David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Synthese 100 (1):49 - 94 (1994)
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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References found in this work BETA
Michael A. E. Dummett (1991). The Logical Basis of Metaphysics. Harvard University Press.
Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
Neil Tennant (1987). Anti-Realism and Logic: Truth as Eternal. Oxford University Press.
Citations of this work BETA
Nils Kürbis (2015). Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality. Journal of Philosophical Logic 44 (6):713-727.
Thomas Kroedel (2012). Implicit Definition and the Application of Logic. Philosophical Studies 158 (1):131-148.
Nissim Francez (2014). Harmony in Multiple-Conclusion Natural-Deduction. Logica Universalis 8 (2):215-259.
Peter Milne (1998). Disjunction and Disjunctive Syllogism. Canadian Journal of Philosophy 28 (1):21 - 32.
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