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Erkenntnis

, Volume 81, Issue 6, pp 1243–1252 | Cite as

Restall’s Proof-Theoretic Pluralism and Relevance Logic

  • Teresa KouriEmail author
Original Article

Abstract

Restall (Erkenntnis 79(2):279–291, 2014) proposes a new, proof-theoretic, logical pluralism. This is in contrast to the model-theoretic pluralism he and Beall proposed in Beall and Restall (Aust J Philos 78(4):475–493, 2000) and in Beall and Restall (Logical pluralism, Oxford University Press, Oxford, 2006). What I will show is that Restall has not described the conditions on being admissible to the proof-theoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, one critical component of Restall’s pluralism is that the relevance logic that gets added must have connectives which mean the same thing as the connectives in the already admitted logic. This is what I will show is not possible.

Keywords

Intuitionistic Logic Logical Rule Proof Theory Structural Rule Sequent Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I owe a debt of gratitude to Stewart Shapiro very carefully read and commented on several earlier drafts. I am grateful to comments from several people, including three blind reviewers, Scott Brown, Nathan Kellen, Chris Pincock, Marcus Rossberg, Kevin Scharp, Matt Souba and Neil Tennant. I am also grateful to audiences at the Dubrovnik Conference on Pluralism (2015), the Pacific APA (2015), PhiloSTEM (2014), the Society for Exact Philosophy (2013) and The University of Western Ontario Philosophy of Logic, Math and Physics Graduate Conference (2013).

References

  1. Anderson, A. R., & Belnap, N. D. (1975). Entailment: The logic of relevance and neccessity (Vol. I). USA: Princeton University Press.Google Scholar
  2. Beall, J., & Restall, G. (2000). Logical pluralism. Australian Journal of Philosophy, 78(4), 475–493.CrossRefGoogle Scholar
  3. Beall, J., & Restall, G. (2006). Logical pluralism. Oxford: Oxford University Press.Google Scholar
  4. Belnap, N. (1982). Display logic. Journal of Philosophical Logic, 11, 375–417.Google Scholar
  5. Dunn, J. M., & Restall, G. (1992). Relevance logic 1. Handbook of Philosophical Logic, 6, 1–192.Google Scholar
  6. Hjortland, O. T. (2014). Verbal disputes in logic: Against minimalism for logical connectives. Logique et Analyse, 227, 463–486.Google Scholar
  7. Paoli, F. (2014). Semantic minimalism for logical constants. Logique et Analyse, 227, 439–461.Google Scholar
  8. Read, S. (1982). Disjunction. Journal of Semantics, 1(3), 275–285.CrossRefGoogle Scholar
  9. Read, S. (2006). Monism: The one true logic. In D. Devidi & T. Kenyon (Eds.), A logical approach to philosophy (pp. 193–209). Netherlands: Springer.CrossRefGoogle Scholar
  10. Restall, G. (2000). An introduction to substructural logic. New York: Routledge.CrossRefGoogle Scholar
  11. Restall, G. (2014). Pluralism and proofs. Erkenntnis, 79(2), 279–291.CrossRefGoogle Scholar
  12. Tennant, N. (1984). Perfect validity, entailment and paraconsistency. Studia Logica, 43(1–2), 181–200.CrossRefGoogle Scholar
  13. Tennant, N. (1992). Autologic. Edinburgh information technology series. Edinburgh: Edinburgh University Press.Google Scholar
  14. Tennant, N. (forthcoming). Core Logic.Google Scholar
  15. Urbas, I. (1996). Dual-intuitionistic logic. Notre Dame Journal of Formal Logic, 37(3), 440–451.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Ohio State UniversityColumbusUSA

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