About the Book
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 the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past.
The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass.
All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited.
Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.
Table of Contents:
Gödel's life and workSolomon Feferman:
A Gödel chronologyJohn W. Dawson, Jr.:
Gödel 1929: Introductory note to 1929, 1930 and 1930aBurton Dreben and Jean van Heijenoort:
Über die Vollständigkeit des Logikkalküls
On the completeness of the calculus of logic
Gödel 1930: (See introductory note under Gödel 1929.)
Die Vollständigkeit der Axiome des logischen Funktionenkalküls
The completeness of the axioms of the functional calculus of logic
Gödel 1930a: (See introductory note under Gödel 1929.)
Über die Vollständigkeit des Logikkalküls
On the completeness of the calculus of logic
Gödel 1930b: Introductory note to 1930b, 1931 and 1932bStephen C. Kleene:
Einige metamathematische Resultate über Entscheidungs-definitheit und Widerspruchsfreiheit
Some metamathematical results on completeness and consistency
Gödel 1931: (See introductory note under Gödel 1930b.)
Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I
On formally undecidable propositions of Principia mathematica and related systems I
Gödel 1931a: Introductory note to 1931a, 1932e, f and gJohn W. Dawson, Jr.:
Diskussion zur Grundlegung der Mathematik
Discussion on providing a foundation for mathematics
Gödel 1931b: Review of Neder 1931
Gödel 1931c: Introductory note to 1931cSolomon Feferman:
Review of Hilbert 1931
Gödel 1931d: Review of Betsch 1926
Gödel 1931e: Review of Becker 1930
Gödel 1931f: Review of Hasse and Scholz 1928
Gödel 1931g: Review of von Juhos 1930
Gödel 1932: Introductory note to 1932A. S. Troelstra:
Zum intuitionistischen aussagenkalkül
On the intuitionistic propositional calculus
Gödel 1932a: Introductory note to 1932a, 1933i and lWarren D. Goldfarb:
Ein Spezialfall des Enscheidungsproblems der theoretischen Logik
A special case of the decision problem for theoretical logic
Gödel 1932b: (See introductory note under Gödel 1930b.)
Über Vollständigkeit und Widerspruchsfreiheit
On completeness and consistency
Gödel 1932c: Introductory note to 1932cW. V. Quine:
Eine Eigenschaft der Realisierungen des Aussagenkalküls
A property of the realizations of the propositional calculus
Gödel 1932d: Review of Skolem 1931
Gödel 1932e: (See introductory note under Gödel 1931a.)
Review of Carnap 1931
Gödel 1932f: (See introductory note under Gödel 1931a.)
Review of Heyting 1931
Gödel 1932g: (See introductory note under Gödel 1931a.)
Review of von Neumann 1931
Gödel 1932h: Review of Klein 1931
Gödel 1932i: Review of Hoensbroech 1931
Gödel 1932j: Review of Klein 1932
Gödel 1932k: Introductory note to 1932k, 1934e and 1936bStephen C. Kleene:
Review of Church 1932
Gödel 1932l: Review of Kalmár 1932
Gödel 1932m: Review of Huntington 1932
Gödel 1932n: Review of Skolem 1932
Gödel 1932o: Review of Dingler 1931
Gödel 1933: Introductory note to 1933W. V. Quine:
[[Über die Parryschen Axiome]]
[[On Parry's axioms]]
Gödel 1933a: Introductory note to 1933aW. V. Quine:
Über Unabhängigkeitsbeweise im Aussagenkalkül
On independence proofs in the propositional calculus
Gödel 1933b: Introductory note to 1933b, c, d, g and hJudson Webb:
Über die metrische Einbettbarkeit der Quadrupel des R[3 in Kugelflächen
On the isometric embeddability of quadruples of points of R[3 in the surface of a sphere
Gödel 1933c: (See introductory note under Gödel 1933b.)
Über die Waldsche Axiomatik des Zwichenbegriffes
On Wald's axiomization of the notion of betweenness
Gödel 1933d: (See introductory note under Gödel 1933b.)
