Proceedings of the XXIII World Congress of Philosophy

Volume 55, 2018

Philosophy of Logic

S7. Iterated Modalities: Are there Possible Impossibilities?

Following Halldén, we define S7 as the system generated by the addition of ↓ ↓ p to S3. Initial motivation for the extension comes from Halldén’s paradox. In addition to resolving the paradox, the resulting system generates a helpful framework for comparing classical propositional logic (CPL) with otherwise incommensurable logics, including paraconsistent logics such as LP. S7, although non-regular and non-normal, thus turns out to be preferable to systems such as S4 and S5 as an account of alethic modality.