Mathematical “Small Things” and the Quadrivium

What did early mathematical education look like in the Middle Ages? As is commonly known, the ideal Liberal Arts curriculum of the Middle Ages featured both the Trivium (dedicated to the study of words) and Quadrivium (dedicated to the study of nature in the form of mathematical arts). The Trivium included Grammar, Logic, and Rhetoric. The Quadrivium consisted of Music, Astronomy, Geometry, and Arithmetic. These seven ways (viae) of liberal arts learning prepared students who studied them diligently to “comprehend everything that they read, elevat[ing] their understanding to all things and empower[ing] them to cut through the knots of all problems possible of solution” (John of Salisbury, Metalogicon I.12). Even today, the concept of a Liberal Arts education that prepares a student for life and whatever (foreseen and unforeseen) challenges lay aheadremains. And yet, for anyone who has educated a child, the idea of delaying mathematical education until the early teen years (which is when the formal Quadrivium was taught) seems completely impractical and misguided.

Unknown Miniaturist, French (active 1190s Paris). Bodleian Library, MS Laud Misc. 409 (Oxford Manuscript ) f.3v.

Did medieval educators really wait until students had a full understanding of the Trivium before introducing mathematics? The difficulty here comes in part from the lack of extensive knowledge of the curriculum of early childhood medieval education, including mathematical instruction. The institutions for learning changed over time and even geographic region. Early childhood education could take place in a home, in a monastery, or at a local cathedral school. Another difficulty may also be that our cultures mean slightly different things when we talk about the discipline of mathematics.

The “paper trail” for exactly what early childhood mathematical education might have looked like is not vast. But one tiny, but vivid, glimpse of what boyhood mathematical pursuits might have looked like can be seen in the writings of Hugh of St. Victor, an early twelfth century canon regular who wrote a book on the Liberal Arts called the Didascalicon. In this work, Hugh of St. Victor gives a rare view of his own early mathematical education:

I laid out pebbles for numbers, and I marked the pavement with black coals and by a model placed right before my eyes, I plainly showed what difference there is between an obtuse-angled, and an acute triangle. Whether or not an equilateral parallelogram would yield the same area as a square when two of its sides were multiplied together, I learned by walking both figures and measuring them with my feet. Often I kept watch outdoors through the winter nights like one of the fixed stars by which we measure time. Often I used to bring out my strings, stretched to their number on the wooden frame, both that I might note wih my ear the difference among the tones and that I might at the same time delight my soul with the sweetness of the sound. These were boyish pursuits…yet not without their utility for me, nor does my present knowledge of them lie heavy upon my stomach. (VI.3)

Hugh describes these activities as grounding him “in things small” so that he could “safely strive for all” later in life.

Notice how many of the activities mentioned by Hugh of St. Victor do not require a textbook at all, especially with a charismatic teacher, or in the case of Hugh’s own life, a particularly inquisitive child. Counting and the study of angles required only pebbles. The figuring of surface area required only the measurement of feet. An early acquaintance with the stars required actually going out to look at the night sky, even when it was cold, and the study of the relationship between musical notes came from literally fiddling around with a simple stringed instrument. To these activities, we might presumably add the common medieval practices of singing (cantus) and possibly dancing in set patterns. Or the calculating of times and seasons (computus). Or measurements of land and sea masses for commerce or geography. Or ratios for cooking. Many of these activities can be conveyed orally through constant interaction with numbers in the physical world. That is not to say that no formal study or book learning could or was be done in these areas, but the bulk of early mathematical learning did not need to take place in a school environment with a textbook. All that was needed was a student, the physical world, and a teacher with mathematical knowledge.

Christine and the Sybil pointing to a ladder from the heavens, from the Book of the Queen, France (Paris), c. 1410-1414, Harley MS 4431, f. 189v.

What Hugh recognized was that these mathematical activities, whether for play or practical application, were essential for what he and his contemporaries would have considered the formal discipline of mathematics as a liberal art (i.e. the Quadrivium), which would have taken place during the teenage years at higher level schools. Hugh distinguishes arts and disciplines in the following manner: “Knowledge can be called an art ‘when it comprises the rules and precepts of an art’ as it does in the study of how to write; knowledge can be called a discipline when it is said to be ‘full’ as it is in the ‘instructional’ science, or mathematics” (II.1).

A table used for Computus. Harley MS 3667 f 001v.