Zur Axiomatik der elementargeometrischen Verknüpfungs-relationen
On the axiomatization of the relations of connection in elementary geometry
Gödel 1933e: Introductory note to 1933eA. S. Troelstra:
Zur institutionistischen Arithmetik und Zahlentheorie
On intuitionistic arithmetic and number theory
Gödel 1933f: Introductory note to 1933fA. S. Troelstra:
Eine Interpretation des institutionistischen Aussagenkalküls
An interpretation of the intuitionistic propositional calculus
Gödel 1933g: (See introductory note under Gödel 1933b.)
Bemerkung über projektive Abbildungen
Remark concerning projective mappings
Gödel 1933h: (See introductory note under Gödel 1933b.)
Diskussion über koordinatenlose Differentialgeometrie
Discussion concerning coordinate-free differential geometry
Gödel 1933i: (See introductory note under Gödel 1932a.)
Zum Enscheidungsproblem des logischen Funktionenkalküls
On the decision probelm for the functional calculus of logic
Gödel 1933j: Review of Kaczmarz 1932
Gödel 1933k: Review of Lewis 1932
Gödel 1933l: (See introductory note under Gödel 1932a.)
Review of Kalmár 1933
Gödel 1933m: Review of Hahn 1932
Gödel 1934: Introductory note to 1934Stephen C. Kleene:
On undecidable propositions of formal mathematical systems
Gödel 1934a: Review of Skolem 1933
Gödel 1934b: Introductory note to 1934bW. V. Quine:
Review of Quine 1933
Gödel 1934c: Introductory note to 1934c and 1935Robert L. Vaught:
Review of Skolem 1933a
Gödel 1934d: Review of Chen 1933
Gödel 1934e: (See introductory note under Gödel 1932k.)
Review of Church 1933
Gödel 1934f: Review of Notcutt 1934
Gödel 1935: (See introductory note under Gödel 1934c.)
Review of Skolem 1934
Gödel 1935a: Introductory note to 1935aW. V. Quine:
Review of Huntington 1934
Gödel 1935b: Review of Carnap 1934
Gödel 1935c: Review of Kalmár 1934
Gödel 1936: Introductory note to 1936John W. Dawson, Jr.:
Diskussionsbemerkung
Discussion remark
Gödel 1936a: Introductory note to 1936aRohit Parikh:
Über die Länge von Beweisen
On the length of proofs
Gödel 1936b: (See introductory note under Gödel 1932k.)
Review of Church 1935
Textual notes
References
Index
Review :
"Gödel would probably have been pleased with the systematic and neat presentation. The set should be of interest to professionals and students in the areas of logic, mathematics, [and] philosophy....For all university level libraries and for large public and college library collections....Will also be a treasure in the hands of the individual who can afford and understand a good part of the contents." --New Technical Books, The New York Public
Library
"The editors are to be wholeheartedly congratulated on bringing to the public work which deserves careful study and which ought to do something to revitalise the philosophy of mathematics by presenting a point of view that, unusually, combines intellectual rigour with a willingness to make bold and sweeping metaphysical claims." --The Times Higher Education Supplement
"Should find a place in all academic libraries where mathematical logic is taught....The editors deserve the highest praise for the design of the edition."--Choice
"Anyone interested in the life and work of Kurt Gödel, or in the history of mathematical logic in this century, is indebted to all of the contributors to this volume for the care with which they have presented Gödel's work. They have succeeded in using their own expertise to elucidate both the nature and significance of what Gödel and, in turn, mathematical logic have accomplished in this century."--Isis
"A marvel of selfless scholarly teamwork. Under the leadership of Solomon Feferman, many of the world's most eminent logicians and historians of logic have pooled their talents to produce lucid and informative introductions, helpful notes, and clear facing-page translations. It is no small tribute to Gödel to recognize that he deserves this coordination of patient work by brilliant scholars. Equally, it is no small tribute to those who have worked on
this volume to say that their efforts are worthy of their subject." --Times Literary Supplement
"From the example of this first volume, the edition promises to be a model of its kind; virtually nothing could be bettered....The whole is beautifully produced...the translations are clear and accurate....Anyone interested in mathematical logic must...wish to own this first volume of [Gödel's] collected works, which is a worthy tribute to a great man. Feferman and his team are to be congratulated on the care, sureness of touch, and scholarly accuracy
with which they have carried out their task, and we must look forward to the appearance of the subsequent volumes."--Mind
"Beautifully prepared, meticulously edited collection." --The Journal of Symbolic Logic
"The publication of this book is a significant scientific event not only in mathematical logic...but also in formal computing systems, recursive computing theory, and the possibility and limits of mechanical theorem proving...This volume is a splendid text. The original German and an excellent English translation are printed on facing pages. The introductory notes add much to the reader's understanding of the primary material, and the list of editors and
