Aþum Swerian: Swearers of Oaths?

Beowulf is a story about a doomed people who are destined for annihilation as a result of depredation, feuding, and cyclical inter-tribal violence. Yet, the violence described in the poem is not always outward but often occurs from within, as acts of intra-tribal violence frame much of the narrative. Even seemingly positive events are thus generally short-lived. Accordingly, in the eminence of King Hrothgar’s glorious construction of Heort, the narrator reveals the hall’s imminent doom:  

Sele hlifade  
heah ond horn-geap.   Heaðo-wylma bad
laðan liges.                Ne wæs hit lenge þa gen  
þæt se ecg-hete aþum swerian 
æfter wæl-niðe wæcnan scolde. (81-5)

The hall sheared upward, high and horn-vaulted. For the battle-surge it waited, loathsome fire. Nor was it long before the edge hate of aþum swerian must awaken for slaughter-spite.

Beowulf Manuscript, excerpt with aþum swerian.” BL, Cotton Vitellius a.vx. MS 130v, BL 133v.

This dire prediction identifies the causal agents of disaster as aþum-swerian. But given that this term is unattested and grammatically invalid, we are bound to ask: Who are these aþum-swerian? The conventional approach solves this conundrum by creating a new term in imitation of such copulatives as suhtergefaedaran (“nephew and uncle” from Beowulf), gisunfader (“son and father” from Heliand), and sunufatarungo (“son and father” from Hildebrandslied). Following these models, the editors of Klaeber 4 (120, 350, 437) emend the term to aþum-sweoran, thereby conjoining aþum (sons-in-law) and sweoran (fathers-in-law). Because this solution apparently predicts the sundering of vows between Ingeld and Hrothgar (2022-66), this emendation has become the dominant convention. 

Nevertheless, there are problems. First, the emended term, glossed as “sons-in-law and fathers-in-law,” differs markedly from the models, which are glossed as “nephew and uncle” and “son and father.” And though the term is indeed attested with the gloss “son-in-law,” the rendering aþum-sweoran is a hapax legomenon attested nowhere in the extant corpus of Old English literature. Making the invention yet more suspect is the well-attested phrase, sweor ond aþum (father-in-law and son-in-law), which would seem to preclude a need for the copulative. 

The proposed term also falls short in its narratological salience. There are no “sons-in-law” implicated in the violence that erupts at Ingeld’s wedding, only one “son-in-law.” Yet more problematic, this single crisis cannot account for the apocalyptic imagery that frames Heorot’s catastrophe. Prior to the prediction of calamity, the hall’s construction is marked by an array of tropes that suggest the Tower of Babel. As Tristan Major observes, “Hrothgar’s rise to power [64-79] and the building of his hall, Heorot, echoes Nimrod and the Tower of Babel” (242).” Likewise, as Daniel Anlezark observes, the hall’s destruction is marked by retributive images of Flood and Hellfire (336-7). In sum, the proposed solution leaves important problems unresolved. It inaccurately predicts “sons-in-law” in respect to Ingeld. And it does not account for the apocalyptic imagery of idolatry, flame, and fire that marks Heorot’s doom.

The Tower of Babel. London, British Library, Cotton Claudius B.IV, fol 19r. 

In this review, we promote an alternative initially proposed by Michael Alexander. This alternative interprets aþum as the plural dative “oaths” and emends swerian to the plural dative -swaran (swearers). The rendering “swearers of oaths,” acknowledged by Klaeber 4 as possible, has the advantage of relying on attested terms. The plural dative form aþum (oaths) occurs not only in the corpus but also in Beowulf, and the second term (-swara) occurs in a similar compound, man-swaran (criminal swearers). Yet more support for this construct can be found in the oath-swearing between Hengest and Finn. Here the term aðum also occurs as a plural dative, framing a parallel scenario in which oaths will be broken and a hall destroyed:

Fin Hengeste
elne, unflitme aðum benemde
þæt he þa wealafe weotena dome 
arum heolde, þæt ðær ænig mon 
wordum ne worcum wære ne bræce . . . .  (1097-100)

“Fin with Hengest without quarrel declared his oath that he would by his council’s judgment hold [the truce] with honor that any man there by word or deeds should not break the covenant . . . .”

