Journal of Philosophical Logic

, Volume 47, Issue 2, pp 227–257 | Cite as

On the Costs of Nonclassical Logic

  • Volker Halbach
  • Carlo NicolaiEmail author


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.


Formal theories of truth Semantic paradoxes Logical pluralism 



We would like to thank Leon Horsten and an anonymous referee. The work of the second author was supported by the European Commission, Grant 658285 FOREMOTIONS.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.University of Oxford and New CollegeOxfordUK
  2. 2.Ludwig-Maximilans-UniversitätMunich Center for Mathematical PhilosophyMünchenGermany

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