Classification and deontic explosion for contrary-to-duty obligations
For researchers in deontic logic, the paper highlights a limitation in a recent system and offers a structural insight into an earlier, stronger system.
The paper identifies a deontic explosion problem in Carmo and Jones' most recent axiom system for conditional obligation, where a student not achieving the highest grade makes any passing grade acceptable. It also provides a classification of all satisfying models for the strongest 1997 system, characterized by a single forbidden possible world.
Carmo and Jones have presented a sequence of candidate axiom systems for conditional obligation between 1997 and 2022. For their most recent system we demonstrate a limited form of deontic explosion: given that a student does not get the highest possible grade on a test, any other passing grade is acceptable. In addition to that negative result, we give a positive one: revisiting the strongest version of Carmo and Jones' 1997 system, we provide a surprising classification of all satisfying models in terms of a single forbidden possible world.