Wednesday, 12 May 2021
Shawn Standefer (Slovak Academy of Sciences, Bratislava)
Varieties of necessity in a non-classical setting

Abstract: In standard modal logics, there are three common conceptions of necessity:, the universal conception, the equivalence relation conception, and the axiomatic conception. theses provide distinct presentations of the modal logic S5, commonly used in metaphysics and epistemology. In standard settings, these presentations coincide, giving three views of a single, unified logic. I will explore these different conceptions in the context of the relevant logic R, explaining when they come apart and why that matters. This reveals that there are many options for being an S5-ish extension of R. It further reveals a divide between the universal conception of necessity on the one hand, and the axiomatic conception on the other: The latter is consistent with motivations for relevant logics while the former is not. For the committed relevant logician, necessity cannot be truth in all possible worlds.