Collected Works: Volume II: Publications 1938-1974

ISBN-13: 9780195039726 / Angielski / Twarda / 1989 / 432 str.

Kurt Godel; Stephen C. Kleene; Solomon Feferman

Opis

Kurt Godel was the most outstanding logician of the twentieth century, famous for his work 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 computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting "time-travel" into the past.
This second volume of a comprehensive edition of Godel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.
Collected Works is 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. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century.

Recenzje

This is the second volume of this impressive series of Gödel's works ... this second volume of his published works is really fundamental, as it was only in this period that Gödel decided to make public some traits of his philosophical position ... The introductory note to these writings, by R. Solovay, seems to me historically and technically superb. I congratulate the editorial team for including in this volume the improved 1972 version of the Dialectica paper of 1958 on finitary mathematics ... As a whole, the book is absolutely indispensable for anyone interested in Gödel's ideas, or generally on the history and philosophy of logic and mathematics.

Spis treści

Gödel 1938: Introductory note to 1938, 1939, 1939a, and 1940 by Robert M. Solovay; The consistency of the axiom of choice and of the generalized continuum hypothesis; Gödel 1939: the consistency of the generalized continuum hypothesis; Gödel 1939a: Consistency proof for the generalized continuum hypothesis; Gödel 1940: the consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory; Gödel 1944: Introductory note to 1944 by Charles Parsons; Russell's mathematical logic; Gödel 1946: Introductory note to 1946 by Charles Parsons; Remarks before the Princeton bicentennial conference on problems in mathematics; Gödel 1947: Introductory note to 1947 and 1964 by Gregory H. Moore; What is Cantor's continuum problem?; Gödel 1949: Introductory note to 1949 and 1952 by S.W. Hawking; An example of a new type of cosmological solutions of Einstein's field equations of gravitation; Gödel 1949a: Introductory note to 1949a by Howard Stein; A remark about the relationship between relativity theory and idealistic philosophy; Gödel 1952: Rotaoting universes in general relativity theory; Gödel 1958: Introductory note to 1958 and 1972 by A.S. Troelstra; Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes; On a hitherto unutilized extension of the finitary standpoint; Gödel 1962: postscript to Spector 1962; Gödel 1964: What is Cantor's continuum problem? Gödel 1972: On an extension of finitary mathematics which has not yet been used; Gödel 1972a: Introductory note to 1972a by Solomon Feferman, Robert M. Solovay, and Judson C. Webb; Some remarks on the undecidability results; Gödel 1974: Introductory note to 1974 by Jens Erik Fenstad; Remark on non-standard analysis; Textual notes; References.