Kurt Gödel (goedel-k)

Contributions to Philosophie.ch

Bibliography

Carnap, Rudolf, Hahn, Hans, Neumann, John von, Heyting, Arend, Gödel, Kurt and Reidemeister, Kurt. 1931. “Diskussion zur Grundlegung der Mathematik.” Erkenntnis 2: 135–149. Reprinted in Gödel (1986).
Gödel, Kurt. 1929. “Über die Vollständigkeit des Logikkalküls.” in Collected Works. Volume I: Publications 1929–1936, pp. 60–101. Oxford: Oxford University Press. Doctoral thesis, University of Vienna, doi:10.1093/oso/9780195147209.001.0001.
Gödel, Kurt. 1930a. “Die Vollständigkeit der Axiome des logischen Funktionenkalküls.” Monatshefte für Mathematik und Physik 37: 349–360. Reprinted in Gödel (1986, 102–123) and translated by Stefan Bauer-Mengelberg in van Heijenoort (1967, 582–591), doi:10.1007/BF01696781.
Gödel, Kurt. 1930b. “Einige metamathematische Resultate über Entscheidungsdefinitheit und Widerspruchsfreiheit.” Anzeiger der Akademie der Wissenschaften in Wien, Mathematisch-naturwissenschaftliche Klasse 67: 214–215. Reprinted in Gödel (1986, 140–143) and translated by Stefan Bauer-Mengelberg in van Heijenoort (1967, 595–596).
Gödel, Kurt. 1930c. “Vortrag über Vollständigkeit des Funktionenkalküls.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 16–29. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1930d. “Ein Spezialfall des Entscheidungsproblems der theoretischen Logik.” Ergebnisse eines mathematischen Kolloquiums 2: 27–28. Reprinted and translated in Gödel (1986, 230–233), reprinted, with the original page numbers, in Menger (1998, 145–146).
Gödel, Kurt. 1931a. “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.” Monatshefte für Mathematik und Physik 38: 173–198. English translation in van Heijenoort (1967, 596–616); reprinted in Gödel (1986, 145–195), doi:10.1007/BF01700692.
Gödel, Kurt. 1931b. “Besprechung von Hilbert (1931).” Zentralblatt für Mathematik und ihre Grenzgebiete 1: 260. English translation in van Heijenoort (1967, 596–616); reprinted in Gödel (1986, 213/214).
Gödel, Kurt. 1931c. “Über unentscheidbare Sätze.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 30–35. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1931d. “Über Vollständigkeit und Widerspruchsfreiheit.” Ergebnisse eines mathematischen Kolloquiums 3: 12–13. Translated in van Heijenoort (1967, 616–617), reprinted in Gödel (1986, 234–237), reprinted, with the original page numbers, in Menger (1998, 168).
Gödel, Kurt. 1932a. “Zum intuitionistischen Aussagenkalkül.” Anzeiger der Akademie der Wissenschaften in Wien, Mathematisch-naturwissenschaftliche Klasse 69: 65–66. Reprinted and translated in Gödel (1986, 222–225).
Gödel, Kurt. 1932b. “Zur intuitionistischen Arithmetik und Zahlentheorie.” Ergebnisse eines mathematischen Kolloquiums 4: 34–38. Reprinted and translated in Gödel (1986, 286–295), reprinted, with the original page numbers, in Menger (1998, 216–220).
Gödel, Kurt. 1933a. “Vereinfachter Beweis eines Steinitzschen Satzes.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 56–61. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1933b. “Eine Interpretation des intuitionistischen Aussagenkalküls.” Ergebnisse eines mathematischen Kolloquiums 4: 39–40. Reprinted and translated in Gödel (1986, 300/301), reprinted, with the original page numbers, in Menger (1998, 221–222).
Gödel, Kurt. 1933c. “Zum Entscheidungsproblem des Funktionenkalküls.” Monatshefte für Mathematik und Physik 40: 433–443. Reprinted and translated in Gödel (1986, 306–326), doi:10.1007/BF01708881.
Gödel, Kurt. 1933d. “The Present Situation in the Foundations of Mathematics.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 45–53. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1934. “On Undecidable Propositions of Formal Mathematical Systems.” Lecture notes by Stephen Cole Kleene and John Barkley Rosser, reprinted with revisions in Davis (1965, 39–74) and in Gödel (1986, 346–372).
Gödel, Kurt. 1935. “Über die Länge von Beweisen.” Ergebnisse eines mathematischen Kolloquiums 7: 23–24. Reprinted and translated in Gödel (1986, 396–398), reprinted, with the original page numbers, in Menger (1998, 341–342).
Gödel, Kurt. 1938a. “The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis.” Proceedings of the National Academy of Sciences of the U.S.A. 24: 556–557. Reprinted in Gödel (1990, 26).
Gödel, Kurt. 1938b. “Vortrag bei Zilsel.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 86–113. Oxford: Oxford University Press. Translation by Charles Parsons, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1939a. “The Consistency of the Generalized Continuum Hypothesis.” Bulletin of the American Mathematical Society 45: 93. Reprinted in Gödel (1990, 27).
Gödel, Kurt. 1939b. “Consistency-Proof of the Generalized Continuum-Hypothesis.” Proceedings of the National Academy of Sciences of the U.S.A. 25: 220–224. Reprinted in Gödel (1990, 28).
Gödel, Kurt. 1939c. “Vortrag Göttingen.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 126–155. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1940. “The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory.” Annals of Mathematical Studies 3. Lecture notes taken by George W. Brown, reprinted with additional notes as Gödel (1951b) and with further notes as Gödel (1966); reprinted in Gödel (1990, 33–101).
Gödel, Kurt. 1941. “In What Sense is Intuitionistic Logic Constructive?” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 189–201. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1944. “Russell’s Mathematical Logic.” in The Philosophy of Bertrand Russell, edited by Paul Arthur Schilpp, pp. 125–154. The Library of Living Philosophers n. 5. LaSalle, Illinois: Open Court Publishing Co. Reprinted in Pears (1972, 192–226) and Gödel (1990, 119–143).
