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The formal construction of the second-order logic or predicate calculusessentially adds quantifiers to propositional logic. Why second-order logiccannot be reduced to that of the first order? How to demonstrate that certainpredicates are of higher-order? What type of order matches the naturallanguage? Is there a philosophical position behind every logic, even forclassical ones? What philosophical position for what logic in connection to itsexpressive power? These are the questions we ask and that we very brieflysketch as a first reflection. (paper in French)

Tr\`es courte enqu\^ete sur l'extension non-triviale de la logique de propositions \`a la logique du premier et deuxi\`eme ordre