David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 163 (2):187 - 198 (2008)
Prawitz proved a theorem, formalising 'harmony' in Natural Deduction systems, which showed that, corresponding to any deduction there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can extend the theorem to the classical case. Properly arranged there is a thoroughgoing 'harmony', in the classical rules. Indeed, as we shall see, they are, all together, far more 'harmonious' in the general sense than has been commonly observed. As this paper will show, the appearance of disharmony has only arisen because of the illogical way in which natural deduction rules for Classical Logic have been presented
|Keywords||No keywords specified (fix it)|
No categories specified
(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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
Torben Braüner (2004). Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW] Journal of Logic, Language and Information 13 (1):1-23.
Stephen Read (2000). Harmony and Autonomy in Classical Logic. Journal of Philosophical Logic 29 (2):123-154.
Sara Negri & Jan von Plato (2001). Sequent Calculus in Natural Deduction Style. Journal of Symbolic Logic 66 (4):1803-1816.
Peter Milne (1994). Classical Harmony: Rules of Inference and the Meaning of the Logical Constants. Synthese 100 (1):49 - 94.
M. W. Bunder (1982). Deduction Theorems for Weak Implicational Logics. Studia Logica 41 (2-3):95 - 108.
Yannis Delmas-Rigoutsos (1997). A Double Deduction System for Quantum Logic Based on Natural Deduction. Journal of Philosophical Logic 26 (1):57-67.
James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.
Added to index2009-01-28
Total downloads39 ( #48,806 of 1,140,379 )
Recent downloads (6 months)1 ( #140,193 of 1,140,379 )
How can I increase my downloads?