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RUSSELL AND GÖDEL

Published online by Cambridge University Press:  30 December 2016

ALASDAIR URQUHART
ALASDAIR URQUHART*
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF TORONTO SANDFORD FLEMING BUILDING 10 KING’S COLLEGE ROAD TORONTO, ON M5S 3G4, CANADA E-mail: [email protected]
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Abstract

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This paper surveys the interactions between Russell and Gödel, both personal and intellectual. After a description of Russell’s influence on Gödel, it concludes with a discussion of Russell’s reaction to the incompleteness theorems.

Keywords

01A6003-03Bertrand RussellKurtG&DotodelPrincipia Mathematicaincompleteness theorem
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 22 , Issue 4 , December 2016 , pp. 504 - 520
Copyright
Copyright © The Association for Symbolic Logic 2016 

References

REFERENCES

Anellis, I., Did Gödel’s result come as a surprise to Bertrand Russell? Posting to the FOM email list, March 30, 2010.Google Scholar
Church, A., Russell’s theory of identity of propositions . Philosophia Naturalis, vol. 21 (1984), pp. 513–522.Google Scholar
Crawshay-Williams, R., Russell Remembered, Oxford University Press, London, New York, 1970.Google Scholar
Dawson, J. W., Logical Dilemmas: The Life and Work of Kurt Gödel, A.K. Peters, Wellesley, MA, 1997.Google Scholar
Feinberg, B. and Kasrils, R. (eds.), Dear Bertrand Russell… A Selection of his Correspondence with the General Public 1950–1968, George Allen and Unwin Ltd, London, 1969.Google Scholar
Frege, G., Philosophical and Mathematical Correspondence (Gabriel, G., Hermes, H., Kambartel, F., Thiel, C., and Veraart, A., editors), University of Chicago Press, Chicago, 1980, Abridged from the German edition by Brian McGuinness and translated by Hans Kaal.Google Scholar
Gödel, K., Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I . Monatshefte für Mathematik und Physik, vol. 38 (1931), pp. 173–198.CrossRefGoogle Scholar
Gödel, K., Russell’s mathematical logic , The Philosophy of Bertrand Russell (Library of Living Philosophers Volume 5) (Schilpp, P. A., editor), Northwestern University, Evanston, 1944, pp. 123–153, [10, pp. 119–141].Google Scholar
Gödel, K., What is Cantor’s continuum problem? American Mathematical Monthly, vol. 54 (1947), pp. 515–525, [10, pp. 176–187].CrossRefGoogle Scholar
Gödel, K., Collected Works, Volume II: Publications 1938–1974 (Feferman, S., Dawson, J. W. Jr., Kleene, S. C., Moore, G. H., Solovay, R. M., and van Heijenoort, J., editors), Oxford University Press, New York, 1990.Google Scholar
Gödel, K., Collected Works, Volume III: Unpublished Essays and Lectures (Feferman, S., Dawson, J. W. Jr., Goldfarb, W., Parsons, C., and Solovay, R. M., editors), Oxford University Press, New York, 1995.Google Scholar
Gödel, K., Collected Works, Volume IV: Correspondence A-G (Feferman, S., Dawson, J. W. Jr. (Editors-in-chief), Goldfarb, W., Parsons, C., and Sieg, W., editors), Oxford University Press, New York, 2003.Google Scholar
Gödel, K., Collected Works, Volume V: Correspondence H-Z (Feferman, S., Dawson, J. W. Jr. (Editors-in-chief), Goldfarb, W., Parsons, C., and Sieg, W., editors), Oxford University Press, New York, 2003.Google Scholar
Grattan-Guinness, I., The Search for Mathematical Roots, 1870–1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel, Princeton University Press, Princeton, NJ, 2000.Google Scholar
Henkin, L., Are logic and mathematics identical? Science, vol. 138 (1962), pp. 788–794.CrossRefGoogle ScholarPubMed
Irvine, A. (ed.), Bertrand Russell: Critical Assessments, Volume II: Logic and Mathematics, Routledge, London, New York, 1999.Google Scholar
Pelham, J. and Urquhart, A., Russellian propositions , Logic, Methodology and Philosophy of Science IX, Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science, Uppsala, Sweden, August 7–14, 1991, North Holland, Amsterdam, New York, 1994, pp. 307–326.Google Scholar
