An Outline of Bergson’s Philosophy of Mathematics

  • Milič Čapek
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 7)

Abstract

Is it possible to speak of Bergson’s philosophy of mathematics except in a negative sense? This is the usual, textbook interpretation of his philosophy and the fact that he insisted so much on the inapplicability of the concept of arithmetical multiplicity not only to psychology, but also, as we shall see, to physics apparently substantiates it. Yet, this is an oversimplification which does not stand a critical and attentive reading of the relevant texts.

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Notes

  1. 3.
    Norman Kemp Smith, A Commentary to Kant’s ‘Critique of Pure Reason’Humanities Press, New York, 1962, p. 129.Google Scholar
  2. 7.
    Robert Blanché, ‘Psychologie de la duree et physique du champ’, Journal de psychologie normale et pathologique 44(1951) 420:9Google Scholar
  3. 9.
    Aron Gurwitch, The Field of Consciousness, Duquesne University Press, Pittsburgh, 1964, pp. 140ff.Google Scholar
  4. 10.
    Bertrand Russell, The Philosophy of BergsonMacmillan, London, 1912, pp. 14–15. n T.F.W., pp. 77–79; 86–87; 104–105; 121–123; 127–128.Google Scholar
  5. 13.
    Cf. M. Čapek, The Philosophical Impact of Contemporary Physics, pp. 23–241.Google Scholar
  6. 14.
    J. J. Baumann, Die Lehre von Raum, Zeit und Mathematik, Berlin 1869, II, pp. 668–671; F. A. Lange, Logische Studien, Iserlohn 1877, pp. 141ff. The reference to G. Noel is in Bergson, T.F.W., p. 75; that to Paul Du Bois-Reymond Allgemeine Funktionstheorieis in Helmholtz-Schlick, op. cit., p. 72Google Scholar
  7. J. Tannery’s article ’Principes fondamentaux de l’arithmetique’ is in Halsted’s Introduction to the English translation of Helmholt’s Counting and Measuring, Van Nostrand, Princeton, 1931, p. I X.Google Scholar
  8. 15.
    H. Poincaré, ‘Les fondements de la geometrie’, The Monist VII(1898) 57.Google Scholar
  9. 16.
    E. W. Beth and J. Piaget, L’epistemologie mathematique et psychologie, Etudes de psychologie genetique, Presses Universitaires de France, Paris, 1961 [Vol. XIV], p. 112. On Beth’s change of attitude toward epistemology cf. Jean Piaget, Genetic Epistemology(Columbia University Press, 1970 ), p. 12.Google Scholar
  10. 17.
    On Brouwer’s opposition to the Cantorian atomization of continuum and his view of continuum as “the medium of free becoming” (ein Medium des freien Werdens) cf. A. Fränkel, Einleitung in die Mengenlehre(Dover, New York, 1946), pp. 238–239;Google Scholar
  11. on Brouwer in general cf. Max Black, The Nature of Mathematics, Littlefield, Adams amp; Co., New York, 1959, pp. 186–210.Google Scholar
  12. On the relation of Weyl’s view of continuum to that of Bergson see Chapter 9 of this part, Note 14.Google Scholar
  13. 18.
    L.J.E. Brouwer, ‘Consciousness, Philosophy and Mathematics,’ quoted by E. W. Beth, The Foundations of Mathematics, Harper Torchbooks, New York, 1966, p. 618.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1971

Authors and Affiliations

  • Milič Čapek

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