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The Nature of Mathematical Knowledge

Philip Kitcher

Published in print April 1985 | ISBN: 9780195035414
Published online November 2003 | e-ISBN: 9780199833368 | DOI: http://dx.doi.org/10.1093/0195035410.001.0001
The Nature of Mathematical Knowledge

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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.

Keywords: kitcher; a priori knowledge; analysis; apriorism; conceptualism; epistemology; history of mathematics; mathematical knowledge; philosophy of mathematics

Book.  300 pages.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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Table of Contents

Introduction in The Nature of Mathematical Knowledge

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Epistemological Preliminaries in The Nature of Mathematical Knowledge

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The Apriorist Program in The Nature of Mathematical Knowledge

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Mathematical Intuition in The Nature of Mathematical Knowledge

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Conceptualism in The Nature of Mathematical Knowledge

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Toward a Defensible Empiricism in The Nature of Mathematical Knowledge

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Mathematical Reality in The Nature of Mathematical Knowledge

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Mathematical Change and Scientific Change in The Nature of Mathematical Knowledge

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Mathematical Changes in The Nature of Mathematical Knowledge

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Patterns of Mathematical Change in The Nature of Mathematical Knowledge

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