contributors reads like a Who's Who of modern logic. The bibliographic references are extensive and worth explaining in themselves; they probably constitute a guide to the subject in their own right...it
is an opportunity to experience firsthand the complexity, elegance, and rigor of one of the great minds of the twentieth century. I look forward to coming volumes."--Computing Reviews
"Both books are models of what scholarly editions of this kind should be like. . .no one working in logic or in the philosophy of mathematics should be without their own copies." --Philosophia Mathematica
"The writing throughout exemplifies the clarity, care and incisiveness for which its author is renowned. This is a stimulating book that can be read and reread with intellectual pleasure and profit."--Modern Logic
"Gödel would probably have been pleased with the systematic and neat presentation. The set should be of interest to professionals and students in the areas of logic, mathematics, [and] philosophy....For all university level libraries and for large public and college library collections....Will also be a treasure in the hands of the individual who can afford and understand a good part of the contents." --New Technical Books, The New York Public
Library
"The editors are to be wholeheartedly congratulated on bringing to the public work which deserves careful study and which ought to do something to revitalise the philosophy of mathematics by presenting a point of view that, unusually, combines intellectual rigour with a willingness to make bold and sweeping metaphysical claims." --The Times Higher Education Supplement
"Should find a place in all academic libraries where mathematical logic is taught....The editors deserve the highest praise for the design of the edition."--Choice
"Anyone interested in the life and work of Kurt Gödel, or in the history of mathematical logic in this century, is indebted to all of the contributors to this volume for the care with which they have presented Gödel's work. They have succeeded in using their own expertise to elucidate both the nature and significance of what Gödel and, in turn, mathematical logic have accomplished in this century."--Isis
"A marvel of selfless scholarly teamwork. Under the leadership of Solomon Feferman, many of the world's most eminent logicians and historians of logic have pooled their talents to produce lucid and informative introductions, helpful notes, and clear facing-page translations. It is no small tribute to Gödel to recognize that he deserves this coordination of patient work by brilliant scholars. Equally, it is no small tribute to those who have worked on
this volume to say that their efforts are worthy of their subject." --Times Literary Supplement
"From the example of this first volume, the edition promises to be a model of its kind; virtually nothing could be bettered....The whole is beautifully produced...the translations are clear and accurate....Anyone interested in mathematical logic must...wish to own this first volume of [Gödel's] collected works, which is a worthy tribute to a great man. Feferman and his team are to be congratulated on the care, sureness of touch, and scholarly accuracy
with which they have carried out their task, and we must look forward to the appearance of the subsequent volumes."--Mind
"Beautifully prepared, meticulously edited collection." --The Journal of Symbolic Logic
"The publication of this book is a significant scientific event not only in mathematical logic...but also in formal computing systems, recursive computing theory, and the possibility and limits of mechanical theorem proving...This volume is a splendid text. The original German and an excellent English translation are printed on facing pages. The introductory notes add much to the reader's understanding of the primary material, and the list of editors and
contributors reads like a Who's Who of modern logic. The bibliographic references are extensive and worth explaining in themselves; they probably constitute a guide to the subject in their own right...it
is an opportunity to experience firsthand the complexity, elegance, and rigor of one of the great minds of the twentieth century. I look forward to coming volumes."--Computing Reviews
"Both books are models of what scholarly editions of this kind should be like. . .no one working in logic or in the philosophy of mathematics should be without their own copies." --Philosophia Mathematica
"The writing throughout exemplifies the clarity, care and incisiveness for which its author is renowned. This is a stimulating book that can be read and reread with intellectual pleasure and profit."--Modern Logic
"A comprehensive edition of the 20th-century logician's work, in facing pages of German and English. This first volume covers published writings in the period 1929-36, beginning with his dissertation, which was previously only available through the University of Vienna. Each selection or group of selections is introduced. In addition, mathematician and philosopher Solomon Feferman contributes a biographical essay on Gödel's life and work."--SciTech
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