Skip to main content

Interpretations of Leibniz’s Mathesis Universalis at the Beginning of the XXth Century

  • Chapter
  • First Online:
New Essays on Leibniz Reception

Abstract

In his doctoral dissertation, completed in 1922 under the direction of Edmund Husserl and published in 1925 in the Jahrbuch für Philosophie und Phänomenologische Forschungen, Dietrich Mahnke proposed a very valuable overview of the so-called “Leibniz Renaissance”. As indicated by the choice of his title: Leibnizens Synthese von Universalmathematik und Individualmetaphysik, this renaissance was seen by Mahnke as marked by a tension between two Leibnizian programs: that of a “universal mathematics” and that of a “metaphysics of individuation”. His agenda was to propose a way of reconciling these two programs through a point of view inspired by the development of Husserlian phenomenology. In this paper, I will concentrate on the first program, “universal mathematics” or mathesis universalis, and see how the interpretation of this Leibnizian theme was indeed a key point in the demarcation between different ways of articulating logic, mathematics and philosophy at the beginning of the XXth century.

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 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. Brunschvicg, Léon, Les étapes de la philosophie mathématique, Paris, Alcan, 1912.

    Google Scholar 

  2. Burkhardt, Hans, Logik und Semiotik in der Philosophie von Leibniz, München, Philosophia, 1980.

    Google Scholar 

  3. Cassirer, Ernst, Leibniz’ System in seinen wissenschaftlichen Grundlagen (1902) [including, as its first part : Descartes’s Kritik der mathematischen und Naturwissenschaftlichen Erkenntnis (1899)], reed. Gesammelte Werke, t. I, Hamburg, F. Meiner, 1998.

    Google Scholar 

  4. Cassirer, Ernst, Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, vol. I, (1906), reed. Gesammelte Werke t. II, Hamburg, F. Meiner, 1999.

    Google Scholar 

  5. Couturat, Louis, La Logique de Leibniz d’après des documents inédits, Paris, Alcan, 1901.

    Google Scholar 

  6. Couturat, Louis, Opuscules et fragments inédits de Leibniz, extraits des manuscrits de la Bibliothèque de Hannovre, Paris, Alcan, 1903, rééd. Hildesheim, New-York, Olms, 1988.

    Google Scholar 

  7. Couturat, Louis, Les Principes des mathématiques (1905), reed. Paris, Albert Blanchard, 1980.

    Google Scholar 

  8. Descartes, René, OEuvres de Descartes, publiées par C. Adam et P. Tannery, 11 vol., nouvelle présentation en coédition avec le CNRS, Paris, Vrin, 1964–1974 [AT].

    Google Scholar 

  9. Fédi, Laurent, “L’esprit en marche contre les codes: philosophie des sciences et dépassement du kantisme chez Léon Brunschvicg”, in Les philosophies françaises et la science: dialogue avec Kant, sous la dir. de L. Fedi et J.-M. Salanskis, Cahiers d’Histoire et de Philosophie des Sciences n◦ 50, ENS éditions Lille, 2001, pp. 119–142.

    Google Scholar 

  10. Hintikka, Jaakko, Lingua Universalis vs. Calculus Ratiocinator. An ultimate presupposition of Twentieth-century philosophy, Dordrecht, Kluwer Academic Publishers, 1997.

    Google Scholar 

  11. Husserl, Edmund, Logische Untersuchungen I (1900), reed. Husserliana, vol. XVIII, Den Haag, Martinus Nijhoff, 1975.

    Google Scholar 

  12. Husserl, Edmund, Die Krisis der europäischen Wissenschaften und die transzendantale Phänomenologie (1934–1937), La Haye, M. Nijhoff, 1954.

    Google Scholar 

  13. Klein, Jacob, “Die griechische Logistik und die Entstehung der Algebra”, in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik; Abteilung B: Studien, 3, n. 1 (1934), pp. 18–105 and n. 3 (1936), pp. 122–235.

    Google Scholar 

  14. Leibniz, Gottfried Wilhelm von, Nouvelles lettres et opuscules inédits, éd. Foucher de Careil, 1857, rééd. Olms, Hildesheim-N.Y, 1971.

    Google Scholar 

  15. Leibniz, Gottfried Wilhelm von, Nouveaux Essais sur l’entendement humain (1704), transl. Peter Remnant and Jonathan Bennett: New Essays on Human Understanding, Cambridge, Cambridge University Press, 1981.

    Google Scholar 

  16. Grosholz, Emily and Yakira, Elhanan, Leibniz’s Science of the Rational, Studia Leibnitiana Sonderheft 26, Steiner Verlag, 1998 (with a transcription and a commentary of LH XXXV, I, 9).

    Google Scholar 

  17. Kneale, William & Martha, The Development of Logic, Oxford, Clarendon Press, 1962, rééd..

    Google Scholar 

  18. Mahnke, Dietrich, Leibnizens Synthese von Universalmathematik und Individualmetaphysik, Max Niemeyer, Halle, 1925, Jahrbuch für Philosophie und Phänomenologische Forschungen, pp. 305–612 (reed. fac-simile, Stuttgart, 1964).

    Google Scholar 

  19. Rabouin, David, “Logique, mathématique et imagination dans la philosophie de Leibniz”, Corpus, n. 49, “Logiques et philosophies à l’âge classique”, hiver 2005, p. 165–198.

    Google Scholar 

  20. Russell, Bertrand, A Critical Exposition of the Philosophy of Leibniz, London, Unwin,1900.

    Google Scholar 

  21. Russell, Bertrand, “ Recent Work on The Philosophy of Leibniz ”, Mind, vol. 12, n. 46, 1903, pp. 177–201.

    Article  Google Scholar 

  22. Schneider, Martin, “Funktion und Grundlegung der Mathesis Universalis im Leibnizschen Wissenschaftsystem ”, Studia Leibnitiana Sonderheft 15, 1988.

    Google Scholar 

  23. Van Heijenoort, Jean, “Logic as Calculus and Logic as Language”, Synthese, vol. 17 (1967), pp. 324–330.

    Article  MATH  Google Scholar 

  24. Weyl, Hermann, Philosophie der Mathematik und Naturwissenschaft, Munich, R. Oldenbourg (Handbuch der Philosophie), 1926.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Rabouin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Basel AG

About this chapter

Cite this chapter

Rabouin, D. (2012). Interpretations of Leibniz’s Mathesis Universalis at the Beginning of the XXth Century. 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_9

Download citation

Publish with us

Policies and ethics