Conclusion: Pure Mathematics

Christopher Pincock

in Mathematics and Scientific Representation

Published in print January 2012 | ISBN: 9780199757107
Published online May 2012 | e-ISBN: 9780199932313 | DOI:

Series: Oxford Studies in the Philosophy of Science

Conclusion: Pure Mathematics

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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

Chapter.  10897 words. 

Subjects: Philosophy of Science

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