The emendation to aþum-swaran also offers much stronger alignment with the narrative arc. Notably, this alignment begins with the paired disclosures that define Fitt I: Whereas the history of Grendel’s origin locates Cain’s act of murder as a calamity in the past, the prediction of murderous oath-swearers locates Heorot’s destruction as a calamity in the future. This parallel design is highly significant: In effect, it forges a link between Cain’s crime of kinship murder and the internecine violence that spells Heorot’s doom. This linkage, moreover, not only intimates the Danes’ ongoing state of iniquity but also explains the apocalyptic tropes that frame the hall’s calamity. Accordingly, Heorot’s doom emerges not as a circumstantial event caused by brawling Danes and Heathobards but as an in-kind retributive event that aligns perfidious Nordic warriors with the curse of exile from human joys, entailed in Cain’s crime and punishment.

Cain killing Abel with a scythe. Bible Historiale. British Library, MS Harley 4381, f.10r, 1403-1404.

Notably, also, the intimation of Danish perfidy is borne out across the narrative arc. Beowulf and the narrator declare Unferth’s fratricidal treachery; the narrator insinuates Hrothulf’s possible resentment against his uncle, Hrothgar; the lay of Finn and Hildeburh recounts the Danes’ violation of peace oaths in favor of murderous revenge; Hrothgar’s adoption of Beowulf sparks Wealhtheow’s resistance and her appeals to warriors in the hall; and Hrothgar violates his promise of protection to the Geats, potentially inciting Beowulf’s revenge. This surfeit of Danish treachery, in other words, aligns perfectly with the narrator’s revelation that “swearers of oaths” will soon incite violence.

For this reason, also, the reference to oath-swearers functions as a formula for suspense—a design that impels the audience to consider, in a fictive world replete with perfidy and oath-making, which of the oath-swearers will incite a conflagration? Will Unferth the fratricide murder again? Will Hrothulf avenge his displacement from the throne? Will one of the Danes retaliate against Hrothgar’s covenant with Beowulf, the foreigner? Will Wealhtheow incite the same kind of intertribal violence that erupts in the Frisians’ hall? Will Beowulf retaliate against Hrothgar for deserting his men?

The emendation to aþum-swaran presents a solution that is better attested and more meaningful than the conventional emendation to aþum-sweoran. As noted above, the gloss of “sons-in-law” does not possess predictive value regarding Ingeld, and the sundering of vows between Ingeld and Hrothgar cannot explain the apocalyptic imagery surrounding the disclosure of Heorot’s doom. Conversely, that same apocalyptic imagery aligns perfectly with a depiction of Danish society as inherently unstable, doomed to self-destruction, as the unchecked impulses of egoistic aggrandizement overcome the covenants that bind social order. Likewise, the depiction of Danish perfidy permeates the narrative arc. Accordingly, the disclosure of violent oath-swearers functions within an ingenious narrative design. It affords the schadenfreude of dramatic irony, as the audience anticipates a disaster the characters know not of. And it thus generates a game of blind corners, in which the audience’s knowledge of impending violence from oath-swearers charges subsequent events with anticipation and suspense. 

Chris Vinsonhaler & Richard Fahey
Medieval Institute
CUNY University & University of Notre Dame


Selected Bibliography & Further Reading

Alexander, Michael. Beowulf: A Glossed Text. Penguin Classics, 1995.

Anlezark, Daniel. Water and Fire: The Myth of the Flood in Anglo-Saxon England. Manchester U Press, 2006. 

Major, Tristan. Undoing Babel: The Tower of Babel in Anglo-Saxon Literature. U Toronto Press, 2018. 

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.

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.

“Philosophy Presenting the Seven Liberal Arts to Boethius,” about 1460–1470, Coëtivy Master (Henri de Vulcop?), Ms. 42, leaf 2v (91.MS.11.2.verso), Getty Museum Collection.

Boethius (c.480-525) not only established the seven liberal arts as the traditional curriculum for the Middle Ages, but he also wrote treatises on all of the trivium as well as arithmetic, music, and geometry (the latter work is now lost).  He, coined the term, “quadrivium” in his attempt to translate the tessares methodoi (four methods) of the Neopythagorean, Nicomachus of Gerasa (c.60-120). Boethius’ own De institutione arithmetica largely draws upon the work of Nicomachus. Modern day history of mathematics textbooks often observe that Nicomachus’ work is one of the first to distinguish arithmetic and geometry as separate disciplines but that the actual quality of the mathematics contains basic errors. Unlike Euclid, Nicomachus doesn’t always give his proofs. Nicomachus presents arithmetic as the principle mathematical art and as a result, so does Boethius. While Boethius was unlikely to have gotten the problem of irrational numbers from Nicomachus because Nicomachus presents arithmetic as the highest mathematical art, Boethius adopts his fourfold division of the mathematical arts along with the belief that arithmetic was the principle mathematical art (De institutio arithmetica 1,1,8).

Image from Boethius’ De institutione arithmetica in British Library, Harley MS 549.

