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

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. Pt. 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 -- Pt. 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. Edited By Paolo Mancosu. Includes Bibliographical References And Index. Most contemporary work in the foundations of mathematics takes its start from the groundbreaking contributions of, among others, Hilbert, Brouwer, Bernays, and Weyl. This book offers an introduction to the debate on the foundations of mathematics during the 1920s and presents the English reader with a selection of 25 translated articles central to the debate. It is intended for undergraduate and graduate courses in the philosophy of mathematics Offering an introduction to the debate on the foundations of mathematics during the 1920s, this volume contains 25 articles central to the debate. It begins with the contributions of Hilbert, and others and is intended for undergraduate and graduate courses in the philosophy of mathematics Luitzen Egbertus Jan Brouwer (1881-1966) is a central figure in the history of contemporary mathematics and philosophy.