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Dialetheism and the Impossibility of the World

Martin, BJL; (2015) Dialetheism and the Impossibility of the World. Australasian Journal of Philosophy , 93 (1) 10.1080/00048402.2014.956768. Green open access

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Abstract

This paper first offers a standard modal extension of dialetheic logics that respect the normal semantics for negation and conjunction in an attempt to adequately model absolutism, the thesis that there are true contradictions at metaphysically possible worlds. It is shown, however, that the modal extension has unsavoury consequences for both absolutism and dialetheism. While the logic commits the absolutist to dialetheism, it commits the dialetheist to the impossibility of the actual world. A new modal logic AV is then proposed which avoids these unsavoury consequences by invalidating the interdefinability rules for the modal operators with the use of two valuation relations. However, while using AV carries no significant cost for the absolutist, the same isn’t true for the dialetheist. Although using AV allows her to avoid the consequence that the actual world is an impossible world, it does so only on the condition that the dialetheist admits that she cannot give a dialetheic solution to all self-referential semantic paradoxes. Thus, unless there are any further available modal logics that don’t commit her to the impossibility of the actual world, the dialetheist is faced with a dilemma. Either admit that the actual world is an impossible world, or admit that her research programme cannot give a comprehensive solution to the self-referential paradoxes.

Type: Article
Title: Dialetheism and the Impossibility of the World
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/00048402.2014.956768
Publisher version: http://dx.doi.org/10.1080/00048402.2014.956768
Language: English
Additional information: © 2014 The Author(s). Published by Taylor & Francis. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: dialetheism, impossible worlds, paraconsistent logics, contradictions
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/1447207
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