Très courte enquête sur l'extension non-triviale de la logique de propositions à la logique du premier et deuxième ordre

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are of higher-order? What type of order matches the natural language? Is there a philosophical position behind every logic, even for classical ones? What philosophical position for what logic in connection to its expressive power? These are the questions we ask and that we very briefly sketch as a first reflection. (paper in French)