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HARMONISING HARMONY

Published online by Cambridge University Press:  15 May 2015

LUCA TRANCHINI
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Abstract

The term ‘harmony’ refers to a condition that the rules governing a logical constant ought to satisfy in order to endow it with a proper meaning. Different characterizations of harmony have been proposed in the literature, some based on the inversion principle, others on normalization, others on conservativity. In this paper we discuss the prospects for showing how conservativity and normalization can be combined so to yield a criterion of harmony equivalent to the one based on the inversion principle: We conjecture that the rules for connectives obeying the inversion principle are conservative over normal deducibility. The plausibility of the conjecture depends in an essential way on how normality is characterized. In particular, a normal deduction should be understood as one which is irreducible, rather than as one which does not contain any maximal formula.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 3 , September 2015 , pp. 411 - 423
Copyright
Copyright © Association for Symbolic Logic 2015 

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