On the Costs of Nonclassical Logic

Volker Halbach; Carlo Nicolai

doi:10.1007/s10992-017-9424-3

On the Costs of Nonclassical Logic

Volker Halbach, Carlo Nicolai

Philosophy

University of Oxford

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

183 Downloads (Pure)

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.

Original language	English
Pages (from-to)	227-257
Journal	JOURNAL OF PHILOSOPHICAL LOGIC
Volume	47
Issue number	2
Early online date	2 Mar 2017
DOIs	https://doi.org/10.1007/s10992-017-9424-3
Publication status	Published - Apr 2018

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10.1007/s10992-017-9424-3

On the costs of_HOLBACH_Accepted3January2017Publishedonline2March2017_GREEN AAMAccepted author manuscript, 259 KB

https://ora.ox.ac.uk/objects/uuid:d73fb7fc-b68e-4a30-9ce9-91741cfe1b78

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On the Costs of Nonclassical Logic

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