Le opere dei sei giorni: aritmetica e esegesi secundum physicam in Teodorico di Chartres

L'elaborato si concentra sul Tractatus de sex dierum operibus di Teodorico di Chartre. Si è quindi analizzata la tipologia esegetica dell'autore: da una parte vi è un metodo naturalistico - in base al quale la Genesi è letta secondo categorie fisiche - dall'altra un metodo aritmetico - che rilegge la creazione biblica secondo parametri quadriviali

The medieval latin reception of the Pseudo-Aristotelian on indivisible lines: reassessing the state of the art

Este artículo trata de la primera recepción latina de Sobre las líneas indivisibles de Pseudo-Aristóteles y de su impacto en el debate medieval sobre el continuo. La referencia de Robert Grosseteste y Alberto Magno a este texto pone en evidencia que esta obra pseudoaristotélica podría ser tomada tanto como fuente para encontrar información sobre el principio de indivisibilidad como ampliación de las críticas antiatomistas de Aristóteles dispersas en sus obras auténticas. El uso de Sobre las líneas indivisibles que hacen Enrique de Harclay y Adán de Wodeham confirma que la lectura de este texto podría ser doble según el principio defendido: mientras que Enrique toma el argumento pseudoaristotélico de la división de las líneas en partes iguales y lo replica, Adán amplía este argumento mostrando las incongruencias que implican sus adversarios indivisibilistas.This article deals with the first Latin reception of Pseudo-Aristotle’s On Indivisible Lines and its impact on the medieval debate about the continuum. Robert Grosseteste’s and Albert the Great’s references to this pseudo-Aristotelian text show that it could be regarded as a source for where to find information about the indivisibilist tenet, as well as an expansion of Aristotle’s anti-atomistic critiques scattered throughout his authentic works. The use of On Indivisible Lines made by Henry of Harclay and Adam of Wodeham confirms this trend: the reading of this text could be twofold according to the tenet defended. While Henry argues against Pseudo-Aristotle to defend indivisibilism, Adam expands on pseudo-Aristotelian arguments to show the incongruities implied by indivisibilism

La recepción latina medieval del pseudoaristotélico 'Sobre las líneas indivisibles': Reevaluación del estado de la cuestión

This article deals with the first Latin reception of Pseudo-Aristotle’s On Indivisible Lines and its impact on the medieval debate about the continuum. Robert Grosseteste’s and Albert the Great’s references to this pseudo-Aristotelian text show that it could be regarded as a source for where to find information about the indivisibilist tenet, as well as an expansion of Aristotle’s anti-atomistic critiques scattered throughout his authentic works. The use of On Indivisible Lines made by Henry of Harclay and Adam of Wodeham confirms this trend: the reading of this text could be twofold according to the tenet defended. While Henry argues against Pseudo-Aristotle to defend indivisibilism, Adam expands on pseudo-Aristotelian arguments to show the incongruities implied by indivisibilism.Este artículo trata de la primera recepción latina de Sobre las líneas indivisibles de Pseudo-Aristóteles y de su impacto en el debate medieval sobre el continuo. La referencia de Robert Grosseteste y Alberto Magno a este texto pone en evidencia que esta obra pseudoaristotélica podría ser tomada tanto como fuente para encontrar información sobre el principio de indivisibilidad como ampliación de las críticas antiatomistas de Aristóteles dispersas en sus obras auténticas. El uso de Sobre las líneas indivisibles que hacen Enrique de Harclay y Adán de Wodeham confirma que la lectura de este texto podría ser doble según el principio defendido: mientras que Enrique toma el argumento pseudoaristotélico de la división de las líneas en partes iguales y lo replica, Adán amplía este argumento mostrando las incongruencias que implican sus adversarios indivisibilistas. &nbsp

Diferencias espaciales absolutas: la lectura de Grosseteste del 'Sobre los cielos' de Aristóteles

This article deals with Robert Grosseteste’s account of ‘spatial differences’, such as ‘up’, ‘down’, ‘right’, ‘left’, ‘before’, and ‘behind’. More specifically, attention is focused on Grosseteste’s De differentiis localibus, which is a concise scientific treatise arguing for the objectiveness of the differences of place pertaining to all living bodies, including heavenly ones. The article has a two-fold goal: to present the contents of such an understudied opuscule, and to check if there is some compelling reliance on any of the Latin versions of Aristotle’s On the Heavens. Such an analysis reveals that Grosseteste’s reading of Aristotle’s On the Heavens is angled by Averroes’ Long Commentary on the Physics, on which Grosseteste relies as well to build his conception of mathematical and natural differences.Este artículo trata sobre la descripción de las ‘diferencias espaciales’ de Roberto Grosseteste, como ‘arriba’, ‘abajo’, ‘derecha’, ‘izquierda’, ‘antes’ y ‘detrás’. Más específicamente, se presta especial atención al De differentiis localibus de Grosseteste, que es un breve tratado científico que defiende la objetividad de las diferencias de lugar y su pertenencia a todos los cuerpos vivos, incluidos los celestiales. El artículo tiene un doble objetivo: presentar el contenido de este opúsculo tan poco estudiado y comprobar si presenta alguna dependencia respecto a alguna de las versiones latinas del Sobre el cielo de Aristóteles. Este análisis revela que la lectura de Grosseteste de Sobre el cielo de Aristóteles está condicionada por el Comentario largo sobre la Física de Averroes, en el que Grosseteste también se basa para fundar su concepción de las diferencias matemáticas y naturales

“Theological Arithmetism” in the 10th and the 11th Centuries : Abbo of Fleury and the Explanatio in Calculo Victorii

