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date: 03 August 2020

Abstract and Keywords

This article examines the statement that a property is true for ‘almost all’ considered objects, in a precise mathematical sense, by referring to Henri Poincaré’s reflections on the generality of recurring trajectories. In 1890, Poincaré introduces a statement of a new type in which he formulates mathematically the remark that he had previously made in vague terms: ‘the trajectories that have this property [of stability, AR] are more general than those that do not’. This article first considers how Poincaré adapts the calculus of probability to show that the non-recurring trajectories are exceptional before analyzing the proofs of the recurrence theorem and the corollary that Poincaré added to the theorem. It also discusses the change of status of the recurrence theorem between 1889 and 1891 and suggests that the confinement inside the trajectory surfaces seemed to be the key property for the definition of stability.

Keywords: property, Henri Poincaré, generality, recurring trajectories, stability, calculus of probability, non-recurring trajectories, recurrence theorem, corollary, trajectory surfaces

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