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Symmetry: Culture and Science
Volume 33, Number 2, pages 155-171 (2022)
https://doi.org/10.26830/symmetry_2022_2_155

BERGSON’S NOTION OF NUMBER AND SOME RUSSELLIAN OBJECTIVES^[1]

Dóra Dergez-Rippl

Department of Cultural Theory and Applied Communication Sciences, Faculty of Cultural Sciences, Education and Regional Development, University of Pécs, 1 Rákóczi Str., Szekszárd 7100, Hungary.
Email: ripdor@gmail.com, rippl.dora@pte.hu
ORCID: 0000-0001-8694-2311

Abstract: Bergson’s theory of intuition is based on a notion of irrationality which is free from causality. Starting from this he was seeking the method of philosophy. Many of his notions serve this theory: intuition, duration, motion, creative evolution, and space but first of all the notion of time. Bergson’s theory of time leads us to live in the experience of philosophy, especially through art. This is the reason why his works are the basis for artistic investigations as well. So this topic gives free vent to deep theoretical investigations in Bergson’s philosophy such as the difference between intuition and intellect, the special notion of order applied in art, or the essence of life in the light of artistic creativity. Besides, in the centre of his philosophy is the notion of time. He differentiated objective and subjective time and while the former is the notion of the physicists the latter is the basis of philosophy. Bergson has made this distinction with the help of a mathematical problem: the notion and origin of ‘number’. This attracted Russell’s attention who totally refused Bergson’s explanatory method and made a lecture in 1913 at Trinity College on the topic. This caused a debate between him and one of Bergson’s disciples the British philosopher Wildon Carr. In my paper, I give a summarization of this debate focusing on the notion of number. Besides I want to show how Russell has misunderstood Bergson for the latter did not want to give the criticism of mathematics but he wanted to develop his metaphysical investigations on philosophical intuition. Regarding this one cannot say with Russell that Bergson did not know what a number is but instead must take into consideration the implicitness of Bergson’s notional distinctions and the general consequences of it, namely reviving the old philosophical questions of the problem of number and counting: set theory, the paradox of Zeno, mathematical Platonism or intuition in mathematics.

Keywords: theory of number, Bergson, Russell, intuition, philosophy

References:
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^[1] This paper is the edited version of my earlier lecture (Bergson’s mathematical indiscretion – Russell’s Criticism on Bergson) at the conference „Axiomatics: Ancient and Contemporary Perspectives” 31st Novembertagung on the History and Philosophy of Mathematics, University of Humboldt, 26th-28th 11. 2020.