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The Philosophy of Mathematics: An Introductory Essay

Publisher: 
Dover Publications
Number of Pages: 
198
Price: 
10.95
ISBN: 
0486250482
Date Received: 
Monday, July 17, 2006
Reviewable: 
No
Include In BLL Rating: 
Yes
Reviewer Email Address: 
Stephan Körner
Series: 
Hutchinson University Library: Philosophy.
Publication Date: 
1986
Format: 
Paperback
Category: 
Monograph

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
Publish Book: 
Modify Date: 
Monday, July 17, 2006

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