Journal article
On the costs of nonclassical logic
- 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 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
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(Preview, Accepted manuscript, pdf, 259.1KB, Terms of use)
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- Publisher copy:
- 10.1007/s10992-017-9424-3
Authors
- Publisher:
- Springer Netherlands
- Journal:
- Journal of Philosophical Logic More from this journal
- Volume:
- 47
- Issue:
- 2
- Pages:
- 227–257
- Publication date:
- 2017-03-02
- Acceptance date:
- 2016-12-29
- DOI:
- EISSN:
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1573-0433
- ISSN:
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0022-3611
- Keywords:
- Pubs id:
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pubs:667503
- UUID:
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uuid:d73fb7fc-b68e-4a30-9ce9-91741cfe1b78
- Local pid:
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pubs:667503
- Source identifiers:
-
667503
- Deposit date:
-
2016-12-29
Terms of use
- Copyright holder:
- Springer Science+Business Media Dordrecht
- Copyright date:
- 2017
- Notes:
- Copyright © Springer Science+Business Media Dordrecht. This is the accepted manuscript version of the article. The final version is available online from Springer at: https://doi.org/10.1007/s10992-017-9424-3
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