Workshop: The Concept of Motion in Late Medieval Philosophy (5 November 2021)
Idea & Motivation
Our meeting will assemble a group of scholars to explore the concept of motion, the central notion in the history of physics and natural philosophy. We will focus on the late medieval Aristotelian tradition considering above all the different definitions and classifications of motion, the impetus theory, the force/resistance rules for speed, motion in a vacuum and its connection to the notions of infinity and continuity. In addition, we intend to discuss the conceptual significance and the diffusion of this intellectual tradition for the Renaissance and the scientific revolution of the 17th century.
- Cristina Cerami, Paris
- Valérie Cordonier, Paris
- Philippe Debroise, Paris
- Daniel A. Di Liscia, München
- José Higuera Rubio
- Edit Anna Lukács, Wien
- Aurora Panzica, Fribourg/Leuven
- Sabine Rommevaux-Tani, Paris
|09:15 - 09:30||Daniel A. Di Liscia (München): Welcome and introduction to the meeting|
|09:30 - 10:10||Cristina Cerami (Paris): Alteratio substantialis: Averroes' theory of substantial generation as a kind of motion|
|10:10 - 10:50||José Higuera Rubio (Porto): The Intermediate Parts of Motion According to Ramon Llull: The Dynamic of Logical Relations|
|10:50 - 11:10||Coffee Break|
|11:10 - 11:50||Aurora Panzica (Leuven): An apparent exception in the Aristotelian physics: antiperistasis as concentration by the contrary quality and its interpretation in the medieval commentary tradition|
|11:50 - 12:30||Edit Anna Lukács (Vienna): Robert of Halifax on the Velocity of Moving Bodies that Follow Shadows|
|12:30 - 14:00||Lunch Break|
|14:00 - 14:40||Sabine Rommevaux-Tani (Paris): The paradoxes caused by the different ways of determining the speed of motion in the anonymous treatise De sex inconvenientibus.|
|14:40 - 15:20||Valérie Cordonier (Paris): The contribution of [Pseudo-]Aristotle’s Liber de bona fortuna to the Latin debates on motion between Paris and Oxford (1310-1360)|
|15:20 - 15:40||Coffee Break|
|15:40 - 16:20||Philippe Debroise (Paris): Motion and continuity in Nicole Oresme’s works|
|16:20 - 17:00||Daniel A. Di Liscia (München): The Concept of Motion in Jacques Legrand´s Compendium utriusque philosophie|
|17:00 - 18:00||Final discussion|
Cristina Cerami (Paris): Alteratio substantialis: Averroes' theory of substantial generation as a kind of motion.
One of the fundamental principles of Aristotle's physics is the clear distinction of substantial generation from other possible types of change, both ontologically and epistemologically. Aristotle explains that the generation of a substance has a specific nature that cannot be expressed or analysed with the same theoretical and linguistic tools used for other changes. Although Aristotle considers the possibility of identifying an explanatory paradigm and principles common to any kind of change, he ensures that substantial generation is, in several respects, an exception. Through the analysis of a series of texts of Averroes' Long Commentary on Aristotle's Physics I would like to show that Averroes does not defend such a rigid theory of substantial generation. On the contrary, it will be seen that Averroes' greatest effort is to assimilate generation as much as possible to a movement, while safeguarding its unique nature.
José Higuera Rubio (Porto): The Intermediate Parts of Motion According to Ramon Llull: The Dynamic of Logical Relations.
The schematic description of motion in Aristotelian Physics is a line (C) bounded by one starting point (A) and one ending point (B). In his Commentarium magnum, Averroes spots the issue about motion intermediate divisions -on the line (C)- and its physical instances. Following Aristotle, Averroes rejects the atomistic solution and the line’s (C) infinite division. Thus, his arguments dealt with the continuity and contiguity of the non-atomic parts of motion/change. He vindicated the perceptual aspect of physical movement that shows itself like in-progress-path between points A and B, in which there is a middle part where qualitative, local, or quantitative changes suddenly happen. To overcome this issue, Albert the Great introduced a proportional relation between intermediate motion parts inspired by the Pythagorean strings division, quoted by Boethius. This geometrical solution was embraced by Ramon Llull but without Albert’s expertise. He took the geometrical points as “motion units” (sine punctum nullus motus est possibilis). Points are intermediate divisions that represent physical phenomena by the continuity of geometrical lines, surfaces, and figures. Also, he appeals to relational logic to spot the middle parts between A and B into the in-progress-path of motion. Those middle parts are signified by a dynamic vocabulary, called: correlative language. This contribution focuses on the conceptual environment of Llull’s assumptions, in which Averroes’ Latin readers explored the geometry and the vocabulary of the motion intermediate parts.
