v. 41 n. 2 (2021)
Seção temática

Inferentialism and Relevance: The case of Connexivity

Damián Szmuc
IIF -SADAF - CONICET / Universidad de Buenos Aires, Argentina

Publicado 2021-11-01

Resumo

This paper provides an inferentialist motivation for a logic belonging in the connexive family, by borrowing elements from the bilateralist interpretation for Classical Logic without the Cut rule, proposed by David Ripley. The paper focuses on the relation between inferentialism and relevance, through the exploration of what we call relevant assertion and denial, showing that a connexive system emerges as a symptom of this interesting link. With the present attempt we hope to broaden the available interpretations for connexive logics, showing they can be rightfully motivated in terms of certain relevantist constraints imposed on assertion and denial.

Referências

  1. Anderson, A. R., & Belnap, N. (1975). Entailment: The logic of relevance and necessity, volume 1. Princeton University Press.
  2. Belnap., N. (1977). A useful four-valued logic. In M. Dunn & G. Epstein (Eds.), Modern uses of multiple-valued logic (vol. 2, pp. 5-37). Springer.
  3. Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41(2), 347-385.
  4. Cobreros, P., Égré, P., Ripley, D. & van Rooij, R. (2013). Reaching transparent truth. Mind, 122(488), 841-866. https://doi.org/10.1093/mind/fzt110
  5. Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2017). Tolerant reasoning: nontransitive or nonmonotonic? Synthese, 2017. https://doi.org/10.1007/s11229-017-1584-8
  6. Deutsch, H. (1984). Paraconsistent analytic implication. Journal of Philosophical Logic, 13(1), 1-11.
  7. Dicher, B., & Paoli, F. (2017). ST, LP, and tolerant metainferences. In C. Başkent & T. M. Ferguson (Eds.), Graham Priest on dialetheism and paraconsistency (pp. 383-407). Springer. https://doi.org/10.1007/978-3-030-25365-3_18
  8. Dunn, M. (1976). Intuitive semantics for first-degree entailments and ‘coupled trees’. Philosophical Studies, 29(3), 149-168.
  9. Estrada-Gonzalez, L., & Ramirez-Camara, E. (2016). A comparison of connexive logics. IFCoLog Journal of Logics and their Applications, 3(3), 341-355.
  10. Ferguson, T. M. (2015). Logics of nonsense and Parry systems. Journal of Philosophical Logic, 44(1), 65-80.
  11. French, R. (2016). Structural reflexivity and the paradoxes of self-reference. Ergo, 3(5):113-131, 2016.
  12. Gentzen, G. (1935a). Untersuchungen uber das logische Schliessen. I. Mathematische Zeitschrift, 39(1), 176-210.
  13. Gentzen G. (1935b). Untersuchungen uber das logische Schlissen. II. Mathematische Zeitschrift, 39(1), 405-431.
  14. Kapsner, A. (2012). Strong connexivity. Thought, 1(2), 141-145.
  15. Kleene, S. C. (1952). Introduction to metamathematics. North-Holland.
  16. McCall, S. (1966). Connexive implication. Journal of Symbolic Logic, 31(3), 415-433.
  17. Priest, G. (1999a). Negation as cancellation, and connexive logic. Topoi, 18(2), 141-148.
  18. Priest, G. (1999b). What not? A defence of a dieletheic account of negation. In D. M. Gabbay & H. Wansing (Eds.), What is Negation? (pp. 101-120). Kluwer.
  19. Restall, G. (2005). Multiple conclusions. In P. Hajek, L. Valdes-Villanueva & D. Westerstahl (Eds.), Logic, methodology, and philosophy of science: Proceedings of the Twelfth International Congress (pp. 189-205). College Publications.
  20. Ripley, D. (2012). Conservatively extending classical logic with transparent truth. Review of Symbolic Logic, 5(02), 354-378.
  21. Ripley, D. (2013). Paradoxes and failures of cut. Australasian Journal of Philosophy, 91(1), 139-164.
  22. Ripley, D. (2018). Uncut. Manuscript.
  23. Routley, R., & Routley, V. (1985). Negation and contradiction. Revista Colombiana de Matemáticas, 19(1-2), 201-230.
  24. Rumfitt, I. (2000). ‘Yes’ and ‘No’. Mind, 109(436), 781-823.
  25. Wansing, H. (2004). Connexive modal logic. In R. Schimdt, I. Pratt-Hartmann, M. Reynolds, & H. Wansing (Eds.), Advances in modal logic (vol. 5, pp. 387-399). College Publications.
  26. Wansing, H. (2016). Connexive logic. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring ed.). Stanford University.
  27. Wansing, H., & Skurt, D. (2018). Negation as cancellation, connexive logic, and qLPm. Australasian Journal of Logic, 15(2), 476-488.
  28. Wansing, H., Omori, H., & Ferguson, T. M. (2016). The tenacity of connexive logic: Preface to the special issue. IFCoLog Journal of Logics and their Applications, 3(3), 279-296.