Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. Pincock tackles this perennial question by asking how mathematics contributes to the success of our best scientific representations.

• 1 Introduction


• 1.1 A Problem


• 1.2 Classifying Contributions


• 1.3 An Epistemic Solution


• 1.4 Explanatory Contributions


• 1.5 Other Approaches


• 1.6 Interpretative Flexibility


• 1.7 Key Claims


• I Epistemic Contributions


• 2 Content and Confirmation


• 2.1 Concepts


• 2.2 Basic Contents


• 2.3 Enriched Contents


• 2.4 Schematic and Genuine Contents


• 2.5 Inference


• 2.6 Core Conceptions


• 2.7 Intrinsic and Extrinsic


• 2.8 Confirmation Theory


• 2.9 Prior Probabilities


• 3 Causes


• 3.1 Accounts of Causation


• 3.2 A Causal Representation


• 3.3 Some Acausal Representations


• 3.4 The Value of Acausal Representations


• 3.5 Batterman and Wilson


• 4 Varying Interpretations


• 4.1 Abstraction as Variation


• 4.2 Irrotational Fluids and Electrostatics


• 4.3 Shock Waves


• 4.4 The Value of Varying Interpretations


• 4.5 Varying Interpretations and Discovery


• 4.6 The Toolkit of Applied Mathematics


• 5 Scale Matters


• 5.1 Scale and ScientificRepresentation


• 5.2 Scale Separation


• 5.3 Scale Similarity


• 5.4 Scale and Idealization


• 5.5 Perturbation Theory


• 5.6

Christopher Pincock received his Ph.D. in philosophy from the University of California, Berkeley in 2002. After eight years at Purdue University, he recently joined the philosophy department at the University of Missouri as an Associate Professor.