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On the Costs of Nonclassical Logic

Research output: Contribution to journalArticle

Volker Halbach, Carlo Nicolai

Original languageEnglish
Pages (from-to)227-257
JournalJOURNAL OF PHILOSOPHICAL LOGIC
Volume47
Issue number2
Early online date2 Mar 2017
DOIs
Accepted/In press3 Jan 2017
E-pub ahead of print2 Mar 2017
PublishedApr 2018

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Abstract

Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: (a variant) of the system KF of Feferman (The Journal of Symbolic Logic, 56, 1–49, 1991) formulated in classical logic, and (a variant of) the system PKF of Halbach and Horsten (The Journal of Symbolic Logic, 71, 677–712, 2006), formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.

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