Review of Symbolic Logic 13 (1):80-104 (2020)

Authors
Damian Szmuc
Universidad de Buenos Aires (UBA)
Federico Pailos
Universidad de Buenos Aires (UBA)
Eduardo Alejandro Barrio
University of Buenos Aires
Abstract
In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities.
Keywords Substructural Logics  Cut Rule  Recovery Operator  Paradoxes
Categories (categorize this paper)
DOI 10.1017/s1755020318000369
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
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

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.
On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.

View all 38 references / Add more references

Citations of this work BETA

Expressing Consistency Consistently.Lucas Rosenblatt - 2021 - Thought: A Journal of Philosophy 10 (1):33-41.

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.
The Suszko Operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1):181-231.
The Suszko Operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1-2):181 - 231.
Comparing Substructural Theories of Truth.David Ripley - 2015 - Ergo: An Open Access Journal of Philosophy 2.
Too Good to Be “Just True”.Marcus Rossberg - 2013 - Thought: A Journal of Philosophy 2 (1):1-8.
Naive Modus Ponens and Failure of Transitivity.Andreas Fjellstad - 2016 - Journal of Philosophical Logic 45 (1):65-72.
Restriction by Noncontraction.Elia Zardini - 2016 - Notre Dame Journal of Formal Logic 57 (2):287-327.
Meeting Strength in Substructural Logics.Yde Venema - 1995 - Studia Logica 54 (1):3-32.
Can the Classical Logician Avoid the Revenge Paradoxes?Andrew Bacon - 2015 - Philosophical Review 124 (3):299-352.
Meeting Strength in Substructural Logics.Yde Venema - 1995 - Studia Logica 54 (1):3 - 32.
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.

Analytics

Added to PP index
2018-10-03

Total views
354 ( #23,494 of 2,433,123 )

Recent downloads (6 months)
37 ( #21,243 of 2,433,123 )

How can I increase my downloads?

Downloads

My notes