Logo Logo
Switch Language to German

Halbach, Volker and Nicolai, Carlo (2018): On the Costs of Nonclassical Logic. In: Journal of Philosophical Logic, Vol. 47, No. 2: pp. 227-257

Full text not available from 'Open Access LMU'.


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.

Actions (login required)

View Item View Item