On the Metainferential Solution to the Semantic Paradoxes

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Substructural solutions to the semantic paradoxes have been broadly discussed in recent years. In particular, according to the non-transitive solution, we have to give up the metarule of Cut, whose role is to guarantee that the consequence relation is transitive. This concession—giving up a meta rule—allows us to maintain the entire consequence relation of classical logic. The non-transitive solution has been generalized in recent works into a hierarchy of logics where classicality is maintained at more and more metainferential levels. All the logics in this hierarchy can accommodate a truth predicate, including the logic at the top of the hierarchy—known as CMω—which presumably maintains classicality at all levels. CMω has so far been accounted for exclusively in model-theoretic terms. Therefore, there remains an open question: how do we account for this logic in proof-theoretic terms? Can there be found a proof system that admits each and every classical principle—at all inferential levels—but nevertheless blocks the derivation of the liar? In the present paper, I solve this problem by providing such a proof system and establishing soundness and completeness results. Yet, I also argue that the outcome is philosophically unsatisfactory. In fact, I’m afraid that in light of my results this metainferential solution to the paradoxes can hardly be called a “solution,” let alone a good one.

Original languageEnglish
Pages (from-to)797-820
Number of pages24
JournalJournal of Philosophical Logic
Issue number3
StatePublished - 1 Jun 2023


  • Metainferences
  • Proof theory
  • ST hierarchy
  • Semantics paradoxes

ASJC Scopus subject areas

  • Philosophy


Dive into the research topics of 'On the Metainferential Solution to the Semantic Paradoxes'. Together they form a unique fingerprint.

Cite this