v. 41 n. 2 (2021)
Seção temática

Why a Logic is not only its Set of Valid Inferences

Eduardo A. Barrio
Instituto de Investigaciones Filosóficas, Sociedad Argentina de Análisis Filosófico, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Federico Pailos
Instituto de Investigaciones Filosóficas, Sociedad Argentina de Análisis Filosófico, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina

Publicado 2021-11-01

Resumo

The main idea that we want to defend in this paper is that the question of what a logic is should be addressed differently when structural properties enter the game. In particular, we want to support the idea according to which it is not enough to identify the set of valid inferences to characterize a logic. In other words, we will argue that two logical theories could identify the same set of validities (e.g. its logical truths and valid inferences), but not be the same logic.

Referências

  1. Barrio, E., Pailos, F., & Szmuc. D. (2017). A paraconsistent route to semantic closure. Logic Journal of the IGPL, 25(4), 387-407. https://doi.org/10.1093/jigpal/jzx009
  2. Barrio, E., Pailos, F., & Szmuc. D. (2018). What is a paraconsistent logic? In W. Carnielli & J. Malinowski (Eds.), Contradictions, from consistency to inconsistency (pp 89-108). Springer. https://doi.org/10.1007/978-3-319-98797-2_5
  3. Barrio, E., Pailos, F., & Szmuc, D. (2019). (Meta)inferential levels of entailment beyond the Tarskian paradigm. Synthese. https://doi.org/10.1007/s11229-019-02411-6
  4. Barrio, E., Pailos, F., & Szmuc, D. (2020a). Hierarchies of para-consistency and classicality. Journal of Philosophical Logic, 49(1), 93-120. https://doi.org/10.1007/s10992-019-09513-z
  5. Barrio, E., Pailos, F., & Szmuc. D. (2020b). A recovery operator for non- transitive approaches. The Review of Symbolic Logic, 13(1), 80-104. https://doi.org/10.1017/S1755020318000369
  6. Barrio, E., Pailos, F., & Szmuc, D. (2021). Substructural logics, pluralism and collapse. Synthese, 198, 4991–5007. https://doi.org/10.1007/s11229-018-01963-3
  7. Barrio, E., Rosenblatt, L., & Tajer, D. (2015). The logics of strict-tolerant logic. Journal of Philosophical Logic, 44(5), 551–571. https://doi.org/10.1007/s10992-014-9342-6
  8. Barrio, E., Rosenblatt, L., & Tajer, D. (2016). Capturing naive validity in the cut-free approach. Synthese. https://doi.org/10.1007/s11229-016-1199-5
  9. Beall, J. (2013a). Lp+, k3+, fde+, and their ‘classical collapse’. Review of Symbolic Logic, 6(4), 742-754. https://doi.org/10.1017/S1755020313000142
  10. Beall, J. (2013b). A simple approach towards recapturing consistent theories in a paraconsistent setting. Review of Symbolic Logic, 6(4):755-754, 2013. https://doi.org/10.1017/S1755020313000208
  11. 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
  12. 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
  13. Frankowski. S. (2004a). Formalization of a plausible inference. Bulletin of the Section of Logic, 33(1), 41-52, 2004.
  14. Frankowski.S. (2004b). p-consequence versus q-consequence operations. Bulletin of the Section of Logic, 33(4), 197-207.
  15. French. R. (2006). Structural reflexivity and the paradoxes of self-reference. Ergo, 3(5), 113-131.
  16. Hlobil, U. (2018). The cut-free approach and the admissibility-curry. Thought, 7(1), 40-48. https://doi.org/10.1002/tht3.267
  17. Hlobil, U. (2019). Faithfulness for naive validity. Synthese, 196, 4759–4774. https://doi.org/10.1007/s11229-018-1687-x
  18. Humberstone. L. (1996). Valuational semantics of rule derivability. Journal of Philosophical Logic, 25(5), 451-461.
  19. Malinowski, G. (1990). Q-consequence operation. Reports on Mathematical Logic, 24(1), 49-59.
  20. Pailos, F. (2020). A fully classical truth theory characterized by substructural means. The Review of Symbolic Logic, 13(2), 249-268. https://doi.org/10.1017/S1755020318000485
  21. Restall, G. (2021). Proof theory: Rules & meaning. Manuscript.
  22. Ripley, D. (2013). Paradoxes and failures of cut. Australasian Journal of Philosophy, 91(1), 139-164.
  23. Ripley, D. (2018). Uncut. Manuscript.
  24. Rosenblatt, L. (2017). Naive validity, internalization and substructural approaches to paradox. Ergo, 4(4), 93-120. https://doi.org/10.3998/ergo.12405314.0004.004
  25. Tajer, D. (2020). LFIs and methods of classical recapture. Logic Journal of the IGPL, 28(5), 807-816, https://doi.org/10.1093/jigpal/jzy060
  26. Zardini, E. (2011). Truth without contra(di)ction. The Review of Symbolic Logic, 4(4), 498-535. https://doi.org/10.1017/S1755020311000177
  27. Zardini, E. (2013). Naive modus ponens. Journal of Philosophical Logic, 42(4), 575-593. http://www.jstor.org/stable/42001176