Abstract : Franciscus de Mayronis develops a correlational account of cognition and thus, of intentionality - to think or to cognize are relational predicates, that is to say: they always involve a relation to an object. However, correlational theories of intentionality are possible only within the framework of an ontology that offers a non-reductionist conception of being and a sophisticated account of relations. The aim of the present study is to present Franciscus' correlational theory of intentionality, and to sketch its ontological consequences. First, some preliminary, systematic remarks will be made; second, the case of Franciscus de Mayronis will be considered in detail.