David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
E. J. Lemmon (1965). Beginning Logic. Monograph Collection (Matt - Pseudo).
Citations of this work BETA
Thomas Kroedel (2012). Implicit Definition and the Application of Logic. Philosophical Studies 158 (1):131-148.
Nils Kürbis (forthcoming). Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality. Journal of Philosophical Logic:1-15.
Nissim Francez (2014). Harmony in Multiple-Conclusion Natural-Deduction. Logica Universalis 8 (2):215-259.
Similar books and articles
Ruy J. G. B. De Queiroz (2008). On Reduction Rules, Meaning-as-Use, and Proof-Theoretic Semantics. Studia Logica 90 (2):211 - 247.
Ruy J. G. B. de Queiroz (2008). On Reduction Rules, Meaning-as-Use, and Proof-Theoretic Semantics. Studia Logica 90 (2):211-247.
Peter Milne (2007). Existence, Freedom, Identity, and the Logic of Abstractionist Realism. Mind 116 (461):23-53.
Hartley Slater (2008). Harmonising Natural Deduction. Synthese 163 (2):187 - 198.
Julien Murzi & Ole Thomassen Hjortland (2009). Inferentialism and the Categoricity Problem: Reply to Raatikainen. Analysis 69 (3):480-488.
Stephen Read (2000). Harmony and Autonomy in Classical Logic. Journal of Philosophical Logic 29 (2):123-154.
Stephen Read (2010). General-Elimination Harmony and the Meaning of the Logical Constants. Journal of Philosophical Logic 39 (5):557-76.
Added to index2009-01-28
Total downloads96 ( #33,383 of 1,726,249 )
Recent downloads (6 months)9 ( #74,830 of 1,726,249 )
How can I increase my downloads?