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Oxford Calculators Oxford’S Medieval Philosophers Deserve Greater Recognition, Says Mark Thakkar

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Oxford Calculators Oxford’S Medieval Philosophers Deserve Greater Recognition, Says Mark Thakkar The Oxford calculators Oxford’s medieval philosophers deserve greater recognition, says Mark Thakkar observing, however, that Bradwardine and RARY Swineshead were both originally Balliol ib L men. Balliol’s founding statutes restricted its itish scholars to studies in the faculty of Arts, so BR he that those who wished to study in the higher T faculties of Theology and Law were obliged to leave after taking their MA. Merton, by contrast, was founded with the specific aim of fostering study in the faculty of Theology. Then, as now, Oxford was a centre of academic excellence. Indeed, if Paris was the capital of scholasticism, Oxford was its second city. But the life of the mind was pursued in a manner quite unlike that of today: the best work in philosophy was pro- duced by men who went on to enjoy high- profile careers in politics or the Church. This led the powerful patron and wealthy bibliophile Bishop Richard de Bury to com- plain of being ‘deprived of the bodily com- panionship of some of these shining lights when, justice looking down from heaven, the ecclesiastical preferments and dignities that they deserved fell to their portion’. Bradwardine provides the most strik- ing illustration of this phenomenon. His career was initially that of an Oxford aca- demic, which brought with it administrative responsibilities; in 1328, for instance, as a University proctor, he successfully defended our disciplinary autonomy from the Church. He left Merton in 1335 to join de Bury’s household in Durham, but two years later he was appointed Chancellor of St Paul’s, and subsequently became chaplain to Edward III. His period of royal service cul- minated in the French expedition of 1346, xford has such a long intellectual heat, colour, density and light. But their where he witnessed the Battle of Crécy; he history that even the episodes experiments were those of the imagination; was later appointed to negotiate peace with that made it illustrious are liable practical experiments would have been of Philip VI. He was consecrated Archbishop O to be forgotten. One such took little help in any case without suitable meas- of Canterbury in 1349, just over a month place in the second quarter of the four- uring instruments. Indeed, some of the cal- before succumbing to the Black Death. teenth century, when a group of Oxonians culators’ works, although ostensibly dealing Nowadays, Bradwardine is known developed a battery of new techniques for with the natural world, may best be seen as primarily for his views on free will and dealing with philosophical problems, the advanced exercises in logic. strikingly mathematical nature of their They have been dubbed ‘the Merton approach earning them the epithet of ‘cal- School’, because several of them – includ- above: Oxford mathematician Richard of culators’. ing the most notable, Thomas Bradwardine, Wallingford (1292–1336), a contemporary These scholars busied themselves with William Heytesbury and Richard Swineshead of the Merton calculators, though any quantitative analyses of qualities such as – were Fellows of Merton. I cannot resist evidence of a connection is lost 24 OXF O R D T O DAY . Trinity Issue 2007 The Oxford calculators predestination, which earned him a men- late one of the calculators’ most famous photos tion alongside Augustine and Boethius in results: the mean-speed theorem, also S The Canterbury Tales. But for centuries he known as the Merton rule. The theorem A thom was famed for his Treatise on Proportions says that if a moving object accelerates at / (1328), which, among other things, sought a uniform rate for a certain time, it covers ollege to establish the relationship between the the same distance as it would by moving C force applied to an object, the resistance to for the same time at its mean speed. This ton R its motion and its resulting velocity. means, for instance, that a lorry travelling at E F M O Some remarks of Aristotle’s suggested 30 mph will be caught up by a car accelerat- that velocity was proportional to force and ing smoothly from a standstill as soon as the Fellows inversely proportional to resistance, so that car reaches 60 mph. Unlike Bradwardine’s D N doubling the force would double the velocity, law, which falls foul of the physical facts, the A while doubling the resistance would halve Merton rule is a mathematically demonstra- en the velocity. But, as Bradwardine objected, ble truth, and is thought to have indirectly WARD this fails to predict a velocity of zero when influenced Galileo’s treatment of free fall. the resistance matches or exceeds the force, The last and the greatest of the calcula- as when one struggles with a stiff door. tors was Richard Swineshead, known