The Philosophy of Mathematics: An Introductory Essay

Stephan Körner

Publisher:

Dover Publications

Publication Date:

1986

Number of Pages:

198

Format:

Paperback

Series:

Hutchinson University Library: Philosophy.

Price:

10.95

ISBN:

0486250482

Category:

Monograph

MAA Review
Table of Contents

We do not plan to review this book.

Preface; Introduction
I. Some older views
	1. Plato's account
	2. Some views of Aristotle
	3. Leibniz's philosophy of mathematics
	4. Kant: some of his views
II. Mathematics as Logic: Exposition
	1. The programme
	2. The logic of truth-functions
	3. On the logic of classes
	4. On the logic of quantification
	5. On logicist systems
III. Mathematics as Logic: Criticism
	1. The ligicist account of logic
	2. The logist conflation of empirical and non-empirical concepts
	3. The logicist theory of mathematical infinity
	4. The logicist account of geometry
IV. Mathematics as the Science of Formal Systems: Exposition
	1. The programme
	2. Finite methods and infinite totalities
	3. Formal systems and formalizations
	4. Some results of metamathematics
V. Mathematics as the Science of Formal Systems: Criticism
	1. The formalist account of pure mathematics
	2. The formalist account of applied mathematics
	3. The concept of actual infinity
	4. The formalist conception of logic
VI. Mathematics as the Activity of Intuitive Constructions: Exposition
	1. The programme
	2. Intuitionist mathematics
	3. Intuitionist logic
VII. Mathematics as the Activity of Intuitive Constructions: Criticism
	1. Mathematical theorems as reports on intuitive constructions
	2. Intuitionism and the logical status of applied mathematics
	3. The intuitionist conception of mathematical infinity
	4. Interrelations between formalism and intuitionism
VIII. The nature of pure and applied mathematics
	1. Exact and inexact concepts
	2. Pure mathematics disconnected from perception
	3. Mathematical existence-propositions
	4. The nature of applied mathematics
	5. Mathematics and philosophy
Appendix A. On the classical theory of real numbers
Appendix B. Some suggestions for further reading
Index