Description
Book SynopsisMathematics 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 mathematics contributes 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
Trade Reviewa rare and fairly comprehensive philosophical account of the success of mathematics in science and after reading it you may be left with the impression that something like this should have been published years ago. This book is a major contribution to an otherwise underdeveloped area in the philosophy of science and is most likely to be well referenced ... this book is at the cutting-edge. * Stuart Rowlands, Science & Education *
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, exemplify exciting and fertile scholarly 'border-hopping'. * Juha Saatsi, Notre Dame Philosophical Reviews *
Pincocks writing style is engaging, and the book is structured in a way that makes it easy to follow the contours of the main lines of argumentan...an impressive book and one that repays detailed reading and re-reading. * Alan Baker, The British Journal for the Philosophy of Science *
Pincock's book is an excellent analysis of some of the most important topics in philosophy of science and philosophy of mathematics, and is well worth a read for any philosopher interested in the issue of mathematical application. * Ashley Graham Kennedy, International Studies in the Philosophy of Science *
Table of Contents1 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
