Arithmetic was one of the seven liberal arts taught in the French schools just before the middle of the twelfth century, and Boethius’s De arithmetica was the principal textbook for this art. This volume provides an edition of a commentary on the De arithmetica; the accompanying introduction identifies the author of the commentary as Thierry of Chartres, and provides a careful consideration of how the commentary reflects his philosophy.
Unlike the commentaries on Plato's Timaeus and on Boethius's Consolatio philosophiae, medieval exegesis of Boethius's De arithmetica has seldom been subjected to comprehensive and systematic enquiry. Inhabiting the shifting boundary between philosophy and history of science, the De arithmetica itself has been neglected by most medievalists. Yet, from the Carolingian renaissance onward, when the scholarly curriculum came to be based on the seven liberal arts, Boethius's work soon became a canonical text for the study of arithmetic. Indeed, the growing interest in it during the twelfth century is attested by the large number of surviving commentaries in manuscript.
The commentary on the De arithmetica preserved in Stuttgart, Württembergische Landesbibliothek, Cod. math. 4° 33 and edited here for the first time can be securely attributed to Thierry of Chartres. It belongs to a phase when the Chartrian master's interests were mainly directed toward the liberal arts. We can also discern in Thierry's commentary on the De arithmetica themes and problems developed in his Tractatus de sex dierum operibus and more elaborately in his commentaries on Boethius's Opuscula sacra. Indeed, the discovery of this commentary on the De arithmetica might legitimately be said to clarify not only the more intractable passages in the theological writings but also to illuminate Thierry's philosophical project as a whole. At the heart of that vision is a developing trend in twelfth-century philosophy that places number and proportion at the heart of the physical cosmos. In this profoundly 'mathematical Platonism,' all things are based on number and follow the rule of number; or, to quote Thierry himself, “creatio numerorum, rerum est creatio.”
A specialist in the history of medieval philosophy as well as the history of science, Irene Caiazzo received her doctorate in 1999 and her Habilitation in 2012 from the Ecole pratique des Hautes Etudes, Paris. She is currently directeur de recherche at the Centre national de la recherche scientifique.
Thierry of Chartres and the School of Chartres
Commentary and Commentator
Thought, Language, Philosophy
Traditions of Commentary on the De arithmetica
Some Concluding Reflections
The Present Work: From Manuscript to Edition
TEODORICUS CARNOTENSIS: Commentum super Arithmeticam Boethii
Appendix: A Handlist of Medieval Commentaries on Boethius's De arithmetica
“The importance of mathematics for Thierry of Chartres’s theological, specifically Trinitarian, reflections on Boethius’s Opuscula sacra has engaged generations of scholars. Irene Caiazzo’s discovery of Thierry’s commentary on Boethius’s De institutione arithmetica, edited for the first time in this volume, finally allows scholars to study the formation and development of crucial elements in Thierry’s mathematical theology through his detailed and bold explication of Boethius’s arithmetical handbook. Accompanied by an introductory study that forcefully argues for Thierry’s authorship of the anonymously transmitted commentary by measuring it against the shifting but coherent doctrinal positions staked out in Thierry’s theological commentaries, Caiazzo’s meticulous edition will substantially reshape and refine our understanding of the Breton master, extolled by John of Salisbury as the artium studiosissimus investigator and acclaimed by Hermann of Carinthia as the soul of Plato reincarnate.”