David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 37 (4):696-702 (1972)
In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system.
|Keywords||Aristotle syllogistic completeness natural deduction indirect deduction axiom-free underlying logic semantics syntax multi-premise syllogisms|
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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.
John Corcoran (2009). Aristotle's Demonstrative Logic. History and Philosophy of Logic 30 (1):1-20.
Robin Smith (1982). What Is Aristotelian Ecthesis? History and Philosophy of Logic 3 (2):113-127.
Klaus Glashoff (2010). An Intensional Leibniz Semantics for Aristotelian Logic. Review of Symbolic Logic 3 (2):262-272.
Ian Pratt-Hartmann (2013). The Syllogistic with Unity. Journal of Philosophical Logic 42 (2):391-407.
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