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Seventeenth-Century Indivisibles Revisited
The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods a...
The Collapse of Mechanism and the Rise of Sensibility
Understanding the emergence of a scientific culture - one in which cognitive values generally are modelled on, or subordinated to, scientific ones - is one of the foremost historical and philosophical problems with which we are now confronted. The significance of the emergence of such scientific values lies above all in their ability to provide the criteria by which we come to appraise cognitive enquiry, and which shape our understanding of what it can achieve. The period between the 1680s and the middle of the eighteenth century is a very distinctive one in this development. It is then that we witness the emergence of the idea that scientific values form a model for all cognitive claims. It...
Force and Geometry in Newton's Principia
In this book François De Gandt introduces us to the reading of Newton's Principia in its own terms. The path of access that De Gandt proposes leads through the study of the geometrization of force. The result is a highly original meditation on the sources and meaning of Newton's magnum opus. In Chapter I De Gandt presents a translation of and detailed commentary on an earlier and simpler version of what in 1687 became Book I of the Principia; here in clearer and starker outline than in the final version, the basic principles of Newton's dynamics show forth. Chapter II places this dynamics in the intellectual context of earlier efforts--the first seeds of celestial dynamics in Kepler, Galile...
Geometrical Landscapes
This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the 16th century. Leading mathematicians began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. Many of those who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period?the infinitesimal methods, which the author shows was no coincidence.
The Principia
In his monumental 1687 work Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts ...
The Principia: The Authoritative Translation and Guide
In his monumental 1687 work,ÊPhilosophiae Naturalis Principia Mathematica, known familiarly as theÊPrincipia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised ...
Science and Speculation
Studies the impact that the advances in philosophy and science had on each other in Greece between 300 B.C. and A.D. 200.
The Phenomenological Critique of Mathematisation and the Question of Responsibility
This edited collection discusses phenomenological critiques of formalism and their relevance to the problem of responsibility and the life-world. The book deals with themes of formalization of knowledge in connection to the life-world, the natural world, the history of science and our responsibility for both our epistemic claims and the world in which we live. Readers will discover critiques of formalization, the life-world and responsibility, and a collation and comparison of Patočka’s and Husserl’s work on these themes. Considerable literature on Husserl is presented here and the two themes of epistemic responsibility and the life-world are discussed together. This work specificall...
Conflicts Between Generalization, Rigor, and Intuition
This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
