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Mark Colyvan - The Indispensability of Mathematics

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Mark Colyvan The Indispensability of Mathematics
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The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.

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Colyvan Mark Lecturer School of Philosophy University of Tasmania The - photo 1
Colyvan, Mark Lecturer, School of Philosophy, University of Tasmania
The Indispensability of Mathematics
Publication date 2001 (this edition)
Print ISBN-10: 0-19-513754-X
Print ISBN-13: 978-0-19-513754-5
doi:10.1093/019513754X.001.0001
Abstract: Looks at the Quine-Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to our best scientific theories. The indispensability argument has come under serious scrutiny in recent times, with many influential philosophers unconvinced of its cogency. This book outlines the indispensability argument in considerable detail, before defending it against various challenges.Although the focus is squarely on the indispensability argument, in order to appreciate the argument's full force, it is necessary to consider many other interesting and related topics. These include questions about ontological commitments and the applications of mathematics to physical theories. Of particular interest here is the Quinean backdrop from which the indispensability argument emerges. This backdrop consists of the doctrines of holism and naturalism. The latter is crucial to the whole indispensability debate, so a considerable portion of this work is spent discussing naturalism.
Keywords: applied mathematics,Mark Colyvan,holism,indispensability argument,mathematics,naturalism,ontological commitment,philosophy of mathematics,philosophy,Putnam,Quine
The Indispensability of Mathematics
end p.i
end p.ii
The Indispensability of Mathematics
Picture 2
2001
end p.iii
Picture 3

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Copyright 2001 by Mark Colyvan
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Library of Congress Cataloging-in-Publication Data
Colyvan, Mark.
The indispensability of mathematics / Mark Colyvan.
p. cm.
Includes bibliographical references and index.
ISBN 0-19-513754-X
1. Mathematics Philosophy. I. Title.
QA8.4 .C65 2000
510dc21 00-037346
end p.iv
Acknowledgments
I'd like to thank Jody Azzouni, Alan Baker, Paul Benacerraf, John Bigelow, Brian Birchall, James Chase, Colin Cheyne, Stephen Ferguson, Hartry Field, Peter Forrest, Jay Garfield, Philip Gerrans, Ian Gold, Geoffrey Hellman, Frank Jackson, Drew Khlentzos, Keith Lehrer, Bernard Linsky, Penelope Maddy, Peter Menzies, Bob Meyer, Alan Musgrave, Daniel Nolan, Alex Oliver, Graham Oppy, Philip Pettit, Michael Potter, W. V. Quine, Helen Regan, Mike Resnik, Peter Roeper, Gideon Rosen, David Ryan, Jack Smart, and Ed Zalta. All of these people have made significant intellectual contributions to this work.
This book draws upon material which has been published elsewhere, so I'd like to thank the relevant publishers for their permission to use that material again here. The copyright for previously published material remains with the relevant journals. Much of chapter )) in The Australian Journal of Philosophy.
M. C.
Hobart, Tasmania
October 2000
end p.v
end p.vi
Contents
Mathematics and Its Applications
1.1
Realism and Anti-realism in Mathematics
1.2
Indispensability Arguments
1.3
The Road Ahead
The Quinean Backdrop
2.1
Introducing Naturalism
2.2
Quinean Naturalism
2.3
The Methodologies of Philosophy and Science
2.4
The Causal Version of Naturalism
2.5
Holism
2.6
The First Premise Revisited
The Eleatic Principle
3.1
The Inductive Argument
3.2
The Epistemic Argument
3.3
The Argument from Causal Explanation
3.4
Causal Relevance
3.5
Rejecting Inference to the Best Explanation
3.6
The Content of Scientific Theories
3.7
The Moral
3.8
Recapitulation
Field's Fictionalism
4.1
The Science without Numbers Project
4.2
What Is It to Be Indispensable?
4.3
The Role of Confirmation Theory
4.4
The Role of Mathematics in Physical Theories
4.5
Review of Field's Fictionalism
end p.vii
Maddy's Objections
5.1
The Objections
5.2
Maddy's Naturalism
5.3
Defending the Indispensability Argument
5.4
Review of Maddy's Objections
The Empirical Nature of Mathematical Knowledge
6.1
The Obviousness of Some Mathematical Truth
6.2
The Unfalsifiability of Mathematics
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