Journal of Philosophical Logic

, Volume 44, Issue 5, pp 551–571 | Cite as

The Logics of Strict-Tolerant Logic

  • Eduardo BarrioEmail author
  • Lucas Rosenblatt
  • Diego Tajer


Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP.


Transparent truth Strict-tolerant logic Semantic paradoxes Transitivity Substructural logic 



We owe thanks to Norbert Gratzl, Ole Hjortland, Francesco Paoli, Lavinia Picollo, Dave Ripley, Thomas Schindler, and Johannes Stern for very helpful comments on previous versions of this paper. Some of this material was presented at conferences in Barcelona (Logos), Munich (MCMP) and Buenos Aires (Buenos Aires Logic Group). We are very grateful to the members of these audiences for their valuable feedback. We are also specially grateful to Jose Martinez and Elia Zardini for organizing the Substructural Approaches to Paradox Workshop and to Thomas Meier for organizing the 1st MCMP Munich-Buenos Aires Workshop.


  1. 1.
    Avron, A. (1988). The semantics and proof theory of linear logic. Theoretical Computer Science, 57.Google Scholar
  2. 2.
    Baaz, M., Fermüller, C., Salzer, G., Zach, R. (1998). Labeled calculi and finite-valued logics. Studia Logica, 61, 7–33.CrossRefGoogle Scholar
  3. 3.
    Baaz, M., Fermüller, C., Zach, R. (1993). Systematic construction of natural deduction systems for many-valued logics. In 23rd international symposium on multiple valued logic, Sacramento, (pp. 208–213). Los Alamitos: IEEE Press.Google Scholar
  4. 4.
    Beall, J.C. (2009). Spandrels of truth. New York: Oxford University Press.CrossRefGoogle Scholar
  5. 5.
    Beall, J.C., & Murzi, J. (2013). Two flavors of curry’s paradox. Journal of Philosophy, 110(3), 143–165.CrossRefGoogle Scholar
  6. 6.
    Cobreros, P., Egre, P., Ripley, D., van Rooij, R. (2012). Tolerance and mixed consequence in the S’valuationist setting. Studia Logica, 100(4), 855–877.CrossRefGoogle Scholar
  7. 7.
    Cobreros, P., Egré, P., Ripley, D., van Rooij, R. (2012). “Tolerant, Classical, Strict”. Journal of Philosophical Logic, 41(2), 347–385.CrossRefGoogle Scholar
  8. 8.
    Cobreros, P., Egré, P., Ripley, D., van Rooij, R. (2014). Vagueness, truth and permissive consequence. In T. Achourioti et al. (Eds.), Unifying the philosophy of truth. Springer. (forthcoming).Google Scholar
  9. 9.
    Cobreros, P., Egre, P., Ripley, D., van Rooij, R. (2013). Reaching transparent truth. Mind, 122(488), 841–866.CrossRefGoogle Scholar
  10. 10.
    Field, H. (2008). Saving truth from paradox. Oxford: Oxford University Press.CrossRefGoogle Scholar
  11. 11.
    Hjortland, O. (2014). Verbal disputes in logic: against minimalism for logical connectives. Logique et Analyse, 277, 463–486.Google Scholar
  12. 12.
    Hjortland, O. (2013). Logical pluralism, meaning-variance, and verbal disputes. Australasian Journal of Philosophy, 91(2), 355–373.CrossRefGoogle Scholar
  13. 13.
    Kripke, S. (1975). Outine of a theory of truth. Journal of Philosophy, 690–716(19).Google Scholar
  14. 14.
    Leitgeb, H. (2007). What theories of truth should be like (but cannot be). Philosophy Compass, 2(2), 276–290.CrossRefGoogle Scholar
  15. 15.
    Mares, E., & Paoli, F. (2014). Logical consequence and the paradoxes. Journal of Philosophical Logic, 43(2-3), 439–469.CrossRefGoogle Scholar
  16. 16.
    Paoli, F. (2007). Implicational paradoxes and the meaning of logical constants. Australasian Journal of Philosophy, 85(4), 553–579.CrossRefGoogle Scholar
  17. 17.
    Paoli, F. (2003). Quine and Slater on paraconsistency and deviance. Journal of Philosophical Logic, 32, 531–548.CrossRefGoogle Scholar
  18. 18.
    Paoli, F. (2002). Substructural logics: a primer. Dordrecht: Kluwer.CrossRefGoogle Scholar
  19. 19.
    Priest, G. (2006). In contradiction: a study of the transconsistent: Oxford University Press.Google Scholar
  20. 20.
    Restall, G. (2000). An introduction to substructural logic . Routledge.Google Scholar
  21. 21.
    Ripley, D. (2013). Paradoxes and failures of cut. Australasian Journal of Philosophy, 91(1), 139–164.CrossRefGoogle Scholar
  22. 22.
    Ripley, D. (2012). Conservatively extending classical logic with transparent truth. Review of Symbolic Logic, 5(2), 354–378.CrossRefGoogle Scholar
  23. 23.
    Rousseau, G. (1967). Sequents in many-valued logic I. Fundamenta Mathematicae, 60, 23–131.Google Scholar
  24. 24.
    Zardini, E. (2011). Truth without contra(di)ction. Review of Symbolic Logic, 4(4), 498–535.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.National Scientific and Technical Research CouncilUniversity of Buenos AiresCiudad de Buenos AiresArgentina
  2. 2.National Scientific and Technical Research CouncilUniversity of Buenos AiresCiudad de Buenos AiresArgentina

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