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 into his philosophy, this article invites us to re-imagine Bergson’s place in the history of Western philosophy.

ABSTRACT This article examines Bergson’s critique of intensive magnitude in Time and Free Will. I demonstrate how his rejection of a different kind of quantity that is ordinal and does not allow measurement, and the underlying strict dualism of quantity and quality, is inconsistent with both the letter and the spirit of his later philosophy. I dismantle two main strategies for explaining these inconsistencies. Furthermore, I argue that Bergson’s simplistic conception of quantity in terms of homogeneous multiplicity, which is operative (...) in his rejection of an alternative conception of quantity, lacks justification in the face of the transformations that the concept of quantity underwent in the history of mathematics and physics. (shrink)

This article attempts to show that, in opposition to analytical and phenomenological traditions, when Bergson examines the epistemological problem of the measurement of sensations, he tries to connect it with the philosophical question of human freedom, which science cannot solve. It is not possible to conclude that every philosophical problem is a scientific problem. But philosophy does not come first. It needs an indirect approach and a metaphorical language. As Bergson says, intuition is riding intelligence. The problem of measuring sensation (...) concerns the difficulty of establishing sensation as a mental object or a representation that can be compared or distinguished from others. What sensation does is not separate from what it does to us. It is not only something thought, it is something lived and connected with duration, like human freedom, which is nothing but a specific feeling. This living is not a phenomenological illusion, it is a naturalistic puzzle. If we take the Bergsonian conclusion, sensation is simply a spiritualistic reality. We contest this dual approach, but we try to separate this wrong solution from the very accurate puzzle that Bergson presents us with. (shrink)