Completeness of an ancient logic

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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DOI 10.2307/2272415
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Neil Tennant (2014). Aristotle's Syllogistic and Core Logic. History and Philosophy of Logic 35 (2):120-147.
John Corcoran (2009). Aristotle's Demonstrative Logic. History and Philosophy of Logic 30 (1):1-20.
John M. Martin (1997). Aristotle'S Natural Deduction Reconsidered. History and Philosophy of Logic 18 (1):1-15.

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