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Philosophy of Mathematics

Philosophy of Mathematics
Selected Readings

2nd Edition

CAD$56.95 (G)

Rudolf Carnap, Arend Heyting, Johann von Neumann, L. E. J. Brouwer, Michael Dummett, Gottlob Frege, Bertrand Russell, David Hilbert, Haskell B. Curry, Georg Kreisel, Paul Bernays, Paul Benacerraf, Hilary Putnam, Alfred Jules Ayer, W. V. Quine, Carl G. Hempel, Henri Poincaré, Kurt Gödel, George Boolos, Hao Wang
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  • Date Published: January 1984
  • availability: Available
  • format: Paperback
  • isbn: 9780521296489

CAD$ 56.95 (G)
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  • 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.

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    Product details

    • Edition: 2nd Edition
    • Date Published: January 1984
    • format: Paperback
    • isbn: 9780521296489
    • length: 612 pages
    • dimensions: 232 x 153 x 39 mm
    • weight: 0.91kg
    • availability: Available
  • 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 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.

  • Editors

    Paul Benacerraf

    Hilary Putnam

    Contributors

    Rudolf Carnap, Arend Heyting, Johann von Neumann, L. E. J. Brouwer, Michael Dummett, Gottlob Frege, Bertrand Russell, David Hilbert, Haskell B. Curry, Georg Kreisel, Paul Bernays, Paul Benacerraf, Hilary Putnam, Alfred Jules Ayer, W. V. Quine, Carl G. Hempel, Henri Poincaré, Kurt Gödel, George Boolos, Hao Wang

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