In his work on arithmetic, Boethius explains that the order of the quadrivium he offers (music, astronomy, geometry, and arithmetic) both reflects the true nature of the universe and is the proper pedagogical order for the study of mathematics as a preparation for philosophy. Progression through each of the arts trains the mind to move from sense perception to intelligible reality.

Philosophy Instructing Boethius on the Role of God. Coëtivy Master (Henri de Vulcop?), about 1460–1470. Ms. 42, leaf 3 (91.MS.11.3.recto), J. Paul Getty Museum.

This progression of the soul can be seen in the Consolation of Philosophy, where Boethius begins with music and is drawn to philosophy upward by means of astronomy, geometry, and finally arithmetic.

While Boethius’ highly influential order of the quadrivium was adopted by both Cassiodorus and Isidore, Calcidiuswrites very clearly in his commentary on Plato’s Timaeus that geometry is the foundation of all other mathematical arts (Commentum 2.32). His influence throughout the Middle Ages was also extensive. Calcidius’ translation and commentary of Plato’s Timaeus, was one of the only texts of Plato available throughout much of the Middle Ages. Although there were other translations of the Timaeus available, Calcidius’ commentary, as Reydams-Schils has demonstrated, was actually a very good introduction to Platonism as a whole because it was designed to introduce the reader to Platonic doctrine in a pedagogically sequenced way from mathematics to physics and then theology. Throughout the earlier Middle Ages, as Somfai has shown, the commentary was used to teach the quadrivium itself, and earlier versions contained numerous geometrical diagrams. While interest in his geometrical figures appears to fall out of favor in the twelfth century and in newer commentaries on the Timaeus, Nicholas of Cusa in the fourteenth century has both the old Calcidius’ commentaries and the newer commentaries, and geometry clearly plays a major role in his understanding of infinity and kinds of infinity.

Early tenth century manuscript of Calcidius’ Latin translation of Plato’s Timaeus from Italy. Reg. lat. 1308 fols. 21 verso – 22 recto medbio01 NAN.10.

The third line of quadrivial tradition can be found in Martianus Capella whose Marriage of Philology and Mercury, places music as the highest of the seven liberal arts, the culmination of his entire work. As Michael Masi has observed, this ordering can be found in many visual depictions of the quadrivium, including most famously, the Incarnation Portal at Chartres Cathedral, where arithmetic is paired with geometry as a mathematical study and music with astronomy as a study in harmony. While the complete reasons for this preference are too numerous to identify in a blog, there is a certain kind of Pythagorean logic even here. Music, for Pythagoras and his followers, was thought to be the best evidence for number being at the foundation of the universe. Even the movement of the stars and planets were considered to be one example of many kinds of music in the universe.

Charles Nègre (French, 1820 – 1880), photographer [Chartres Cathedral, Royal Portal (The Incarnation Portal), South Lateral Doorway], 1857. HeliogravureImage: 59.8 × 45.3 cm (23 9/16 × 17 13/16 in.),  Sheet: 71.6 × 55.1 cm (28 3/16 × 21 11/16 in.) The J. Paul Getty Museum, Los Angeles,  84.XM.692.4

The stakes for getting the order of the quadrivium right in the Middle Ages may not have risen to the level of murder (although that might make a nice monastic murder mystery written by Umberto Eco, Murder Most Irrational….). And yet, three sources for the quadrivial tradition in the Middle Ages did present the idea that the order of the mathematical arts reflects the most fundamental nature of the universe itself. Furthermore, this fundamental order of the universe has implications for the order of education in the mathematical arts. These stakes, the metaphysical order of the universe and of education, would still have been considered pretty high for most thinkers throughout the Middle Ages.

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

Further Reading:

Albertson, David. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford University Press, 2014. https://doi.org/10.1093/acprof:oso/9780199989737.001.0001.

Boethius. Boethian Number Theory: A Translation of the “De Institutione Arithmetica” with Introduction and Notes. Translated by Michael Masi. Studies in Classical Antiquity; v. 6. Amsterdam: Rodopi, 1983.

Boethius. The Consolation of Philosophy. Translated by Victor Watts. London: Penguin, 1999.

Burton, David M. The History of Mathematics: An Introduction. Dubuque, Iowa: Wm. C. Brown Publishers, 1988.

Caiazzo, Irene. “Teaching the Quadrivium in the Twelfth-Century Schools.” In A Companion to Twelfth-Century Schools, edited by Cédric Giraud, translated by Ignacio Duran, 88:180–202. Brill’s Companions to the Christian Tradition. Brill, 2019. https://doi.org/10.1163/9789004410138_010.

