Mathematics as a Tool

Tracing New Roles of Mathematics in the Sciences

  • Johannes Lenhard
  • Martin Carrier

Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 327)

Table of contents

  1. Front Matter
    Pages i-x
  2. Johannes Lenhard, Martin Carrier
    Pages 1-19
  3. Organizing Science

  4. Conceptual Re-evaluation

    1. Front Matter
      Pages 91-91
    2. Nicolas Fillion
      Pages 137-155
    3. Anouk Barberousse
      Pages 157-173
  5. Reflections on the Tool Character

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.


Scientific Practice Mathematical instrument Computer Modelling Mathematical practice Simulation Mathematical Engineering Mathematization Mathematics mediator Data driven Research Mathematical Tuning Mathematical idealization Mathematical representation

Editors and affiliations

  • Johannes Lenhard
    • 1
  • Martin Carrier
    • 2
  1. 1.Department of PhilosophyBielefeld UniversityBielefeldGermany
  2. 2.Department of PhilosophyBielefeld UniversityBielefeldGermany

Bibliographic information