simply Bradwardine proposed a new formula- as ‘the Calculator’. The sixteenth-century tion which focused on changes in veloc- polymath Girolamo Cardano placed him ity: in order to double the velocity we must in the top ten intellects of all time, along- square the ratio of the force to the resistance; side Archimedes, Aristotle and Euclid, eighteenth century Leibniz could complain in order to triple the velocity we must cube while according to Robert Burton, writing that Swineshead’s works were little known this ratio; and so on. In modern notation we The Anatomy of Melancholy some 75 years and hard to find, and these days his name might express Aristotle’s theory as V ∝ F/R later, he ‘well nigh exceeded the bounds is familiar only to students of medieval and Bradwardine’s as V ∝ log F/R; math- of human genius’. Sadly, by the turn of the philosophy. ematically inclined readers can confirm that the latter does indeed give a zero velocity th R when F = R. Bradwardine’s law was extremely lwo A influential, and widely accepted throughout W A Europe until the late sixteenth century. uli Bradwardine’s younger contemporary, : J photo Heytesbury, played an active role in life at / Merton, where he was a bursar in the late ollege 1330s. We have his record of an arduous C journey to administer the college properties ton R in Northumberland; it took him eight days E F M O to get to Ponteland, averaging more than 30 miles per day. In his later life he also had Fellows one or two stints as Chancellor of Oxford, D N and as a churchman he held a number of A en benefices in Kent. In his Rules for Solving Sophismata WARD (1335), Heytesbury was the first to articu- top: 17th-century depiction of Merton’s medieval buildings, from the memorial to mathematician Henry Savile right: Opening of Bradwardine’s Treatise on Proportions (Venice, 1505) OXF O R D T O DAY . Trinity Issue 2007 25 The Oxford calculators Swineshead’s magnum opus, and per- came instead from its devastating effect From the student’s point of view, how- haps the crowning achievement of the group on primary education, which meant that ever, the analytical facility developed by as a whole, was a series of treatises known students from the 1360s onwards were not such technical study would have proved use- as the Book of Calculations (c.1350). These sufficiently well prepared to cope with work ful for careers in an increasingly monetised dealt in exhausting detail with problems of as advanced and sophisticated as that of the society. It is notable that even today Oxford quantitative physics, including more than 50 calculators. (Oxford, with its overwhelm- bills its Mathematics and Philosophy joint variations on Bradwardine’s ingly English demographic, degree as involving ‘two of the most fun- law. While supposedly wres- suffered more in this respect damental and widely applicable intellectual tling with such subtle prob- Swineshead ... than the cosmopolitan univer- skills’. lems, Swineshead took part was subsequently sity of Paris.) Moreover, with hindsight we can see in a brawl over the election ordered to return Subsequently the abstruse that the calculators made an important of the Provost of Oriel as nature of the calculators’ writ- advance by treating qualities such as heat Chancellor of Oxford, and several items ings earned them ridicule and force as quantifiable at all, even if only was subsequently ordered seized from the from some quarters. While theoretically. Although the problems they by the Crown to return sev- University Chest the Italian universities enthu- set themselves stemmed from imaginary eral items seized from the siastically adopted an Oxonian situations rather than actual experiments, University Chest. It seems approach, the humanists of the they nonetheless ‘introduced mathemat- he favoured the Mertonian candidate, John Renaissance heaped scorn on what they ics into scholastic philosophy’, as Leibniz Wyliot, who was installed when the Provost called quisquiliae suiceticae, ‘Swinehead’s put it. This influential move facilitated the died a month later. rubbish’. One particularly vicious critic full-scale application of mathematics to the Oxford scholastic philosophy is thought complained that ‘the scholastics hit upon real world that characterised the Scientific to have declined in brilliance after 1350. It cavillations of the most stupid subtlety and Revolution and culminated triumphantly in is tempting to see this as an immediate con- called them calculations’, and asked: ‘What Newton’s laws of motion. sequence of the Black Death, but the plague science can there be in subjects so remote Mark Thakkar (Balliol) is studying for a actually claimed the lives of comparatively and divorced from all intelligence and com- DPhil in medieval philosophy. He is also few Oxonians. The real blow probably mon sense?’ Oxford Today’s crossword editor Project2 15/1/07 13:05 Page 1 26 OXF O R D T O DAY . Trinity Issue 2007.
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