The Modal Logic of Arithmetic Potentialism and the Universal Algorithm
Abstract
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.
Fields of Study & Subjects
Logic
Reasoning
and Knowledge
Advanced Algebra and Logic
Philosophy and Theoretical Science
Publication details
- Journal / source
- Philosophia Mathematica
- Publisher
- Oxford University Press (OUP)
- Volume
- 34
- Issue
- 1
- Pages
- 137–182
- Publication date
- 8 January 2026
- Language
- EN