The Journal of Symbolic Logic

Research Article

Completeness of an ancient logic

John Corcoran

State University of New York at Buffalo, Amherst, New York 14226

In previous articles ([4], [5]) it has been shown that the deductive system developed by Aristotle in his “second logic” (cf. Bochenski [2, p. 43]) is a natural deduction system and not an axiomatic system as previously had been thought [6]. It was also pointed out 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 formable in the language of the system is demonstrable 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 Aristotélian system.

(Received January 07 1972)