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

Journal of Philosophical Logic 1:1-31 (forthcoming)
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I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in. 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. Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity. Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis ) that the validity predicate introduced in by Beall and Murzi in, 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc.
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Archival date: 2021-07-26
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