On the costs of nonclassical logic

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 [Fefe...

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Main Authors: Halbach, V, Nicolai, C
Format: Journal article
Published: Springer Netherlands 2017
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author Halbach, V
Nicolai, C
author_facet Halbach, V
Nicolai, C
author_sort Halbach, V
collection OXFORD
description 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 1991] formulated in classical logic, and (a variant of) the system PKF of [Halbach & Horsten 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: KPF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.
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spelling oxford-uuid:d73fb7fc-b68e-4a30-9ce9-91741cfe1b782022-03-27T08:39:42ZOn the costs of nonclassical logicJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d73fb7fc-b68e-4a30-9ce9-91741cfe1b78Symplectic Elements at OxfordSpringer Netherlands2017Halbach, VNicolai, CSolutions 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 1991] formulated in classical logic, and (a variant of) the system PKF of [Halbach & Horsten 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: KPF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.
spellingShingle Halbach, V
Nicolai, C
On the costs of nonclassical logic
title On the costs of nonclassical logic
title_full On the costs of nonclassical logic
title_fullStr On the costs of nonclassical logic
title_full_unstemmed On the costs of nonclassical logic
title_short On the costs of nonclassical logic
title_sort on the costs of nonclassical logic
work_keys_str_mv AT halbachv onthecostsofnonclassicallogic
AT nicolaic onthecostsofnonclassicallogic