 In other words, the sorts of activities Hugh describes himself doing as a boy were not mathematical disciplines in his terminology. Instead, his boyish mathematical play was both pleasant at the time and useful as he grew up to study the mathematical disciplines. For this reason, Hugh praised such activity as best because it aids one’s movement “step by step” rather than “fall[ing] head over heels when [attempting] to make a great leap ahead” (VI.2). This learning process mirrors the original discovery of the disciplines themselves by humanity. As Hugh writes:

Such was the origin of all the arts; scanning them all, we find this true. Before there was grammar, men both wrote and spoke; before there was dialectic, they distinguished the true from the false by reasoning; before there was rhetoric, they discoursed upon civil laws; before there was arithmetic, there was knowledge of counting; before there was an art of music, they sang; before there was geometry, they measured fields; before there was astronomy, they marked off periods of time from the courses of the stars. But then came the arts, which, though they took their rise in usage, nonetheless excel it. (I.11)

Early childish mathematical play was not the Quadrivium, but Hugh considered it a necessary preparation for the later study of the Quadrivial arts. Just as Boethius argued in Institutio arithmetica 1,1,7 that the quadrivium provides steps (gradus) by which the mind is progressively illuminated and can raise itself from its immediate sensible circumstances to the certainty of intelligible truth, so Hugh argued that the humble mathematical play of childhood was one step on the way to learning the discipline of mathematics. Computus, stargazing, learning to sing, learning to dance, and making geometric shapes with pebbles—none of this was Quadrivium. These activities could be boyhood pursuits…or in some cases, ends in themselves practiced into adulthood, but activities of this sort were, in Hugh’s opinion, a necessary preparatory step for the Quadrivial disciplines.

Lesley-Anne Dyer Williams
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

Lesley-Anne Dyer Williams is a Professor for Memoria College’s Masters of Arts in Great Books program and graduated with her doctorate from the University of Notre Dame’s Medieval Institute in 2012. She was also the founding director Liberal Arts Guild at LeTourneau University. Her research focuses upon twelfth-century Platonism and poetry, especially Thierry of Chartres and Bernard Silvestris.

Further Reading:

Hugh of St. Victor. The Didascalicon of Hugh of St. Victor:  A Medieval Guide to the Arts. Edited & translated by Jerome Taylor, Columbia University Press, 1991.

Jaeger, C. Stephen. The Envy of Angels: Cathedral Schools and Social Ideals in Medieval Europe, 950-1200. University of Pennsylvania Press, 1994.

John of Salisbury. Metalogicon. Translated by C.C.J. Webb, Clarendon Press, 1929.

Orme, Nicholas. Medieval Children. Yale University Press, 2001.

Orme, Nicholas. Medieval Schools. Yale University Press, 2006.

Plato, Mathematician and Myth-Maker

Pisano, Giovanni, 1240?-1320?. c.1284. Siena Duomo: det.: Plato. Place: Museo dell’Opera del Duomo (Siena, Italy). https://library-artstor-org.proxy.library.nd.edu/asset/ARTSTOR_103_41822000532257.

The Republic, The Symposium, The Phaedrus, The Apology, and The Phaedo––these are just a few of the works of Plato that were not widely available throughout most of the Middle Ages. No extended depiction of the most just city in the Republic. No discussion of love in The Symposium and The Phaedrus. No self-defense for Socrates at his trial as found in The Apology, and no final dialogue before his suicide as found in The Phaedo. For lovers of great texts, especially Plato, such news can be shocking. What kind of Plato does a person know if they don’t have these key works? How much of Socrates’ life and Plato’s philosophy could even be known? These are the questions that many medieval scholars of the Latin Platonist tradition have dedicated their lives and careers to answering, and the answers can be quite surprising.

One aspect of this research that ought to be appreciated by the wider reading public (outside of the narrow confines of medievalists) is that Plato’s Timaeus wasthe most widely available Platonic work throughout most of the Middle Ages. In fact, examining the text of the Timaeus and why itwas such one of the few Platonic texts preserved reveals how peculiarly modern our current canon of Platonic literature is.

What we value in Plato was not necessarily what late antique or medieval readers valued, and yet, their ability to read well meant that they understood a lot more than might be supposed. An attention to the reception history of Plato’s Timaeus can give modern readers of Plato a better appreciation for the importance of both mathematics and poetry in Platonic philosophy.

