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Connexive class logic

Published online by Cambridge University Press:  12 March 2014

Storrs McCall
Storrs McCall*
Affiliation:
Makerere University College, Kampala, Uganda
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Extract

Student. I've been studying the logic of classes, and can't see how any class can be included in its own complement.

Teacher. Surely you've heard of the null class, which is included in every class, and hence in its own complement?

Student. That also strikes me as somehow implausible. How do you define ‘inclusion’?

Teacher. In the usual way. a is included in b if and only if the intersection of a with the complement of b is null.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 83 - 90
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]McCall, Storrs, Connexive implication, this Journal, Vol. 31 (1966), pp. 415–433.Google Scholar
[2]McCall, Storrs, The completeness of Boolean algebra, forthcoming in Zeitschrift für Mathematische Logik und Grundlagen der Mathematik.Google Scholar
[3]Shepherdson, J. C., On the interpretation of Aristotelian syllogistic, this Journal, vol. 21 (1956), pp. 137–147.Google Scholar
[4]Smiley, Timothy, Syllogism and quantification, this Journal, vol. 27 (1962), pp. 58–72.Google Scholar