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.

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Citations of this work BETA

An Argument for Minimal Logic.Nils Kürbis - 2019 - Dialectica 73 (1-2):31-63.
What is Wrong with Classical Negation?Nils Kurbis - 2015 - Grazer Philosophische Studien 92 (1):51-86.
Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria : An International Journal for Theory, History and Fundations of Science 24 (2):147-168.
Implicit Definition and the Application of Logic.Thomas Kroedel - 2012 - Philosophical Studies 158 (1):131-148.

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