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The Indispensability of Mathematics$
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Mark Colyvan

Print publication date: 2001

Print ISBN-13: 9780195137545

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/019513754X.001.0001

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(p.141) 7 Conclusion
The Indispensability of Mathematics

Mark Colyvan

Oxford University Press

The varieties of mathematical realism that are consistent with the indispensability argument are outlined. It is shown that the argument is silent on many issues such as whether numbers are sets, and whether mathematical entities are causally inert or not. Paul Benacerraf's two objections to mathematical realism are also considered. Finally, the use of indispensability arguments outside the philosophy of mathematics is considered, and, in particular, an indispensability argument for modal realism is discussed.

Keywords:   Benacerraf, mathematical entities, mathematical realism, modal realism, numbers, sets

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