Reflexiones acerca de la necesidad lógica

Abstract

It is known that logicians and philosophers have been interested on modal sentences since Aristotle and that it was Leibniz who gave the first definition of logical necessity: a necessary truth is the one that is true in every possible world. More than three centuries later, in the first half of the XX century, C. I. Lewis developed the first modal systems capable to formulate old Aristotelian definitions of modal operators in modern logic. However, it is only with Kripke's semantic of possible worlds that it was possible to get the first characterization of Leibnizian concept of necessary truth. Later on, David Lewis built a new semantics, also based on the notion of possible world, that allowed to give truth conditions of counterfactual conditionals and define necessary truth from them. The present paper intends to show: 1) that the modal systems built on Kripke classic semantic don't realize strictly the Leibnizian concept of necessary truth despite the fact that they were inspired by it ; 2) in addition, in the posterior developments of Kripkian semantic, the modal systems -and particularly the meaning of modal operators -have gradually lost their original philosophical content, and 3) despite David Lewis's semantics of counterfactual conditional was more fruitful for the philosophical logic than the modal systems based on the traditional semantics of possible worlds, however it was not successful to express appropriately the Leibnizian idea of necessary truth.