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The Reception of Gödel's Incompleteness Theorems

Published online by Cambridge University Press:  28 February 2022

John W Dawson Jr.
John W Dawson Jr.*
Affiliation:
Penn State/York and The Institute for Advanced Study
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Extract

“Die Arbeit über formal unentscheidbare Sätze wurde wie ein Erdbeben empfunden; insbesondere auch von Carnap.” - - (Popper 1980).

“Kurt Gödel's achievement in modern logic … is a landmark which will remain visible far in space and time.” - - John von Neumann

It is natural to invoke geological metaphors to describe the impact and the lasting significance of Gödel's incompleteness theorems. Indeed, how better to convey the impact of those results - - whose effect on Hilbert's program was so devastating and whose philosophical reverberations have yet to subside - - than to speak of tremors and shock waves? The image of shaken foundations is irresistible.

Type
Part VI. Invited Paper: History of Logic
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1984 , Issue 2: Volume Two: Symposia and Invited Papers 1984 , 1984 , pp. 252 - 271
Copyright
Copyright © 1985 by the Philosophy of Science Association

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References

Anderson, Alan Ross (1958). “Mathematics and the ‘Language Game'.” The Review of Metaphysics 11: 446-458. (As reprinted in Benacerraf and Putnam (1964). Pages 481-490.)Google Scholar
Barzin, Marcel (1940). “Sur la Portée du Théorème de M. Gödel.” Académie Royale de Be1gioue, Bulletin de la Classe des Sciences, Series 5, 26: 230-239.Google Scholar
Benacerraf, Pau and Putnam, Hilar (eds.). (1964). Philosophy of Mathematics: Selected Readings. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
Bernays, Paul (1959). “Comments on Ludwig Wittgenstein's ‘Remarks on the Foundations of Mathematics’.” Ratio II: 1-22. (A3 reprinted in Benacerraf and Putnam (1964). Pages 510-528.)Google Scholar
Birkhoff, Garrett (1940). Lattice Theory. (American Mathematical Society Colloquium Publications. Volume 25.) New York: American Mathematical Society.Google Scholar
Church, Alonzo (1946). Review of Finsler (1944). Journal of Symbolic Logic 11: 131-132.Google Scholar
Davis, Marti. (ed.). (1965). The Undecidable. Hewlett, N.Y.: Raven Press .Google Scholar
Davis, Martin (1982). “Why Gödel Didn't Have Church's Thesis.” Information and Control 54: 3-24 .CrossRefGoogle Scholar
Dawson, Jr., John, W (1984). “Discussion on the Foundation of Mathematics.” History and Philosophy of Logic 5: 111-129.Google Scholar
Davis, Marti (1985). “Completing the Gödel-Zermelo Correspondence.” Historla Mathematica 12: 66-70.Google Scholar
Dummet, Michael (1959). “Wittgenstein's Philosophy of Mathematics.” Philosophical Review LXVIII: 324-348. (As reprinted in Benacerraf and Putnam (1964). Pages 491-509.)Google Scholar
Feferman, Solomon (1985). “Conviction and Caution: A Scientific Portrait of Kurt Gödel.” PhilosOPhia Naturalis 21: 546-562.Google Scholar
Finsler, Paul (1926). “Formale Beweise und die Entscheidbarkeit.” Mathematische Zeitschrift 25: 676-682. (English translation in van Heijenoort (1967). Pages 440-445.)CrossRefGoogle Scholar
Finsler, Paul (1944). “Gibt es unentscheldbare Sätze?” Commentarli Mathematici Helvetici 16: 310-320.CrossRefGoogle Scholar
Gödel, Kurt (1930). “Einige metamathematische Resultate über Entscheidungsdefinitheit und Widerspruchsfreiheit.” Anzeiger der Akademie der Wissenschaft in Wien 67: 214-215. (English translation in jran Heijenoort (1967). Pages 595-596.)Google Scholar
Gödel, Kur. (1930/31). “Über Vollständigkeit und Hiderspruehsfreiheit.” Ergebnisse eines mathematischen Kolloquiums 3: 12-13. (English translation in van Heijenoort (1967). Pages 616-617.Google Scholar
Gödel, Kurt (1931). “Über formal unentschuldbare Sätze der Principia Mathematica und verwandter Systeme I.” Monatshefte für Mathematik und Physik 38: 173-198. (English translation in van Heijenoort (1967).; Pages 596-616.)CrossRefGoogle Scholar
Gödel, Kurt (1934). “On Undecidable Propositions of Formal Mathematical Systems.” Mimeographed notes by S.C. KLeene and J.B. Hosser of lectures by Kurt Gödel at the Institute for Advanced Study. (As reprinted in Davis (1965). Pages 39-74.)Google Scholar
Gonseth, Ferdinan (ed.).; (1941). Les Entretlens de Zürich sur les Fondements et la methode des sciences mathematioues 6-9 Decembre 1938. Zurich: Leeman.Google Scholar