Gödel, Kurt. 1946. “Remarks before the Princeton Bicentennial Conference on Problems in Mathematics.” in The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Fonctions, edited by Martin Davis, pp. 84–87. Hewlett, New York: Raven Press. Reprinted in Gödel (1990, 150–153).
Gödel, Kurt. 1947. “What is Cantor’s Continuum Problem?” American Mathematical Monthly 54: 515–525. Revised and expanded version in Benacerraf and Putnam (1964, 258–273), reprinted in Gödel (1990, 176–188).
Gödel, Kurt. 1949a. “A Remark about the Relationship between Relativity Theory and Idealistic Philosophy.” in Albert Einstein: Philosopher-Scientist, edited by Paul Arthur Schilpp, pp. 555–562. The Library of Living Philosophers n. 7. LaSalle, Illinois: Open Court Publishing Co. Reprinted in Gödel (1990, 202–207).
Gödel, Kurt. 1949b. “Lecture on Rotating Universes.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 269–289. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1951a. “Some Basic Theorems on the Foundations of Mathematics and their Philosophical Implications (1951).” in Kurt Gödel: Unpublished Philosophical Essays, edited by Francisco A. Rodrı́guez Consuegra, pp. 129–158. Basel: Birkhäuser. Reprinted in Gödel (1990, 304–323).
Gödel, Kurt. 1951b. The Consistency of the Continuum Hypothesis. Princeton, New Jersey: Princeton University Press. Lectures notes taken by George W. Brown, 2nd printing, with additional notes.
Gödel, Kurt. 1953. “Is Mathematics Syntax of Language?” in Kurt Gödel: Unpublished Philosophical Essays, edited by Francisco A. Rodrı́guez Consuegra, pp. 171–218. Basel: Birkhäuser. Also in Gödel (1995, 334–363).
Gödel, Kurt. 1958. “Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes.” Dialectica 12(47–48): 280–287. English translation published as Gödel (1980); reprinted in Gödel (1990, 241–252), doi:10.1111/j.1746-8361.1958.tb01464.x.
Gödel, Kurt. 1961. “The Modern Development of the Foundations of Mathematics in the Light of Philosophy.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 374–387. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1965a. “On Formally Undecidable Propositions of Principia Mathematica and Related Systems I.” in The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Fonctions, edited by Martin Davis, pp. 4–38. Hewlett, New York: Raven Press. Translation, by Elliott Mendelsohn, of Gödel (1931a).
Gödel, Kurt. 1965b. “On Intuitionistic Arithmetic and Number Theory.” in The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Fonctions, edited by Martin Davis, pp. 75–81. Hewlett, New York: Raven Press. Translation, by Martin Davies, of Gödel (1933a).
Gödel, Kurt. 1965c. “On the Length of Proofs.” in The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Fonctions, edited by Martin Davis, pp. 82–83. Hewlett, New York: Raven Press. Translation, by Martin Davies, of Gödel (1935).
Gödel, Kurt. 1966. The Consistency of the Continuum Hypothesis. Princeton, New Jersey: Princeton University Press. Lectures notes taken by George W. Brown, 3rd printing, with further notes.
Gödel, Kurt. 1970. “Ontological Proof.” in Collected Works. Volume III: Unpublished Essays and Lectures, pp. 403–404. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1972a. “La complétude des axiomes du calcul fonctionnel.” in Logique mathématique, Textes, edited by Jean Largeault, pp. 175–185. U Epistémologie. Paris: Armand Colin. Traduction de Gödel (1930a).
Gödel, Kurt. 1972b. “Some Remarks on the Undecidability Results.” in Collected Works. Volume II: Publications 1938–1974, pp. 305–306. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay and Jean van Heijenoort, doi:10.1093/oso/9780195147216.001.0001.
Gödel, Kurt. 1980. “On a Hitherto Unexploited Extension of the Finitary Standpoint.” The Journal of Philosophical Logic 9(2): 133–142. Reprinted in Gödel (1990, 271–280), doi:10.1007/bf00247744.
Gödel, Kurt. 1986. Collected Works. Volume I: Publications 1929–1936. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay and Jean van Heijenoort, doi:10.1093/oso/9780195147209.001.0001.
Gödel, Kurt. 1989. “Sur les propositions formellement indécidables des Principia Mathematica et des systèmes apparentés I.” in Le théorème de Gödel, edited by Jean-Baptiste Scherrer, pp. 107–143. Paris: Éditions du Seuil. Traduction de Gödel (1931a) par Jean-Baptiste Scherrer.
Gödel, Kurt. 1990. Collected Works. Volume II: Publications 1938–1974. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay and Jean van Heijenoort, doi:10.1093/oso/9780195147216.001.0001.
Gödel, Kurt. 1995. Collected Works. Volume III: Unpublished Essays and Lectures. Oxford: Oxford University Press. Edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay, doi:10.1093/oso/9780195072556.001.0001.
Gödel, Kurt. 1996. “Ensayos inéditos / Unpublished Philosophical Essays.” in Encyclopedia and Utopia. The Life and Work of Otto Neurath (1882-1945), edited by Elisabeth Nemeth and Friedrich Stadler, pp. 368. Vienna Circle Institute Yearbook n. 4. Dordrecht: Kluwer Academic Publishers. Edited by A. Rodrı́guez-Consuegra.
Gödel, Kurt. 2003a. Collected Works. Volume IV: Correspondence A–G. Oxford: Oxford University Press. Edited by Feferman, Solomon and Dawson, Jr, John W. and Warren Goldfarb and Charles Parsons and Wilfried Sieg.
Gödel, Kurt. 2003b. Collected Works. Volume V: Correspondence H–Z. Oxford: Oxford University Press. Edited by Feferman, Solomon and Dawson, Jr, John W. and Warren Goldfarb and Charles Parsons and Wilfried Sieg.

