Kilvington, Richard (c. 1302–1361)

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KILVINGTON, RICHARD
(c. 1302–1361)

Richard Kilvington, Master of Arts (c. 1325) and Doctor of Theology (c. 1335) at Oxford, was a member of Richard de Bury's household, later becoming archdeacon and finally dean of Saint Paul's Cathedral in London. Along with Thomas Bradwardine, Kilvington formed the first academic generation of the school known as the "Oxford Calculators." All of Kilvington's philosophical works—Sophismata and Quaestiones super De generationeet corruptione (written before 1325), Quaestiones super Physicam (c. 1326) and Quaestiones super libros Ethicorum (before 1332)—and his theological questions on Lombard's Sentences (c. 1334) stem from lectures at Oxford. In his Physics, Kilvington found an original way to apply the Euclidean theory of ratios to a new formula relating speeds, forces, and resistances in motions. Because the new rule avoided a serious weakness in Aristotle's theory of motion, nearly everyone adopted it, including the most famous Oxford Calculator, Thomas Bradwardine, in his renowned treatise on velocities in motions, written in 1328.

Following William of Ockham, Kilvington refuted the Aristotelian prohibition against metabasis and was convinced that mathematics is useful in all branches of scientific inquiry. He made broad use of the most popular fourteenth-century calculative techniques to solve physical, ethical, and theological problems. Four types of measurement are present in his works: by limits, that is, by the first and last instants of continuous processes, and by the intrinsic and extrinsic limits of capacities of passive and active potencies; by latitude or degree of forms, to measure intensive changes; by a calculus of compounding ratios, to determine speed of motion; and by one to one correspondence, to compare different infinities. Having adopted Ockham's position of ontological minimalism, Kilvington claimed that absolutes—that is, substances and qualities—are the only subjects that change and therefore all other terms, such as "motion," "time," "latitude," or "degree," are modes of speech. Accordingly, he contrasted things that are really distinct with things that are merely distinct rationally or in imagination. Because imaginable means possible—that is, not self-contradictory—in physics Kilvington discussed secundum imaginationem (according to imagination) counterfactual cases, such as the rectilinear motion of the earth or motion in a vacuum, and pondered questions that would never arise from direct observation, because the structure of nature can only be uncovered by highly abstract analysis.

Like many Oxford Calculators, Kilvington refrained from including God in the speculations of natural science. However, like almost everyone in the fourteenth-century, he distinguished between God's absolute power (potentia Dei absoluta ) and ordained power (potentia Dei ordinata ). The laws of nature reflect God's ordained power. Thanks to his absolute power and will, a presently active power, God might intervene to change or contradict the order of things that he had established. Therefore, it is possible for the past to have been otherwise, because all past events are contingent. Kilvington's teaching on logic, natural philosophy, and theology was markedly influential both in England and elsewhere in Europe. He inspired both the next generation of Oxford Calculators and important Parisian masters such as Nicolas Oresme.

Bibliography

works by kilvington

The Sophismata of Richard Kilvington, edited by Norman Kretzmann and Barbara E. Kretzmann. Oxford: Oxford University Press, 1990.

The Sophismata of Richard Kilvington. Introduction, translation, and commentary by Norman Kretzmann and Barbara E. Kretzmann. Cambridge, U.K.: Cambridge University Press, 1990.