Aurora Panzica (Leuven): An apparent exception in the Aristotelian physics: antiperistasis as concentration by the contrary quality and its interpretation in the medieval commentary tradition.
This paper explores the scholastic debate about antiperistasis, a mechanism in Aristotle’s dynamics described in Meteorology as an intensification of a quality caused by the action of the contrary one. After having distinguished this process from a homonymous, but more general, principle concerning the dynamics of fluids that Aristotle describes in Physics, I focus on the medieval reception of the former. Scholastic commentators oriented their exegetical effort in combining the two different – and somewhat discordant – versions of this theory presented in the two Latin translations of Aristotle’s Meteorology, as well as in elaborating a consistent explanation of an apparently paradoxical process like the intensification of a quality by the opposite one. From the fourteenth century onwards, most of the commentators resorted to the theory of the multiplication of species, according to which each entity acts through the emission of virtual rays (species) that spread spherically in the medium. When these rays encounter an obstacle, such as a contrary quality, they are pushed back towards their source. The reflection of the virtual rays determined by the surrounding and opposite quality produces a concentration of the first one, which as a consequence intensifies. Therefore, the theory of multiplication of species provided scholastic commentators on Aristotle’s Meteorology with a powerful tool to reinsert an apparent exception in the Aristotelian dynamics into a consistent model of physical causation.
Edit Anna Lukács (Vienna): Robert of Halifax on the Velocity of Moving Bodies that Follow Shadows.
In this talk, I am going to discuss the astronomical evidence in favour of the Oxford Calculatorsʼ theorem of mean speed Robert of Halifax proposes in the first question of his Sentences commentary. In an astonishing and rich argument, Halifax calculates the motion of two pairs of luminous and obscure bodies, the decrease of their shadows, and the space they traverse in a given interval of time, and concludes their equal velocity despite their unequally evolving motion. This evidence significantly challenges many of our assumptions, in particular concerning the Oxford Calculatorsʼ astronomy and the role it played in the shaping of new theories in natural philosophy. Yet, given that Halifaxʼs argument is imbedded in a wider context, it has even more to reveal about how the concept of motion was understood at Oxford in the 1330s. Halifaxʼs chief analogy was theological in nature, and concerned the commensuration of virtue and merit, of sin and due punishment. In introducing the human will in the form of two equally virtuous and then unequally evolving moral beings into the cones of shadows, Halifax merges very different motions in what seems to be a “general theorem of mean speed” and a multi-purpose proportional calculation of velocity. I shall thus argue that the theological perspective on motion proves as essential as the astronomical one.
Sabine Rommevaux-Tani: The paradoxes caused by the different ways of determining the speed of motion in the anonymous treatise De sex inconvenientibus.
By privileging quantitative over ontological aspects, the anonymous treatise De sex inconvenientibus is a good example of the calculatores’ approach when dealing with the concept of motion. The treatise is organised around four main questions relating to the determination of velocity in the four kinds of changes, i.e. in the generation of elementary forms, in alteration, in increase and decrease, and, of course, in local motion. For each of the subjects treated in these questions and in the articles attached to them, the author proposes six arguments against the theses he expounds (whether he supports them or not), hence the title of the treatise (About six difficulties). My presentation will focus on some of these arguments contra, in which the author points out the paradoxes to which the two ways of determining the velocity of a motion can lead: on the one hand, the velocity results from the effect produced (the degree of quality generated, the space covered, etc.); on the other hand, it can also be measured by the ratio between the moving power and the resistance of the mobile or patient. While this twofold approach to determining the velocity of motion appears in the majority of calculator texts, the two points of view - the analysis according to its effects and the analysis according to its causes - have rarely been confronted. We will see how the author responds to the contradictions he identifies.
Valérie Cordonier (Paris): The contribution of [Pseudo-]Aristotle’s Liber de bona fortuna to the Latin debates on motion between Paris and Oxford (1310-1360).
In this paper, I will present some discussions held during the 14th century in Paris and Oxford concerning the pseudo-Aristotelian Liber de bona fortuna, a Latin compilation of the chapters on good fortune taken from the Magna Moralia and the Eudemian Ethics that was produced in the 1260s. In analyzing the key concepts of these discussions (casus, fortuna, bona fortuna, motus, impetus, impulsus and inclinatio), my aim is to emphasize a line of reflection that was part of the doctrine of motion in the later Middle Ages and early modernity. Here are the works on the basis of which I hope to shed light on this somewhat neglected side of Peripatetic philosophy of nature: the Questiones super de bona fortuna attributed to John of Jandun and / or to Francesco Caracciolo, the commentaries on the Sentences by Peter Auriol, Adam Wodeham and Richard FitzRalph, the treatise De Causa Dei by Thomas Bradwardine and, above all, Nicole Oresme’s Questiones super Physicam, his De Configurationibus Qualitatum et Motuum, his Livre de Divinacions and his Problemata.
