Relevant Implication and the case for a Weaker Logic^\ast

Author: Brady R.T.¹

Source: Journal of Philosophical Logic, Volume 25, Number 2, April 1996 , pp. 151-183(33)

Publisher: Springer

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Abstract:

We collect together some misgivings about the logic {\rm R} of relevant inplication, and then give support to a weak entailment logic {\rm DJ^d}. The misgivings centre on some recent negative results concerning {\rm R}, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for {\rm DJ^d} with respect to a content semantics, which embraces the concept of meaning containment.

Language: English

Document Type: Regular paper

Affiliations: 1: Philosophy Department, La Trobe University, Bundoora, Victoria, Australia

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