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META-CLASSICAL NON-CLASSICAL LOGICS

Part of: General logic

Published online by Cambridge University Press:  16 May 2024

EDUARDO BARRIO Open the ORCID record for EDUARDO BARRIO [Opens in a new window] ,
CAMILLO FIORE Open the ORCID record for CAMILLO FIORE [Opens in a new window]  and
FEDERICO PAILOS Open the ORCID record for FEDERICO PAILOS [Opens in a new window]
EDUARDO BARRIO
Affiliation:
IIF-SADAF-CONICET-UNIVERSITY OF BUENOS AIRES BULNES 642, C1176ABL BUENOS AIRES ARGENTINA E-mail: [email protected]
CAMILLO FIORE
Affiliation:
IF-SADAF-CONICET-UNIVERSITY OF BUENOS AIRES BULNES 642, C1176ABL BUENOS AIRES ARGENTINA E-mail: [email protected]
FEDERICO PAILOS*
Affiliation:
IIF–SADAF–CONICET–UNIVERSITY OF BUENOS AIRES BULNES 642, C1176ABL BUENOS AIRES ARGENTINA and DEPARTMENT OF COMPUTER SCIENCE EBERHARD KARLS UNIVERSITÄT TÜBINGEN SAND 13, 72076 TÜBINGEN GERMANY
*
E-mail: [email protected]
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Abstract

Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of ‘increasingly classical’ logics—that is, logics that are classical at the level of inferences and of increasingly higher metainferences—all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by taking a somehow different route. We explore logics that are different from classical logic at the level of inferences, but recover some important aspects of classical logic at every metainferential level. We dub such systems meta-classical non-classical logics. We argue that the systems presented deserve to be regarded as logics in their own right and, moreover, are potentially useful for the non-classical logician.

Keywords

non-classical logicsmetainferencesclassical logicmixed logicsparadoxes

MSC classification

Primary: 03B60: Other nonclassical logic
Secondary: 03B50: Many-valued logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 4 , December 2024 , pp. 1146 - 1171
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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