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

Journal of Philosophical Logic 51 (6):1295–1325 (2022)
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Abstract

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.

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Rea Golan
Ben-Gurion University of the Negev

Citations of this work

Bilateralism, coherence, and incoherence.Rea Golan - forthcoming - Philosophy and Phenomenological Research.
On the Metainferential Solution to the Semantic Paradoxes.Rea Golan - 2023 - Journal of Philosophical Logic 52 (3):797-820.
Inferential Constants.Camillo Fiore, Federico Pailos & Mariela Rubin - 2022 - Journal of Philosophical Logic 52 (3):767-796.

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References found in this work

The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.

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