Synthese:1-32 (2019)

Authors
Tore Fjetland Øgaard
University of Bergen
Abstract
Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing.
Keywords Disjunctive syllogism  Entailment  Modality  Paraconsistency  Relevant logics  Suppression
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Reprint years 2019, 2020
DOI 10.1007/s11229-019-02507-z
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Farewell to Suppression-Freedom.Tore Fjetland Øgaard - 2020 - Logica Universalis 14 (3):297-330.

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