v. 40 n. 2 (2020)
Artigos

Las Lógicas Mixtas como escape al Problema del Colapso y al Desafío de Quine

Joaquín Santiago Toranzo Calderón
Universidad de Buenos Aires, Buenos Aires, Argentina / Universidad Tecnológica Nacional, Buenos Aires, Argentina

Publicado 2020-11-01

Resumo

En este trabajo presentaré una forma de evitar los problemas más recurrentes en cierta versión del pluralismo lógico, aquella que defiende que incluso considerando un lenguaje fijo existen múltiples sistemas lógicos legítimos. Para ello, será necesario considerar los puntos de partida del programa pluralista y explicitar los problemas que de ellos surgen, principalmente el Desafío de Quine y el Problema del Colapso. Luego, propondré una modificación respecto de lo que se entiende por consecuencia lógica, para poder considerar una familia de sistemas lógicos, las lógicas mixtas, que abarcan tanto a las lógicas puras como a las impuras. Finalmente, mostraré que con una interpretación razonable del formalismo se puede eludir aquellos problemas a la vez que se respeta el espíritu del programa pluralista.

Referências

  1. Barrio, E. A., Pailos, F., & Szmuc, D. (2018). Substructural Logics, Pluralism and Collapse. Synthese. https://doi.org/10.1007/s11229-018-01963-3
  2. Barrio, E. A., Pailos, F., & Szmuc, D. (2020). A Hierarchy of Classical and Paraconsistent Logics. Journal of Philosophical Logic, 49, 93-120. https://doi.org/10.1007/s10992-019-09513-z
  3. Beall, J. C., & Restall, G. (2000). Logical Pluralism. Australasian Journal of Philosophy, 78(4), 475-493. https://doi.org/10.1080/ 00048400012349751
  4. Beall, J. C., & Restall, G. (2001). Defending Logical Pluralism. En B. Brown & J. Woods (Eds.), Logical consequence: Rival approaches. Proceedings of the 1999 Conference of the Society of Exact Philosophy (pp. 1-22). Hermes.
  5. Beall, J. C., & Restall, G. (2006). Logical pluralism. Clarendon Press.
  6. Bou, F., Esteva, F., Font, J. M., Gil, A., Godo, L., Torrens, A., & Verdú, V. (2009). Logics preserving degrees of truth from varieties of residuated lattices. Journal of Logic and Computation, 19(6), 1031-1069. https://doi.org/10.1093/logcom/exp030
  7. Bou, F., Esteva, F., Font, J. M., Gil, A., Godo, L., Torrens, A., & Verdú, V. (2012). Logics preserving degrees of truth from varieties of residuated lattices. Journal of Logic and Computation, 22(3), 661-665. https://doi.org/10.1093/logcom/exr003
  8. Bueno, O., & Shalkowski, S. (2009). Modalism and logical pluralism. Mind, 118(470), 295-321. https://www.jstor.org/stable/20532763
  9. Caret, C. R. (2017). The collapse of logical pluralism has been greatly exaggerated. Erkenntnis, 82(4), 739-760. https://doi.org/10.1007/s10670-016-9841-7
  10. Chemla, E., Egré, P., & Spector, B. (2017). Characterizing logical consequence in many-valued logic. Journal of Logic and Computation, 27(7), 2193-2226. https://doi.org/10.1093/logcom/exx001
  11. Cobreros, P., Egré, P., Ripley, D., & van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41(2), 347-385. https://doi.org/10.1007/s10992-010-9165-z
  12. Cobreros, P., Egré, P., Ripley, D., & van Rooij, R. (2014). Reaching transparent truth. Mind, 122(488), 841-866. https://www.jstor.org/stable/24489584
  13. Da Ré, B., Pailos, F., Szmuc, D., & Teijeiro, P. (2020). Metainferential duality. Journal of Applied Non-classical Logics. https://doi.org/10.1080/11663081.2020.1826156
  14. Dummett, M. (1975). The philosophical basis of intuitionistic logic. En H. E. Rose & J. C. Shepherdson (Eds.), Logic Colloquium ‘73 Proceedings of the Logic Colloquium, Studies in Logic and the Foundations of Mathematics, 80 (pp. 5-40). North Holland. https://doi.org/10.1016/S0049-237X(08)71941-4
  15. Ferrari, F. & Moruzzi, S. (2020). Logical pluralism, indeterminacy and the normativity of logic. Inquiry, 63(3-4), 323-346. https://doi.org/10.1080/0020174X.2017.1393198
  16. French, R. (2016). Structural reflexivity and the paradoxes of self-reference. Ergo, 3(5), 113-131. https://doi.org/10.3998/ergo.12405314.0003.005
  17. Haack, S. (1978). Philosophy of logics. Cambridge University Press.
  18. Humberstone, L. (2011). The connectives. The MIT Press. https://doi.org/10.7551/mitpress/9055.001.0001
  19. Kouri Kissel, T. (2018a). Connective meaning in Beall and Restall’s logical pluralism. En J. Wyatt, N. Pedersen & N. Kellen (Eds.), Pluralisms in truth and logic (pp. 217-235). Palgrave Macmillan. https://doi.org/10.1007/978-3-319-98346-2_10
  20. Kouri Kissel, T. (2018b). Logical Pluralism from a Pragmatic Perspective. Australasian Journal of Philosophy, 96(3), 578-591. https://doi.org/10.1080/00048402.2017.1399151
  21. Pailos, F. (2020). Disjoint logics. Logic and Logical Philosophy. http://dx.doi.org/10.12775/LLP.2020.014
  22. Pailos, F. (manuscrito). Pure logics.
  23. Price, H. (1983). Sense, assertion, Dummett, and denial. Mind, 92(366), 161-173. https://www.jstor.org/stable/2253778
  24. Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8(1), 219-241. http://www.jstor.org/stable/30227165
  25. Priest, G. (2001). Logic: one or many? En B. Brown & J. Woods (Eds.), Logical consequence: Rival approaches. Proceedings of the 1999 Conference of the Society of Exact Philosophy (pp. 23-28). Hermes.
  26. Quine, W. V. (1970). Filosofía de la Lógica. Alianza.
  27. Read, S. (2006). Monism: The one true logic. En D. DeVidi & T. Kenyon (Eds.), A logical approach to philosophy: Essays in memory of Graham Solomon (pp. 193-209). Springer. https://doi.org/10.1007/1-4020-4054-7_10
  28. Restall, G. (2005). Multiple conclusions. En P. Hájek, L. Valdés-Villanueva & D. Westerståhl (Eds.), Logic, methodology, and philosophy of science: Proceedings of the Twelfth International Congress (pp. 189-205). Kings’ College Publications. https://doi.org/10.1093/philmat/nkn004
  29. Ripley, D. (2012). Conservatively extending classical logic with transparent truth. Review of Symbolic Logic, 5(2), 354-378. https://doi.org/10.1017/S1755020312000056
  30. Rumfitt, I. (2000). ‘Yes’ and ‘no’. Mind, 109(436), 781-823. https://doi.org/10.1093/mind/109.436.781
  31. Smiley, T. (1996). Rejection. Analysis, 56(1), 1-9. https://doi.org/10.1111/j.0003-2638.1996.00001.x
  32. Stei, E. (2020). Rivalry, normativity, and the collapse of logical pluralism. Inquiry, 63(3-4), 411-432. https://doi.org/10.1080/ 0020174X.2017.1327370
  33. Steinberger, F. (2011). Why conclusions should remain single. Journal of Philosophical Logic, 40(3), 333-355. https://doi.org/10.1007/s10992-010-9153-3