David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 18 (1):1-15 (1997)
John Corcoran?s natural deduction system for Aristotle?s syllogistic is reconsidered.Though Corcoran is no doubt right in interpreting Aristotle as viewing syllogisms as arguments and in rejecting Lukasiewicz?s treatment in terms of conditional sentences, it is argued that Corcoran is wrong in thinking that the only alternative is to construe Barbara and Celarent as deduction rules in a natural deduction system.An alternative is presented that is technically more elegant and equally compatible with the texts.The abstract role assigned by tradition and Lukasiewicz to Barbara and Celarent is retained.The two ? perfect syllogisms? serve as ?basic elements? in the construction of an inductively defined set of valid syllogisms.The proposal departs from Lukasiewicz, and follows Corcoran, however, in construing the construction as one in natural deduction.The result is a sequent system with fewer rules and in which Barbara and Celarent serve as basic deductions.To compare the theory to Corcoran?s, his original is reformulated in current terms and generalized.It is shown to be equivalent to the proposed sequent system, and several variations are discussed.For all systems mentioned, a method of Henkin?style completeness proofs is given that is more direct and intuitive than Corcoran?s original
|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
No references found.
Citations of this work BETA
Edgar Andrade-Lotero & Catarina Dutilh Novaes (2012). Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW] Journal of Philosophical Logic 41 (2):387-418.
Klaus Glashoff (2010). An Intensional Leibniz Semantics for Aristotelian Logic. Review of Symbolic Logic 3 (2):262-272.
Ian Pratt-hartmann & Lawrence S. Moss (2009). Logics for the Relational Syllogistic. Review of Symbolic Logic 2 (4):647-683.
John N. Martin (2013). Distributive Terms, Truth, and thePort Royal Logic. History and Philosophy of Logic 34 (2):133-154.
Ian Pratt-Hartmann (2011). The Hamiltonian Syllogistic. Journal of Logic, Language and Information 20 (4):445-474.
Similar books and articles
Torben Braüner (2004). Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW] Journal of Logic, Language and Information 13 (1):1-23.
Phil Corkum (forthcoming). Is Aristotle's Syllogistic a Logic? History and Philosophy of Logic.
Allard Tamminga & Koji Tanaka (1999). A Natural Deduction System for First Degree Entailment. Notre Dame Journal of Formal Logic 40 (2):258-272.
Sara Negri & Jan von Plato (2001). Sequent Calculus in Natural Deduction Style. Journal of Symbolic Logic 66 (4):1803-1816.
Maria Luisa Bonet & Samuel R. Buss (1993). The Deduction Rule and Linear and Near-Linear Proof Simulations. Journal of Symbolic Logic 58 (2):688-709.
Michael Gabbay, Some Formal Considerations on Gabbay's Restart Rule in Natural Deduction and Goal-Directed Reasoning.
Greg Restall & Francesco Paoli (2005). The Geometry of Non-Distributive Logics. Journal of Symbolic Logic 70 (4):1108 - 1126.
Andrzej Indrzejczak (2003). A Labelled Natural Deduction System for Linear Temporal Logic. Studia Logica 75 (3):345 - 376.
David J. Pym (1995). A Note on the Proof Theory the λII-Calculus. Studia Logica 54 (2):199 - 230.
Yannis Delmas-Rigoutsos (1997). A Double Deduction System for Quantum Logic Based on Natural Deduction. Journal of Philosophical Logic 26 (1):57-67.
Added to index2010-08-10
Total downloads18 ( #98,490 of 1,101,947 )
Recent downloads (6 months)1 ( #306,569 of 1,101,947 )
How can I increase my downloads?