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Quadrivium

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.

This blog post is excerpted from the University of Notre Dame’s Medieval Institute Research Blog.

Categories
Medieval Platonism Quadrivium

The Quadrivium and the Stakes for Ordering the Mathematical Arts

 Fyodor Bronnikov, Pythagoreans’ Hymn to the Rising Sun, 1869. Oil on canvas.

Legend has it that Pythagoras sentenced the first person to discover irrational numbers, Hippasus of Metapontum (c.530-450 BC), to death. He was tossed overboard a ship to drown. Why? Pythagoras taught that number was the essence and cause of all things, and for Pythagoras and his followers, numbers meant integers. Hippasus’ discovery of irrational numbers appeared to undermine the very core of Pythagoras’ teachings about the numerical nature of the universe. The secret could not get out. Hippasus had to die.

Imaginary engraving of the philosopher Hippasus of Metapontum. From the 1580 book Illustrium philosophorum et sapientum effigies ab eorum numistatibus extractae, by Girolamo Olgiati. Reprinted 1583.

The existence of irrational numbers became a Pythagorean secret. They were called “unutterables” because in Greek, the ratio between two integers was called logos, and so, irrational numbers were called, alogos, which can be translated as either “irrational” or “not spoken.” The worry caused by this secret knowledge was somewhat alleviated by Eudoxus of Cnidos (408-355 BC) when he argued that the basis of reality was a ratio of magnitudes. In effect, Eudoxus made geometry replace arithmetic as the highest mathematical discipline, the foundation of all others. Geometry and arithmetic were hardly even separate disciplines at the time. This change of emphasis allowed Pythagorean teachings about the numeric nature of the universe to continue.

Philosophia et septem artes liberales (Philosophy and the Seven Liberal Arts), as illustrated in the Hortus deliciarum. The order of the arts here are: grammar, rhetoric, dialectic, music, arithmetic, geometry, and astronomy. A more detailed study of this image can be found here and here.

         The idea that the mathematical disciplines have some orderly relationship between each other is essential for understanding the medieval concept of “quadrivium.” While it is well known that the medieval liberal arts curriculum, at least in its ideal established by Boethius, taught that a student must study both the trivium and quadrivium before progressing to philosophy and theology, the exact nature and rationale for the quadrivium is often less understood. Lists of the arts comprising the quadrivium (arithmetic, geometry, astronomy, and music/harmony) are consistent, but the exact order for these lists can vary. While there is no doubt that sometimes there is truly no rationale for a given order of the mathematical arts, attention to the mathematical art considered the principle or highest can reveal at least three identifiable streams of quadrivial traditions coming from the ancient world (similar to Chenu’s identification of different kinds of Platonism): the Boethian, the Calcidean, and the Capellan. The mathematical art considered “principle” is the one closest to metaphysical reality of the universe and serves as the foundation for all other mathematical disciplines. While the problem of irrational numbers may not have been on the forefront of anyone’s mind in the Middle Ages…it was a closely guarded Pythagorean secret after all…the problem of the principle mathematical art, inherited from Pythagoreanism, was readily available in the source texts.

This content is excerpted. Read the full article here at the University of Notre Dame’s Research Blog