Arystoteles na nowo odczytany. Ryszarda Kilvingtona „Kwestie o ruchu”
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The impulse to this book was a question that I was asked after my talk on God and science in the Middle Ages, whether I was able to give a positive answer to the problem, which I had signalled in my previous book Między filozofią przyrody a nowożytnym przyrodoznastwem. Ryszard Kilvington i fizyka matematyczna w średniowieczu, namely that I did not know what medieval science had been and what respect it had to the modern science. I have decided that the best way to answer that question is to show the readers on the example of one of the medieval texts dealing with physics and, more specifically, one of the fourteenth century commentaries to Aristotle’s Physics. My choice, with regard to my long standing interest in Richard Kilvington, was obvious. I decided to present a Polish translation of his Question on motion along with a monograph. The main purpose of this study is to verify, through detailed analyses, the commonly accepted view about the revolutionary character of the new theory of motion invented and developed by the members of the so-called school of Oxford Calculators, which was founded by Richard Kilvington and Thomas Bradwardine. The book consists of two parts. The first one presents results of research concerning Richard Kilvington’s biography and dating of his works, a description of his four questions on motion, methods he used in philosophy of nature, and his theories set against the background of two famous fourteenth century thinkers: William of Ockham and Thomas Bradwardine. The second part presents a Polish translation of Kilvington’s four questions – a result of his lectures on Aristotle’s Physics. These questions are: 1) Whether an active potency exceeds a passive potency of a body in motion; 2) Whether a quality takes degrees of more and less; 3) Whether a simple body can move equally fast in a plenum and a vacuum; 4) Whether that which has changed in the moment when it has first changed, is in that to which it has changed. Richard Kilvington was born in the beginning of the fourteenth century in the village of Kilvington in Yorkshire. He studied at Oxford, where he became Master of Arts (1324/1325) and then Doctor of Theology (ca. 1335). His academic career was followed by a diplomatic and ecclesiastical one. It culminated in his service as Dean of St. Paul’s Cathedral in London. Along with Richard Fitzralph, Kilvington was involved in the battle against mendicant friars almost until his death in 1361. Except for a few sermons, all of Kilvington’s known works stem from his lectures at Oxford. His philosophical works, the Sophismata and Quaestiones super De generatione et corruptione, both composed before 1325, were the result of lectures given as a Bachelor of Arts; his Quaestiones super Physicam (Questions on motion) composed in 1325/26 and Quaestiones super Libros Ethicorum composed in 1326/1332 come from the period he was a Master of Arts; finally, he composed eight questions on Peter Lombard’s Sentences at the Faculty of Theology before 1335. One of the most notable achievements of Kilvington’s theory is his awareness of the different levels of abstraction involved in the problem he analyzes. Although his account frequently proceeds secundum imaginationem in the direction of “speculative physics”, it never renounces empirical verification. Nevertheless, Kilvington ponders questions, which would never arise as a result of direct observation, since the structure of nature can only be uncovered by highly abstract analyses. Such abstractions, however, arise from genuine realities and cannot contradict them. He sees physics and mathematics as complementary, i.e., as two different ways of describing natural phenomena. Reality provides the starting point for the more complicated mental constructions, which in turn make it comprehensible. While mathematics is the proper way to solve the problems, logic remains the most convenient way to pose them. These different methods together guarantee the objective and demonstrative character of the natural sciences. On the one hand, Kilvington never abandons the realm of Aristotelian physics or rejects the principles laid down in his natural philosophy. But on the other, his tendency to combine mathematics and physics frequently led him beyond Aristotle’s theories to seek solutions to many paradoxes which resulted from Aristotelian principles. Kilvington pointed to two different conditions which have to be met: one referring to the everyday use of language, which describes real, physical phenomena; and another referring to the formal, i.e. logico-mathematical, language that deals with the questions in the realm of speculative, i.e., mathematical, physics. Like a great many Oxford thinkers of the period, Kilvington is convinced that mathematics is useful in any branch of scientific inquiry that deals with measurable subjects. He makes a broad use of the most popular fourteenthcentury calculative techniques to solve not only physical but also ethical and theological problems. Three types of calculations can be found in Kilvington’s Quaestions on motion. The most predominant is the measure by limits, i.e., by the first and last instants beginning and ending a continuous process, and by the intrinsic and extrinsic limits of capacities of passive and active potencies. The second type of calculation, by a latitude of forms, covers processes in which accidental forms or qualities are intensified or diminished, e.g., in the distribution of such natural qualities as heat or whiteness. Finally, the third type of calculation is more properly mathematical and employs a new calculus of compounding ratios in order to measure the speed of local motion. Although Kilvington subscribes to the general Aristotelian principles of motion, he follows Ockham in accepting substance and quality as the only two kinds of really existing things. Beyond doubt, Kilvington follows Ockham’s understanding of the works of