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A FULLY CLASSICAL TRUTH THEORY CHARACTERIZED BY SUBSTRUCTURAL MEANS

Published online by Cambridge University Press:  04 January 2019

FEDERICO MATÍAS PAILOS
FEDERICO MATÍAS PAILOS*
Affiliation:
Philosophy Department, University of Buenos Aires
*
*NATIONAL SCIENTIFIC AND TECHNICAL RESEARCH COUNCIL SARMIENTO 440 C104AA7 BUENOS AIRES, ARGENTINA and DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BUENOS AIRES PUÁN 480 C1406CQJ BUENOS AIRES, ARGENTINA E-mail: [email protected]
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Abstract

We will present a three-valued consequence relation for metainferences, called CM, defined through ST and TS, two well known substructural consequence relations for inferences. While ST recovers every classically valid inference, it invalidates some classically valid metainferences. While CM works as ST at the inferential level, it also recovers every classically valid metainference. Moreover, CM can be safely expanded with a transparent truth predicate. Nevertheless, CM cannot recapture every classically valid meta-metainference. We will afterwards develop a hierarchy of consequence relations CMn for metainferences of level n (for 1 ≤ n < ω). Each CMn recovers every metainference of level n or less, and can be nontrivially expanded with a transparent truth predicate, but cannot recapture every classically valid metainferences of higher levels. Finally, we will present a logic CMω, based on the hierarchy of logics CMn, that is fully classical, in the sense that every classically valid metainference of any level is valid in it. Moreover, CMω can be nontrivially expanded with a transparent truth predicate.

Keywords

03BXX03B4703B5003B6003B53logicmetainferencesmetainferential validitysubstructural logicsempty logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 2 , June 2020 , pp. 249 - 268
Copyright
Copyright © Association for Symbolic Logic 2019 

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