Divergent Potentialism : A Modal Analysis With an Application to Choice Sequences

Ethan BRAUER*, Øystein LINNEBO, Stewart SHAPIRO

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

Abstract

Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we overcome those challenges. Finally, we apply our modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms.
Original languageEnglish
Article numbernkab031
JournalPhilosophia Mathematica
DOIs
Publication statusE-pub ahead of print - 27 Dec 2021

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