Kitcher P. The Nature of Mathematical Knowledge

New York; Oxford: Oxford University Press, 1984. — 300 p. — ISBN: 0-19-503541-0.This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.Epistemological Preliminaries
The Apriorist Program
Mathematical Intuition
Conceptualism
Toward a Defensible Empiricism
Mathematical Reality
Mathematical Change and Scientific Change
Mathematical Changes
Patterns of Mathematical Change
The Development of Analysis: A Case Study