Calcidius. On Plato’s Timaeus. Dumbarton Oaks Medieval Library 41. Cambridge, Massachusetts; London, England: Harvard University Press, 2016.

Chenu, M. D. Nature, Man, and Society in the Twelfth Century: Essays on New Theological Perspectives in the Latin West. Chicago and London: University of Chicago Press, 1957.

Eco, Umberto. The Name of The Rose. Reprint edition. Boston: HarperVia, 2014.

Evans, Gillian R. “The Influence of Quadrivium Studies in the Eleventh- and Twelfth-Century Schools.” Journal of Medieval History 1, no. 2 (July 1975): 151–64.

Fassler, Margot E. The Virgin of Chartres: Making History through Liturgy and the Arts. Yale University Press, 2010.

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

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

Martianus Capella. Martianus Capella and the Seven Liberal Arts. Translated by William Harris Stahl, Richard Johnson, and E.L. Burge. Vol. II: The Marriage of Philology and Mercury. 2 vols. Records of Western Civilization 84. Columbia University Press, 1992.

Masi, Michael. “Boethius and the Iconography of the Liberal Arts.” Latomus 33, no. 1 (January 1, 1974): 57–75.

Nicholas of Cusa. Nicholas of Cusa on Learned Ignorance: A Translation and an Appraisal of De Docta Ignorantia. Edited by Jasper Hopkins. Minneapolis: The Arthur Banning Press, 1985.

Oosterhoff, Richard. Making Mathematical Culture: University and Print in the Circle of Lefèvre d’Étaples. Oxford-Warburg Studies. Oxford: University Press, 2018. https://doi.org/10.1093/oso/9780198823520.001.0001.

Reydam-Schils, Gretchen. “Meta-Discourse: Plato’s Timaeus According to Calcidius.” Phronesis 52 (2007): 301–27.

Somfai, Anna. “Calcidius’ Commentary on Plato’s Timaeus and Its Place in the Commentary Tradition: The Concept of Analogia in Text and Diagrams.” Bulletin of the Institute of Classical Studies 47, no. Supplement_83_Part_1 (January 1, 2004): 203–20. https://doi.org/10.1111/j.2041-5370.2004.tb02303.x.

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

Stahl, William H. “The Quadrivium of Martianus Capella: Its Place in the Intellectual History of Western Europe.” In Arts libéraux et philosophie au moyen âge, 959–67. Actes du IVe Congrès internationl de philosophie médiévale. Montreal Paris, 1969.

Stahl, William Harris, Richard Johnson, and E.L. Burge. Martianus Capella and the Seven Liberal Arts. Vol. I: The Quadrivium of Martianus Capella. 2 vols. Records of Civilization, Sources and Studies 84. New York: Columbia University Press, 1971.

Weigh Your Books! An Interview with Dr. Andrew Irving

This week, we’re revisiting the first published episode of “Meeting in the Middle Ages.” Back in 2022, we sat down with Dr. Andrew Irving, assistant professor of religion and heritage at the University of Groningen. We spoke to him about his journey to Medieval Studies, his work on the 11th century Uta Codex, why one should always weigh their books, and why liturgy is like a Wagnerian opera.

Dr. Irving’s story is one of a truly international scholar. A native of New Zealand who moved to the US to study for his PhD at Notre Dame, he now works in Europe on a broad range of medieval subjects. His stories of archival work highlight some of the unexpected challenges that researchers can face: limited access to resources, unconducive weather (it helps to examine books in “raking light”), or flat out denied permission to consult a manuscript. Traveling to another country to visit a library and examine its rarest materials can be intimidating, especially for young scholars. But Dr. Irving demonstrates that a personal connection and diligent preparation can pave the way for a smooth experience. It’s an instructive tale for young scholars, and sheds light on a part of scholarly work that may seem mysterious to the uninitiated.

Dr. Irving’s work is about place. His career has taken him all over the world, of course. But the place in which texts exist is also paramount. Through his work on texts like the Uta Codex, he provides some great examples of how a manuscript has to be considered in terms of its home. Where was it kept? What was the environment? What was the history of that home? Was it ever destroyed, raided, burned? If it was a written document, was it read aloud? To whom? Was it carried about? How much did it weigh? All of these questions must be asked to get at the truth of an object. A text has to be wrestled with on its own terms—in isolation—but this is only half the story. Each historical artifact is living history: it was created by someone for someone or something. We have to be prepared to engage with it in a multitude of ways. We must be historians, linguists, theologians, art historians, literary critics, and more. That is what it is to be a medievalist.

Thanks for listening. See you next time in the Middle Ages.

Will Beattie & Ben Pykare