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Relevant implication and the case for a weaker logic

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Abstract

We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic DJd. The misgivings centre on some recent negative results concerning 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 DJd with respect to a content semantics, which embraces the concept of meaning containment.

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Authors and Affiliations

  1. Philosophy Department, La Trobe University, Bundoora, Victoria, Australia

    Ross T. Brady

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  1. Ross T. Brady
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Additional information

Dedicated to Robert K. Meyer on the occasion of his 60th birthday

This paper was presented to the Australasian Association for Logic Conference, A.N.U., Canberra, in July, 1992. This Conference commemorated the 60th birthday of Robert K. Meyer, in recognition of the enormous contribution he has made to Logic, especially to Relevant Logic, and of the general lift he has given to the field in his adopted country, Australia. This paper owes its inspiration to Robert Meyer's “Farewell to Entailment” [37] and his earlier “Why I am not a Relevantist” [35]. This paper also owes a great deal to Richard Sylvan who has consistently supported weaker relevant logics at a time when stronger relevant logics were in vogue (see especially [47], Chapter 3). In writing this paper, I have also benefited from conversations with Nuel Belnap, Michael Dunn, Kit Fine and Alasdair Urquhart during a period of study leave in 1991. I also thank Robert Meyer, Michael Dunn, Martin Bunder and John Slaney for useful comments on my conference paper. I would also like to thank the referees of this Journal for their helpful comments, which led me to make substantial improvements to this paper.

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Brady, R.T. Relevant implication and the case for a weaker logic. J Philos Logic 25, 151–183 (1996). https://doi.org/10.1007/BF00247002

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