Philippe Debroise: Motion and continuity in Nicole Oresme’s works
If the 14th century begot a new mathematical science of motion, it is not only because motion was quantified, either quantum ad causam or quantum ad effectum, but also because motion became a decisive tool in the mathematician toolbox. Nicole Oresme had a pre-eminent role in this process, as one can see in his numerous and inventive mathematical works. For him, motion was not only an object of observation as natural motion, but also an object of active imagination as mathematical motion. Anyway, the understanding of the nature of motion implied by those methods, particularly in regard to continuity, were at odds with the traditional Aristotelian doctrine according to which the continuum cannot be made up of indivisibles. However, could not the mathematician imagine continuity as composed of an infinite number of indivisibles? Would not this imagination be useful to analyze motion mathematically? In my talk, I shall show that the ontological problem of the unity of such a res successiva as motion was of major concern for Oresme, a concern that was fundamentally based on his mathematical approach. I shall argue that his solution, the understanding of motion as a real fluxus internal to the mobile and distinct from its continuous succession of appearances, was not fully satisfactory. Finally, I intend to explain that, on the contrary, the concept of motion the new mathematics needed was a challenge to human reason only comparable to theological mysteries.
Daniel A. Di Liscia (München): The Concept of Motion in Jacques Legrand´s Compendium utriusque philosophie.
Following the path opened in the 13th century by Albert the Great, many authors from the 14th century onward used to discuss the nature of motion in terms of the alternative theses “forma fluens” and “fluxus formae”. Under the influence of Ockham’s natural philosophy, a strong logic-linguistic approach was added to the controversy: Does the concept of “motus” refer to a special kind of entity besides the moving body and the “terminus” reached by it, or is it nothing but a kind of “shortcut” meaning “this body is here, and later it is there, and always in another place”? According to Anneliese Maier, Buridan and other members of his “school” accepted this latter view in regard to the qualitative and quantitave motions, but they decidely rejected it for the special case of the local motion. And this is - underlines Maier - the view which, together with a more empirical approach in physics, prevailed later.
In my paper, I will critically examine Maier’s view offering a case study of the physical textbook composed by Jacques Legrand at the beginning of the 15th century. First, I will discuss Legrand‘s original division of change, transmutation and motion, and explain the place it assumes in this Compendium. Secondly, I will present Legrand’s arguments sustaining the extraordinary – perhaps even weird – idea of a motion “according to the time”. Finally, I will delve into a series of arguments trying to show that, precisely and in good “nominalistic manner”, for Legrand motion is nothing different from the moving body and the place it ocuppies.
In order to register for the conference, please send an email to email@example.com.
The meeting is organized by the Munich Center for Mathematical Philosophy in collaboration with the Laboratoire SPHère (Université de Paris; CNRS).
The conference is generously funded by Deutsche Forschungsgemeinschaft.
- From Aristoteles / Averroes /Marco Antonio Zimara: Libri Physicorum octo, Lugdunum, 1520. München, Bayerische Staatsbibliothek A.gr.b.696; available in: https://reader.digitale-sammlungen.de/de/fs1/object/display/bsb10169855_00154.html. Some rights reserved (desaturated from original).
- From Auctor sex inconvenientium, Venetiis, 1505. München, Bayerische Staatsbibliothek, Res/2 Anat. 44 d#Beibd.2; available in: https://reader.digitale-sammlungen.de//de/fs1/object/display/bsb10196069_00005.html. Some rights reserved (desaturated from original).
- From Dominici Soto Segoviensis, Philosophi […] Super octo libros physicorum Aristotelis subtilissimae Quaestiones, Venetiis, 1582; Augsburg, Staats- und Stadtbibliothek, 4 LG 347#(Beibd, available in: https://reader.digitale-sammlungen.de//de/fs1/object/display/bsb11217347_00001.html. Some rights reserved (desaturated from original).
- From Calculator: Subtilissimi Richardi Suiseth Anglici Calculationes, Venetiis, 1520. München, Bayerische Staatsbibliothek, 2 P.lat.1518m#Beibd.2, available in: https://reader.digitalesammlungen.de/resolve/display/bsb10149301.html. Some rights reserved (desaturated from original).
- From Basel, Universitätsbibliothek, Ms. F-VI-60, f. 187r (with permission from the Library. https://www.e-codices.unifr.ch/de; https://www.e-manuscripta.ch/).
- From Paris, Bibliothèque nationale de France, Ms. Latin 4935, f. 19v, available in https://gallica.bnf.fr/ark:/12148/btv1b8455934w/f48.item# (with permission from the library. https://gallica.bnf.fr/edit/und/conditions-dutilisation-des-contenus-de-gallica.)
- Description Workshop Motion (269 KByte)