图书简介

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 Multiple Scales; 5.7 Interpreting Multiscale Representations; 5.8 Summary; 6 Constitutive Frameworks; 6.1 A Different Kind of Contribution; 6.2 Carnap’s Linguistic Frameworks; 6.3 Kuhn’s Paradigms; 6.4 Friedman on the Relative A Priori; 6.5 The Need for Constitutive Representations; 6.6 The Need for the Absolute A Priori; 7 Failures; 7.1 Mathematics and Scientific Failure; 7.2 Completeness and Segmentation Illusions; 7.3 The Parameter Illusion; 7.4 Illusions of Scale; 7.5 Illusions of Traction; 7.6 Causal Illusions; 7.7 Finding the Scope of a Representation; II Other Contributions; 8 Discovery; 8.1 Semantic and Metaphysical Problems; 8.2 A Descriptive Problem; 8.3 Description and Discovery; 8.4 Defending Naturalism; 8.5 Natural Kinds; 9 Indispensability; 9.1 Descriptive Contributions and Pure Mathematics; 9.2 Quine and Putnam; 9.3 Against the Platonist Conclusion; 9.4 Colyvan; 10 Explanation; 10.1 Explanatory Contributions; 10.2 Inference to the Best Mathematical Explanation; 10.3 Belief and Understanding; 11 The Rainbow; 11.1 Asymptotic Explanation; 11.2 Angle and Color; 11.3 Explanatory Power; 11.4 Supernumerary Bows; 11.5 Interpretation and Scope; 11.6 Batterman and Belot; 11.7 Looking Ahead; 12 Fictionalism 413; 12.1 Motivations; 12.2 Literary Fiction; 12.3 Mathematics; 12.4 Models; 12.5 Understanding and Truth; 13 Facades; 13.1 Physical and Mathematical Concepts; 13.2 Against Semantic Finality; 13.3 Developing and Connecting Patches; 13.4 A New Approach to Content; 13.5 Azzouni and Rayo; 14 Conclusion: Pure Mathematics; 14.1 Taking Stock; 14.2 Metaphysics .; 14.3 Structuralism; 14.4 Epistemology; 14.5 Peacocke and Jenkins; 14.6 Historical Extensions; 14.7 Non-conceptual Justification; 14.8 Past and Future; Appendices; A Method of Characteristics; B Black-Scholes Model; C Speed of Sound; D Two Proofs of Euler’s Formula

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