Skip to main content

The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number

  • Chapter
From Dedekind to Gödel

Part of the book series: Synthese Library ((SYLI,volume 251))

Abstract

From 1897 to 1913, during the entire period when Russell made his major contributions to mathematical logic, he corresponded regularly with the French philosopher, Louis Couturat. Almost 200 letters passed between them, ranging over a myriad of topics, from the politics of the Boer War to the usefulness of an international language. The heart of this correspondence, however, is not its political themes but its logical, mathematical, and philosophical ones.

I wish to thank Jeffrey Zucker for his comments on this paper. I thank the Bertrand Russell Archives at McMaster University for kindly giving permission to quote from Russell’s unpublished manuscripts and letters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Bibliography

  • Burali-Forti, Cesare: 1897, ‘Una questione sui numeri transfiniti’, Rendiconti del Circolo Matematico di Palermo 11, 154–164. Translated in van Heijenoort 1967, pp. 169179.

    Google Scholar 

  • Cantor, Georg: 1883, Grundlagen einer allgemeinen Mannichfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen, Teubner, Leipzig.

    Google Scholar 

  • Cantor, Georg: 1891, ‘Über eine elementare Frage der Mannigfaltigkeitslehre’, Jahresbericht der Deutschen Mathematiker-Vereinigung 1, 75–78.

    Google Scholar 

  • Cantor, Georg: 1897, ‘Beiträge zur Begründung der transfiniten Mengenlehre. II’, Mathematische Annalen 49, 207–246.

    Article  Google Scholar 

  • Couturat, Louis: 1896, De l’Infini mathématique, Alcan, Paris.

    Google Scholar 

  • Couturat, Louis: 1898, ‘Sur les rapports du nombre et de la grandeur’, Revue de métaphysique et de morale 6, 422–447.

    Google Scholar 

  • Couturat, Louis: 1901, La logique de Leibniz, Alcan, Paris.

    Google Scholar 

  • Dugac, Pierre: 1983, ‘Louis Couturat et Georg Cantor’, L’oeuvre de Louis Couturat ( 1868–1914 ), Ecole Normale Supérieure, Paris, pp. 55–61.

    Google Scholar 

  • Frege, Gottlob: 1976, Nachgelassene Schriften und wissenschaftlicher Briefwechsel vol. 2, Felix Meiner, Hamburg.

    Google Scholar 

  • Frege, Gottlob: 1980, Philosophical and Mathematical Correspondence,edited by

    Google Scholar 

  • Gottfried Gabriel et al. Translated by Hans Kaal, University of Chicago Press, Chicago. Grattan-Guinness, Ivor: 1977, Dear Russell - Dear Jourdain,Duckworth, London.

    Google Scholar 

  • Griffin, Nicholas: 1989, ‘The Tiergarten Programme’, Russell: The Journal of the Bertrand Russell Archives 8 (1–2), 19–34.

    Google Scholar 

  • Jourdain, Philip: 1913, ‘A Correction and Some Remarks’, The Monist 23, 145–148.

    Article  Google Scholar 

  • Lackey, Douglas P.: 1972, ‘The Whitehead Correspondence’, Russell: The Journal of the Bertrand Russell Archives 5, 14–16.

    Google Scholar 

  • Moore, Gregory H.: 1978, ‘The Origins of Zermelo’s Axiomatization of Set Theory’, Journal of Philosophical Logic 7, 307–329.

    Article  Google Scholar 

  • Moore, Gregory H.: 1989, ‘The Roots of Russell’s Paradox’, Russell: The Journal of the Bertrand Russell Archives 8 (1–2), 46–56.

    Google Scholar 

  • Moore, Gregory H., and Alejandro Garciadiego: 1981, ‘Burali-Forti’s Paradox: A Reappraisal of Its Origins’, Historia Mathematica 8, 319–350.

    Article  Google Scholar 

  • Peckhaus, Volker: 1990, Hilbertprogramm und kritische Philosophie. Das Göttinger Modell interdisziplinärer Zusammenarbeit zwischen Mathematik und Philosophie, Vandenhoeck & Ruprecht, Göttingen.

    Google Scholar 

  • Russell, Bertrand: 1896, ‘Notes on Cantor’, unpublished notes printed in his 1990, 460–481.

