Lenhard J., Carrier M. (Eds.) Mathematics as a Tool: Tracing New Roles of Mathematics in the Sciences

Springer International Publishing AG, 2017. — 285 p. — (Boston Studies in the Philosophy and History of Science 327) — ISBN: 3319544683This 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.Introduction: Mathematics as a Tool
Organizing Science
Rational and Empirical Cultures of Prediction
Mathematization in Synthetic Biology: Analogies, Templates, and Fictions Trigonometry, Construction by Straightedge and Compass, and the Applied Mathematics of the Almagest
Shaping Mathematics as a Tool: The Search for a Mathematical Model for Quasi-crystals
Conceptual Re-evaluation
Boon and Bane: On the Role of Adjustable Parameters
in Simulation Models
Systems Biology in the Light of Uncertainty: The Limits of Computation
The Vindication of Computer Simulations
Empirical Bayes as a Tool
Reflections on the Tool Character
On the Epistemic and Social Foundations of Mathematics as Tool and Instrument in Observatories, 1793–1846
Approaching Reality by Idealization: How Fluid Resistance Was Studied by Ideal Flow Theory
Idealizations in Empirical Modeling
Forcing Optimality and Brandt’s Principle
Object Oriented Models vs. Data Analysis – Is This the Right Alternative?