Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Gödel, Leibniz and “Russell’s Mathematical Logic”

  • Chapter
  • First Online:
New Essays on Leibniz Reception

Abstract

Kurt Gödel explicitly mentioned Leibniz in only one paper, “Russell’s mathematical logic”, which appeared in 1944 in the volume of the Library of Living Philosophers devoted to Bertrand Russell and edited by A. Schilpp.1 Nevertheless, the tribute paid by Godel to Leibniz in this text is so important that this alone suffices in attesting to the role that Leibniz’s work played in Godel’s thought.

Since the first draft of this paper, a considerable amount of new transcriptions of Godel’s manuscripts is now available thanks to the project ANR-09-BLA-0313, under my direction. Therefore, the formulations given here could be improved in several places, but the conjectures advanced are confirmed by the new texts.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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.

References

  1. Angelelli, I., Studies on Gottlob Frege and traditional philosophy. Reidel, Dortrecht, 1967.

    Google Scholar 

  2. Audureau, E., Kurt Gödel, critique de la théorie de la relativité générale. Doctoral thesis of the University of Aix-Marseille 1. November 2004

    Google Scholar 

  3. Bernays, P., ‘Review of Gödel’s “Russell’s mathematical logic”’, The Journal of Symbolic logic 11 (1946), 75–79.

    Article  Google Scholar 

  4. Buldt, B. et al. (eds), Kurt Gödel. Wahrheit und Beweisbarkeit. öbv&hpt, Wien 2002.

    Google Scholar 

  5. Church, A., “A set of postulates for the foundations of logic” Annals of mathematics, 2, n. 33, 1932, pp. 346–366.

    Google Scholar 

  6. Church, A., “A set of postulates for the foundations of logic (second paper)” Annals of mathematics, 2, n. 34, 1933, pp. 839–864.

    Google Scholar 

  7. Church, A., “Review to Carnap’s Introduction to semantics”, Philosophical Review, vol 52, n. 3, May 1943, pp. 298–304.

    Article  Google Scholar 

  8. Church, A., Introduction to mathematical logic, Princeton University Press, 1956.

    Google Scholar 

  9. Crocco, G., “Gödel, Carnap and the Fregean Heritage”, Synthese, 137, n◦1–2, 2003, pp. 21–41.

    Google Scholar 

  10. Crocco, G., “Gödel on concepts”, History and Philosophy of Logic, 27 Mai 2006, pp. 171–191

    Google Scholar 

  11. Frege, G., “Funktion und Begriff” in Kleine Schriften Angelleli I. ed. Hildesheim, Georg Olms, (1967) pp. 125–142. First edition 1891.

    Google Scholar 

  12. Frege, G., “Über Begriff und Gegenstand” in Kleine Schriften Angelleli I. ed. Hildesheim Georg Olms, (1967) pp. 167–178. First edition 1892.

    Google Scholar 

  13. Davidson, D., Inquiries into Truth and Interpretation, Oxford University Press 1984.

    Google Scholar 

  14. Gödel, K., “The present situation in the foundations of mathematics”, in [Gödel CW III] pp. 45–53.

    Google Scholar 

  15. Gödel, K., “Russell’s mathematical logic” in The philosophy of Bertrand Russell, P.A. Schilpp ed. Library of living philosophers, Open Court La Salle 1944, pp. 123–153. Reprinted in [Gödel CW II] pp. 119–141

    Google Scholar 

  16. Gödel, K., “Some observations about the relationship between theory of relativity and Kantian philosophy” in [Gödel CW III] pp; 230–246.

    Google Scholar 

  17. Gödel, K., “A remark about the relationship between relativity theory and idealistic philosophy” in Albert Einstein, philosopher – scientist P.A. Schilpp ed. Library of living philosophers Open Court La Salle 1949, pp. 555–562; reprinted in [Gödel CW II] pp. 202–207,

    Google Scholar 

  18. Gödel, K., “Some basic theorems on the foundations of mathematics and their philosophical implications” in [Gödel CW III] pp. 304–323.

    Google Scholar 

  19. Gödel, K., “Is mathematics syntax of language ?” version III, in [Gödel CW III] pp. 334–356, version V, in [Gödel CW III] pp. 356–362.

    Google Scholar 

  20. Gödel, K., “The modern development of the foundations of mathematics in the light of philosophy” in [Gödel CW III] pp. 374–387.

