Metainferences from a Proof-Theoretic Perspective, and a Hierarchy of Validity Predicates

Springer Science and Business Media LLC - Tập 51 - Trang 1295-1325 - 2021
Rea Golan1
1Institut für Philosophie, Freie Universität, Berlin, Germany

Tóm tắt

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic, 49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy, 110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc.

Tài liệu tham khảo

Avron, A. (1991). Simple consequence relations. Information and Computation, 92, 105–139.

Barrio, E., Rosenblatt, L., & Tajer, D. (2015). The logics of strict-tolerant logic. Journal of Philosophical Logic, 44(5), 551–571.

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.

Barrio, E., 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.

Beall, J. (2011). Multiple-conclusion LP and default classicality. Review of Symbolic Logic, 4(2), 326–336. https://doi.org/10.1017/S1755020311000074.

Beall, J., & Murzi, J. (2013). Two flavors of Curry paradox. Journal of Philosophy, 110(3), 143–165.

Blok, W., & Jónsson, B. (2006). Equivalence of consequence operations. Studia Logica, 83(1), 91–110.

Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2013). Reaching transparent truth. Mind, 122(488), 841–866.

Dicher, B., & Paoli, F. (2019). ST, LP, and tolerant metainferences. In Başkent, C., & Ferguson, T.M. (Eds.) Graham Priest on Dialetheism and Para consistency. Dordrecht: Springer, pp.383–407.

Hlobil, U. (2018). The Cut-free approach and the admissibility-Curry. Thought: a Journal of Philosophy, 7: 40–48. https://doi.org/10.1002/tht3.267.

Hlobil, U. (2019). Faithfulness for Naive Validity. Synthese, 196, 4759–4774.

Lewis, D. (1974). Tensions. In Munitz, M.K. & Unger, P.K. (Eds.), SemanticsandPhilosophy. New York: New York University Press, pp. 49–61.

Pailos, F. (2020). A fully classical truth theory characterized by substructural means. Review of Symbolic Logic, 13(2), 249–268.

Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8, 219–241.

Priest, G. (2008). An Introduction to Non-Classical Logic, second edition. Cambridge, MA: Cambridge University Press.

Ripley, D. (2012). Conservatively extending classical logic with transparent truth. Review of Symbolic Logic, 5(2), 354–378.

Ripley, D. (2013). Paradoxes and Failures of Cut. Australasian Journal of Philosophy, 91(1), 139–164.

Scambler, C. (2020). Classical logic and the strict tolerant hierarchy. Journal of Philosophical Logic, 49, 351–370.

Wansing, H., & Priest, G. (2015). External Curries. Journal of Philosophical Logic, 44(4), 453–471.

Woods, J. (2018). Intertranslatability, theoretical equivalence, and perversion. Thought: a Journal of Philosophy, 7, 58–68.

Thông tin
Thông tin xuất bản

Springer Science and Business Media LLC

Tập 51

1295-1325

Thông tin tác giả