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Abstract
In a long question, "Whether there is motion to quality," (Utrum ad qualitatem sit motus) which became part of his Oxford Expositio omnium librorum Physicorum cum questionibus optime disputatis, composed before 1310, Walter Burley supported the succession-of-forms theory of qualitative change. After commenting on Peter Lombard's Sentences at Paris, Burley took part in disputations on controversial questions in the early 1320s, resulting in his De primo et ultimo instanti and his Tractatus Primus and Tractatus Secundus de intensione et remissione formarum. In these independent controversial works, Burley advanced and defended the succession-of-forms theory with greater detail and precision. This paper examines the treatment of the mathematics of alteration in Burley's final Parisian Expositio in libros octo de physico auditu in light of this earlier controversial work.
The core Oxford Calculators (here William Heytesbury, John Dumbleton, and Richard Swineshead) developed a science of kinematics in which the key concept was the “latitude of velocity.” Based upon the concept of “latitude,” the Calculators developed parts of a mathematical physics in deductive format that could be applied to quite various situations.
Abstract
In this paper I examine what John Buridan has to say in his Quaestiones in Analytica Posteriora relevant to the subalternate mathematical sciences, particularly astronomy. Much previous work on the scholastic background to the Scientific Revolution relies on texts that were written in the late sixteenth or seventeenth centuries. Here I am interested in texts that might reflect the context of Copernicus, and, in particular those before 1500. John Buridan and Albert of Saxony were fourteenth century authors influential in Cracow in the fifteenth century, whose conception of science may be characterized as "critical realism." Their view would support the autonomy of astronomy, as well as the idea that sciences may progress over time.
In his De primo et ultimo instanti, Walter Burley paid careful attention to continuity, assuming that continua included and were limited by indivisibles such as instants, points, ubi (or places), degrees of quality, or mutata esse (indivisibles of motion). In his Tractatus primus, Burley applied the logic of first and last instants to reach novel conclusions about qualities and qualitative change. At the end of his Quaestiones in libros Physicorum Aristotelis, William of Ockham used long passages from Burley’s Tractatus primus, sometimes agreeing with Burley and sometimes disagreeing. How may this interaction between Burley and Ockham be understood within its historical context?
Jacob Bernoulli’s Lettre à un Amy sur les Parties du Jeu de Paume employs the sorts of mathematical techniques that had been applied to games of chance by Pascal and Huygens to a game, now called Court Tennis or Royal Tennis, the outcomes of which depended, as he thought, not on chance but on athletic skill. He assumed that the players’ relative strengths could be determined a posteriori or by observation. Bernoulli’s work shows an alternate route by which mathematics was applied to the real world in the seventeenth century, one which did not involve Platonic conceptions of the role of mathematics, but rather the techniques of commercial arithmetic and, in particular, of algebra.
Abstract
In his De primo et ultimo instanti, Walter Burley paid careful attention to continuity, assuming that continua included and were limited by indivisibles such as instants, points, ubi (or places), degrees of quality, or mutata esse (indivisibles of motion). In his Tractatus primus, Burley applied the logic of first and last instants to reach novel conclusions about qualities and qualitative change. At the end of his Quaestiones in libros Physicorum Aristotelis, William of Ockham used long passages from Burley’s Tractatus primus, sometimes agreeing with Burley and sometimes disagreeing. How may this interaction between Burley and Ockham be understood within its historical context?