The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. Preface to the second edition Introduction Part I. The Foundations of Mathematics: 1. The logicist foundations of mathematics Rudolf Carnap 2. The intuitionist foundations of mathematics Arend Heyting 3. The formalist foundations of mathematics Johann von Neumann 4. Disputation Arend Heyting 5. Intuitionism and formalism L. E. J. Brouwer 6. Consciousness, philosophy, and mathematics L. E. J. Brouwer 7. The philosophical basis of intuitionistic logic Michael Dummett 8. The concept of number Gottlob Frege 9. Selections from Introduction to Mathematical Philosophy Bertrand Russell 10. On the infinite David Hilbert 11. Remarks on the definition and nature of mathematics Haskell B. Curry 12. Hilbert's programme Georg Kreisel Part II. The Existence of Mathematical Objects: 13. Empiricism, semantics, and ontology Rudolf Carnap 14. On Platonism in mathematics Paul Bernays 15. What numbers could not be Paul Benacerraf 16. Mathematics without foundations Hilary Putnam Part III. Mathematical Truth: 17. The a priori Alfred Jules Ayer 18. Truth by convention W. V. Quine 19. On the nature of mathematical truth Carl G. Hempel 20. On the nature of mathematical reasoning Henri Poincar&#233 21. Mathematical truth Paul Benacerraf 22. Models and reality Hilary Putnam Part IV. The Concept of Set: 23. Russell's mathematical logic Kurt G&#246 del 24. What in Cantor's continuum problem? Kurt G&#246 del 25. The iterative concept of set George Boolos 26. The concept of set Hao Wang Bibliography.