The Timaeus is Plato’s work on the origins of the universe. It begins with a dialogue between Timaeus, Socrates, Hermocrates, and Critias, in which Socrates expresses a desire for a “moving image” of the city they had been talking about the day before. The summary of the previous day’s discussion appears to bear some resemblance to the conversation found in the Republic although scholars are divided over whether this summary perfectly matches the Republic that we now possess. Regardless of its accuracy, this summary would have been the closest a medieval reader would have had to a taste of the Republic. The opening dialogue covers all sorts of fascinating topics from Solon’s visit to Egypt, oral culture, the mythic origins of writing, and the myth of Atlantis, but the bulk of the work features a narration about the origins of the universe recounted by the Pythagorean, Timaeus.

The Timaeus was received in the Middle Ages through three main channels of Latin translations: the translation of Calcidius (which ends at 53b), the translation of Cicero (available but not widely used or even known, which ends at 42b), and the excerpts from the Ciceronian translation of the Timaeus that can be found in Augustine’s City of God. Although it does not contain the whole text of the Timaeus, Calcidius’ translation is much more complete than Cicero’s: rather than giving merely the speech of Timaeus like Cicero’s translation does, it includes the opening dialogue (even though the commentary itself ignores it).

Most modern Plato scholars would probably not choose The Timaeus as theone and only work they could save from destruction for all time. But, a better understanding of who Calcidius was and why he wrote the commentary on the Timaeus suggests that the preservation of the Timaeus in the Latin West was not an accident of fate. Rather, the results of Gretchen Reydams-Schills’ lifelong study of Calcidius give a plausible reason for why Calcidius’ commentary may have been the Platonic work of choice for many late antique philosophers.

Reydams-Schils argues that Calcidius wrote his commentary as an introduction to the Platonic corpus, essentially reversing the Middle Platonic curriculum, which traditionally ended with the Timaeus. One major piece of evidence for this theory is that Calcidius’ commentary often reserves discussion of harder philosophical concepts for the end of the commentary.Furthermore, unlike the Neoplatonists, Calcidius did not read the Timaeus synoptically and believed strongly in the importance of sequential reading of the Platonic corpus. In Calcidus’ Platonic curriculum, the Timaeus came first with its teachings on natural justice, then the Republic with its teaching of positive justice, and finally, the Parmenides came with its teaching of the forms and intelligible realities. Calcidius believed that a thorough understanding of mathematics was necessary for understanding of almost all of the Platonic works, which is why his commentary on the Timaeus turns out to be something like a crash course in Pythagorean mathematics.

Thus, although the Timaeus was one of the only Platonic works available throughout the early Middle Ages, Calcidius’ commentary gave readers some introduction to the entire Platonic corpus as well as a great deal of Pythagorean mathematics. Perhaps there might be good reason for a philosopher to save The Timaeus (especially a copy with Calcidius’ commentary)from a burning building!

Plato; Chalcidius (translation). Timaeus. Manuscript. Place: Bodleian Library, University of Oxford, <a href=’http://www.bodley.ox.ac.uk/’>http://www.bodley.ox.ac.uk/</a>. https://library-artstor-org.proxy.library.nd.edu/asset/BODLEIAN_10310768399.

Medievalists who study the textual reception of the various translations of The Timaeus have been able to identify a shift in kinds of interest in Plato over time. The primary Latin translation of the Timaeus used until the eleventh century was Cicero’s. Medieval scholars used to assume that the revival of Calcidius began with the twelfth century Platonists, but Anna Somfai has demonstrated that the proliferation of copies of Calcidius’ text and commentary began in the eleventh century when championed by Lanfranc of Bec (c.1050). The late twelfth-century actually experienced a decline of copying the Timaeus as interests shifted towards other texts.

What motivated the eleventh-century interest in Calcidius appears to have been the mathematical content of the Calcidian commentary because, by the Carolingian period, much of the actual content of the quadrivial arts had been lost, and scholars in the Middle Ages attempted to piece together what scraps of it remained from a variety of sources. Calcidius’ commentary on the Timaeus appears to have been particularly valued as a source text for the quadrivial (or mathematical) arts. As my two previous MI blogs have explored here and here, medieval thinkers in the traditional liberal arts tradition recognized that the quadrivial arts were the foundation for philosophical thought, even if they had few textual sources for actually studying them.

