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In Baroque scholasticism the medieval semantic theory of connotation as a property of terms, originally elaborated by Ockham and others, received an ontological application or re-interpretation in the context of the theory of relations. The main proponent of this ontologized “doctrina de connotatis” seems to have been Suárez. Subsequently, this doctrine was severely criticised by the Jesuits Pedro Hurtado de Mendoza and Rodrigo de Arriaga, but also by the “princeps Scotistarum” Bartholomeo Mastri; whereas another Scotist, John Punch, adopted a theory of relations close to this doctrine. The fates of the original semantic theory of connotation, the ontologized “doctrina de connotatis” and the broader context of the relevant discussions (especially the new res–modus ontology established around 1600) document the complexity of the history of scholastic ideas, irreducible to any simple paradigm (like that of the realism–nominalism strife).