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 (sec. 1). 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 (sec. 2–5). 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.
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Acknowledgements
For important discussion and help I am indebted to Heinrich Wansing, Diderik Batens, Graham Priest, Manuel Bremer, Hannes Leitgeb, Alexandre Costa-Leite, Jean-Yves Beziau, Corina Strößner and two unknown referees.
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Open Access funding enabled and organized by Projekt DEAL. This work was supported by the DFG (Deutsche Forschungsgemeinschaft), research unit FOR 2495.
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Schurz, G. Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism. J Philos Logic 51, 27–55 (2022). https://doi.org/10.1007/s10992-021-09608-6
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DOI: https://doi.org/10.1007/s10992-021-09608-6