Recently, several authors have pointed out that substructural logics are adequate for developing naive theories that represent semantic concepts such as truth. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, nowhere in the substructural literature has anyone proposed rejecting the structural rule of weakening, while accepting the other rules. Some theorists have even argued that this task was not possible, since weakening plays no role in the derivation of semantic paradoxes. In this article, I introduce a theory for naive truth based on the logic resulting from dropping the rule of weakening from classical logic, and maintaining the other structural rules.
"Structural Weakening and Paradoxes." Notre Dame J. Formal Logic 62 (2) 369 - 398, May 2021. https://doi.org/10.1215/00294527-2021-0018