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From Brouwer To Hilbert

The Debate on the Foundations of Mathematics in the 1920s

Edited by Paolo Mancosu

Publication Date - September 1997

ISBN: 9780195096323

352 pages
6-1/8 x 9-1/4 inches

In Stock


From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. The articles have been translated for the first time from Dutch, French, and German, and the volume is divided into four sections devoted to (1) Brouwer, (2) Weyl, (3) Bernays and Hilbert, and (4) the emergence of intuitionistic logic. Each section opens with an introduction which provides the necessary historical and technical context for understanding the articles. Although most contemporary work in this field takes its start from the groundbreaking contributions of these major figures, a good, scholarly introduction to the area was not available until now. Unique and accessible, From Brouwer To Hilbert will serve as an ideal text for undergraduate and graduate courses in the philosophy of mathematics, and will also be an invaluable resource for philosophers, mathematicians, and interested non-specialists.

About the Author(s)

Paolo Mancosu is Assistant Professor of Philosophy at the University of California at Berkeley. His main interests are in mathematical logic and philosophy of mathematics. He is the author of Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (OUP, 1996).

Table of Contents

    Part I. L. E. J. Brouwer
    Brouwer's Intuitionist Programme Walter P. van Stigt
    1. Brouwer, Intuitionist Set Theory
    2. Brouwer, Does Every Real Number Have a Decimal Expansion?
    3. Brouwer, Proof that Every Full Function is Uniformly Continuous
    4. Brouwer, Intuitionist Reflections on Formalism
    5. Brouwer, Mathematics, Science, and Language
    6. Brouwer, The Structure of the Continuum
    Part II. H. Weyl
    Hermann Weyl: Predicativity and an Intuitionistic Excursion Paolo Mancosu
    7. Weyl, On the New Foundational Crisis of Mathematics
    8. Brouwer, Comments on Weyl 1921
    9. Weyl, The Current Epistemological Situation in Mathematics
    10. Holder, The Alleged Circulus Vitiosus and the So-Called Foundational Crisis in Analysis
    Part III. P. Bernays and D. Hilbert
    Hilbert and Bernays on Mathematics Paolo Mancosu
    11. Bernays, Hilbert's Significance for the Philosophy of Mathematics
    12. Hilbert, The New Grounding of Mathematics: First Report
    13. Bernays, On Hilbert's Thoughts Concerning the Grounding of Arithmetic
    14. Bernays, Reply to the Note by Mr. Aloys Muller "On Numbers as Signs"
    15. Hilbert, Problems of the Grounding of Mathematics
    16. Bernays, The Philosophy of Mathematics and Hilbert's Proof Theory
    17. Hilbert, The Grounding of Elementary Number Theory
    Part IV. Intuitionistic Logic
    Intuitionistic Logic Paolo Mancosu and Walter P. van Stigt
    18. Brouwer, Intuitionist Splitting of the Fundamental Notions of Mathematics (Dutch Version)
    19. Brouwer, Intuitionist Splitting of the Fundamental Notions of Mathematics (German Version)
    20. Brouwer, Addendum to "Intuitionist Splitting of the Fundamental Notions of Mathematics"
    21. Borel, Concerning the Recent Discussion between Mr. R. Wavre and Mr. P. Levy
    22. Glivenko, On Some Points of the Logic of Mr. Brouwer
    23. Heyting, On Intuitionistic Logic
    24. Heyting, The Formal Rules of Intuitionistic Logic
    25. Kolmogorov, On the Interpretation of Intuitionistic Logic