Introduction by The Guest Editor – 4th Filomena Workshop.

Abstract:Three half-leaves of the final manuscript of Principia Mathematica have come to light in the Bertrand Russell Archives. They were originally tucked in Russell’s own copy but avoided archival notice because their versos had been employed for an index of propositions used in theorem *350·62. The leaves form the whole of a folio 152 and the top half of 153 and include *336·51 through part of *336·52, on pages 400–1 of Volume iii. Markings by the Cambridge University Press add (...) to our knowledge of the typesetting and proofreading of PM and give some indication of the fate of the remainder of the approximately 5–6,000 manuscript leaves, of which only one had been known to have survived. (shrink)

A philosopher may develop ideas on his or her own or follow them in the works of others. Different kinds of documentary threads will develop. Historians of a subject may follow either kind. In the period of _Toward “Principia Mathematica”, 1905–08_, Russell engaged with developments in the writings of Poincaré, Haldane, Schiller and Berry, among others. What follows are remarks on supplementary documents (one being on-line) for a fuller study of logical and philosophical threads in the period.

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)

Teaching Newtonian physics involves the replacement of students’ ideas about physical situations with precise concepts appropriate for mathematical applications. This paper focuses on the concepts of ‘matter’ and ‘mass’. We suggest that students, like some pre-Newtonian scientists we examine, use these terms in a way that conflicts with their Newtonian meaning. Specifically, ‘matter’ and ‘mass’ indicate to them the sorts of things that are tangible, bulky, and take up space. In Newtonian mechanics, however, the terms are defined by Newton’s Second (...) Law: ‘mass’ is simply a measure of the acceleration generated by an impressed force. We examine the relationship between these conceptions as it was discussed by Newton and his editor, Roger Cotes, when analyzing a series of pendulum experiments. We suggest that these experiments, as well as more sophisticated computer simulations, can be used in the classroom to sufficiently differentiate the colloquial and precise meaning of these terms. (shrink)

Editorial: 20 Years of Principia, dedicated to the memory of Prof. Oswaldo Porchat. Interview with Luiz Henrique Dutra.

Editorial: 20 Years of Principia, dedicated to the memory of Prof. Oswaldo Porchat. Interview with Luiz Henrique Dutra.

I. Bernard Cohen (1914–2003), the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton, founder of Isis and the History of Science Society. He went on to succeed Sarton as editor of Isis (1952–1958) and, later, president of the Society (1961–1962); he was also a president of the International Union of the History and Philosophy of Science. Cohen was an internationally recognized Newton scholar; (...) his interests were encyclopedic, ranging from science and public policy to the history of computers, with several decades as a special consultant for history of computing with IBM. Among his hundreds of publications were such major books as Franklin and Newton (1956), The Birth of a New Physics (1959; rpt., 1985), The Newtonian Revolution (1980), Revolution in Science (1985), Science and the Founding Fathers (1995), Howard Aiken: Portrait of a Computer Pioneer (1999), and his last book, The Triumph of Numbers (2005), not to mention two jointly authored contributions, the variorum edition and new English translation of Newton's Principia, which will surely still be read a century from now. (shrink)