The Modal Logic of Arithmetic Potentialism and the Universal Algorithm
Joel David Hamkins · Philosophia Mathematica · 2026
Abstract I investigate the modal commitments of the various conceptions of arithmetic potentialism that arise from the models of arithmetic by taking them as realms of feasibility with respect to their natural extension concepts, such as end extensions and arbitrary extensions, thereby shedding light on the range of differing philosophical positions available for arithmetic potentialism. The main analysis makes fundamental use of the universal algorithm, of which this article provides a simplified, self-contained account.