Collected Works Volume III: Unpublished Essays and Lectures

by Godel, Kurt; Feferman, S.; Dawson, John W.; Goldfarb, Warren; Parsons, Charles; Solovay, R.

• ISBN13: 9780195147223
• ISBN10: 0195147227
• Format: Paperback
• Copyright: 2001-05-31
• Publisher: Oxford University Press

Summary

Kurt Godel (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 notedfor 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 creativeaccomplishment. The first two volumes were devoted to Godel'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 This third volume features a wide selection of unpublished articles and lecture texts found in Godel's Nachlass, documents that enlarge considerably our appreciation of hisscientific and philosophical thought and add a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 ofmaterial originally written in German (some transcribed from Gabelsberger shorthand), and a complete bibliography. A succeeding volume is to contain a comprehensive selection of Godel's scientific correspondence and a complete inventory of his Nachlass. The books are designed to be accessible anduseful 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 computerscience.

Table of Contents

List of illustrations	xvii
The Nachlass of Kurt Godel: an overview	1	(6)
John W. Dawson, Jr
Godel's Gabelsberger shorthand	7	(6)
Cheryl A. Dawson
Godel *1930c: Introductory note to *1930c	13	(17)
Warren Goldfarb
Vortrag uber Vollstandigkeit des Funktionenkalkuls	16	(1)
Lecture on completeness of the functional calculus	17	(13)
Godel *1931?: Introductory note to *1931?	30	(6)
Stephen C. Kleene
[Uber unentscheidbare Satze]	30	(1)
[On undecidable sentences]	31	(5)
Godel *1933o: Introductory note to *1933o	36	(18)
Solomon Feferman
The present situation in the foundations of mathematics	45	(9)
Godel *1933?: Introductory note to *1933?	54	(8)
Israel Halperin
Vereinfachter Beweis eines Steinitzschen Satzes	56	(1)
Simplified proof of a theorem of Steinitz	57	(5)
Godel *1938a: Introductory note to *1938a	62	(52)
Wilfried Sieg
Charles Parsons
Vortrag bei Zilsel	86	(1)
Lecture at Zilsel's	87	(27)
Godel *1939b: Introductory note to *1939b and *1940a	114	(42)
Robert M. Solovay
Vortrag Gottingen	126	(1)
Lecture at Gottingen	127	(29)
Godel *193?: Introductory note to *193?	156	(19)
Martin Davis
[Undecidable diophantine propositions]	164	(11)
Godel *1940a: (See Introductory note under Godel *1939b.) Lecture [on the] consistency [of the] continum hypothesis (Brown University)	175	(11)
Godel *1941: Introductory note to *1941	186	(16)
A.S. Troelstra
In what sense is intuitionistic logic constructive?	189	(13)
Godel *1946/9: Introductory note to *1946/9	202	(59)
Howard Stein
Some observations about the relationship between theory of relativity and Kantian philosophy
---[Version B2]	230	(17)
---[Version C1]	247	(14)
Godel *1949b: Introductory note to *1949b	261	(29)
David B. Malament
Lecture on rotating universes	269	(21)
Godel *1951: Introductory note to *1951	290	(34)
George Boolos
Some basic theorems on the foundations of mathematics and their implications	304	(20)
Godel *1953/9: Introductory note to *1953/9	324	(40)
Warren Goldfarb
Is mathematics syntax of language?
---Version III	334	(22)
---Version V	356	(8)
Godel *1961/?: Introductory note to *1961/?	364	(24)
Dagfinn Follesdal
The modern development of the foundations of mathematics in the light of philosophy [German transcript]	374	(1)
The modern development of the foundations of mathematics in the light of philosophy [English translation]	375	(13)
Godel *1970: Introductory note to *1970	388	(17)
Robert M. Adams
Ontological proof	403	(2)
Godel *1970a: Introductory note to *1970a, *1970b and *1970c	405	(21)
Robert M. Solovay
Some considerations leading to the probable conclusion that the true power of the continuum is N2	420	(2)
Godel *1970b: (See introductory note under Godel *1970a.)
A proof of Cantor's continuum hypothesis from a highly plausible axiom about orders of growth	422	(2)
Godel *1970c: (See introductory note under Godel *1970a.)
[Unsent letter to Alfred Tarski]	424	(2)
Appendix A: Excerpt from *1946/9-A	426	(3)
Appendix B: Texts relating to the ontological proof	429	(10)
Textual notes	439	(40)
References	479	(38)
Addenda and corrigenda to Volumes I and II	517	(3)
Addendum to this volume	520	(1)
Index	521