Grattai-Guinness, Ivor (1979). “In Memoriam Kurt Gödel: His 1931 Correspondence with Zermelo on his Incompletability Theorem.” Historia Mathematioa 6: 294-304.CrossRefGoogle Scholar
Grattai-Guinness, Ivor (1981). “On the Development of Logics Between the Two World Wars.” American Mathematical Monthly 88: 495-509.CrossRefGoogle Scholar
Grelling, Kur. (1937/38). “Gibt es eine Gödelsche Antinomie?” Theorie 3: 297-306. “Zusätze und Berichtigungen.” Theoria 4: 68-69.Google Scholar
Hahn, Han et al. (1931). “Diskussion zur Grundlegung der Mathematik.” Erkenntnis 2: 135-151. (English translation in Dawson (1984). Pages 116-128.)Google Scholar
Helmer, Olaf (1937). “Perelman versus Godel.” Mind 46: 58-60.CrossRefGoogle Scholar
Hubert, Davi and Bernays, Paul (1934). Die Grundlagen der Mathematik Volume 1. Berlin: Springer.Google Scholar
Hubert, Davi and Bernays, Paul (1939). Die Grundlagen der Mathematik, Volume 2. Berlin: Springer.Google Scholar
Kleene, Stephen C (1937a). Review of Perelman (1936). Journal of Symbolic Logic 2: 40-41.Google Scholar
Kleene, Stephen C (1937b). Review of Helmer (1937). Journal of Symbolic Logic 2: 48-49.Google Scholar
Kleene, Stephen C.. (1976). “The Work of Kurt Gödel.” Journal of Symbolic Logic 41: 761-778.CrossRefGoogle Scholar
Kleene, Stephen C (1978). “Addendum.” Journal of Symbolic Logic 43: 613.CrossRefGoogle Scholar
Kleene, Stephen C (1981a). “Origins of Recursive Function Theory.” Annals of the History of Computing 3: 52-67. (Corrigenda in Davis (1982), footnotes 10 and 12.)CrossRefGoogle Scholar
Kleene, Stephen C (1981b). “The Theory of Recursive Functions, Approaching its Centennial.” Bulletin of the American Mathematical Society (n.s.) 5:1, 43-61.CrossRefGoogle Scholar
Kreisel, Georg (1979). Review of Kleene (1978). Zentralblatt für Mathematik und ihre Grenzgebiete 401: 12-13. Review #03001.Google Scholar
Kuczyński, Jerzy (1938). “0 Twierdzeniu Gödla.” Kwartalnik Filozofiozny 14: 74-80.Google Scholar
Ladrière, Jean (1957). Les Limitations Internes des Formalismes. Louvain: E. Nauwelaerte. Paris: Gauthier-Villars.Google Scholar
Menger, Karl (1978). Selected Papers in Logic and Foundations, Didactics, Economics. (Vienna Circle Collection, Number 10.) D. Reidel: Dordrecht-Boston-London.Google Scholar
Mostowski, AndrzeJ (1938). Review of Kuczynski (1938). Journal of Symbolic Logic 3: 118.CrossRefGoogle Scholar
Perelman, Charles (1936). L'Antinomie de M. Gödel.” Academic Royale de Belgioue, Bulletin de la Classe des Sciences. Serie 5, 22: 730-736.Google Scholar
Popper, Karl R (1980). “Der wichtigste Beitrag seit Aristoteles.” Wissenschaft aktuell (4): 50-51.Google Scholar
Post, Emil L (1965). “Absolutely ünsolvable Problems and Relatively ündecidable Propositions: Account of an Anticipation.” In Davis (1965). Pages 338-433.Google Scholar
Quine, Willard V (1978). “Kurt Gödel, (1906-1978).” Year Book of the American Philosophical Society 1978: 81-84.Google Scholar
Reichenbach, Hans (1930). “Tagung für Erkenntnislehre der exakten Wissenschaften.” Die Naturwissenschaften 18: 1093-1094.CrossRefGoogle Scholar
Rosser, J. Barkley (1936). “Extensions of Some Theorems of Gödel and Church.” Journal of Symbolic Logic 1: 87-91. (Reprinted in Davis (1965). Pages 231-235.)CrossRefGoogle Scholar
Rosser, J. Barkley (1938). Review of Grelling (1937/38). Journal of Symbolic Logic 3: 86.Google Scholar
Russell, Bertrand (1959). My Philosophical Development. London: Allen and Unwin.Google Scholar
Tarski, Alfred (1956). Logic, Semantics, Metamathematics. (ed.) and (trans.) Moodger, J.H. Oxford: Oxford University Press.Google Scholar
Turing, Alan M (1936/37). “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, Series 2, 42: 230-265. Corrigenda, 43: 544-546. (Reprinted in Davis (1965). Pages 115-154.)Google Scholar
van Heijenoort, Jea. (ed.). (1967). From Frege to Gödel. A Source Book In Mathematical Logic. 1879-1931. Cambridge, Mass.: Harvard university Press.Google Scholar
Wang, Hao (1981). “Some Facts About Kurt Gödel.” Journal of Symbolic Logic 16: 653-659.CrossRefGoogle Scholar
Wittgenstein, Ludwig (1956). “Appendix I.” In Remarks on the Foundations of Mathematics. New York: MacMillan Co. Pages 19-54. (As reprinted in Benacerraf and Putnam (1961). Pages 131-135.)Google Scholar
Zermelo, Ernst (1932). “Über Stufen der Qualifikation und die Logik des Unendlichen.” Jahresbericht der deutschen Mathematiker-Vereinigung 41, part 2: 85-88.Google Scholar