Cette thèse porte sur l’Explanatio in Calculo Victorii d’Abbon de Fleury, un commentaire aux tables de multiplication de Victorius d’Aquitaine (fl. 450). En considérant l’oeuvre d’Abbon comme le témoin par excellence de la tradition philosophique, que je qualifie d’« arithmétisme théologique », ma thèse se veut une contribution à l’histoire du néo-pythagorisme médiéval des Xe et XIe siècles. Les thèmes suivants y sont abordés : l’interprétation d’Abbon du verset Sap. 11, 21 et son arrière-plan philosophique (ch. III) ; son hénologie (théorie de l’unité) à l’égard de l’unité divine et créée (ch. IV) ; sa conception de la composition – ontologique et matérielle – des créatures (ch. V) ; ses compétences computistes et arithmétiques qui prennent appui sur la théorie boécienne des nombres et sur les méthodes de calcul (ch. VI). Dans le cadre bien néopythagoricien de l’Explanatio, certaines notions péripatéticiennes sont employées par Abbon dans l’étude des phénomènes physiques (ch. VII). De plus, la thèse entend situer la pensée abbonienne dans un contexte culturel qui se caractérise par un renouvellement dans l’étude des arts libéraux, tout particulièrement du quadrivium, qui est favorisé par la redécouverte progressive du De arithmetica de Boèce et par la diffusion en Occident de nouveaux instruments de calcul (ch. I). Les traditions manuscrites de l’Explanatio d’Abbon ainsi que du Calculus de Victorius sont également examinées, dans le but de dégager deux voies possibles par lesquelles l’oeuvre de Victorius est arrivée à l’abbaye de Fleury. Ensuite, on montre la place du commentaire d’Abbon dans l’histoire de l’arithmétique en tant que théorie des nombres autour de l’an mil (ch. II). La thèse étudie les sources philosophiques d’Abbon, tout en analysant sa façon de comprendre et d’harmoniser les différentes approches platoniciennes, notamment d’après le De statu animae de Claudien Mamert, le Commentaire au Timée de Calcidius, le Commentaire au Songe de Scipion et les Saturnalia de Macrobe, le De arithmetica et le De institutione musica de Boèce.This thesis deals with the arithmetical commentary by Abbo of Fleury on the series of multiplication tables ascribed to Victorius of Aquitaine (fl. 450): the Explanatio in Calculo Victorii. My research aims to shed light on the history of medieval Neopythagoreanism between the 10th and 11th centuries, in which Abbo’s work stands as a peculiar testimony of what my work indicates as “theological arithmetism”. The organization of my thesis follows this overall structure. In the first two chapters Abbo’s life and works are presented with a special emphasis on his educational training and learning. Then, the main topics of his “mathematism” are presented, starting with Abbo’s interpretation of the Biblical passage on God who created everything in number, wheight and measure (Wisd. 11, 21), which is discussed at chapter 3, also by illustrating its philosophical background. Then, I present Abbo’s “henology”, namely his consideration of Unity, with regard to both divine and created unity (chapter 4); moving next to his conception of ontological and material compositeness, which Abbo ascribed to creatures (chapter 5) and finally to his arithmetical and computistical knowledge grounded on Boethius’ number theory and his methods of reckoning (chapter 6). To this overall exposition of Abbo’s Neopythagoreanism, it follows a section devoted to Peripatetic approach to the analysis of the natural phenomena (chapter 7). The methodology applied to my research intends to place Abbo’s thought in its cultural context: the renewal of the liberal studies and particularly of the quadrivium, which was stimulated by a progressive rediscovery of Boethius’ De arithmetica together with the introduction of new calculation tools in the Latin West. If this is the general background from which Abbo’s peculiar “Pythagorism” emerges, the philological analysis of his commentary confirms how Fleury was an outstanding centre for high-level mathematical studies. The manuscript tradition of both Abbo’s Explanatio and Victorius’ Calculus, let us envisage two possible paths through which the latter reached Fleury Abbey. A final goal of my work is also to consider Abbo’s commentary within the history of theoretical arithmetics during the first Millennium. Tracking Abbo’s philosophical sources and showing his distinctive comprehension and harmonization of different Platonic accounts, namely those spelt out in Mamertus’ De statu animae, Calcidius’ Commentary on Timaeus, Macrobius’ Commentary on the Dream of Scipio and Saturnalia and Boethius’ De arithmetica and De institutione musica, has been a stimulating research and a confirmation of Abbo’s outstanding role in the not yet sufficiently explored history of high medieval “mathematical” approach to theology and world vision

Rappresentazioni della natura nel Medioevo, a cura di Giovanni Catapano e Onorato Grassi

Scopo del volume e\u300 evidenziare con un approccio multidisciplinare e interdisciplinare come le rappresentazioni della natura si trasformino, nei contenuti e nei modi, fra il V e il XV secolo. Accanto alle rappresentazioni concettuali, proprie delle discipline teoretiche, viene dato ampio spazio alle rappresentazioni figurative, letterarie e musicali. Non solo concezioni e teorie della natura, dunque, ma anche immagini, simboli, suoni che nel Medioevo riproducono, evocano o fingono mondi naturali. Rispetto agli studi gia\u300 esistenti sull\u2019argomento, il volume si propone di suggerire letture innovative che possano mettere in discussione i paradigmi storico-critici vigenti e le nozioni date per acquisite, contribuendo cosi\u300 a reimpostare l\u2019intera questione in una nuova ottica, capace di superare le tradizionali frontiere disciplinari