And although some of the interest in the kinds of mathematics found in the Timaeus and Calcidius’ commentary may have declined after the twelfth century, it was by no means lost completely. As David Albertson has demonstrated, the mathematical interest in Plato found in the work of the twelfth-century scholar, Thierry of Chartres, would eventually be picked up by the fifteenth-century scholar, Nicholas of Cusa, and many scholars have noted resonances of Cusa’s quadrivial agenda in the thinking of Leibniz, the founder of calculus:

It seems that God, when he bestowed these two sciences [arithmetic and algebra] on humankind, wanted to warn us that a much greater secret lay hidden in our intellect, of which these were but shadows. (Leibniz as quoted by Albertson, p.2)

Bernardus Silvester. Liber fortunae, also known as Experimentarius.. Manuscript. Place: Bodleian Library, University of Oxford, <a href=’http://www.bodley.ox.ac.uk/’>http://www.bodley.ox.ac.uk/</a>. https://library-artstor-org.proxy.library.nd.edu/asset/BODLEIAN_10310765350.

Even though the interest in scribal copying of the Timaeus seems to have declined somewhat by the twelfth-century, another kind of imitatio or translatio studii was being enacted by a different kind of scholar, Bernard Silvestris. He wrote a prosi-metric telling of the creation of the world that emulates Plato’s Timaeus. The title of his work, Cosmographia, roughly translates as “universe writing,” and Bernard delivered an oral performance of itbefore Pope Eugenius III in 1147. Bernard’s creative retelling of the Timaeus poetically depicts the role of imitation in the divine creation of the world in the form of “divine writing.” Performatively, the Cosmographia demonstrates that this divine writing is then imitated by poets in the form of human writing. In other words, Bernard values Plato’s Timaeus here not merely for its insights into mathematics or even the structure of the universe, but also what this mathematics in the universe implies about the mimetic nature of poetry itself.

As many literary scholars have demonstrated, much of the European literary tradition follows suit in seeing the value of Timaean Platonism for the production of literature. This interest can be seen in such diverse authors as Alan of Lille, Chrétien de Troyes, and Dante.

While I would personally be loath to give up the access to the Platonic corpus that I possess, the medieval reception of the Timaeus constantly pushes me to reconsider how I am reading that corpus. Having a large corpus of texts actually places an onus on the modern reader to ask the question of where to place the textual emphasis: Which texts of Plato should be considered central (and which ones periphery) and why? For example, should Plato’s Republic be considered his last word on poets and poetry? What would happen if Plato’s Timaeus were given more weight?

C.S. Lewis once wrote in his introduction to On the Incarnation by Athanasius:

Every age has its own outlook. It is specially good at seeing certain truths and specially liable to make certain mistakes. We all, therefore, need the books that will correct the characteristic mistakes of our own period. And that means the old books.

These words about reading the great books can also apply to reading the old books as they were read by past readers. Understanding medieval readings of Plato might very well be a good counterweight to modern presuppositions about who Plato was and what he was about. How might the idea of Plato as both a mathematician and myth-maker transform our modern understanding of Platonism and its history?

Lesley-Anne Dyer Williams is a Professor for Memoria College’s Masters of Arts in Great Books program and graduated with her doctorate from the University of Notre Dame’s Medieval Institute in 2012. She was also the founding director Liberal Arts Guild at LeTourneau University. Her research focuses upon twelfth-century Platonism and poetry, especially Thierry of Chartres and Bernard Silvestris.

Lesley-Anne Dyer Williams
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

For Further Reading:

Albertson, David. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford University Press, 2014.

Baxter, Jason M. The Infinite Beauty of the World: Dante’s Encyclopedia and the Names of God. Peter Lang, 2020.

Bernardus Silvestris. Poetic Works. Edited by Winthrop Wetherbee, vol. 38, Harvard University Press, 2015.

Caiazzo, Irene. “Teaching the Quadrivium in the Twelfth-Century Schools.” A Companion to Twelfth-Century Schools, edited by Cédric Giraud, translated by Ignacio Duran, vol. 88, Brill, 2019, pp. 180–202.

Calcidius. On Plato’s Timaeus. Edited by John Magee, vol. 41, Harvard University Press, 2016.

Chenu, M. D. “The Platonisms of the Twelfth Century.” Nature, Man and Society in the Twelfth Century: Essays on New Theological Perspectives in the Latin West, translated by Jerome Taylor and Lester K. Little, vol. 37, University of Toronto Press, 1997.

