Logical Consequence and the Paradoxes

Journal of Philosophical Logic 43 (2-3):439-469 (2014)
  Copy   BIBTEX

Abstract

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

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

Paradoxes of intensionality.Dustin Tucker & Richmond H. Thomason - 2011 - Review of Symbolic Logic 4 (3):394-411.
Substructural Logics.Greg Restall - forthcoming - Stanford Encyclopedia of Philosophy.
Implicational paradoxes and the meaning of logical constants.Francesco Paoli - 2007 - Australasian Journal of Philosophy 85 (4):553 – 579.
Informational interpretation of substructural propositional logics.Heinrich Wansing - 1993 - Journal of Logic, Language and Information 2 (4):285-308.
Meeting strength in substructural logics.Yde Venema - 1995 - Studia Logica 54 (1):3 - 32.
Definability and the Structure of Logical Paradoxes.Haixia Zhong - 2012 - Australasian Journal of Philosophy 90 (4):779 - 788.
Modal translations in substructural logics.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (3):283 - 336.
Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.

Analytics

Added to PP
2013-03-17

Downloads
220 (#88,149)

6 months
36 (#96,981)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Francesco Paoli
Universita di Cagliari
Edwin Mares
Victoria University of Wellington

Citations of this work

Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
Properties.Francesco Orilia & Michele Paolini Paoletti - 2020 - Stanford Encyclopedia of Philosophy.
What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency. Cham, Switzerland: Springer.
The Logics of Strict-Tolerant Logic.Eduardo Barrio, Lucas Rosenblatt & Diego Tajer - 2015 - Journal of Philosophical Logic 44 (5):551-571.

View all 49 citations / Add more citations

References found in this work

In contradiction: a study of the transconsistent.Graham Priest - 1987 - New York: Oxford University Press.
Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.

View all 56 references / Add more references