Varieties of Relevant S5

Logic and Logical Philosophy 32 (1):53–80 (2023)
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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.

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Shawn Standefer
National Taiwan University

Citations of this work

What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
Stratified Restricted Universals.Michael Calasso & Shay Allen Logan - 2023 - Asian Journal of Philosophy 2 (2):44.
One Variable Relevant Logics are S5ish.Nicholas Ferenz - 2024 - Journal of Philosophical Logic 53 (4):909-931.

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References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Depth Relevance and Hyperformalism.Shay Allen Logan - 2022 - Journal of Philosophical Logic 51 (4):721-737.
Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.

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