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Abstract

I am not a Relevantist. But, were I one, I might speak something like this. β€œIn their epochal work Entailment (vol. I, Anderson and Belnap, 1975, with others), Relevant Logicians have led us out of the Material dominions of the great Boole. They wave the Archetypal Form of Inference A β†’ A, and the Truth-functional Sea parts, that the Children of Relevance might reach the far side in safety, there to practice Natural Deduction according to the systems of their choice in peace, tranquility, and mathematical exactitude. But the Sea returns to claim the pursuing Official Logicians, who are weighed down by false theorems. Just is the fate of these Officials. For they have bowed down before Irrelevant Entailments in which antecedents and consequents share no variable. And they have allowed the Accidental Premiss to beget the Necessitive Conclusion. Drowned are they in their own Paradoxes and Contradictions; and in the Flood of Nonsense that follows therefrom.”

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References

  • Ackermann, W., 1956, BegrΓΌndung einer strengen” Implikation, Journal of Symbolic Logic, 21:113–128.

    ArticleΒ  Google ScholarΒ 

  • Anderson, A. R. and Belnap, N. D. Jr., 1962, The Pure Calculus of Entailment, Journal of Symbolic Logic, 27:19–52.

    ArticleΒ  Google ScholarΒ 

  • Anderson, A. R. and Belnap, N. D. Jr., 1975, β€œEntailment, the Logic of Relevance and Necessity,” vol. 1, Princeton University Press, Princeton.

    Google ScholarΒ 

  • Bacon, J., 1966, β€œBeing and Existence: Two Ways of Formal Ontology,” Ph.D. thesis, Yale University, New Haven.

    Google ScholarΒ 

  • Belnap, N. D. Jr., 1959, β€œThe Formalization of Entailment,” Ph.D. thesis, Yale University, New Haven.

    Google ScholarΒ 

  • Belnap, N. D. Jr., 1967, Intensional Models for First Degree Formulas, Journal of Symbolic Logic, 32:1–22.

    ArticleΒ  Google ScholarΒ 

  • Belnap, N. D. Jr., 1984, Return to Relevance, typescript, Pittsburgh.

    Google ScholarΒ 

  • Belnap, N. D. Jr. and Dunn, J. M., 1981, Entailment and the Disjunctive Syllogism, in: β€œContemporary Philosophy: A New Survey,” G. Floistad and G. H. von Wright, eds., Martinus Nijhoff, The Hague.

    Google ScholarΒ 

  • Brady, R. T., 1982, Non-Triviality of Dialectical Set Theory, in: β€œParaconsistent Logic,” R. Routley, G. Priest and J. Norman, eds., Philosophia Verlag, Munich (forthcoming).

    Google ScholarΒ 

  • Church, A., 1951, The Weak Theory of Implication, in: β€œKontrolliertes Denken, Untersuchungen zum LogikkalkΓΌl und der Logik der Einzelwissenschaften,” A. Menne, A. Wilhelmy, and H. Angstl, eds., Alber, Munich.

    Google ScholarΒ 

  • Coffa, J. A., 1975, Fallacies of Modality, in: β€œEntailment, the Logic of Relevance and Necessity,” A. R. Anderson and N. D. Belnap Jr., eds., Princeton University Press, Princeton.

    Google ScholarΒ 

  • Curry, H. B. and Feys, R., 1958, β€œCombinatory Logic,” vol. 1, North-Holland, Amsterdam.

    Google ScholarΒ 

  • Dunn, J. M., 1966, β€œThe Algebra of Intensional Logics,” Ph.D. thesis, University of Pittsburgh, Ann Arbor.

    Google ScholarΒ 

  • Kripke, S. A., The Problem of Entailment, Journal of Symbolic Logic, 24:324.

    Google ScholarΒ 

  • Maximova, L., 1973, Semantics for the Calculus E of Entailment, Bulletin of the Section of Logic, Polish Academy of Sciences, 2:18–21.

    Google ScholarΒ 

  • Martin, E. P., 1978, β€œThe P-W Problem,” Ph.D. thesis, Australian National University, Canberra.

    Google ScholarΒ 

  • McRobbie, M. A., 1979, β€œA Proof Theoretic Investigation of Relevant and Modal Logics,” Ph.D. thesis, Australian National University, Canberra.

    Google ScholarΒ 

  • Meyer, R. K., 1975, Arithmetic Formulated Relevantly, typescript, Australian National University, Canberra.

    Google ScholarΒ 

  • Meyer, R. K., 1979, Why I am Not a Relevantist, Research Paper No. 1, Logic Group, Australian National University, Canberra.

    Google ScholarΒ 

  • Meyer, R. K. and Dunn, J. M., 1969, E, R and Ξ³, Journal of Symbolic Logic, 34:460–474.

    ArticleΒ  Google ScholarΒ 

  • Meyer, R. K. and Martin, E. P., 1984, Logic on the Australian Plan, typescript, Australian National University, Canberra.

    Google ScholarΒ 

  • Meyer, R. K. and McRobbie, M. A., 1982, Multisets and Relevant Implication I and II, Australasian Journal of Philosophy, 60:107–139, 265-281.

    ArticleΒ  Google ScholarΒ 

  • Meyer, R. K. and Routley, R., 1973, Classical Relevant Logics I, Studia Logica, 32:51–66.

    ArticleΒ  Google ScholarΒ 

  • Mortensen, C., 1983, The Validity of Disjunctive Syllogism is Not So Easily Proved, Notre Dame Journal of Formal Logic, 24:35–40.

    ArticleΒ  Google ScholarΒ 

  • Routley, R., 1983, Relevantism and the Problem as to When Material Detachment and the Disjunctive Syllogism Argument Can be Correctly Used, Research Paper No. 12, Logic Group, Australian National University, Canberra.

    Google ScholarΒ 

  • Routley, R., and Meyer, R. K., 1973, The Semantics of Entailment I, in: β€œTruth, Syntax and Modality,” H. Leblanc, ed., North-Holland, Amsterdam.

    Google ScholarΒ 

  • Routley, R. and Routley, V., 1969, A Fallacy of Modality, Nous, 3:129–153.

    ArticleΒ  Google ScholarΒ 

  • Routley, R. and Routley, V., 1972, Semantics of First Degree Entailment, Nous, 6:335–359.

    ArticleΒ  Google ScholarΒ 

  • Routley, R. with Meyer, R. K., Plumwood, V. and Brady, R. T., 1984, β€œRelevant Logics and Their Rivals, Part 1: the Basic Philosophical and Semantical Theory,” Ridgeview, Atascadero, California.

    Google ScholarΒ 

  • Slaney, J. K., 1982, The Irrationality of the Square Root of 2, typescript, University of Queensland, Brisbane.

    Google ScholarΒ 

  • Thistlewaite, P. B., 1984, β€œAutomated Theorem-Proving in Non-Classical Logics,” Ph.D. thesis, Australian National University, Canberra.

    Google ScholarΒ 

  • Urquhart, A., 1972, β€œThe Semantics of Entailment,” Ph.D. thesis, University of Pittsburgh, Ann Arbor.

    Google ScholarΒ 

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Meyer, R.K. (1985). A Farewell to Entailment. In: Dorn, G., Weingartner, P. (eds) Foundations of Logic and Linguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0548-2_25

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  • DOI: https://doi.org/10.1007/978-1-4899-0548-2_25

  • Publisher Name: Springer, Boston, MA

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