Synthese 100 (1):49 - 94 (1994)

Peter Milne
University of Stirling
The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified from this proof-theoretic perspective. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the standard logical constants cannot all be given by their introduction and/or elimination rules; negation, in particular, comes under close scrutiny.
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DOI 10.1007/BF01063921
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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Elements of Intuitionism.Michael Dummett - 1977 - Oxford University Press.
The Foundations of Frege’s Logic.Pavel Tichý - 1988 - Berlin and New York: De Gruyter.
Anti-Realism and Logic: Truth as Eternal.Neil Tennant - 1987 - Oxford, England: Oxford University Press.
The Runabout Inference-Ticket.A. Prior - 1960 - Analysis 21 (2):38.

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Citations of this work BETA

What is Wrong with Classical Negation?Nils Kürbis - 2015 - Grazer Philosophische Studien 92 (1):51-86.
An Argument for Minimal Logic.Nils Kürbis - 2019 - Dialectica 73 (1-2):31-63.
Speech Acts, Categoricity, and the Meanings of Logical Connectives.Ole Thomassen Hjortland - 2014 - Notre Dame Journal of Formal Logic 55 (4):445-467.

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