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The Nature of Mathematical Knowledge

Online ISBN:
9780199833368
Print ISBN:
9780195035414
Publisher:
Oxford University Press
Book

The Nature of Mathematical Knowledge

Philip Kitcher
Philip Kitcher

Professor of Philosophy

University of Minnesota
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Published online:
1 November 2003
Published in print:
11 April 1985
Online ISBN:
9780199833368
Print ISBN:
9780195035414
Publisher:
Oxford University Press

Abstract

The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical knowledge is viable. It then constructs an approach to the content of mathematical statements, viewing mathematics as grounded in our manipulations of physical reality. From these crude beginnings, mathematics unfolds through the successive modifications of mathematical practice, spurred by the presence of unsolved problems. This process of unfolding is considered in general, and illustrated by considering the historical development of analysis from the seventeenth century to the end of the nineteenth.

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