    Google Scholar 

  • Russell, Bertrand: 1896a, Review of Hannequin 1895, Mind 5, 410–417. Reprinted in his 1990, pp. 35–43.

    Google Scholar 

  • Russell, Bertrand: 1896b, ‘Notes on the Relations between Number and Quantity’, unpublished notes printed in his 1990, 13.

    Google Scholar 

  • Russell, Bertrand: 1896c, ‘On Some Difficulties of Continuous Quantity’, unpublished manuscript, printed in his 1990, pp. 44–58.

    Google Scholar 

  • Russell, Bertrand: 1897, Review of Couturat 1896, Mind 6, 112–119. Reprinted in his 1990, pp. 59–67.

    Google Scholar 

  • Russell, Bertrand: 1897a, ‘On the Relations of Number and Quantity’, Mind 6, 326–341. Reprinted in his 1990, pp. 68–82.

    Google Scholar 

  • Russell, Bertrand: 1898, ‘Les axiomes propres à Euclide, sont-ils empiriques?’, Revue de métaphysique et de morale 6, 759–776.

    Google Scholar 

  • Russell, Bertrand: 1899, The Fundamental Ideas and Axioms of Mathematics,unpublished book manuscript, printed in his 1990, pp. 261–305, and in his 1993, pp. 54–74.

    Google Scholar 

  • Russell, Bertrand: 1899a, ‘Sur les axiomes de la géométrie’, Revue de métaphysique et de morale 7, 684–707.

    Google Scholar 

  • Russell, Bertrand: 1900, A Critical Exposition of the Philosophy of Leibniz, Allen & Unwin, London.

    Google Scholar 

  • Russell, Bertrand: 1900a, The Principles of Mathematics (Draft of 1899–1900),unpublished book manuscript, printed in his 1993, pp. 3–180.

    Google Scholar 

  • Russell, Bertrand: 1901, ‘Recent Work on the Principles of Mathematics’, International Monthly 4, 83–101. Reprinted in his 1993, pp. 363–379.

    Google Scholar 

  • Russell, Bertrand: 1903, The Principles of Mathematics, Cambridge University Press, Cambridge.

    Google Scholar 

  • Russell, Bertrand: 1926, Education and the Good Life, Boni & Liveright, New York.

    Google Scholar 

  • Russell, Bertrand: 1956, Portraits from Memory and Other Essays, Simon and Schuster, New York.

    Google Scholar 

  • Russell, Bertrand: 1959, My Philosophical Development, Allen and Unwin, London. Russell, Bertrand: 1967, The Autobiography of Bertrand Russell, 1872–1914, vol. 1, Allen & Unwin, London.

    Google Scholar 

  • Russell, Bertrand: 1990, Philosophical Papers 1896–99,edited by Nicholas Griffin and Albert C. Lewis, Unwin Hyman, London. Vol. 2 of The Collected Papers of Bertrand Russell.

    Google Scholar 

  • Russell, Bertrand: 1993, Toward the Principles of Mathematics, 1900–1902,edited by GregoryH.Moore, Routledge, London. Vol. 3 of The Collected Papers of Bertrand Russell.

    Google Scholar 

  • Schmid, Anne-Françoise: 1983, ‘La correspondance inédite Couturat-Russell’, L’ oeuvre de Louis Couturat (1868–1914), Ecole Normale Supérieure, Paris, pp. 81–96.

    Google Scholar 

  • Spadoni, Carl: 1978, ‘Philosophy in Russell’s Letters to Alys’, Russell: The Journal of the Bertrand Russell Archives 29–32, 17–31.

    Google Scholar 

  • Van Heijenoort, Jean: 1967, From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Winchester, Ian: 1989, ‘The Antinomy of Dynamical Causation in Leibniz and the Principles and Russell’s Early Picture of Physics’, Russell: The Journal of the Bertrand Russell Archives 8 (1–2), 35–45.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Moore, G.H. (1995). The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number. In: Hintikka, J. (eds) From Dedekind to Gödel. Synthese Library, vol 251. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8478-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8478-4_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4554-6

  • Online ISBN: 978-94-015-8478-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics