Logic and Logical Philosophy:1-28 (forthcoming)

Authors
Shawn Standefer
National Taiwan University
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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DOI 10.12775/llp.2022.011
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Actual Issues for Relevant Logics.Shawn Standefer - 2020 - Ergo: An Open Access Journal of Philosophy 7.

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Citations of this work BETA

What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.

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