Oxford Calculators

‘Oxford Calculators’ is a modern label for a group of thinkers at Oxford in the mid-fourteenth century, whose approach to problems was noticed in the immediately succeeding centuries because of their tendency to solve by ‘calculations’ all sorts of problems previously addressed by other methods. If for example the question was, what must a monk do to obey the precept of his abbot to pray night and day, a ‘calculator’ might immediately rephrase the question to ask whether there is a minimum time spent in prayer that would be sufficient to fulfil the abbot’s precept, or a maximum time spent that would be insufficient to fulfil the precept. Or, if grace was supposed to be both what enables a Christian to act meritoriously and a reward for having so acted, then a calculator might ask whether the degree of grace correlated with a meritorious act occurs at the moment of the meritorious act, before the act when the decision to act is being made, or after the act when the reward of increased grace is given. If a body was hot at one end but cold at the other, then a calculator might ask not whether it is to be labelled hot or cold, but how hot it is as a whole. Finally, if it was asked whether a heavy body acts as a whole or as the sum of its parts, then a calculator might take the case of a long thin rod falling through a tunnel pierced through the centre of the earth and attempt to calculate how the rod’s velocity would decrease as parts of the rod passed the center of the cosmos, if it acted as the sum of its parts. Of these four questions, the last two were asked by Richard Swineshead, a mid-fourteenth century fellow of Merton College, Oxford, whose Liber calculationum (Book of Calculations) led to his being given the name ‘Calculator’. By association with Richard Swineshead, other Oxford masters including Thomas Bradwardine, Richard Kilvington, William Heytesbury, Roger Swineshead and John Dumbleton have been labelled the ‘Oxford Calculators’. Their work contains a distinctive combination of logical and quantitative techniques, which results from the fact that it was often utilized in disputations on sophismata (de sophismatibus). This same group of thinkers, with emphasis on their mathematical rather than logical work, has been called the ‘Merton School’, because many but not all of the Calculators were associated with Merton College, Oxford. Besides calculatory works, the same authors wrote works in which calculatory techniques are not so prominent, including commentaries on Aristotle, mathematical compendia and commentaries on Peter Lombard’s Sentences.