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RELEVANCE FOR THE CLASSICAL LOGICIAN

  • ETHAN BRAUER (a1)
Abstract

Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection.

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*DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITY 350 UNIVERSITY HALL 230 N. OVAL MALL COLUMBUS, OH 43210, USA E-mail: eebrauer@gmail.com
References
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Abramsky, S. (1993). Computational interpretations of linear logic. Theoretical Computer Science, 111, 357.
Anderson, A. R. & Belnap, N. D. (1962). Tautological entailments. Philosophical Studies, 13 (1), 924.
Anderson, A. R. & Belnap, N. D. (1975). Entailment: The Logic of Relevance and Entailment, Vol. I. Princeton: Princeton University Press.
Anderson, A. R., Belnap, N. D., & Dunn, J. M. (1992). Entailment: The Logic of Relevance and Entailment, Vol. II. Princeton: Princeton University Press.
Avron, A. (1984). Relevant entailment—Semantics and formal systems. Journal of Symbolic Logic, 49(2), 334342.
Avron, A. (2014). What is a relevance logic? Annals of Pure and Applied Logic, 165, 2648.
Bennett, J. (1965). Review: T. J. Smiley, Entailment and Deducibility and Alan Ross Anderson and Nuel D. Belnap, The Calculus of Pure Entailment. Journal of Symbolic Logic, 30(2), 240241.
Boolos, G., Burgess, J., & Jeffrey, R. (2007). Computability and Logic (fifth edition). New York: Cambridge University Press.
Burgess, J. (1981). Relevance: A fallacy? Notre Dame Journal of Formal Logic, 22, 97104.
Chang, C. & Keisler, H. J. (2012). Model Theory (third edition). Mineola, NY: Dover.
Conan Doyle, A. (1976). The adventure of the priory school. In The Original Illustrated Sherlock Holmes. Edison, NJ: Castle Books, pp. 508526.
Copeland, B. (1980). The trouble Anderson and Belnap have with relevance. Philosophical Studies, 37, 325334.
Copeland, B. (1984). Horseshoe, hook, and relevance. Theoria, 50, 148164.
Diaz, M. R. (1981). Topics in the Logic of Relevance. Munich: Philosophia Verlag.
Dunn, J. M. & Restall, G. (2002). Relevance logic. In Gabbay, D. and Geunther, F., editors. Handbook of Philosophical Logic, Vol. 6. Dordrecht: Kluwer Academic, pp. 1136.
Feferman, S. (1960). Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae, 49(1), 3592.
Frege, G. (1879). Begriffsschrift. In van Heijenoort, J., editor. From Frege to Gödel, Cambridge, MA: Harvard University Press, pp. 182.
Friedman, H. & Flagg, R. C. (1990). A framework for measuring the complexity of mathematical concepts. Advances in Applied Mathematics, 11, 134.
Geach, P. (1958). Entailment. Proceedings of the Aristotelian Society, Supplementary Volumes, 32, 157172.
Geach, P. (1970). Entailment. Philosophical Review, 79(2), 237239.
Gemes, K. (2007). Irrelevance: Strengthening the bayesian requriements. Synthese, 157(2), 161166.
Krämer, S. (2017). A hyperintensional criterion of irrelevance. Synthese, 194(8), 29172930.
Krämer, S. & Roski, S. (2017). Difference-making grounds. Philosophical Studies, 174, 11911215.
Lambek, J. (1958). The mathematics of sentence structure. American Mathematical Monthly, 65(3), 154170.
Lapara, N. (1976). Semantics for a natural notion of entailment. Philosophical Studies, 29(2), 91113.
Lehrer, K. (1973). Relevant deduction and minimally inconsistent sets. Philosophia, 3(3), 153165.
Lewis, C. I. & Langford, C. H. (1959). Symbolic Logic. New York: Dover.
Makinson, D. (2017). Relevance via decomposition: A project, some results, an open question. Australasian Journal of Logic, 14(3), 356377.
Mares, E. (2014). Relevance logic. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Spring 2014 edition). Available at: https://plato.stanford.edu/archives/spr2014/entries/logic-relevance/.
Meyer, R. (1971). Entailment. Journal of Philosophy, 68(21), 808818.
Prawitz, D. (2006). Natural Deduction: A Proof-Theoretical Study. Mineola, NY: Dover. Original published 1965.
Read, S. (1988). Relevant Logic. Oxford: Blackwell.
Restall, G. (2000). An Introduction to Substructural Logic. New York: Routledge.
Shapiro, L. (2017). Lp, k3, and fde as substructural logics. In Arazim, P. and Lavic˘ka, T., editors. The Logica Yearbook 2016. London: College Publications.
Smiley, T. (1959). Entailment and deducibility. Proceedings of the Aristotelian Society, 59, 233254.
Tennant, N. (1979). Entailment and proofs. Proceedings of the Aristotelian Society, 79, 167189.
Tennant, N. (1984). Perfect validity, entailment and paraconsistency. Studia Logica, 43, 179198.
Tennant, N. (1987). Anti-Realism and Logic. Oxford: Clarendon Press.
Tennant, N. (2005). Relevance in reasoning. In Shapiro, S., editor. The Oxford Handbook of Philosophy of Logic and Mathematics. New York: Oxford University Press, pp. 696726.
Tennant, N. (2015). The relevance of premises to conclusions of core proofs. Review of Symbolic Logic, 8, 743784.
Verdée, P. & de Bal, I. (2015). A new approach to classical relevance. Studia Logica, 103, 919954.
von Wright, G. (1957). The concept of entailment. In Logical Studies. London: Routledge and Kegan Paul, pp. 166191.
Woods, J. (1964). Relevance. Logique et Analyse, 7(27), 130137.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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