CLASSICAL HARMONY - RULES OF INFERENCE AND THE MEANING OF THE LOGICALCONSTANTS

The thesis that, in a system of natural deduction, the meaning of a lo gical constant is given by some or all of its introduction and elimina tion rules has been developed recently in the work of Dummett, Prawitz , Tennant, and others, by the addition of harmony constraints. Introdu ction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logic s no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified from this proof-theoretic perspecti ve. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the st andard logical constants cannot all be given by their introduction and /or elimination rules; negation, in particular, comes under close scru tiny.