Journal of Philosophical Logic 51 (1):27-55 (2022)

Authors
Gerhard Schurz
Heinrich Heine University Düsseldorf
Abstract
In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language. Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10992-021-09608-6
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,307
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - University of Chicago Press.
The Structure of Empirical Knowledge.Laurence BonJour - 1985 - Cambridge, MA, USA: Harvard University Press.
Inference to the Best Explanation.Peter Lipton - 1991 - London and New York: Routledge/Taylor and Francis Group.

View all 67 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Modal Translations in Substructural Logics.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (3):283 - 336.
Universal Logic as a General Theory of Logic.Musa Akrami - 2012 - Journal of Philosophical Investigations at University of Tabriz 6 (10):44-61.
The Classical Constraint on Relevance.Arnon Avron - 2014 - Logica Universalis 8 (1):1-15.
On Some Interpretations of Classical Logic.Branislav R. Boričić & B. R. Boričić - 1992 - Mathematical Logic Quarterly 38 (1):409-412.
Note on Grammatical Translations of Logical Calculi.Stanislaw Krajewski - 1992 - Archive for Mathematical Logic 31 (4):259-262.
Pluralismo, Monismo e Relativismo Lógico.Diogo Dias - 2018 - Revista de Filosofia Moderna E Contemporânea 6 (2):21-36.
Judgement Aggregation in Non-Classical Logics.Daniele Porello - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):106-139.

Analytics

Added to PP index
2021-09-06

Total views
30 ( #381,417 of 2,507,870 )

Recent downloads (6 months)
14 ( #55,518 of 2,507,870 )

How can I increase my downloads?

Downloads

My notes