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Mathematics and Reality$
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Mary Leng

Print publication date: 2010

Print ISBN-13: 9780199280797

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199280797.001.0001

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Conclusion

Conclusion

Chapter:
(p.253) 10 Conclusion
Source:
Mathematics and Reality
Author(s):

Mary Leng (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199280797.003.0010

This chapter sums up the argument of the book, and ties up a few loose ends. In particular, it considers Michael Resnik's alternative ‘pragmatic’ version of the indispensability argument, and shows how this argument, while not relying on confirmational holism, can be responded to from the fictionalist perspective developed in this book. It also considers the question of whether one should reject the existence of mathematical objects or merely remain agnostic about their existence, and argues for the stronger position which rejects the existence of such things. Finally, it considers a sense in which the view of the axioms of set theory with non‐mathematical objects as urelements as generative of a fiction can be considered to be a revival of a version of conventionalism about our mathematical hypotheses, as analytic ‘truths’ which are not in fact truths.

Keywords:   pragmatic indispensability argument, Michael Resnik, agnosticism, anti‐platonism, analyticity, conventionalism

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