Kurt Godël Collected Works - Volume III

Kurt Gödel (1906-1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory and stronger systems, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, the foundations of computation theory, unusual cosmological models, and for the strong individuality of his writings on the philosophy of mathematics. The Collected Works is a landmark resource that draws together a lifetime of creative accomplishment. The first two volumes were devoted to Gödel's publications in full (both in the original and translation). This third volume features a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass, documents that enlarge considerably our appreciation of his scientific and philosophical thought and add a great deal to our understanding of his motivations. Continuing the format of the earlier volumes, the present volume includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, English translations of material originally written in German (some transcribed from Gabelsberger shorthand), and a complete bibliography. A succeeding volume is to contain a comprehensive selection of Gödel's scientific correspondence and a complete inventory of his Nachlass. The books are designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science.

Contents

• 1 John W. Dawson, Jr.: The Nachlass of Kurt Gödel: an overview
• 2 Cheryl A. Dawson: Gödel's Gabelsberger shorthand
• 3 Warren Goldfarb: Gödel *1930c: Introductory note to *1930c
• 4 Lecture on completeness of the functional calculus
• 5 Stephen C. Kleene: Gödel *1931?: Introductory note to *1931?
• 6 On undecidable sentences
• 7 Solomon Feferman: Godel *1933c: Introductory note to *1933c
• 8 The present situation in the foundations of mathematics
• 9 Israel Halperin: Godel *1933?: Introductory note to *1933?
• 10 Simplified proof of a theorem of Steinitz
• 11 Wilfried Sieg and Charles Parsons: Godel *1938a: Introductory note to *1938a
• 12 Lecture at Zilsel's
• 13 Robert M. Solovay: Godel *1939b: Introductory note to *1939b and *1940a
• 14 Lecture at Göttingen
• 15 Martin Davis: Godel *193?: Introductory note to *193?
• 16 Undecidable diophantine propositions
• 17 Godel *1940a
• 18 Lecture on the consistency of the continuum hypothesis
• 19 A.S. Troelstra: Godel *1941: Introductory note to *1941
• 20 In what sense is intuitionistic logic constructive?
• 21 Howard Stein: Godel *1946/9: Introductory note to *1946/9
• 22 Some observations about the relationship between theory of relativity and Kantian philosophy
• 23 David B. Malament: Godel *1949b: Introductory note to *1949b
• 24 Lecture on rotating universes
• 25 George Boolos: Godel *1951: Introductory note to *1951
• 26 Some basic theorems on the foundations of mathematics and their implications
• 27 Warren Goldfarb: Godel *1953/9: Introductory note to *1953/9
• 28 Is mathematics syntax of language? Version III
• 29 Is mathematics syntax of language? Version V
• 30 Dagfinn Føllesdal: Godel *1961/?: Introductory note to *1961/?
• 31 The modern development of the foundations of mathematics in the light of philosophy
• 32 Robert M. Adams: Godel *1970: Introductory note to *1970
• 32 Ontological proof
• 33 Robert M. Solovay: Godel *1970a: Introductory note to *1970a, *1970b and *1970c
• 34 Some considerations leading to the probable conclusion that the true power of the continuum is N[2
• 35 Godel *1970b
• 36 A proof of Cantor's continuum hypothesis from a highly plausible axiom about orders of growth
• 37 Godel *1970c
• 38 Unsent letter to Alfred Tarski
• Appendix A: Excerpt from *1946/9-A
• Appendix B: Texts relating to the ontological proof </</body>