Chapter

Conclusion

Mark Colyvan

in The Indispensability of Mathematics

Published in print April 2001 | ISBN: 9780195137545
Published online November 2003 | e-ISBN: 9780199833139 | DOI: http://dx.doi.org/10.1093/019513754X.003.0007
                   Conclusion

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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

Chapter.  6957 words. 

Subjects: Philosophy of Mathematics and Logic

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