2024/07/31 by Sylvia Wenmackers · 1 voice
Arts and Humanities · Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis #Philosophy and History of Science
paper · pdf · doi:10.1007/s11229-024-04622-y
openalex publication_date 2024/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
Abstract To analyse contingent propositions, this paper investigates how branching time structures can be combined with probability theory. In particular, it considers assigning infinitesimal probabilities—available in non-Archimedean probability theory—to individual histories. This allows us to introduce the concept of ‘remote possibility’ as a new modal notion between ‘impossibility’ and ‘appreciable possibility’. The proposal is illustrated by applying it to a future contingent and a historical counterfactual concerning an infinite sequence of coin tosses. The latter is a toy model that is used to illustrate the applicability of the proposal to more realistic physical models.