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

From Brouwer to Hilbert

The Debate on the Foundations of Mathematics in the 1920s

By: Paolo Mancosu (Editor)

Paperback

Published: 1st September 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 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.

"A first-rate contribution to the field."--Mircea Dumitru, Tulane University "This is an extremely useful collection which makes possible a good course on Intuitionist Logic and Mathematics."--Mary Tiles, University of Hawaii at Manoa

Preface Part I. L. E. J. Brouwer Brouwer's Intuitionist ProgrammeWalter 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 ExcursionPaolo 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 MathematicsPaolo 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 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. 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 Index

ISBN: 9780195096323
ISBN-10: 0195096320
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 352
Published: 1st September 1997
Country of Publication: US
Dimensions (cm): 23.37 x 15.49  x 1.85
Weight (kg): 0.5