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SUBSTITUTION IN RELEVANT LOGICS

Published online by Cambridge University Press:  17 September 2019

TORE FJETLAND ØGAARD
TORE FJETLAND ØGAARD*
Affiliation:
Department of Philosophy, University of Bergen
*
†DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BERGEN PO BOX 7805 5020 BERGEN NORWAY E-mail: Tore.Ogaard@uib.no
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Abstract

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form $s\dot{ = }t \wedge A\left( s \right) \to A\left( t \right)$—as these are put forward in Priest’s books In Contradiction and An Introduction to Non-Classical Logic: From If to Is. The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules is probed and it is argued that Substitution ought to fail.

Keywords

03A0503B4703B5303C0703C9003E70identityLeibniz’s lawsubstitutionrelevant logicstableaux systempossible world semantics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 3 , September 2020 , pp. 655 - 680
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Copyright
Copyright © Association for Symbolic Logic 2019 

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References

BIBLIOGRAPHY

Belnap, N. D. (1960). Entailment and relevance. Journal of Symbolic Logic, 25 (2), 144–146. https://doi.org/10.2307/2964210.CrossRefGoogle Scholar
Berto, F. & Restall, G. (2019). Negation on the Australian plan. Journal of Philosophical Logic. https://doi.org/10.1007/S10992-019-09510-2.CrossRefGoogle Scholar
Brady, R. T. (1989). Depth relevance of some paraconsistent logics. Studia Logica, 43(1–2), 63–73. https://doi.org/10.1007/BF00935740.CrossRefGoogle Scholar
Dunn, J. M. (1979). Relevant Robinson’s arithmetic. Studia Logica, 38(4), 407–418. https://doi.org/10.1007/BF00370478.CrossRefGoogle Scholar
Friedman, H. & Meyer, R. K. (1992). Whither relevant arithmetic? Journal of Symbolic Logic, 57(3), 824–831. https://doi.org/10.2307/2275433.CrossRefGoogle Scholar
Kremer, P. (1999). Relevant identity. Journal of Philosophical Logic, 28(2), 199–222. https://doi.org/10.1023/A:1004323917968.CrossRefGoogle Scholar
Mares, E. D. (2004). Relevant Logic: A Philosophical Interpretation. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511520006.CrossRefGoogle Scholar
Meyer, R. K. & Restall, G. (1996). Linear arithmetic desecsed. Logique & Analyse, 39(155/156), 379–387. http://virthost.vub.ac.be/lnaweb/ojs/index.php/LogiqueEtAnalyse/article/view/1409/.Google Scholar
Meyer, R. K. & Restall, G. (1999). “Strenge” arithmetics. Logique & Analyse, 42(167/168), 205–220. http://virthost.vub.ac.be/lnaweb/ojs/index.php/LogiqueEtAnalyse/article/view/1473/.Google Scholar
Øgaard, T. F. (2016). Paths to triviality. Journal of Philosophical Logic, 45(3), 237–276. https://doi.org/10.1007/s10992-015-9374-6.CrossRefGoogle Scholar
Øgaard, T. F. (2017). Skolem functions in non-classical logics. Australasian Journal of Logic, 14(1), 181–225. https://doi.org/10.26686/ajl.v14i1.4031.CrossRefGoogle Scholar
Øgaard, T. F. (2019). Non-boolean classical relevant logic I, typescript.CrossRefGoogle Scholar
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8(1), 219–241. https://doi.org/10.1007/BF00258428.CrossRefGoogle Scholar
Priest, G. (1992). What is a non-normal world. Logique et Analyse, 35(139/140), 291–302. http://virthost.vub.ac.be/lnaweb/ojs/index.php/LogiqueEtAnalyse/article/view/1296/.Google Scholar
Priest, G. (2006). In Contradiction (second edition). Oxford: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199263301.001.0001.CrossRefGoogle Scholar
Priest, G. (2008). An Introduction to Non-Classical Logic. From If to Is (second edition). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511801174.CrossRefGoogle Scholar
Priest, G. (2011). Paraconsistent set theory. In DeVidi, D., Hallett, M., and Clarke, P., editors. Logic, Mathematics, Philosophy: Vintage Enthusiasms. The Western Ontario Series in Philosophy of Science, Vol. 75. Dordrecht: Springer, pp. 153–169. https://doi.org/10.1007/978-94-007-0214-1.CrossRefGoogle Scholar
Priest, G. & Sylvan, R. (1992). Simplified semantics for basic relevant logic. Journal of Philosophical Logic, 21(2), 217–232. https://doi.org/10.1007/BF00248640.CrossRefGoogle Scholar
Restall, G. (2010). Models for substructural arithmetics. Australasian Journal of Logic, 8, 82–99. https://doi.org/10.26686/ajl.v8i0.1814.CrossRefGoogle Scholar
Routley, R. (1980). Exploring Meinong’s Jungle and Beyond. Departmental Monograph, Philosophy Department, RSSS, Australian National University, Vol. 3. Canberra: RSSS, Australian National University, Canberra. http://hdl.handle.net/11375/14805.Google Scholar
Routley, R. & Routley, V. (1972). The semantics of first degree entailment. Noûs, 6(4), 335–359. https://doi.org/10.2307/2214309.CrossRefGoogle Scholar
Slaney, J. K. (1995). MaGIC, Matrix Generator for Implication Connectives: Release 2.1 notes and guide. Technical Report. http://ftp.rsise.anu.edu.au/techreports/1995/TR-ARP-11-95.dvi.gz.Google Scholar