In this paper, I argue that the most significant contribution of the Jesuits to early modern science (via Galileo) consists in the introduction of a new “image of knowledge.” In contradistinction to traditional Scholasticism, this image of knowledge allows for the possibility of a science (i.e. certain knowledge) of hypothetical entities. This problem became crucial in two specific areas. In astronomy, knowledge of mathematical entities of unclear ontological status (like epicycles and eccentrics) was nevertheless proclaimed certain. In theology, God's knowledge of the future acts of man, logically considered as future contingents, was also proclaimed certain. In both cases the concept of certain knowledge of hypothetical entities was problematic and challenged a central premise of the accepted canons of logic, i.e., that the objects of true knowledge (“scientia”) must be real objects. The main argument of this paper is that the practical orientation of the Jesuit cultural milieu enabled Jesuit scientists and theologians to ignore accepted logical considerations and to modify traditional Thomist images of knowledge. Nevertheless, this modification was not so radical as to change the contemporary organization of knowledge. This was due to the peculiar status of the Jesuits within the church establishment, which exposed them to harsh criticism and created a deep need for legitimation. Thus, the limitations of Jesuit scientific culture are accounted for in institutional, rather than in logical terms.