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Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes

Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes Introduction: Leibniz and the Sciences: Daniel Garber University of Chicago Roger Ariew Virginia Polytechnic Institute and State University In his "Eloge de Monsieur Leibnitz," Bernard de Fontenelle wrote: In somewhat the same way that the ancients could manage simulta­ neously up to eight harnessed horses, Leibniz could manage simul­ taneously all the sciences. Thus we need to split him up here, that is, speaking philosophically, to analyze him. Antiquity made only one person from several Hercules; we will make several savants from only one Leibniz. (Leibniz 1768, vol. 1, p. xx) By "science" here, Fontenelle, of course, does not mean exactly what we do now. Though in the title of this volume we speak of "Leibniz and the Sciences" in the modern sense of the term, meaning to include a variety of studies directed at understanding the natural and mathematical worlds in a systematic way, Leibniz's own notion of a science (and Fontcnellc's as well) was quite different. For Leibniz and his contemporaries, a "science" was a body of doctrine that could be known systematically and with a high degree of certainty; it was contrasted with opinion, that which could only be understood with a lesser degree of certainty, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Perspectives on Science MIT Press

Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes

Perspectives on Science , Volume 6 (1-2): 35 – Jan 5, 1998

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Publisher
MIT Press
Copyright
©1998 by The University of Chicago. All reserved.
ISSN
1063-6145
eISSN
1530-9274
DOI
10.1162/posc_a_00543
Publisher site
See Article on Publisher Site

Abstract

Introduction: Leibniz and the Sciences: Daniel Garber University of Chicago Roger Ariew Virginia Polytechnic Institute and State University In his "Eloge de Monsieur Leibnitz," Bernard de Fontenelle wrote: In somewhat the same way that the ancients could manage simulta­ neously up to eight harnessed horses, Leibniz could manage simul­ taneously all the sciences. Thus we need to split him up here, that is, speaking philosophically, to analyze him. Antiquity made only one person from several Hercules; we will make several savants from only one Leibniz. (Leibniz 1768, vol. 1, p. xx) By "science" here, Fontenelle, of course, does not mean exactly what we do now. Though in the title of this volume we speak of "Leibniz and the Sciences" in the modern sense of the term, meaning to include a variety of studies directed at understanding the natural and mathematical worlds in a systematic way, Leibniz's own notion of a science (and Fontcnellc's as well) was quite different. For Leibniz and his contemporaries, a "science" was a body of doctrine that could be known systematically and with a high degree of certainty; it was contrasted with opinion, that which could only be understood with a lesser degree of certainty,

Journal

Perspectives on ScienceMIT Press

Published: Jan 5, 1998

References