Quine, W. V., The Time of My Life: An Autobiography, MIT Press, Cambridge, MA, 1985.Google Scholar
Richards, I. A., Beyond, Harcourt Brace Jovanovich, New York, 1974.Google Scholar
Rodríguez-Consuegra, F., Russell, Gödel and logicism , Philosophy of Mathematics, Proceedings of the 15th International Wittgenstein Symposium, Part 1, 1993, Reprinted in [16], pp. 320–329, pp. 233–242.Google Scholar
Russell, B., On Denoting . Mind, vol. 14 (1905), pp. 479–493.CrossRefGoogle Scholar
Russell, B., Les paradoxes de la logique . Revue de Métaphysique et de Morale, vol. 14 (1906), pp. 627–650.Google Scholar
Russell, B., Introduction to Mathematical Philosophy, second ed., George Allen and Unwin, London, 1920.Google Scholar
Russell, B., On order in time . Proceedings of the Cambridge Philosophical Society, vol. 32 (1936), pp. 216–228.CrossRefGoogle Scholar
Russell, B., The Principles of Mathematics, George Allen and Unwin, London, 1937, Second Edition: First published 1903.Google Scholar
Russell, B., An Inquiry into Meaning and Truth, first ed., W.W. Norton and Company, Inc., New York, 1940.Google Scholar
Russell, B., Logical positivism . Polemic, vol. 1 (1945), pp. 6–13, Reprinted in [35, pp. 148–155].Google Scholar
Russell, B., Whitehead and Principia Mathematica . Mind, vol. 57 (1948), pp. 137–138, Reprinted in [35, pp. 190–191].Google Scholar
Russell, B., Logical positivism . Revue internationale de philosophie, vol. 4 (1950), pp. 3–19, Reprinted in [30, pp. 323–343].Google Scholar
Russell, B., Logic and Knowledge (Marsh, R. C., editor), George Allen and Unwin, London, 1956.Google Scholar
Russell, B., The Autobiography of Bertrand Russell 1914–1944: Volume II, Little, Brown and Company, Boston, Toronto, 1968, An Atlantic Monthly Press Book.Google Scholar
Russell, B., The Autobiography of Bertrand Russell 1944–1967: Volume III, George Allen and Unwin, London, 1969.Google Scholar
Russell, B., Addendum to my ‘Reply to Criticisms’ , The Philosophy of Bertrand Russell (Schilpp, P. A., editor), The Library of Living Philosophers, Volume V, Fourth Edition, Open Court, La Salle, IL, 1971, pp. xvii–xx.Google Scholar
Russell, B., On ‘Insolubilia’ and their Solution by Symbolic Logic , Essays in Analysis, by Bertrand Russell (Lackey, D., editor), George Braziller, New York, 1973, pp. 190–214.Google Scholar
Russell, B., Collected Papers Volume 11: Last Philosophical Testament 1943–1968 (Slater, J. G. with the assistance of Peter Köllner, editor), Routledge, London, New York, 1997.Google Scholar
Russell, B., Collected Papers Volume 5; Toward “Principia Mathematica” 1905–1908 (Moore, G. H., editor), Routledge, London, New York, 2014.Google Scholar
Arthur Schilpp, P. (ed.), The Philosophy of Bertrand Russell, Library of Living Philosophers, vol. 5, Northwestern University, Evanston, IL, 1944.Google Scholar
Urquhart, A., Logic and denotation , Russell vs. Meinong: The legacy of “On denoting” (Griffin, N. and Jacquette, D., editors), Routledge, New York, 2008.Google Scholar
Urquhart, A., Principia Mathematica: The first 100 years , The Palgrave Centenary Companion to Principia Mathematica (Griffin, N. and Linsky, B., editors), Palgrave Macmillan, Houndmills, Basingstoke, Hampshire, 2013, pp. 3–20.CrossRefGoogle Scholar
Wang, H., Some facts about Kurt Gödel . The Journal of Symbolic Logic, vol. 46 (1981), pp. 653–659.CrossRefGoogle Scholar
Wang, H., Reflections on Kurt Gödel, The MIT Press, Cambridge, Massachusetts, 1987.Google Scholar
North Whitehead, A. and Russell, B., Principia Mathematica, Cambridge University Press, 1910–1913, Volume 1, 1910, Volume 2, 1913, Volume 3, 1913.Google Scholar
North Whitehead, A. and Russell, B., Principia Mathematica Volume 1, second ed., Cambridge University Press, Cambridge, 1927.Google Scholar