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This book puts forward a new role for mathematics in the natural sciences. In the traditional understanding, a strong viewpoint is advocated, on the one hand, according to which mathematics is used for truthfully expressing laws of nature and thus for rendering the rational structure of the world. In a weaker understanding, many deny that these fundamental laws are of an essentially mathematical character, and suggest that mathematics is merely a convenient tool for systematizing observational knowledge.
The position developed in this volume combines features of both the strong and the weak viewpoint. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. Hence the tool perspective is contextual rather than ontological. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others. There is a spectrum of means that will normally differ in how well they serve particular purposes. The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions.
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Boston Studies in the Philosophy and History of Science 327 Johannes Lenhard Martin Carrier Editors Mathematics as a Tool Tracing New Roles of Mathematics in the Sciences Boston Studies in the Philosophy and History of Science Volume 327 Editors Alisa Bokulich, Boston University Robert S. Cohen, Boston University Jürgen Renn, Max Planck Institute for the History of Science Kostas Gavroglu, University of Athens Managing Editor Lindy Divarci, Max Planck Institute for the History of Science Editorial Board Theodore Arabatzis, University of Athens Heather E. Douglas, University of Waterloo Jean Gayon, Université Paris 1 Thomas F. Glick, Boston University Hubert Goenner, University of Goettingen John Heilbron, University of California, Berkeley Diana Kormos-Buchwald, California Institute of Technology Christoph Lehner, Max Planck Institute for the History of Science Peter McLaughlin, Universität Heidelberg Agustí Nieto-Galan, Universitat Autònoma de Barcelona Nuccio Ordine, Universitá della Calabria Sylvan S. Schweber, Harvard University Ana Simões, Universidade de Lisboa John J. Stachel, Boston University Baichun Zhang, Chinese Academy of Science More information about this series at http://www.springer.com/series/5710 Johannes Lenhard • Martin Carrier Editors Mathematics as a Tool Tracing New Roles of Mathematics in the Sciences 123 Editors Johannes Lenhard Department of Philosophy Bielefeld University Bielefeld, Germany Martin Carrier Department of Philosophy Bielefeld University Bielefeld, Germany ISSN 0068-0346 ISSN 2214-7942 (electronic) Boston Studies in the Philosophy and History of Science ISBN 978-3-319-54468-7 ISBN 978-3-319-54469-4 (eBook) DOI 10.1007/978-3-319-54469-4 Library of Congress Control Number: 2017936971 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such n