Dronke, Peter. The Spell of Calcidius: Platonic Concepts and Images in the Medieval West. SISMEL edizioni del Galluzzo, 2008.

Gersh, Stephen. Middle Platonism and Neoplatonism: The Latin Tradition. Vol 1 and Vol 2. University of Notre Dame Press, 1986.

Hoenig, Christina. Plato’s Timaeus and the Latin Tradition. Cambridge University Press, 2018.

Murray, K. Sarah-Jane. From Plato to Lancelot. Syracuse University Press, 2008.

Plato. Plato’s Cosmology: The Timaeus of Plato Translated with Running Commentary. Edited by F. M Cornford, Routledge, 1937.

Reydam-Schils, Gretchen. “Myth and Poetry in the Timaeus.” Plato and the Poets, edited by Pierre Destrée and Fritz-Gregor Herrmann, Brill, 2011.

Reydams-Schils, Gretchen J. Calcidius on Plato’s Timaeus: Greek Philosophy, Latin Reception, and Christian Contexts. Cambridge University Press, 2020.

Somfai, Anna. “The Eleventh-Century Shift in the Reception of Plato’s Timaeus and Calcidius’ Commentary.” Journal of the Warburg and Courtauld Institutes, vol. 65, 2002, pp. 1–21.

Stock, Brian. Myth and Science in the Twelfth Century. Princeton University Press, 1972.

Wetherbee, Winthrop. Platonism and Poetry in the Twelfth Century. Princeton University Press, 1972.

Poetry as a Quadrivial Art?

That ‘Poetry is the cradle of philosophy’ is axiomatic”

(John of Salisbury, Metalogicon I.22).

Coëtivy Master (Henri de Vulcop?) (French, active about 1450 – 1485), Philosophy Presenting the Seven Liberal Arts to Boethius, Google Art Project.

It is a truth generally acknowledged that in the Middle Ages a liberal arts education consisted of the trivium (grammar, logic, and rhetoric) and the quadrivium (arithmetic, music, geometry, astronomy). Poetry –what we might call “literature”– was primarily taught by grammarians and rhetoricians in the Middle Ages. Literary scholars, like Rita Copeland and Marjorie Woods, have therefore been very motivated to study exactly what the language disciplines of Grammar and Rhetoric entailed and precisely how they were taught in order to have a better sense of what the study of literature must have looked like in this period. Their works are indispensable for the study of medieval literature and truly are the bulk of where instruction in poetics lay in the Middle Ages. And yet, once cannot stop there.

Knowing exactly where to put poetry was something that clearly bothered many medieval philosophers. While today we might assume that poetry would clearly be associated with the Trivium, or the arts dedicated to words, specifically grammar and rhetoric, certain medieval thinkers located it within logic and also the Quadrivium, or the arts of number. Understanding why can help us to understand the multi-faceted way in which the medieval mind approached poetry in particular and the literary arts more generally.

Étienne Colaud, “John of Salisbury teaching philosophy,” frontispiece miniature of the Policraticus by John of Salisbury, BnF  Ms.1145, folio 3 recto, Public domain, via Wikimedia Commons.

In the twelfth century when there were major curricular changes afoot in schools and universities, John of Salisbury maintained that poetry belonged to the art of grammar although it was closely allied with rhetoric. “Art,” writes John of Salisbury, “is a system that reason has devised in order to expedite, by its own short cut, our ability to do things within our natural capacities. Reason neither provides nor professes to provide the accomplishment of the impossible;” Instead, reason pursues the possible by means of an efficient plan, what the Greeks would call a methodon (Metalogicon I.11, p.33). As J.J. Murphy writes in the Cambridge History of Literary Criticism, Vol. II: The Middle Ages:

In medieval terminology the Latin word ars (plural: artes) denoted a body of principles relating to a specific activity such as painting, music, preaching, or writing. By extension the term was also used for a written treatise on the subject of a particular art […] The term ‘art’ or ars when applied to such a treatise indicates a discussion of what the ancient Greeks would have called techné ––‘technique’ or ‘craft’ –– rather than an abstract or theoretical discussion of a subject (p.42).

The practitioner of an art is therefore called an artifex or craftsman, and the study of the art consisted of both the intrinsic principles for practice and the extrinsic practice of the art itself.[1] When art is understood in this way, craftsmen generally agree that the person able to produce art is more skilled that the person skilled at conveying the principles underlying art. While poetry was clearly a craft that required a practitioner to study a method of practice, it was by no means clear where it ought to fit in the medieval curriculum of the arts.

