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Mathematics and Scientific Representation$
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Christopher Pincock

Print publication date: 2012

Print ISBN-13: 9780199757107

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780199757107.001.0001

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Conclusion: Pure Mathematics

Conclusion: Pure Mathematics

Chapter:
(p.279) 14 Conclusion: Pure Mathematics
Source:
Mathematics and Scientific Representation
Author(s):

Christopher Pincock

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199757107.003.0014

This final chapter reviews some of the key claims of the book and considers their significance for the interpretation and epistemology of pure mathematics. Building on some of the points from chapter 13, Pincock argues that a more sustained investigation of the history of the development of mathematics is needed to pin down an appropriate interpretation and epistemology. He presents some considerations in favour of structuralism about pure mathematics, but grants that these are not conclusive. Finally, Pincock returns to the point that the a priori justification of some mathematics is a crucial part of the story of how mathematics can contribute so much to the success of science.

Keywords:   platonism, Frege, structuralism, Peacocke, Jenkins, conceptual change in mathematics

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