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HARMONIC INFERENTIALISM AND THE LOGIC OF IDENTITY

Published online by Cambridge University Press:  09 February 2016

STEPHEN READ
STEPHEN READ*
Affiliation:
University of St Andrews
*
*UNIVERSITY OF ST ANDREWS ARCHÉ RESEARCH CENTRE 17-19 COLLEGE ST. ST ANDREWS KY16 9AA SCOTLAND, UK E-mail: [email protected]
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Abstract

Inferentialism claims that the rules for the use of an expression express its meaning without any need to invoke meanings or denotations for them. Logical inferentialism endorses inferentialism specifically for the logical constants. Harmonic inferentialism, as the term is introduced here, usually but not necessarily a subbranch of logical inferentialism, follows Gentzen in proposing that it is the introduction-rules which give expressions their meaning and the elimination-rules should accord harmoniously with the meaning so given. It is proposed here that the logical expressions are those which can be given schematic rules that lie in a specific sort of harmony, general-elimination (ge) harmony, resulting from applying a certain operation, the ge-procedure, to produce ge-rules in accord with the meaning defined by the I-rules. Griffiths (2014) claims that identity cannot be given such rules, concluding that logical inferentialists are committed to ruling identity a nonlogical expression. It is shown that the schematic rules for identity given in Read (2004), slightly amended, are indeed ge-harmonious, so confirming that identity is a logical notion.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 408 - 420
Copyright
Copyright © Association for Symbolic Logic 2016 

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