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SUBSTITUTION IN RELEVANT LOGICS

Published online by Cambridge University Press:  17 September 2019

TORE FJETLAND ØGAARD
TORE FJETLAND ØGAARD*
Affiliation:
Department of Philosophy, University of Bergen
*
†DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BERGEN PO BOX 7805 5020 BERGEN NORWAY E-mail: [email protected]
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Abstract

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form $s\dot{ = }t \wedge A\left( s \right) \to A\left( t \right)$—as these are put forward in Priest’s books In Contradiction and An Introduction to Non-Classical Logic: From If to Is. The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules is probed and it is argued that Substitution ought to fail.

Keywords

03A0503B4703B5303C0703C9003E70identityLeibniz’s lawsubstitutionrelevant logicstableaux systempossible world semantics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 3 , September 2020 , pp. 655 - 680
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Copyright
Copyright © Association for Symbolic Logic 2019 

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