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by Stephan Körner
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ISBN: 0486471853 Dover Publications Price: $9.95 |
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This lucid and comprehensive essay by a distinguished philosopher surveys the views of Plato, Aristotle, Leibniz, and Kant on the nature of mathematics. It examines the propositions and theories of the schools these philosophers inspired, and it concludes by discussing the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
Reprint of the Hutchinson & Co., Ltd., London, 1968 edition.
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Table of Contents for The Philosophy of Mathematics: An Introductory Essay
Preface Introduction SOME OLDER VIEWS Plato's account Some views of Aristotle Leibniz's philosophy of mathematics Kant: some of his views MATHEMATICS AS LOGIC: EXPOSITION The programme The logic of truth-functions On the logic of classes On the logic of quantification On the logicist systems MATHEMATICS AS LOGIC: CRITICISM The logicist account of logic The logicist conflation of empirical and non-empirical concepts The logicist theory of mathematical infinity The logicist account of geometry MATHEMATICS AS THE SCIENCE OF FORMAL SYSTEMS: EXPOSITION The programme Finite methods and infinite totalities Formal systems and formalizations Some results of metamathematics MATHEMATICS AS THE SCIENCE OF FORMAL SYSTEMS: CRITICISM The formalist account of pure mathematics The formalist account of applied mathematics The concept of actual infinity The formalist conception of logic MATHEMATICS AS THE ACTIVITY OF INTUITIVE CONSTRUCTIONS: EXPOSITION The programme Intuitionist mathematics Intuitionist logic MATHEMATICS AS THE ACTIVITY OF INTUITIVE CONSTRUCTIONS: CRITICISM Mathematical theorems as reports on intuitive constructions Intuitionism and the logical status of applied mathematics The intuitionist conception of mathematical infinity Interrelations between formalism and intuitionism THE NATURE OF PURE AND APPLIED MATHEMATICS Exact and inexact concepts Pure mathematics disconnected from perception Mathematical existence-propositions The nature of applied mathematics Mathematics and philosophy Appendix A. On the classical theory of real numbers Appendix B. Some suggestions for further reading Index