The paper shows the debate about the ontological presuppositions of the main cognitive theories in early Jesuit philosophy and their medieval back 181ground: What commitments are necessary for an act of intellectual cognition: species intelligibiles habits of the intellect, or simply the act of intellection, and how the activity of the intellectus agens is seen in each case. The debate concerning these presuppositions includes both the imperfect human cognition and the perfect cognition of Christ. The first part deals with the theories of three “authorities” of the Order: Franciscus Toletus, Benet Perera, who in some aspects follows the school of Padua, and the theological disputations of Gabriel Vázquez, who accepts the intelligible species but in fact reduces them to the act of intellection. The second part descends to the vivacious discussion in the German Jesuit university of Dillingen from 1570 to 1600, where we find a strong influence of Padua, succeeded by alternative theories, and finally by the “opinio communis”, based on arguments from majority and theological preoccupations in the interpretation of the knowledge of Christ, Adam, the angels, and the blessed.