A FULLY CLASSICAL TRUTH THEORY CHARACTERIZED BY SUBSTRUCTURAL MEANS

Abstract

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 CM n for metainferences of level n (for 1 ≤ n < ω ). Each CM n 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 CM ω , based on the hierarchy of logics CM n , that is fully classical , in the sense that every classically valid metainference of any level is valid in it. Moreover, CM ω can be nontrivially expanded with a transparent truth predicate.