To philosophize means to reverse the normal direction of the workings of thought […] The most powerful method of investigation known to the mind, infinitesimal calculus, was born of that very reversal Bergson (1974, p. 190).
[Bergson’s method] must be understood on the model of the calculus Papanicolau and Gunter (1987, p. 2).
Abstract
This article highlights the mathematical structure of Henri Bergson’s method. While Bergson has been historically interpreted as an anti-scientific and irrationalist philosopher, he modeled his philosophical methodology on the infinitesimal calculus developed by Leibniz and Newton in the seventeenth century. His philosophy, then, rests on the science of number, at least from a methodological standpoint. By looking at how he conscripted key mathematical concepts (especially the concepts of “limit” and “approximation”) into his philosophy, this article invites us to re-imagine Bergson’s place in the history of Western philosophy.
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Notes
Others who interpret Bergson as an irrationalist include “Benedetto Croce, Leonard M. Marsak, WalterJ. Slatoff, Gerhardt Lehmann, Egon Friedall, Raymond Bayer, [and] Walter Bruning” (Gunter 1999, p. 268). To this list we must add Georges Lefebvre, George Herbert Mead (Joas 1991, p. 64), and Judith Shklar (Shklar 1998, p. 319). For a rebuttal of this view, see Lefebvre and White (2012, p. 11).
Durie (2004, p. 54).
In general, little scholarly attention has been paid to Bergson’s relationship to mathematics, with the exceptions of Milet (1987, 1974) and Durie (2004). This scarcity is alarming given that Bergson was trained in mathematics and that he regularly conscripted mathematical concepts into his writings.
This is my phrase, not Bergson’s.
Bergson describes space and language as two “facets” of the same prism, which is opposed to the prism of time and intuition (1974, p. 32).
(Barr 1913, 640)
Merleau-Ponty (2013, p. 68).
Ibid., p. 209.
Ibid., p. 58.
Ibid., p. 59. For a comparison between Bergson and Merleau-Ponty’s theories of temporality, see Olkowski (2010).
These acts or events are not conscious acts. They are metaphysically significant events that take place as subjects struggle to move from intuition to language, from image to word.
Shklar (1998, p. 63). This, of course, depends on how we define “anti-scientism.” If scientism refers to the naïve belief that facts speak for themselves independently of theory (empiricism), then Bergson is anti-scientistic. But if scientism entails belief in the essential compatibility of scientific and philosophical modes of thought, then he is a champion of scientism (Bergson 1974, p. 43).
This understanding of time has reigned from the time of Zeno’s paradoxes in the fifth century B.C.E. to the time of Spencer’s social evolutionism in the nineteenth century C.E.
Bergson (1998, p. 48).
Ibid., p. 20.
Bergson (1998, p. 49).
Bergson (1974, p. 14).
Ibid., p. 38.
Bergson (1998, p. 44).
In classical metaphysics, the absolute is defined as that which is truly creative, spontaneous, and free. Typically, the absolute is equated with God. Bergson retains the classical notion of the absolute as well as the properties routinely associated with it, but holds that the absolute (understood as the élan vital) is internal rather than external to human experience (Khandker 2013). Guiding us to this absolute “is just the function of philosophy” (Bergson 1974, p. 30). When we commune with the things of life, we “touch something of the absolute,” he says (1998, p. xi). Riquier (2016) holds that Bergson’s understanding of the absolute inoculates him against the Kantian critique of metaphysics since virtually all pre-critical philosophers, especially the ancients, defined the absolute as something beyond rather than within. A Bergsonian intuition, therefore, isn’t the same kind of intuition that Kant insisted was impossible for creatures with rational but finite intellects.
Bergson (1974, p. x).
Bergson (1998) says that this intuition is more lived than represented (fr. “une intuition vécue plutôt que représentée”). It is given as an embodied feeling rather than an abstract idea.
Bergson (1974, p. 162).
A philosophical intuition is a groundbreaking insight, but it must not be confused with the intuition of duration. The latter is the former’s condition of possibility. The intuition of duration, as Bergson says, “is on the road which leads to philosophical intuition,” but it is not itself a philosophical intuition.
Berkeley’s philosophy, for example, reduces to the image of matter as a thin, transparent screen separating Man from God.
Gunter (1999, p. 1).
“Limit” comes from the Latin limen, meaning “threshold.” Priestley defines the limit by the following telling analogy: “the limit of a function, at a point or near its domain, is like the purpose of a human being at a point in time” (Priestly 2012, p. 14). The concept originates in the writings of Archimedes (p. 43).
This example from the integral calculus focuses on a spatial calculation, but the same logic applies to the differential calculus, which deals with issues of acceleration instead of quadrature.
The calculus also spurred a nasty priority dispute between the British and the Germans about whether it was Newton or Leibniz who “really discovered” this technique. This dispute remained unresolved until after Leibniz’s death in 1716 (Bardi 2009). Today, we teach students that Leibniz and Newton invented the calculus independently and that their disagreement was purely notational. While it’s true that they developed different notational systems, it is not true that their dispute was “purely” about notation. Newton and Leibniz’s disagreement was metaphysical. They disagreed about the metaphysical nature of space, with Newton clinging on to an absolutist conception (for theological reasons) and Leibniz preferring a relational view.
Bergson (1974, p. 190).
Ibid.
Bergson borrowed this claim from Félix Ravaisson-Mollien (Bergson 1974, pp. 220–252).
Ibid., p. 191.
Ibid.
Gunter (1999, p. 1).
Bergson (1974, p. 166).
Bergson (1998, p. 110).
Ibid., 178.
Ibid., 120.
Ibid.
Ibid., 118.
Durant stresses Bergson’s relationship to the German Lebensphilosophie tradition, characterizing him as “the David destined to slay the Goliath of materialism” (Durant 1953, p. 449). Solomon places more value on Bergson’s interest in the metaphysics of change and dubs him “the modern Heraclitus” (Solomon 1911, p. 28). Lefebvre and White focus on the mystical and spiritual elements of Bergsonism and portray him as a “transcendentalist” (Lefebvre and White 2012).
For an account of how contemporary philosophical discourse is policed by the philosophical profession via concepts such as “rationality” and “intelligibility,” see Spera and Peña-Guzmán (2019).
Bergson (1974, p. 66).
Gayon (2005, pp. 50–58).
Gayon calls Bergsonism a “positive metaphysics” (Gayon 2005, p. 43).
Papanicolau and Gunter (1987, p. xiv).
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I would like to thank Tim Johnston, Ellie Anderson, and Rebecca Longtin for giving me feedback on an early draft, the CPR reviewers for their helpful and constructive comments on my original submission, and the editorial staff for the logistical support they offered me along the way.
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Peña-Guzmán, D.M. Bergson’s philosophical method: At the edge of phenomenology and mathematics. Cont Philos Rev 53, 85–101 (2020). https://doi.org/10.1007/s11007-020-09487-9
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DOI: https://doi.org/10.1007/s11007-020-09487-9