Franciscan Studies

410Book Reviews William Heytesbury, Medieval Logic and the Rise of Mathematical Physics. By Curtis Wilson. (Madison, Wisconsin: The University of Wisconsin Press, 1956. Pp. xii—219. $ 4.00). Dr. Curtis Wilson's critical and analytical study of William Heytesbury's Regule solvendi sophismata makes accessible the views of that gifted member of an influential group of logicians and mathematicians at Merton College, Oxford in the first half of the fourteenth century. Heytesbury's Regule and the Liber calculationum of Richard Suiseth (Swineshead) represent the apex of the logical and mathematical discussions about physical problems and these works were influential throughout Europe from about 1350 to the critical years of the sixteenth century. The Regule was produced for the use of firstyear students in logic and for over a century and a half it was the subject of commentary. It presents a late medieval synthesis of logic, mathematics and physics. This is of current interest, particularly in view of the recent trends, which have weakened the connection between mathematics and physics by turning away from the roots of mathematics anchored in intuition, so that there has been a concentration on refinement and an emphasis on the postulational side of mathematics that has at times disregarded, or at least overlooked, the unity of science with mathematics. Not too infrequently have present-day physicists ceased to appreciate the role of mathematics and this rift has unquestionably posed a threat to science as a whole and resulted in divergent and unconnected trends that do not further the organic development of research. Heytesbury's Regule with its logico-physicomathematical emphasis, points out the regard of the Schoolmen for the unity of scientific and mathematical knowledge. The source of the physical aspects of the problems dealt with in the Regule is to be found in Aristotle's Physica and De caelo. Heytesbury's contribution lies in the fact that he employed the devices and distinctions of logic to the mathematization, although it was done verbally, of the physical problems indicated in short passages from Aristotle. Despite the fact that the physical problems covered by Heytesbury are advanced secundum imaginationem and remain without empirical application they are surprisingly close to some of the portions of Mathematical Physics found in textbooks, few in number to be sure, printed today about five hundred years after his death. Pertinent to the twentieth century physicist is the treatise De Maximo et Mínimo which presents the Aristotelian and Scholastic notions about debilitable potencies. Within this same tract is something to engage the mathematician , too; for Heytesbury here develops his views on the types of boundaries . His work in kinematics is of particular interest to both the physicist and the mathematician. Without a knowledge that is available now of a simple mathematical algorithm, Heytesbury attempted to solve by verbal means, problems regarding velocity in local motion as well as intention and remission of such velocity. As Dr. Wilson points out, Heytesbury's analysis of the instantaneous in motion and time "goes about as far as it is possible to go by purely verbal means and without recourse to the symbolic techniques of the calculus." The Regule shows that its author was aware of the ascendency Book Reviews411 involved in the series with the component members: distance traversed, velocity and acceleration. In De Tribus Predicamentis he explains in what terms the velocity of augmentation is to be measured. In addition to his own opinion, he also gives the contrary view of Calculator as expressed in Tractatus VI, "De augmentione" in Liber calculationum. Dr. Wilson's exposition of the Doctrine of Supposition, the Doctrine of Exponible Terms, and the Distinction between Composite and Divisive Sense are of import to those who pursue medieval studies in general and to those who investigate medieval logic in particular. The painstaking study of Dr. Wilson is appendixed by fifty-two pages of valuable notes and by an extremely complete bibliography. Aside from one or two minor inaccuracies the book is remarkably exact, and gives ample evidence that Dr. Wilson used profitably the Fulbright Fellowship (1950—1951) which made it possible for him to view the many manuscripts and texts, the contents of which, he describes in his scholarly...