On the Metainferential Solution to the Semantic Paradoxes

Journal of Philosophical Logic 52 (3):797-820 (2023)
  Copy   BIBTEX


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.



    Upload a copy of this work     Papers currently archived: 91,139

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

John Mair on Semantic Paradoxes.Miroslav Hanke - 2012 - Studia Neoaristotelica 9 (2):154-183.
Semantic Paradoxes and Transparent Intensional Logic.Jiri Raclavsky - 2012 - The Logica Yearbook 2011 (College Publications):239-252.
John Mair on Semantic Paradoxes.Miroslav Hanke - 2013 - Studia Neoaristotelica 10 (1):50-87.
John Mair on Semantic Paradoxes.Miroslav Hanke - 2012 - Studia Neoaristotelica 9 (2):154-183.
Model-theoretic semantics and revenge paradoxes.Lorenzo Rossi - 2019 - Philosophical Studies 176 (4):1035-1054.
Metainferential Reasoning on Strong Kleene Models.Andreas Fjellstad - 2021 - Journal of Philosophical Logic 51 (6):1327-1344.
Definability and the Structure of Logical Paradoxes.Haixia Zhong - 2012 - Australasian Journal of Philosophy 90 (4):779 - 788.
Wittgenstein's Solution of the Paradoxes.Anton Dumitriu - 1974 - Journal of the History of Philosophy 12 (2):227.
The liar paradox and the inclosure schema.Emil Badici - 2008 - Australasian Journal of Philosophy 86 (4):583 – 596.
One Step is Enough.David Ripley - 2021 - Journal of Philosophical Logic 51 (6):1-27.
A new solution to the paradoxes of rational acceptability.Igor Douven - 2002 - British Journal for the Philosophy of Science 53 (3):391-410.


Added to PP

78 (#204,912)

6 months
18 (#124,434)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Rea Golan
Ben-Gurion University of the Negev

Citations of this work

The logics of a universal language.Eduardo Alejandro Barrio & Edson Bezerra - 2024 - Asian Journal of Philosophy 3 (1):1-22.

Add more citations

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.

View all 23 references / Add more references