Completeness of an ancient logic

Journal of Symbolic Logic 37 (4):696-702 (1972)
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Abstract

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.

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Author's Profile

John Corcoran
PhD: Johns Hopkins University; Last affiliation: University at Buffalo

References found in this work

A History of Formal Logic.I. M. Bocheński & Ivo Thomas - 1961 - Science and Society 27 (4):492-494.
Introduction to Mathematical Logic.Max Black - 1956 - Journal of Symbolic Logic 22 (3):286-289.
Archiv für Geschichte der Philosophie.[author unknown] - 1887 - Revue Philosophique de la France Et de l'Etranger 23:551-551.

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