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Entailment and relevance1

Published online by Cambridge University Press:  12 March 2014

Nuel D. Belnap
Nuel D. Belnap*
Affiliation:
Yale University
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Extract

Those who object to the identification of strict implication and entail-ment speak in such a way that for A to entail B, A must be relevant to B. This view of entailment agrees not only with that of the naive student of logic (who tends to think the phrase paradoxes of “implication” more accurate than “paradoxes” of implication), but also with that expressed in the initial chapters of many textbooks in logic under the heading “Fallacies of Relevance.”2

In regard to formal theories proposed as explications of the notion of entailment, it becomes important to have at our disposal some formal account of the demand for relevance as between antecedent and consequent of an entailment.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 25 , Issue 2 , June 1960 , pp. 144 - 146
Copyright
Copyright © Association for Symbolic Logic 1960

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Footnotes

1

This research was supported in part by the Office of Naval Research, Group Psychology Branch, Contract No. SAR/Nonr-609(16).

References

[1]Ackermann, Wilhelm, Begründung einer strengen Implikation, this Journal, vol. 21 (1956) pp. 113–128.Google Scholar
[2]Anderson, Alan Ross, Completeness theorems for the systems E of entailment and EQ of entailment with quantification, forthcoming.Google Scholar
[3]Anderson, Alan Ross and Belnap, Nuel D. Jr., A modification of Ackermann's “rigorous implication” [abstract] this Journal, vol. 23 (1958), pp. 457–458.Google Scholar
[4]Baylis, Charles A., Implication and subsumption, Monist, vol. 41 (1931), pp. 392–399.CrossRefGoogle Scholar
[5]Duncan-Jones, A. E., Is strict implication the same as entailment? Analysis, vol. 2 (1934–1935), pp. 26–35.Google Scholar
[6]Nelson, E. J., Intensional relations, Mind, n.s. vol. 39 (1930), pp. 440–453.CrossRefGoogle Scholar