Zermelian Extensibility
Abstract
ABSTRACT According to an influential idea in the philosophy of set theory, certain mathematical concepts, such as the notion of a well‐order and set, are indefinitely extensible. Following Parsons (1983), this has often been cashed out in modal terms. This paper explores instead an extensional articulation of the idea, formulated in higher‐order logic, that straightforwardly formalizes some remarks of Zermelo. The resulting picture is incompatible with the idea that the entire universe can be well‐ordered, but entirely consistent with the idea that the sets of any set‐theoretic universe can be.
Fields of Study & Subjects
Philosophy and Theoretical Science
Computability
Logic
AI Algorithms
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- Philosophy and Phenomenological Research
- Publisher
- Wiley
- Volume
- 112
- Issue
- 2
- Pages
- 421–436
- Publication date
- 19 January 2026
- Language
- EN