Completeness of an ancient logic

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

Authors
John Corcoran
State University of New York, Buffalo
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.
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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References found in this work BETA

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

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Citations of this work BETA

Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
Logics for the Relational Syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
Aristotle's Syllogistic and Core Logic.Neil Tennant - 2014 - History and Philosophy of Logic 35 (2):120-147.
Logical Foundations and Kant's Principles of Formal Logic.Srećko Kovač - 2019 - History and Philosophy of Logic 41 (1):48-70.

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