits, tinctures, and filters the overwhelming brilliance of the sun. The Quadrivium is the architecture of the temple of God, the pattern and the design of the stained glass.

The Quadrivium course of study is what keeps the sharpness and efficiency of the Trivium from veering away from the stated aims of the Faith, by indissolubly linking it closely to the Logos, Who is the express image of the Father, source of Creation and Re-creation. It is the the link between Reason and Faith, in the context of Christian education; it is the making explicit of what should already be known and understood, but too often, sadly, is not. Without it, the Trivium risks attack from those who see in it an unholy alliance between the “world” and Christ, or perhaps just a slick marketing strategy designed to churn out good Christian rhetoricians who can be culture warriors, even just another smuggling in of anti-Christian doctrines in the form of humanistic reason. Without the Quadrivium, the Trivium is more exposed to charges that it is humanism, paganism, and anti-Christianity, since the glory that was Greece and the grandeur that was Rome can easily be mistaken for the City of God, and indeed was, by people more noble, wiser, and virtuous than many of our day. It is the Quadrivium which argues for a supra-rational Order or divine Reason which is antecedent to the brain and even the mind of Man, but towards which Man's destiny is tending. And it not only argues, it argues by the persuasion of concretely showing, or demonstrating, how that supra-rational Order has moved and is moving through the interstices of Nature to accomplish the divine plan of God.