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