Mathematics and Scientific Representation

Paperback | December 15, 2014

byChristopher Pincock

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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. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematicscontributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated.Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge.In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument formathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of itsinterpretation and epistemology.Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.

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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. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematicscontributes to the success of our best scien...

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.
Format:PaperbackDimensions:352 pages, 9.21 × 6.1 × 0.98 inPublished:December 15, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0190201398

ISBN - 13:9780190201395

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Table of Contents

1. Introduction1.1 A Problem1.2 Classifying Contributions1.3 An Epistemic Solution1.4 Explanatory Contributions1.5 Other Approaches1.6 Interpretative Flexibility1.7 Key ClaimsI Epistemic Contributions2. Content and Confirmation2.1 Concepts2.2 Basic Contents2.3 Enriched Contents2.4 Schematic and Genuine Contents2.5 Inference2.6 Core Conceptions2.7 Intrinsic and Extrinsic2.8 Confirmation Theory2.9 Prior Probabilities3. Causes3.1 Accounts of Causation3.2 A Causal Representation3.3 Some Acausal Representations3.4 The Value of Acausal Representations3.5 Batterman and Wilson4. Varying Interpretations4.1 Abstraction as Variation4.2 Irrotational Fluids and Electrostatics4.3 Shock Waves4.4 The Value of Varying Interpretations4.5 Varying Interpretations and Discovery4.6 The Toolkit of Applied Mathematics5. Scale Matters5.1 Scale and ScientificRepresentation5.2 Scale Separation5.3 Scale Similarity5.4 Scale and Idealization5.5 Perturbation Theory5.6 Multiple Scales5.7 Interpreting Multiscale Representations5.8 Summary6. Constitutive Frameworks6.1 A Different Kind of Contribution6.2 Carnap's Linguistic Frameworks6.3 Kuhn's Paradigms6.4 Friedman on the Relative A Priori6.5 The Need for Constitutive Representations6.6 The Need for the Absolute A Priori7. Failures7.1 Mathematics and Scientific Failure7.2 Completeness and Segmentation Illusions7.3 The Parameter Illusion7.4 Illusions of Scale7.5 Illusions of Traction7.6 Causal Illusions7.7 Finding the Scope of a RepresentationII Other Contributions8. Discovery8.1 Semantic and Metaphysical Problems8.2 A Descriptive Problem8.3 Description and Discovery8.4 Defending Naturalism8.5 Natural Kinds9. Indispensability9.1 Descriptive Contributions and Pure Mathematics9.2 Quine and Putnam9.3 Against the Platonist Conclusion9.4 Colyvan10. Explanation10.1 Explanatory Contributions10.2 Inference to the Best Mathematical Explanation10.3 Belief and Understanding11. The Rainbow11.1 Asymptotic Explanation11.2 Angle and Color11.3 Explanatory Power11.4 Supernumerary Bows11.5 Interpretation and Scope11.6 Batterman and Belot11.7 Looking Ahead12. Fictionalism12.1 Motivations12.2 Literary Fiction12.3 Mathematics12.4 Models12.5 Understanding and Truth13. Facades13.1 Physical and Mathematical Concepts13.2 Against Semantic Finality13.3 Developing and Connecting Patches13.4 A New Approach to Content13.5 Azzouni and Rayo14. Conclusion: Pure Mathematics14.1 Taking Stock14.2 Metaphysics .14.3 Structuralism14.4 Epistemology14.5 Peacocke and Jenkins14.6 Historical Extensions14.7 Non-conceptual Justification14.8 Past and FutureAppendicesA Method of CharacteristicsB Black-Scholes ModelC Speed of SoundD Two Proofs of Euler's Formula

Editorial Reviews

"Mathematics and Scientific Representation is an engaging piece of contemporary philosophy of mathematics and science. Its deeply science-informed approach and focus on applied mathematics, with an aim to seriously tackle also more traditional issues in philosophy of mathematics, exemplifyexciting and fertile scholarly 'border-hopping'." --Juha Saatsi, Notre Dame Philosophical Reviews