Oxford Calculators is a group of 14th-century English philosophers associated with Merton College , Oxford . This group included Thomas Bradwardin , William Heightsbury , Richard Swainshead , John Dumbleton .
These thinkers developed a special discipline - “the doctrine of intension and remission of qualities” , which became [1] one of the most striking pages in the medieval doctrine of movement . In the works of scientists at Merton College, the general logical and mathematical approach was applied to the consideration of a wide variety of qualities that allow continuous change in two opposite directions, their degrees and changes - from physical (such as heat, brightness, speed) to moral and metaphysical (such like sin, lust, mercy, grace). This theme, going back to Plato’s dialogue “Fileb” and to Aristotle ’s treatise “On Origin and Destruction,” was one of the program topics of medieval scholastic physics .
In particular, in the works of the Mertonians, a mathematical apparatus is being built specifically designed to describe mechanical motion ; however, it was a purely abstract construction that did not appeal directly to the sphere of experience [1] . The concepts on the basis of which the Mertonians built their model of movement were the intensity of movement and a degree of speed as a measure of this intensity [2] . Within the framework of this model, the concept of instantaneous velocity was first introduced into mechanics ( W. Heightsbury , 1335) [3] .
Merton thinkers W. Heightsbury and R. Swainshead formulated and proved the mean velocity theorem (in their terminology - the “mean degree of velocity theorem” ), which was later applied by Domingo de Soto [4] and Galileo Galilei [5] in the quantitative analysis of free fall of bodies : the path traveled by the body for some time with equally variable motion is equal to the path traveled by the body for the same time with uniform motion at a speed equal to the arithmetic average of the maximum and minimum values of speed in the equally variable motion [6] [7] . The Mertonians showed that if uniformly accelerated movement starts from a state of rest, then for the first half of the movement time, a path is made up 1/4 of the full path.
In fact, scientists at Merton College laid the foundation — in kinematics and a number of other branches of natural science — for replacing the qualitative concepts characteristic of ancient physics with the quantitative concepts used in the physical sciences to this day [6] . Merton’s ideas were further developed in the “doctrine of the breadth of forms” developed by their French contemporary Nikolai Orem , who taught at the Sorbonne , as well as in the work “On the Speed of Variable Movement” by Italian Giovanni di Casali .
Notes
- ↑ 1 2 Gaidenko, Smirnov, 1989 , p. 288-289.
- ↑ Gaidenko, Smirnov, 1989 , p. 303.
- ↑ Gaidenko, Smirnov, 1989 , p. 301.
- ↑ Moses, 1961 , p. 105.
- ↑ Moses, 1961 , p. 116.
- ↑ 1 2 Truesdell, 1976 , p. 56.
- ↑ Gaidenko, Smirnov, 1989 , p. 315-322.
Literature
- Akhutin A.V. History of the principles of a physical experiment from antiquity to the 17th century. - M .: Nauka, 1976 .-- 292 p.
- Gaidenko V.P., Smirnov G.A. Western European science in the Middle Ages: General principles and the doctrine of movement. - M .: Nauka, 1989 .-- 352 p. - (Library of the World History of Natural History). - ISBN 5-02-007958-8 . .
- Grigoryan A.T. , Zubov V.P. Essays on the development of basic concepts of mechanics. - M .: Publishing House of the Academy of Sciences of the USSR, 1962 .-- 274 p.
- Moiseev N. D. Essays on the history of the development of mechanics. - M .: Publishing house Mosk. University, 1961 .-- 478 p.
- Yushkevich A. P. On the problem of the mathematization of knowledge in the Middle Ages // Problems of the History of Natural Science and Technology, No. 1, 1990. - P. 21–35.
- Sylla E. Medieval Cuantification of Qualities: The “Merton School” // Archive for the History of the Exact Sciencies, 8 , 1971. - P. 9-39.
- Sylla E. Medieval Concept of the Latitude of Forms: the “Oxford Calculators” // Archives d'historie doctrinale et littéraire du moien age, 40 , 1973. - P. 223-283.
- Sylla E. The Oxford Calculators in Context // Science in Context, 1 , 1987. - P. 257—279.
- Truesdell C. History of Classical Mechanics. Part I, to 1800 // Die Naturwissenschaften, 63 (2), 1976. - P. 53-62.