the Philosopher. He explains the reality of motion in terms of the mobile subject and places, qualities, and quantities it acquires successively. Consequently, Kilvington is mostly interested in measuring local motion in terms of its actions or causes, the distance traversed and time consumed, rather than in the “intensity” of its speed. It is his analysis of local motion that places Kilvington among the 14th-century pioneers who considered the problem of motion with respect to its cause (tamquam penes causam), corresponding to modern dynamics, and with respect to its effect (tamquam penes effectum), corresponding to modern kinematics. In his first question, Kilvington, while debating the problem of setting boundaries to capacities or potencies involved in active/passive processes, presents many theories of his colleagues, as well as the Aristotelian and Averroenian solutions of the problem. He articulates most of the issues, which were at stake, and poses questions that influenced the solutions of later Calculators. Kilvington’s most interesting and original idea in the theory of motion concerns the new rule of motion, which relates forces, resistance and speeds in motion and shows that the proper way of measuring the speed of motion is to describe its variations by the double ratio of motive force (F) and resistance (R). In order to produce a mathematically coherent theory, he insists (in agreement with Euclid’s definition from the fifth book of the Elements) that a proper double proportion is the multiplication of a proportion by itself. Kilvington’s function makes it possible to avoid a serious weakness of Aristotle’s theory, which cannot explain the mathematical relationship of F and R in a motion with a speed of less than 1. Local motion considered in its dynamic aspect, i.e., when speed is proportional to the ratios of Fs to Rs, describes the changes of speed, i.e., the accelerate motion. Local motion considered in its kinematic aspect describes the changes of speed with regard to time and traversed distance, and it describes both uniform and uniformly difform motion. Like William of Ockham, Kilvington is convinced that a motion is nothing else than an individual thing in motion. Therefore, speed has to be measured by distances, i.e., latitude of a quality (formal distance) or quantity traversed, and such traversals take time unless the speed is infinitely great. In his questions he considers all sorts of motion, which can occur both in a medium and in a void. Although he holds that the vacuum does not exist in nature, he is nevertheless convinced, contrary to Aristotle, that neither logic nor nature exclude a possible existence of a vacuum. Moreover, using a new rule of motion it is possible to show that a motion in a vacuum would be temporal for both mixed and simple bodies. Ockham’s influence is also confirmed in Kilvington’s considerations of qualitative changes, which was also one of the most frequently discussed issues in the 14th century. Kilvington is convinced that two main Ockhamist principles, namely particularist ontology and economy of thinking, suffice to explain all qualitative changes, such becoming white or cold. Since a quality is a real thing, it is enough to conclude that in the process of becoming hot a body possesses the same quality, which changes from one extreme, i.e., coldness to the other, i.e., hotness. Such terms as the “latitude of a form”, “degree of coldness” etc. are nothing else but sincategorematic terms, which we use to describe qualitative changes. In reality, there are only substances and qualities, the only existing permanent things, while the remaining eight Aristotelian categories serve only to describe various aspects of an individual thing in the outside reality. Kilvington’s teaching on natural philosophy was influential both in England and on the Continent. His Quaestiones de motu were well known to the next generation of the Oxford Calculators and influenced also such prominent Parisian masters as Nicole Oresme and John Buridan. It was Thomas Bradwardine, however, who was the most renowned beneficiary of Kilvington’s work, so much that until recently he was called the Founder of the Oxford Calculators’ School,. The analysis of dispersal of new ideas of mathematical physics point strongly at Kilvington as their primary source. In his famous Treatise on proportions in motion (the best know medieval treatise presenting a new rule of motion) Bradwardine incorporated almost one half of Kilvington’s first and third questions on motion. Extolling of Bradwardine’s treatise by his followers and modern historians of medieval science and swift oblivion of Kilvington’s work were caused by the fact that Bradwardine treatise was a manual for students following the rules for this type of work, i.e., dividing material in chapters, which present general rules based on a theory of proportion, while Kilvington’s questions are the result of his lecturing; one can easily notice that some parts of them are students’ reportata, so their text is difficult in reading. In the present book I reiterate the opinion expressed in my previous book that medieval science was a specific phenomenon of the medieval culture. It can hardly be compared with modern science and its views of the world are clearly incompatible with the modern ones. In its history, medieval science took the Aristotelian course, thoroughly explored that framework exposing its paradoxes and weakness and reached the point, where it was no longer able to overcome the lingering doubt. Its story is finished, so each historian of science is free to write his or her own tale about it. In my opinion, Richard Kilvington, even though he abandoned Aristotle’s prohibition of metabasis, which does not allow to use mathematics as a proper language for physics, and invented a few new methods, still strove to overcome the difficulties and the numerous aporiae of Aristotelian physics, showing how we should properly understand the Philosopher.
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