John of Salisbury reports that some people thought poetry should be its own subject (shockingly!) because so much of it is clearly a “product of nature’s workshop” (Metalogicon I.18). The close tie between poetry and nature formed the basis of their argument, but John of Salisbury warns pragmatically that if poetry is removed from grammar, “its mother and the nurse of its study,” the study of poetry could be “dropped from the roll of liberal studies.” In other words, everyone studies grammar, which in those days often included a careful study of works like Virgil’s Aeneid. If poetry became its own subject, people might not take it at all!

English: Arabic translation of Aristotle’s Poetics by Abu Bishr Matta
Français : Poétique (Aristote) en arabe – Abu Bishr Matta
العربية: فن الشعر لأرسطوطاليس نقل أبي بشر متى – من مخطوطة باريس ٢٣٤٦
http://gallica.bnf.fr/ark:/12148/btv1b8422956q/f273.image

Some philosophers thought that poetry actually belonged to the subject of logic. These people were especially concerned about how to classify Aristotle’s Poetics. In Ancient Greece, Aristotle had written a group of works (one might even say lecture notes) on logic when teaching at the Lyceum. His followers, the Peripatetics, classified these works as the Organon, meaning instrument or tool, because they saw them as instrumental in preparing for the study of philosophy. The Latin West had only select works from the Organon until their increased contact with Arabic philosophers like Avicenna, who wrote a commentary on the Poetics. Following the Greek commentators on Aristotle, most of the Arabic (and subsequently Latin scholastic) commentators saw Aristotle’s Rhetoric and Poetics as the seventh and eighth works of Aristotle’s Organon. In their zeal, therefore, to comment on the entirety of the Organon, some Latin scholastic commentators, like Herman the German, viewed poetics as a part of Logic.

As surprising as it might be to think that poetry should be considered primarily within the context of “logic,” there is strong evidence that poetry was also studied within the context of the quadrivium. And yet, many medieval thinkers, the Pythagorean believed that number lay at the root of creation itself. For example, Dante writes in the Convivio when commenting on the beauty of a canzone:

All of you who cannot perceive the meaning of this canzone, do not reject it on that account, but consider its beauty: considerable for the way it is constructed, which is the concern of the grammarians; the ordering of its discourse, which is the concern of the rhetoricians; and for the metrical numbering of its parts, which is the concern of poets. (II.xi.9–10)

The key word to focus upon here is numbering. Familiarity with the Commedia and its frequent references to the starsis enough to convince a reader that one aspect of the numbering that Dante had in mind was the medieval discipline of astronomy, but there is also good reason to think that Dante had music in mind. Some of this evidence is textual…the numerous references to music in the Purgatorio and Paradiso…, but some of this evidence can be found in Boethius.

The standard textbook for the teaching of music theory in the Middle Ages was Boethius’ Fundamentals of Music, and until 1255, it was not uncommon for most educated men , including Dante, who undertook a liberal arts education to have at least some instruction in the subject.[2] As a result, even 11th and 12th c. philosophers like Anselm and Peter Abelard wrote sacred poetry and song. In this book, Boethius speaks of poetry as a subset of one kind of music.

Boethius begins his work on music with a philosophical justification for its study. Citing Plato and Pythagoras, he observes that music is so deeply engrained in human nature that from a young age it has the power to move human souls, transform their character, and even affect their health and sense of well-being (I.1.180–185). He explains that this phenomenon should leave us with no doubt that “the order of our soul and body seems to be related somehow through those same ratios by which subsequent argument will demonstrate sets of pitches, suitable for melody, are joined together and united” (I.1.186). Since “music is so naturally united with us that we cannot be free from it even if we so desired,” then “the power of the intellect ought to be summoned so that this art, innate through nature, may be mastered, comprehended through knowledge” (I.187). In this way, Boethius justifies the study of music because it reflects something about the fundamental nature of the human soul.

