Structural weakening and paradoxes

BRUNO DA RE

Workshop; Formal Methods in Philosophy: Truth, Paradox, and Mathematics; 2018

Recently, a number of authors have pointed out that substructural logics are suitable for developing naive theories that represent semantical concepts, such as truth, and logical concepts, such as validity. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, as far as I know, in substructural literature no one has proposed to reject the structural rule of weakening, while keeping the others. In this talk, I introduce a theory for naive truth and naive validity based on the logic resulting from dropping weakening from classical logic.