Other significant problem areas to which medieval thinkers addressed themselves are the dynamic and kinematic aspects of motion, that is, motion’s relations to its causes and to distance and time, respectively. In medieval terminology, these aspects concerned the study of motion ‘‘with respect to cause’’ (penes causam) and ‘‘with respect to effect’’ (penes effectum). In the former case, some consideration was given also to the forces acting on bodies to produce motions. Phenomena which fourteenth-century thinkers at Paris and Oxford discussed under these headings, and to which they often took a semantic and quantitative approach, were gravity, accelerated free fall, projectile motion, and also qualitative changes in a given subject, such as heating.
This section discusses the approach of motion with respect to its causes, which roughly corresponds to the dynamic study of motion (as in contrast to kinematics). Aristotle distinguished two kinds of local motion: natural and nonnatural or violent. Natural motion is the motion toward the natural place of the mobile body, which is determined by the proportion of the four elements - water, earth, air, and fire - in it. Bodies in which the elements earth or water predominate are heavy and consequently move downward, whereas bodies in which the elements air and fire predominate are light and move upward. Violent motions are motions in any direction deviating from the moving body’s natural place, for instance upward for bodies mainly consisting of the element earth. Aristotle explained the local motion of inanimate bodies, that is of bodies that do not move themselves, by invoking the principle that motion is never spontaneous but that everything that is in motion ‘‘is moved by something’’ (Physics, 241 b 34; 259 a 29-31). In medieval terminology, this proposition was rendered as “everything that is moved is moved by another’’ (omne quod movetur ab alio movetur). Moreover, Aristotle had argued that there is no action at a spatial distance: the cause of motion and the thing moved need to be in contact (Physics, 243 a 3-4). Both propositions seemed to require that mover and moved were separate entities. When medieval commentators turned to these two basic Aristotelian principles of the explanation of motion, they concentrated their discussions on two problem areas that seemed to present counterexamples to Aristotle’s axioms: one in the field of natural motion, and one in the field of violent motion.
Natural Motion: The Explanation of Gravity and Accelerated Free Fall
In violent motion, it was not difficult to see that an external motive force was involved; but how were mover and moved body to be distinguished in natural motion? Some medieval scholars followed Thomas Aquinas’ lead and concluded that the generator (generans) gave the mobile body its form and everything that followed from that form, including its motive powers and its disposition to move, that is, its heaviness (gravitas) or lightness (levitas). In this way, the generator acted as a kind of remote motive cause in natural motion. A body’s natural motion was conceived of as the consequent of its original generation. In case a body was impeded to move after it was generated, the cause of its natural motion was identified with whatever removed the impediment to its motion (removens impedimentum). The natural motion, for example, of a stone hanging on a rope was caused by the agent that cuts the rope. However, the generator and the remover of the impediment could not explain the continuation of a body’s natural motion, since they were not in continuous simultaneous contact with the moving body. How did fourteenth-century authors solve this problem?
A decisive viewpoint was taken by John Duns Scotus (c. 1265-1308). He concluded that heavy and light bodies are moved by their heaviness and lightness, and in this sense, they move themselves. This was an important deviation from Aristotle, Averroes, and earlier commentators. They had emphasized that the generator was the real cause of the fall of a body, and that the substantial form, heaviness, and lightness were, at best, lower-order instrumental causes. After Duns Scotus, however, authors such as John of Jandun, William Ockham, Walter Burley, John Buridan, Marsilius of Inghen, and Albert of Saxony embraced the position that heaviness and lightness were the proximate causes of a body’s unobstructed natural motion. In this way, they gave up Aristotle’s principle that mover and moved are separate entities. The mover was therefore no longer an extrinsic cause (such as the generator had been), but was now conceived of as an intrinsic principle, inhering in the moving body. As a consequence, the important Aristotelian distinction between the motion of animate and inanimate bodies became blurred. None of these fourteenth-century authors, however, stressed the new turn they had taken, but, on the contrary, tried to justify Aristotle’s views by ‘‘glossing’’ them.
Another question raised in the context of falling bodies was acceleration: a body in natural fall moves with accelerated velocity, not with uniform speed. Discussions about ‘‘heaviness’’ and ‘‘lightness’’ ignored the phenomenon of acceleration. The causal explanation of acceleration took its point of departure from the rules concerning motion, which Aristotle had provided in Book 7 of the Physics (249 b 27-250 a 9) and book 1 of De caelo (273 b 30-275 a 20). In these books, he had discussed the notions of ‘‘quicker,’’ ‘‘slower,’’ and ‘‘of equal speed’’ and formulated the relations that obtain between velocities and the forces and resistances that determine them. Aristotle’s passages are often presented as his ‘‘mechanics’’ and certainly helped to develop late-medieval mechanics.
With respect to natural motion, in which weight acts as the motion’s internal force, and the density of the medium as the resistance, Aristotle states a number of rules. In sum, they provide two options to account for the acceleration ofa falling body: it was caused by either an increase in force or a decrease in resistance. Most late-medieval thinkers, however, eliminated the second option. The most influential theory was proposed by John Buridan. He maintained that the body’s weight not only caused its downward fall, but also generated an impressed force in the falling body, which he called impetus. Since the body’s weight does not expire, but continues to act as a cause, it continues to produce new increments of impetus, which successively increase the falling body’s velocity. This explanation was basically followed by other thinkers in Paris, such as Nicholas Oresme, Albert of Saxony, and Marsilius of Inghen.
