Varieties of Relevant S5
Journal
LOGIC AND LOGICAL PHILOSOPHY
Journal Volume
32
Journal Issue
1
Start Page
53
End Page
80
Date Issued
2023-03
Author(s)
Abstract
In classically based modal logic, there are three common conceptions of necessity, the universal conception, the equivalence relation conception, and the axiomatic conception. They provide distinct presentations of the modal logic S5, all of which coincide in the basic modal language. We explore these different conceptions in the context of the relevant logic R, demonstrating where they come apart. 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 the truth in all possible worlds.
Subjects
relevant modal logic; S5; universal necessity; conceptions of necessity; SIMPLIFIED SEMANTICS
SDGs
Publisher
NICOLAUS COPERNICUS UNIV TORUN
Type
journal article