Inconsistent sets and how to compute them
Journal
Synthese
ISSN
1573-0964
Publisher
Springer Science and Business Media LLC
Date Issued
2026
Author(s)
Weber, Zach
Type
text::journal::journal article
Abstract
The idea of a paraconsistent computability theory has been proposed as a way to work effectively with inconsistent sets of numbers. The viability of such a theory, though—the very coherence of the idea of an ‘inconsistent recursive relation’—has been called into doubt, most recently in (Choi, Synthese 200(5):418, 2022). In this paper we remove some doubt, by setting out a simple model of (naïve) set theory in LP, showing how to compute inconsistent sets in terms of extensions and antiextensions, and establishing further representability results. This suggests a way that a longstanding and apparently impossible-to-answer question—how can inconsistency be computed?—can be answered. ©The author ©Springer.
License
Acceso Restringido
How to cite
Cano-Jorge, F., Weber, Z. Inconsistent sets and how to compute them. Synthese 207, 55 (2026). https://doi.org/10.1007/s11229-025-05388-7