From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s by Paolo Mancosu

From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s

EditorPaolo Mancosu

Paperback | August 1, 1997

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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 inproof 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 articleshave 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 necessaryhistorical 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 ToHilbert 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

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).

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Title:From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920sFormat:PaperbackDimensions:352 pages, 6.1 × 9.09 × 0.71 inPublished:August 1, 1997Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195096320

ISBN - 13:9780195096323

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Table of Contents

PrefacePart I. L. E. J. BrouwerBrouwer's Intuitionist ProgrammeWalter P. van Stigt: 1. Brouwer, Intuitionist Set Theory2. Brouwer, Does Every Real Number Have a Decimal Expansion?3. Brouwer, Proof that Every Full Function is Uniformly Continuous4. Brouwer, Intuitionist Reflections on Formalism5. Brouwer, Mathematics, Science, and Language6. Brouwer, The Structure of the ContinuumPart II. H. WeylHermann Weyl: Predicativity and an Intuitionistic ExcursionPaolo Mancosu: 7. Weyl, On the New Foundational Crisis of Mathematics8. Brouwer, Comments on Weyl 19219. Weyl, The Current Epistemological Situation in Mathematics10. Holder, The Alleged Circulus Vitiosus and the So-Called Foundational Crisis in AnalysisPart III. P. Bernays and D. HilbertHilbert and Bernays on MathematicsPaolo Mancosu: 11. Bernays, Hilbert's Significance for the Philosophy of Mathematics12. Hilbert, The New Grounding of Mathematics: First Report13. Bernays, On Hilbert's Thoughts Concerning the Grounding of Arithmetic14. Bernays, Reply to the Note by Mr. Aloys Muller "On Numbers as Signs"15. Hilbert, Problems of the Grounding of Mathematics16. Bernays, The Philosophy of Mathematics and Hilbert's Proof Theory17. Hilbert, The Grounding of Elementary Number TheoryPart IV. Intuitionistic LogicIntuitionistic LogicPaolo 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. Levy22. Glivenko, On Some Points of the Logic of Mr. Brouwer23. Heyting, On Intuitionistic Logic24. Heyting, The Formal Rules of Intuitionistic Logic25. Kolmogorov, On the Interpretation of Intuitionistic LogicIndex

Editorial Reviews

"This is an extremely useful collection which makes possible a good course on Intuitionist Logic and Mathematics."--Mary Tiles, University of Hawaii at Manoa