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THE RELEVANCE OF PREMISES TO CONCLUSIONS OF CORE PROOFS

Published online by Cambridge University Press:  20 March 2015

NEIL TENNANT
NEIL TENNANT*
Affiliation:
Department of Philosophy, The Ohio State University
*
*DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITY COLUMBUS, OHIO 43210 E-mail: tennant.9@osu.edu
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Abstract

The rules for Core Logic are stated, and various important results about the system are summarized. We describe its relationship to other systems, such as Classical Logic, Intuitionistic Logic, Minimal Logic, and the Anderson–Belnap relevance logic R. A precise, positive explication is offered of what it is for the premises of a proof to connect relevantly with its conclusion. This characterization exploits the notion of positive and negative occurrences of atoms in sentences. It is shown that all Core proofs are relevant in this precisely defined sense. We survey extant results about variable-sharing in rival systems of relevance logic, and find that the variable-sharing conditions established for them are weaker than the one established here for Core Logic (and for its classical extension). Proponents of other systems of relevance logic (such as R and its subsystems) are challenged to formulate a stronger variable-sharing condition, and to prove that R or any of its subsystems satisfies it, but that Core Logic does not. We give reasons for pessimism about the prospects for meeting this challenge.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 743 - 784
Copyright
Copyright © Association for Symbolic Logic 2015 

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