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Notes
The restriction to E is surprising for at least two reasons. First, even though from a historical perspective it should be considered as the original relevance logic (going back to the work of Ackermann), the modern founders of relevance logic did disagree on how one should diagnose the paradoxes of material implication. Anderson found both failures of relevance and failures of necessity, whereas Belnap wanted to treat them exclusively as failures of relevance (Mares, personal communication). Second, there is what Mares (2004) calls the “sad story of E,” namely the fact that R (the logic of relevant implication) cannot be considered as the non-modal basis of E.
References
Anderson, A. R., & Belnap, N. D. (1975). Entailment. The logic of relevance and necessity (Vol. 1). Princeton: Princeton University Press.
Boolos, G. S., Burgess, J. P., & Jeffrey, R. C. (2002). Computability and logic (4th ed.). Cambridge: Cambridge University Press.
Haack, S. (1974). Deviant logic. Some philosophical issues. Cambridge: Cambridge University Press.
Mares, E. (2004). Relevant logic. A philosophical interpretation. Cambridge: Cambridge University Press.
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Allo, P. Donald W. Loveland, Richard E. Hodel, and S. G. Sterrett: Three Views of Logic: Mathematics, Philosophy and Computer Science. Minds & Machines 25, 291–296 (2015). https://doi.org/10.1007/s11023-015-9375-9
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DOI: https://doi.org/10.1007/s11023-015-9375-9