Book

The Indispensability of Mathematics

Mark Colyvan

Published in print April 2001 | ISBN: 9780195137545
Published online November 2003 | e-ISBN: 9780199833139 | DOI: http://dx.doi.org/10.1093/019513754X.001.0001

Series: Oxford Studies in the Philosophy of Science

The Indispensability of Mathematics

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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

Book.  182 pages.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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Table of Contents

Mathematics and Its Applications in The Indispensability of Mathematics

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The Quinean Backdrop in The Indispensability of Mathematics

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The Eleatic Principle in The Indispensability of Mathematics

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Field's Fictionalism in The Indispensability of Mathematics

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Maddy's Objections in The Indispensability of Mathematics

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Conclusion in The Indispensability of Mathematics

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