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Completeness of an ancient logic

Published online by Cambridge University Press:  12 March 2014

John Corcoran
John Corcoran*
Affiliation:
State University of New York at Buffalo, Amherst, New York 14226
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Extract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 37 , Issue 4 , December 1972 , pp. 696 - 702
Copyright
Copyright © Association for Symbolic Logic 1972

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References

REFERENCES

[1] Aristotle, Prior analytics.Google Scholar
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[3]Church, Alonzo, Introduction to mathematical logic. Vol. I, Princeton University Press, Princeton, N.J., 1956.Google Scholar
[4]Corcoran, John, Aristotle's natural deduction system, this Journal, vol. 37 (1972), p. 437. Abstract.Google Scholar
[5]Corcoran, John, A mathematical model of Aristotle's syllogistic, Archiv für Geschichte der Philosophie (to appear).Google Scholar
[6]Łukasiewcz, Jan, Aristotle's syllogistic from the standpoint of modern formal logic, Clarendon Press, Oxford, 1951.Google Scholar
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