Boston Studies in the Philosophy and History of Science

Mathematics as a Tool

Tracing New Roles of Mathematics in the Sciences

Editors: Lenhard, Johannes, Carrier, Martin (Eds.)

  • Shows another level in which the sciences, engineering, and mathematics are intertwined
  • Combines historical and philosophical accounts with a strong emphasis on practices
  • Covers material from ancient periods as well as modern and recent times
  • Focuses on recent, computer-related, developments
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Hardcover $129.00
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About this book

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.

About the authors

Johannes Lenhard does research in philosophy of science with a particular focus on the history and philosophy of mathematics and statistics. During the last years his research concentrated on various aspects of computer and simulation modeling, culminating in his monograph “Calculated Surprises” (in German). Currently, he is senior researcher at the philosophy department of Bielefeld University, Germany. He has held a visiting associate professorship in history at the University of South Carolina, Columbia, long after he had received his doctoral degree in mathematics from the University of Frankfurt, Germany.

Martin Carrier is a professor at the Department of Philosophy, Bielefeld University. He has worked on five different fields in the philosophy of science. History of Early Modern Physical Theory, Theory Change: Problems of Methodological Comparison and Confirmation Theory, Conceptual Relations among Theoretical Systems: cognition, neuronal states, behavior, incommensurability, theory-laden tests, Space-Time Philosophy and Methodological Problems of Applied Research.

Table of contents (14 chapters)

  • Introduction: Mathematics as a Tool

    Lenhard, Johannes (et al.)

    Pages 1-19

  • Rational and Empirical Cultures of Prediction

    Johnson, Ann

    Pages 23-35

  • Mathematization in Synthetic Biology: Analogies, Templates, and Fictions

    Knuuttila, Tarja (et al.)

    Pages 37-56

  • Trigonometry, Construction by Straightedge and Compass, and the Applied Mathematics of the Almagest

    Yavetz, Ido

    Pages 57-67

  • Shaping Mathematics as a Tool: The Search for a Mathematical Model for Quasi-crystals

    Sørensen, Henrik Kragh

    Pages 69-90

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-54469-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-54468-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematics as a Tool
Book Subtitle
Tracing New Roles of Mathematics in the Sciences
Editors
  • Johannes Lenhard
  • Martin Carrier
Series Title
Boston Studies in the Philosophy and History of Science
Series Volume
327
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-54469-4
DOI
10.1007/978-3-319-54469-4
Hardcover ISBN
978-3-319-54468-7
Series ISSN
0068-0346
Edition Number
1
Number of Pages
X, 286
Number of Illustrations and Tables
18 b/w illustrations, 10 illustrations in colour
Topics