The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton’s perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics, but also the problematic aspects of his perfect geometrical (...) methods, more elegant, but less malleable than analytical procedures, of which Newton himself was one of the inventors. Furthermore, we will also consider the way in which Newtonianism was spread before in England and afterwards on continental Europe. In this respect the Geneva Edition plays a fundamental role because of its complete apparatus of notes, and because it appeared only thirteen years after the publication of the third edition of the Principia (1726). Finally, we will also confront some problems connected to the metaphysics of calculus. Therefore, the case of Newton is one of those in which, starting from mathematics applied to physics, it is possible to connect an impressive series of fundamental arguments such as the role of mathematics in science; the comparison between Newton’s geometrical methods and analytical methods; the way in which Newtonianism was spread as well as the philosophical implications of Newton’s mathematical concepts. (shrink)

ABSTRACT Historians of science, inasmuch as they are concerned with knowledges and practices rather than institutions, have tended of late to focus on case studies of common processes such as experiment and publication. In so doing, they tend to treat science as a single category, with various local instantiations. Or, alternatively, they relate cases to their specific local contexts. In neither approach do the cases or their contexts build easily into broader histories, reconstructing changing knowledge practices across time and space. (...) This essay argues that by systematically deconstructing the practices of science and technology and medicine (STM) into common, recurrent elements, we can gain usefully “configurational” views, not just of particular cases and contexts but of synchronic variety and diachronic changes, both short term and long. To this end, we can begin with the customary actors’ disciplines of early modern knowledge (natural philosophy, natural history, mixed mathematics, and experimental philosophy), which can be understood as elemental “ways of knowing and working,” variously combined and disputed. I argue that these same working knowledges, together with a later mode—synthetic experimentation and systematic invention—may also serve for the analysis of STM from the late eighteenth century to the present. The old divisions continued explicitly and importantly after circa 1800, but they were also “built into” an array of new sciences. This historiographic analysis can help clarify a number of common problems: about the multiplicity of the sciences, the importance of various styles in science, and the relations between science and technology and medicine. It suggests new readings of major changes in STM, including the first and second scientific revolutions and the transformations of biomedicine from the later twentieth century. It offers ways of recasting both microhistories and macrohistories, so reducing the apparent distance between them. And it may thus facilitate both more constructive uses of case studies and more innovative and acceptable longer histories. (shrink)

Noting that the doctrine of the general resurrection attracted renewed attention after the Reformation, and after the atomist revival led to the displacement of traditional hylomorphism by alternative matter theories, this article surveys the ways in which the resurrection was discussed by leading natural philosophers in seventeenth‐century England. These include discussion of how bodily resurrection might be possible, what resurrected bodies will be like; as well as the nature of living conditions after the resurrection. It is indicated that the resurrection (...) seems to have played a much less prominent place in the writings of natural philosophers than the doctrine of the immortality of the soul, and other issues of natural theology. Reasons for this lack of prominence are tentatively offered, chiefly focusing on its unsuitability for combatting the perceived atheism of the time. It is hoped that this preliminary survey might inspire others to extend the survey, especially to cover Continental philosophers. (shrink)

Una de las principales razones para el éxito de la filosofía natural de Newton fue el papel que ésta tuvo al desarrollar una teología natural valiosa. Además, Newton mismo publicó las implicaciones teológicas de su propia filosofía natural. Aunque en la primera edición de los Principia no hay ninguna señal de Dios, para la segunda edición (1713) Newton introdujo un "Escolio General" en el que explícitamente discutía la relación entre Dios y su Creación. La obsesión de Newton por la interpretación (...) de las Escrituras durante algún tiempo fue desestimada como embarazosa. Sin embargo, su importancia para una comprensión adecuada de Newton ahora se reconoce y estimula mucha actividad nueva entre los especialistas. El significado de este trabajo permite ver en la actualidad el núcleo de la pregunta de Richard H. Popkin: “¿por qué uno de los más grandes teólogos anti-Trinitarios se dedicó a escribir obras de filosofía natural, como los Principia Mathematica? (shrink)

In this essay, I attempt to assess Henk de Regt and Dennis Dieks recent pragmatic and contextual account of scientific understanding on the basis of an important historical case-study: understanding in Newton’s theory of universal gravitation and Huygens’ reception of universal gravitation. It will be shown that de Regt and Dieks’ Criterion for the Intelligibility of a Theory (CIT), which stipulates that the appropriate combination of scientists’ skills and intelligibility-enhancing theoretical virtues is a condition for scientific understanding, is too strong. (...) On the basis of this case-study, it will be shown that scientists can understand each others’ positions qualitatively and quantitatively, despite their endorsement of different worldviews and despite their convictions as what counts as a proper explanation. (shrink)

Mathematical and philosophical Newton Content Type Journal Article Pages 1-10 DOI 10.1007/s11016-010-9520-2 Authors Steffen Ducheyne, Centre for Logic and Philosophy of Science, Ghent University, Blandijnberg 2, 9000 Ghent, Belgium Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.