The Indispensability of Mathematics

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Although the focus of attention 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 and its relevance to the
debate.
"The book is clearly written and contains many interesting and novel ideas that push forward the horizons of the debate.
Colyvan's defence of the indispensability argument is impressive and powerful yet always fairminded: opponents are given a sympathetic hearing.
Moreover, Colyvan is also an excellent expositor, difficult ideas and positions are explained simply and perspicuously,
and the result is a book that will be of use and interest to undergraduates and researchers alike ...
Colyvan has written an excellent book, and one that everyone interested in the philosophy of mathematics should read."
– Joseph Melia (in Metascience)
"This book will be of particular interest to specialists and advanced
students in the philosophy of mathematics and science, but also to
epistemologists and metaphysicians in general. I do not say that
this book is indispensable – indispensability is a rare commodity,
not easily established. Nor do I say that if it were indispensable it
would be true – I am not convinced of that entailment. I do say
that this book is both useful and pleasurable – like mathematics."
– Colin Cheyne (in The Australasian Journal of Philosophy)
"[T]his book is provocative and interesting ... One important, lasting value of the book is that it presents a clear picture of what the Quinean world view is like.
since Quine's own pronouncements on indispensability are scattered throughout his writings."
– Julian Cole and Stewart Shapiro (in Mind)
Arko, M. (2007) Croatian Journal of Philosophy, 7(9): 118–21.
Castro, E. (2004) Intelectu, 10 (in Portuguese).
Cheyne, C. (2002) Australasian Journal of Philosophy, 80(3):
378–9.
Cole, J. and Shapiro, S. (2003) Mind, 112(446): 331–6.
Decock, L. (2001) Tijdschrift, 63(4): 805–6 (in Dutch).
de Lorenzo, J. (2003) History and Philosophy of Logic, 24(2): 167–9 (in Spanish).
Melia, J. (2003) Metascience, 12(1): 55–8.
Peressini, A. (2003) Philosophia Mathematica (3), 11(2): 208–23.
Sayward, C. (2003) Philosophical Books, 44(3): 293–4.
Shapiro, S. (2004) Mathematical Reviews, http://www.ams.org/mathscinet.