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
Norman Kemp Smith, A Commentary to Kant’s ‘Critique of Pure Reason’Humanities Press, New York, 1962, p. 129.
Robert Blanché, ‘Psychologie de la duree et physique du champ’, Journal de psychologie normale et pathologique 44(1951) 420:9
Aron Gurwitch, The Field of Consciousness, Duquesne University Press, Pittsburgh, 1964, pp. 140ff.
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.
Cf. M. Čapek, The Philosophical Impact of Contemporary Physics, pp. 23–241.
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. 72
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.
H. Poincaré, ‘Les fondements de la geometrie’, The Monist VII(1898) 57.
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.
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;
on Brouwer in general cf. Max Black, The Nature of Mathematics, Littlefield, Adams amp; Co., New York, 1959, pp. 186–210.
On the relation of Weyl’s view of continuum to that of Bergson see Chapter 9 of this part, Note 14.
L.J.E. Brouwer, ‘Consciousness, Philosophy and Mathematics,’ quoted by E. W. Beth, The Foundations of Mathematics, Harper Torchbooks, New York, 1966, p. 618.
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© 1971 D. Reidel Publishing Company, Dordrecht, Holland
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Čapek, M. (1971). An Outline of Bergson’s Philosophy of Mathematics. In: Bergson and Modern Physics. Boston Studies in the Philosophy of Science, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3096-0_25
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