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

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4 Scopus citations

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.

Original languageEnglish
Pages (from-to)1295-1325
Number of pages31
JournalJournal of Philosophical Logic
Volume51
Issue number6
DOIs
StatePublished - 1 Dec 2022
Externally publishedYes

Keywords

  • Metainferences
  • Proof theory
  • Validity predicate

ASJC Scopus subject areas

  • Philosophy

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