Mathematics and Scientific Representation

Erscheinungsjahr 2012
ISBN: 978-0-19-975710-7
Verlag: OXFORD UNIV PR

Buch, Englisch, 348 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 687 g

Reihe: Oxford Studies in Philosophy of Science

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.

Zielgruppe

Professional philosophers, especially in philosophy of science and philosophy of mathematics; graduate students; some advanced undergraduate majors in philosophy; scientists; and mathematicians.

Autoren/Hrsg.

Pincock, Christopher

Fachgebiete

• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

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

Über Autor(innen)

Pincock, Christopher
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.