Philosophy of Mathematics
Selected Readings

Seminal articles in the philosophy of mathematics by Russell, Quine, Gödel and other major thinkers.

Paul Benacerraf (Edited by), Hilary Putnam (Edited by)

9780521296489, Cambridge University Press

Paperback, published 27 January 1984

612 pages
23.2 x 15.3 x 3.9 cm, 0.91 kg

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. 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 Poincaré
21. Mathematical truth Paul Benacerraf
22. Models and reality Hilary Putnam
Part IV. The Concept of Set: 23. Russell's mathematical logic Kurt Gödel
24. What in Cantor's continuum problem? Kurt Gödel
25. The iterative concept of set George Boolos
26. The concept of set Hao Wang
Bibliography.

Subject Areas: Philosophy of mathematics [PBB], Social & political philosophy [HPS]