Journal of Philosophical Logic 29 (2):123-154 (2000)

Stephen Read
University of St. Andrews
Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen's. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic
Keywords classical negation  Dummett  fundamental assumption  Gentzen  multiple-conclusion logic
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Reprint years 2004
DOI 10.1023/a:1004787622057
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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
The Logical Syntax of Language.Rudolf Carnap - 1937 - London: K. Paul, Trench, Trubner & Co..
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Introduction to Mathematical Logic.Alonzo Church - 1944 - London: Oxford University PRess.

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Citations of this work BETA

Inferentialism: Why Rules Matter.Jaroslav Peregrin - 2014 - London and New York: Palgrave-Macmillan.
Weak Assertion.Luca Incurvati & Julian J. Schlöder - 2019 - Philosophical Quarterly 69 (277):741-770.
General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.

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