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Truth in a Logic of Formal Inconsistency: How classical can it get?

Picollo, LM; (2018) Truth in a Logic of Formal Inconsistency: How classical can it get? Logic Journal of the IGPL 10.1093/jigpal/jzy059. (In press). Green open access

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Abstract

Weakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten (2006) have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization KF in classical logic is much stronger than its paracomplete counterpart PKF⁠, not only in terms of semantic but also in arithmetical content. This paper compares the proof-theoretic strength of an axiomatization of Kripke’s construction based on the paraconsistent evaluation scheme of LP⁠, formulated in classical logic with that of an axiomatization directly formulated in LP⁠, extended with a consistency operator. The ultimate goal is to find out whether paraconsistent solutions to the paradoxes that employ consistency operators fare better in this respect than paracomplete ones.

Type: Article
Title: Truth in a Logic of Formal Inconsistency: How classical can it get?
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/jigpal/jzy059
Publisher version: https://doi.org/10.1093/jigpal/jzy059
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Kripke fixed points, LFIs, sequent-calculus truth theories, proof-theoretic strength
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/10066276
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