Mathematics and Scientific Representation
Sorozatcím: Oxford Studies in Philosophy of Science;
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A termék adatai:
- Kiadó OUP USA
- Megjelenés dátuma 2012. április 19.
- ISBN 9780199757107
- Kötéstípus Keménykötés
- Terjedelem348 oldal
- Méret 155x236x33 mm
- Súly 590 g
- Nyelv angol 0
Kategóriák
Rövid leírás:
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.
TöbbHosszú leírás:
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 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 focus of this part of the book is the indispensability argument for mathematical 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 its interpretation 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.
a 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.
Tartalomjegyzék:
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