    Google Scholar 

  21. Gödel, K., Collected Works vol. II. Publications 1938–1974. Feferman S. et al. eds. New York and Oxford. Oxford University Press 1990

    Google Scholar 

  22. Gödel, K., Collected Works vol. III. Unpublished essays and lectures. Feferman S. et al. eds. New York and Oxford. Oxford University Press 1995

    Google Scholar 

  23. Gödel, K., Collected Works vol. IV. Correspondence A–G. Feferman S. et al. eds. New York and Oxford. Oxford University Press 2003

    Google Scholar 

  24. Gödel, K., Collected Works vol. V. Correspondence H–Z. Feferman S. et al. eds. New York and Oxford. Oxford University Press 2003

    Google Scholar 

  25. Gödel, K., Gödel Nachlass, Firestone Library Princeton.

    Google Scholar 

  26. Hintikka, J., “On Gödel’s philosophical assumptions” Synthese 114, 1998, pp. 13–23

    Article  MathSciNet  MATH  Google Scholar 

  27. McCulloch, W., PittsW., “A logical calculus of the ideas immanent in nervous activity”, Bulletin of mathematical biophysics 5, pp. 115–133. 1943

    Google Scholar 

  28. Menger, K., “Memories of Kurt Gödel”. In McGuinness, B. (ed.) Reminiscences of the Vienna Circle and the Mathematical Colloquium. Dordrecht: Kluwer (1994)

    Google Scholar 

  29. Mugnai, M., “Leibniz nominalism and the reality of ideas in the Mind of God” in Heinekamp, Lenzen and Schneider (eds.) Mathesis rationis. Münster, Nodus, 1990 pp. 153–67.

    Google Scholar 

  30. Mugnai, M., Introduzione alla filosofia di Leibniz. Torino, Einaudi 2001.

    Google Scholar 

  31. Nachtomy, O., Possibility, agency, and individuality in Leibniz’s metaphysics. Dordrecht, Springer 2007.

    Google Scholar 

  32. Neale, S. “The philosophical significance of Gödel’s slingshot” Mind, vol. 104, 761–825.

    Google Scholar 

  33. Parsons, Ch., “Platonism and mathematical intuition in Kurt Gödel’s thought” Bulletin of Symbolic logic, 1, n. 1 (1995) pp. 44–74.

    Google Scholar 

  34. Quine,W.V.O., “Whitehead and the rise of modern logic” in The philosophy of Alfred North Whitehead, P.A. Schilpp ed. Open Court La Salle 1941.

    Google Scholar 

  35. Russell, B.,Whitehead, A.N., Principia mathematica, Cambridge, Cambridge university Press 1963. First edition 1910.

    Google Scholar 

  36. Tieszen, R., “Kurt Gödel’s path from the incompleteness theorem (1931) to phenomenology (1961)”, The Bulletin of Symbolic logic, 4 n. 2 1998, pp. 181–203.

    Google Scholar 

  37. Van Atten, M., Kennedy, J., “On the philosophical development of Kurt Gödel”, The Bulletin of Symbolic Logic 9, n. 4, 2003, pp. 425–476.

    Google Scholar 

  38. Wang, Hao, From Mathematics to Philosophy, London, Routledge & Kegan Paul 1974.

    Google Scholar 

  39. Wang, Hao, Reflections on Kurt Gödel Cambridge: The MIT Press (1987)

    Google Scholar 

  40. Wang, Hao, A logical journey from Gödel to philosophy Cambridge: The MIT Press (1996)

    Google Scholar 

  41. Weyl, Hermann, “Review of Schilpp 1944”, American Mathematical Monthly, 53, 208–214 (1946) Reprinted in Weyl’s Gesammelte Abhandlungen, vol. 4, p. 599–605.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre d’Epistémologie et d’Ergologie Comparatives CNRS – CEPERC – UMR 6059, Université de Provence, 29 avenue Robert Schuman, F-13621, AIX EN PROVENCE CEDEX 1, France

    Gabriella Crocco

Authors
  1. Gabriella Crocco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gabriella Crocco .

Editor information

Editors and Affiliations

  1. Ostlandstrasse 33, Siegen, 57080, Germany

    Ralf Krömer

  2. , Archives H. Poincaré, Université Nancy 2, Nancy cedex, 54015, France

    Yannick Chin-Drian

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Basel AG

About this chapter

Cite this chapter

Crocco, G. (2012). Gödel, Leibniz and “Russell’s Mathematical Logic”. In: Krömer, R., Chin-Drian, Y. (eds) New Essays on Leibniz Reception. Publications des Archives Henri Poincaré Publications of the Henri Poincaré Archives(). Springer, Basel. https://doi.org/10.1007/978-3-0346-0504-5_11

Download citation

Publish with us

Policies and ethics

Search

Navigation