# Mathematics as a Tool

## Tracing New Roles of Mathematics in the Sciences

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

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

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

- DOI https://doi.org/10.1007/978-3-319-54469-4
- Copyright Information Springer International Publishing AG 2017
- Publisher Name Springer, Cham
- eBook Packages Earth and Environmental Science
- Print ISBN 978-3-319-54468-7
- Online ISBN 978-3-319-54469-4
- Series Print ISSN 0068-0346
- Series Online ISSN 2214-7942
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