Synthese (8):1-32 (2019)

Tore Fjetland Øgaard
University of Bergen
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
Categories (categorize this paper)
Reprint years 2019, 2020
DOI 10.1007/s11229-019-02507-z
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,037
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.

View all 35 references / Add more references

Citations of this work BETA

Substitution in Relevant Logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic (3):1-26.
Confused Entailment.Tore Fjetland Øgaard - forthcoming - Topoi:1-13.

View all 6 citations / Add more citations

Similar books and articles

A Plea for KR.Alison Duncan Kerr - 2019 - Synthese 198 (4):3047-3071.
Variable Sharing in Substructural Logics: An Algebraic Characterization.Guillermo Badia - 2018 - Bulletin of the Section of Logic 47 (2):107-115.
Halldén Completeness for Relevant Modal Logics.Takahiro Seki - 2015 - Notre Dame Journal of Formal Logic 56 (2):333-350.
Failure of Interpolation in Relevant Logics.Alasdair Urquhart - 1993 - Journal of Philosophical Logic 22 (5):449 - 479.
Skolem Functions in Non-Classical Logics.Tore Fjetland Øgaard - 2017 - Australasian Journal of Logic 14 (1):181-225.
Neighborhoods for Entailment.Lou Goble - 2003 - Journal of Philosophical Logic 32 (5):483-529.


Added to PP index

Total views
13 ( #748,561 of 2,454,419 )

Recent downloads (6 months)
1 ( #449,269 of 2,454,419 )

How can I increase my downloads?


My notes