Further References

Benacerraf, Paul and Putnam, Hilary, eds. 1964. Philosophy of Mathematics: Selected Readings. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. Second edition: Benacerraf and Putnam (1983).
Benacerraf, Paul and Putnam, Hilary, eds. 1983. Philosophy of Mathematics: Selected Readings. 2nd ed. Cambridge: Cambridge University Press. First edition: Benacerraf and Putnam (1964), doi:10.1017/cbo9781139171519.
Davis, Martin, ed. 1965. The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Fonctions. Hewlett, New York: Raven Press.
Ewald, William Bragg, ed. 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Volume II. Oxford: Oxford University Press, doi:10.1093/oso/9780198505365.001.0001.
van Heijenoort, Jan, ed. 1967. From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931. Cambridge, Massachusetts: Harvard University Press.
Hilbert, David. 1931. “Die Grundlegung der elementaren Zahlenlehre.” Mathematische Annalen 104(1): 485–494. Translated as “The Grounding of Elementary Number Theory” in Ewald (1996, 1148–1156), doi:10.1007/BF01457953.
Menger, Karl, ed. 1998. Ergebnisse eines mathematischen Kolloquiums. Wien: Springer. Herausgegeben von E. Dierker, K. Sigmund, mit Beiträgen von J.W. Dawson Jr., R. Engelking und W. Hildenbrand, Geleitwort von G. Debreu, Nachwort von F. Alt, doi:10.1007/978-3-7091-6470-9.
Pears, David F., ed. 1972. Bertrand Russell: A Collection of Critical Essays. Garden City, New York: Anchor Books.