Aristotelian philosophy is generally regarded as incompatible with the mathematical methods and principles that form the basis of modern science. This book offers an entirely new perspective on this presumed incompatibility. It surveys the tradition of the Oxford Calculators from its beginnings in the fourteenth century until Leibniz and the philosophy of the seventeenth century and explores how the Calculators' techniques of quantification expanded the conceptual and methodological limits of Aristotelianism. In the process, it examines a large number of authors, (...) some of them never studied in this context. Exploring the relationship between various late medieval disciplines, the book sheds new light on the problem of continuity vs. discontinuity between scholasticism and modern science. Beyond its historiographical purpose, this book also hopes to be a source of inspiration for present-day philosophers of science. Co-edited by Daniel A. Di Liscia and Edith D. Sylla with the collaboration of Paul Bakker. (shrink)

As its modern edition appears in the Synthese Historical Library, Adam WodehamThis book is an important contribution to the history of philosophy.It will be of interest to all medievalists, particularly to those concerned with medieval science, philosophy, and logic. Theologians and historians of mathematics will also find it useful.Whether charity or [any] other incorruptible form is composed of indivisible forms.Because this difficulty is the same for all composite divisible things, whether intensive or extensive, which are of one and the same (...) species or homogeneous, therefore I will briefly inquire indifferently concerning the former and the latter.” 3 The solutions Wodeham then proposes to the questions he asks rely nearly always on logic. (shrink)

JOHN E. MURDOCH AND EDITH DUDLEY SYLLA INTRODUCTION Conferences and colloquia are held and their results often published, but very rarely is any account ...

In a long question, "Whether there is motion to quality," 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. (shrink)

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, degrees of quality, or mutata esse. 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? (shrink)

As its modern edition appears in the Synthese Historical Library, Adam Wodeham’s Tractatus de indivisibilibus does not appear to belong to any one discipline. With regard to its intended audience, the notice of the book appearing on the back cover states that “This book is an important contribution to the history of philosophy.” But it continues, “It will be of interest to all medievalists, particularly to those concerned with medieval science, philosophy, and logic. Theologians and historians of mathematics will also (...) find it useful.”Adam de Wodeham, Tractatus de indivisibilibus. A Critical Edition with Introduction, Translation, and Textual Notes, ed. Rega Wood (Dordrecht: Kluwer Academic Publishers, 1988). In its medieval context as well, Tractatus de indivisibilibus had ambiguous disciplinary status. It begins with the question, “Whether charity or [any] other incorruptible form is composed of indivisible forms.”Wodeham, Tractatus de indivisibilibus, p. 33. Such a reference to charity signals a connection to the Sentences of Peter Lombard, Book I, dist. 17. In introducing his answer to this question, however, Wodeham states, “Because this difficulty is the same for all composite divisible things, whether intensive or extensive, which are of one and the same species or homogeneous, therefore I will briefly inquire indifferently concerning the former and the latter.”Wodeham, Tractatus de indivisibilibus, pp. 34–35. Here and elsewhere, I occasionally modify Rega Wood’s translation in the interests of exactness. The solutions Wodeham then proposes to the questions he asks rely nearly always on logic. (shrink)

As its modern edition appears in the Synthese Historical Library, Adam Wodeham’s Tractatus de indivisibilibus does not appear to belong to any one discipline. With regard to its intended audience, the notice of the book appearing on the back cover states that “This book is an important contribution to the history of philosophy.” But it continues, “It will be of interest to all medievalists, particularly to those concerned with medieval science, philosophy, and logic. Theologians and historians of mathematics will also (...) find it useful.”Adam de Wodeham, Tractatus de indivisibilibus. A Critical Edition with Introduction, Translation, and Textual Notes, ed. Rega Wood (Dordrecht: Kluwer Academic Publishers, 1988). In its medieval context as well, Tractatus de indivisibilibus had ambiguous disciplinary status. It begins with the question, “Whether charity or [any] other incorruptible form is composed of indivisible forms.”Wodeham, Tractatus de indivisibilibus, p. 33. Such a reference to charity signals a connection to the Sentences of Peter Lombard, Book I, dist. 17. In introducing his answer to this question, however, Wodeham states, “Because this difficulty is the same for all composite divisible things, whether intensive or extensive, which are of one and the same species or homogeneous, therefore I will briefly inquire indifferently concerning the former and the latter.”Wodeham, Tractatus de indivisibilibus, pp. 34–35. Here and elsewhere, I occasionally modify Rega Wood’s translation in the interests of exactness. The solutions Wodeham then proposes to the questions he asks rely nearly always on logic. (shrink)

The ArgumentOur understanding of the predisposing factors, the nature, and the fate of the Oxford Calculatory tradition can be significantly increased by seeing it in its social and institutional context. For instance, the use of intricate imaginary cases in Calculatory works becomes more understandable if we see the connection of these works to undergraduate logical disputations. Likewise, the demise of the Calculatory tradition is better understood in the light of subsequent efforts at educational reform.Unfortunately, too little evidence remains about the (...) Calculators and their context to enable anything like a full reconstruction of the relation of the Oxford Calculators' work to its context. Nevertheless, seeking out and fitting together the bits of information that do remain can add to our insight. Among the topics worth further research are the relation of training incalculationesto later careers in church or government, and the special features of the Calculatory tradition as a tradition consisting of multiple parallel manifestations closely interconnected with other disciplines, ranging from logic and natural philosophy to theology and medicine. (shrink)

The core Oxford Calculators 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.