Journal of Philosophical Logic 49 (2):351-370 (2020)

Chris Scambler
New York University
In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a logic which agrees with classical logic on tautologies, inferences, meta-inferences, meta-meta-inferences, meta-meta-...-meta-inferences, but that disagrees with classical logic on n + 1-meta-inferences. They suggest that this shows that classical logic can only be characterized by defining its valid inferences at all orders. In this article, I invoke some simple symmetric generalizations of BPS’s results to show that the problem is worse than they suggest, since in fact there are logics that agree with classical logic on inferential validity to all orders but still intuitively differ from it. I then discuss the relevance of these results for truth theory and the classification problem.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s10992-019-09520-0
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,417
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Structural Reflexivity and the Paradoxes of Self-Reference.Rohan French - 2016 - Ergo: An Open Access Journal of Philosophy 3.

View all 6 references / Add more references

Citations of this work BETA

A Family of Strict/Tolerant Logics.Melvin Fitting - 2021 - Journal of Philosophical Logic 50 (2):363-394.
Inferences and Metainferences in ST.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2020 - Journal of Philosophical Logic 49 (6):1057-1077.

View all 7 citations / Add more citations

Similar books and articles

The Logics of Strict-Tolerant Logic.Eduardo Barrio, Lucas Rosenblatt & Diego Tajer - 2015 - Journal of Philosophical Logic 44 (5):551-571.
A Family of Metainferential Logics.Federico Matias Pailos - 2019 - Journal of Applied Non-Classical Logics 29 (1):97-120.
Judgement Aggregation in Non-Classical Logics.Daniele Porello - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):106-139.
Game Theoretical Semantics for Some Non-Classical Logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
Logics of Kripke Meta-Models.Sergey Babenyshev & Vladimir Rybakov - 2010 - Logic Journal of the IGPL 18 (6):823-836.
A Problem for a Logic of 'Because'.Savas L. Tsohatzidis - 2015 - Journal of Applied Non-Classical Logics 25 (1):46-49.
Combining Valuations with Society Semantics.Víctor L. Fernández & Marcelo E. Coniglio - 2003 - Journal of Applied Non-Classical Logics 13 (1):21-46.
Nearly Every Normal Modal Logic is Paranormal.Joao Marcos - 2005 - Logique Et Analyse 48 (189-192):279-300.


Added to PP index

Total views
35 ( #309,339 of 2,449,074 )

Recent downloads (6 months)
8 ( #82,403 of 2,449,074 )

How can I increase my downloads?


My notes