Philosophy of Mathematics

Philosophy of Mathematics : Selected Readings

4.34 (69 ratings by Goodreads)
Edited by  , Edited by 

List price: US$195.00

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

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 Godel. 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 Godel 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.show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • Revised
  • 2nd Revised edition
  • 1139171518
  • 9781139171519

Table of contents

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 Poincare; 21. Mathematical truth Paul Benacerraf; 22. Models and reality Hilary Putnam; Part IV. The Concept of Set: 23. Russell's mathematical logic Kurt Godel; 24. What in Cantor's continuum problem? Kurt Godel; 25. The iterative concept of set George Boolos; 26. The concept of set Hao Wang; Bibliography.show more

Rating details

69 ratings
4.34 out of 5 stars
5 49% (34)
4 39% (27)
3 9% (6)
2 3% (2)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X