English: “King David, Lady Music and musicians”. In manuscript “De institutione musica”. Boetius.
Español: “El Rey David, la Señora Música y los músicos”. Del manuscrito “De institutione musica”. Boecio.
Date       Original: 1941 – 1942. Copy upload: 2010.Source: http://images.amazon.com/images/P/B000009OM1.jpg

In this work, Boethius identifies three kinds of music––cosmic, human, and instrumental. This categorization implies that the human response to music is rooted in the nature of not only the human soul but of the cosmos (I.2). Cosmic music, or the music of the spheres, is the harmonious sound produced when the stars in their courses and the diversity of seasons move swiftly together in harmonious union (1.2.187–188). Human music does not concern the music produced by humans. Rather, it is the music found in the harmony of soul and body in a human being. Boethius describes this music as “a careful tuning of low and high pitches as though producing one consonance” (I.2.189). It unites not only the rational and animal parts of the soul, but the parts of the body and the body’s union with soul. Boethius promises to speak about this subject later, but he never returns to it.  Instrumental music, for Boethius, includes the harmonious sounds produced by tension of strengths, human breath, percussion, etc. (I.2.189). This kind of music is what most people today associate with music, but Boethius’ understands this music to operate according to the same mathematical principles of both cosmic and human music. This mathematical concordance explains the reasons for music’s profound effect on the human soul.

            Although the producer of cosmic and human music is ultimately God, instrumental music must be produced by a human musician. Boethius’ definition of a human musician broadens the horizon within which music itself is narrowly considered today. He identifies three classes of musician: the instrumentalist, the poet, and the rational judger of music (I.34.224).

            The instrumentalist is no greater than a “slave” because one does not need the faculty of reason in order to produce music upon an instrument.

            The second class of poets are presumably higher than slaves, but Boethius remarks that even the poets create songs by instinct rather than reason. One might recall here Lady Philosophy’s attack upon the Muses as “harpies” because their base songs only continued to prolong Boethius’ misery.

            The third class of musician is the one with the ability to judge rhythm, melody, and composition. Since this class exercises reason in their experience of music, they alone should be considered worthy of esteem. This final judgment may seem harsh, but it was a common opinion in his day; Augustine repeats a similar idea in De musica.3 In fact, both men express their love of hearing music with some guilt, even though Augustine insists that music should remain in churches (Conf. 9.6, 14 and 10, 33, 49–50; Consol. I.2 and IV.6.6). In other words, Boethius repeats the infamous attack of Plato on the poets, even though he himself writes poetry in the Consolatio.

            It is startling to consider that Boethius includes both poets and song-writers within the class of musicians. Any time a human being takes the mathematics of sound seriously in the construction of a work of verbal art, they are a musician, whether or not the words constructed are intended for accompaniment with music. Second, Boethius boldy asserts that the ability to judge music is superior to the ability to craft and perform music. Within this model of music, the music theorist and literary critic are both superior to the musician and the poet. The ability to judge is always to be preferred over the ability to craft. In the long war between philosophy and poetry, philosophy always wins.

Whether or not poets like Dante would have agreed with Boethius that the practice of their art was inferior to those who judge art, especially since arts are, by definition, intended to be practiced, it is interesting to consider that medieval poets, as a kind of musician, may have conceived themselves to be craftsman that used the tools of grammar, logic, rhetoric, and music (or the entire quadrivium if one is Boethius or Dante!) to construct their art while looking up at the stars.

Lesley-Anne Dyer Williams
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

Further Reading

Ancius Manlius Severinus Boethius. Fundamentals of Music. Edited by Claude V. Palisca. Translated by Calvin M. Bower. New Haven and London: Yale University Press, 1989.

Copeland, Rita, and Ineke Sluiter. Medieval Grammar and Rhetoric: Language Arts and Literary Theory, AD 300 -1475. Oxford: Oxford University Press, 2009.

Dante Alighieri. Dante: Convivio. Translated by Andrew Frisardi. New edition. Cambridge: Cambridge University Press, 2022.

Fournier, Michael. “Boethius and the Consolation of the Quadrivium.” Medievalia et Humanistica, no. 34 (2008): 1–21.

John of Salisbury. The Metalogicon. Translated by Daniel D McGarry. Berkeley: Calif. U.P., 1962.

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Lesley-Anne Dyer Williams is a Professor for Memoria College’s Masters of Arts in Great Books program and graduated with her doctorate from the University of Notre Dame’s Medieval Institute in 2012. She was also the founding director Liberal Arts Guild at LeTourneau University. Her research focuses upon twelfth-century Platonism and poetry, especially Thierry of Chartres and Bernard Silvestris.


[1] Distinctions made by Thierry in the Heptateuchon.

[2] Huglo, “The Study of Ancient Sources of Music Theory in the Medieval University.”