Merton colleges, later confessor to Edwar d III, and eventually archbishop of
Canterbury. Other members of the school, such as William Heytesbury and
Richard Swineshead, were, like Bradwardine, fellows of Merton, so that
members of the group are sometimes known as the Mertonians. They
shared a taste for solving philosophical and theological problems by
mathematical methods, and so they are also called the Oxford Calculators,
after a treatise by Swineshead called the Liber Calculationum (1350).
Bradwardine, in 1328, published a work entitled De Proportionibus Velocitatum
in Motibus (‘On Proportions of Velocity in Motions’). In it he developed a
theory of ratios which he used to present a theory of how forces, resistances,
and velocities were to be correlated in motion. This theory quickly super-
seded Aristotle’s laws of m otion, and it was inXuential not only in Oxford,
but also in Paris, where it was adopted by Oresme. Other Calculators, too,
produced work of importance for natural philosophy, but they devoted
their mathematical talents to the solution of logical and theological prob-
lems rather than to physical research. Questions about maxima and
minima, for instance, were the germ of development towards the diVer-
ential calculus; but they were Wrst raised in connection with the question
what was the minimum, and what the maximum, length of time to be spent
in prayer to fulWl a command to pray night and day. The question of how to
measure non-quantitative qualities, such as heat and cold, was Wrst worked
out in the analysis of the growth of grace in the souls of the faithful and in
measuring the capacity for happiness of souls in heaven.
Many of the developments in physics originated as solutions to logical
puzzles, or sophismata. These were propositions whose content was ambigu-
ous or paradoxical, set as problems to be resolved by logic students, and
solved, or determined, by masters in the arts faculty. One of the most
ingenious sets of these sophismat a was produced, around 1328, by Richard
Kilvington, not himself a Mertonian, but closely associated with the other
Calculators as part of a research group assembled by Richard of Bury,
bishop of Durham and lord chancellor. Kilvington was not himself a
mathematician, but his sophismata were quickly given a mathematical form
by Heytesbury in his Regulae Solvendi Sophismata (1335), in which he worked
out the theory of uniform acceleration.
Sophismata fell into disrepute at the Renaissance, but they came into
fashion again in the twentieth century. At a time when France was a
republic, Bertrand Russell inquired about the truth- value of ‘The king of
THE SCHOOLMEN
98