Violent Motion: The Explanation of Projectile Motion
Buridan also uses his impetus theory to solve another problem in Aristotelian physics, namely that of the explanation of projectile motion. Projectile motion seemed to contradict Aristotle’s principles about movers and mobile bodies: how could the mobile body continue its motion after it had lost contact with the moving force, say, the Hand throwing a stone? Aristotle had claimed that it was the surrounding medium, which accounted for the continuation of the projectile’s motion. Simultaneously with the projectile, the medium too received a motive force from the projector, which it continued to transmit by means of the activation of the medium, thus pushing the projectile along. In this way, Aristotle could uphold his principle that the external force is in continuous contact with the mobile body: the projector’s role had been taken over by the medium.
This account came to be rejected in the fourteenth century. The medium’s role in continuing the projectile’s motion was considered problematic. Francis of Marchia (fl. 1320) pointed out that if the original projector could produce some motive force in the medium, there was no reason why it could not do so also in the projectile itself. Indeed, this ‘‘left-behind force’’ (virtus derelicta) or impressed force (vis impressa) given to the projectile was the real proximate cause of the projectile’s continued motion. This solution had been anticipated by the Greek commentator John Philoponus (d. after 575), who had also found it implausible that the medium should serve as a motive force rather than as resistance to the projectile’s motion. His work, however, was not available in translation, and neither were the several writings of Islamic thinkers who had developed theories of impressed force (mail) in projectile motion.
John Buridan introduced the technical term ‘‘impetus’’ for this impressed force and developed an advanced theory about it. In Buridan’s view, impetus was a motive force transmitted from the initial mover that could act in any direction to which it had been. Buridan took a first step toward the quantification of impetus by declaring that its strength was determined by the velocity with which the initial mover had moved the projectile. Furthermore, he considered its strength proportionate to the projectile’s weight, which in turn depended on its quantity of matter (quantitas materiae). Buridan substantiated this rule by reference to the phenomenon that a leaden projectile can be thrown further than a wooden one of the same volume and shape, because it has a greater capacity to receive impetus.
Buridan applied his impetus theory not only to the explanation of the acceleration of falling bodies, but also to that of celestial motions. He declared that at the moment of creation, God might have imprinted an impetus on the heavens. Since in the case of the heavenly motions, the impetus is not producing a violent motion away from their natural place, and therefore encounters no resistance, it will continue forever. In the sublunar region, however, the impetus is corrupted by the mobile body’s tendency to move to its natural place, and by resistances (from the medium, for instance) acting on the body. In sum, Buridan conceived of impetus as a quasi-permanent quality inherent in the mobile body, which, under terrestrial conditions, interacted with the body’s natural tendencies, and dissipated as a consequence. Albert of Saxony adhered to the same position, even though he avoided the terminology of impetus and spoke instead of‘‘moving force’’ (virtus motiva) or ‘‘moving quality’’ (qualitas motiva). Still other slight variations were introduced by Nicholas Oresme and Marsilius of Inghen. New medieval concepts such as impetus and weight (gravitas) helped abolish Aristotle’s principle that mover and moved are separate entities that must be in contact. Instead, they represent an internalization of Aristotle’s external motive force. The medieval impetus theory was to remain the dominant explanation of projectile motion until the seventeenth century, although it had little impact in Oxford.
The Quantification of the Causes of Motion
At Oxford, scholars took a more quantitative approach toward the causal explanation of motion. The quantitative rules for force and resistance by which Aristotle had tried to capture the interaction between mover and moved (Physics, book 7), came to be criticized at the beginning of the fourteenth century. In his Treatise on Proportions (Tractatus de proportionibus), written in 1328, Thomas Bradwardine gave a general treatment of how one can relate a change of speed of a mobile to a variation in its causes, or as he put it, ‘‘of the proportion between the speeds with which motions take place with respect to both moving and resisting powers.’’
Bradwardine’s mathematical approach had a tremendous influence. At Oxford, Richard Swineshead further developed Bradwardine’s insights by applying them to two new problems. In his Book of Calculations (Liber calculationum), written about 1350, Swineshead specifies, among other things, Bradwardine’s theorem for different kinds of changes in velocity, such as uniform, difform, uniformly difform, and so on. Moreover, he applies Bradwardine’s function to the fall of a heavy body near the center of the universe.
Bradwardine’s theorem of motion was incorporated into the Parisian commentaries on the Physics. Starting with John Buridan, other fourteenth-century scholars at the University of Paris began to show familiarity with Bradwardine’s views. Moreover, Albert of Saxony and Nicholas Oresme elaborated Bradwardine’s function in their Treatise on Proportions (Tractatus proportionum) and Treatise on Ratio of Ratios (Tractatus de proportionibus proportionum), respectively. They abstracted from the physical problems that Bradwardine had discussed and, instead, concentrated on a calculus of proportions as such (see the entries on Oxford Calculators and Richard Swineshead in this volume).
World History
