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.

One of the earliest arguments for Copernicanism was a widely accepted fact: that on a horizontal plane a body subject to no external resistance can be set in motion by the smallest of all possible forces. This fact was contrary to Aristotelian physics; but it was a physical argument (by abduction) for the possibility of the Copernican world system. For it would be explained if that system was true or at least possible.

Galileo argued: only nonviolent motions can be caused by the smallest of all possible forces; hence resistance-free horizontal motions are nonviolent; this confirms Copernicanism insofar as it designates the rotations of celestial spheres (being resistance-free horizontal motions) as nonviolent.

Galileo's argument was compatible with (and supportive of) the specific Copernican version of impetus mechanics; but it was also compatible with a (somewhat qualified) principle of inertia. Thus it promoted decisively the transition from impetus mechanics to classical inertial mechanics.

Our understanding of the predisposing factors, the nature, and the fate of the Oxford Calculatory tradition can be significantly increased by seeing it in its social and institutional context. For instance, the use of intricate imaginary cases in Calculatory works becomes more understandable if we see the connection of these works to undergraduate logical disputations. Likewise, the demise of the Calculatory tradition is better understood in the light of subsequent efforts at educational reform.

Unfortunately, too little evidence remains about the Calculators and their context to enable anything like a full reconstruction of the relation of the Oxford Calculators' work to its context. Nevertheless, seeking out and fitting together the bits of information that do remain can add to our insight. Among the topics worth further research are the relation of training in calculationes to later careers in church or government, and the special features of the Calculatory tradition as a tradition consisting of multiple parallel manifestations closely interconnected with other disciplines, ranging from logic and natural philosophy to theology and medicine.

The development of autonomous theoretical science is often considered a “Greek miracle.” It is argued in the present paper that another “miracle,” necessary for the creation of modern science, took place for the first time in the Islamic Middle Ages, viz. the integration of (still autonomous) theory and (equally autonomous) practice.

The discussion focuses on the mathematical disciplines. It starts by investigating the plurality of traditions which were integrated into Islamic mathematics during its formation, emphasizing practitioners' “sub-scientific” traditions, and shows how these were synthesized in a way virtually unknown in earlier cultures. A discussion of the sociocultural roots of this specific synthesis concludes that a major role was played in the earlier period by the combination of fundamentalist convictions characteristic of Islam – that the most humble daily activity is directly responsible to the highest ontological level, while conversely this highest level is concerned with the humblest ranks of daily existence – with the absence of an institutionalized “Church” able to monopolize the interpretation of the mutual bond of the divine and the everyday levels.

As the institutions of learning crystallized around the turn of the millennium, the integrative attitude to theory and practice was fixated institutionally; the latter process is discussed, first with the example of the madrasah institution as the carrier of an arithmetical textbook tradition, and second with that of the bond between astronomy and theoretical geometry.

Certain authors, in speaking of their works, say: My book, my commentary, my history, etc. They smack of these bourgeois homeowners, with “my house” always on their lips. They should rather speak of: our book, our commentary, our history, etc., since, generally speaking, there is far more in them of others than of their own.

I felt happy but a little apprehensive when I received the suggestion from the editors of Science in Context to write a comment on my book Categories of Medieval Culture quite a few years after its first publication (1972) and translation. It is always difficult to comment on one's own work, for in such a case there is seldom the necessary degree of “distance” between the author and the commentator. I offer this paper rather as a short account of the direction of my thoughts.

Duhem's great contribution to the study of the history of medieval science is indisputable. His book remains an excellent source of information concerning the ideas of the epoch's thinkers about the foundations of the universe. Ariew's painstaking translation of a considerable portion of Duhem's ten-volume work deserves the deep gratitude of all those interested in medieval science. Le Systéme du monde regains its actuality. Nevertheless, to write now about a book produced by this great scholar at the beginning of the century is not an easy undertaking, and involves some risk. Too many changes have taken place in the principles of studying the history of science during the seventy-odd years since the book was written, and some notions that seemed then to be perfectly clear are not so simple and indisputable now. With profound respect for this feat of scholarship, I should like to make some observations in connection with the recent English publication of Duhem's book.

The publication of this volume appears to be the most recent in a group of works whose appearance marks renewed interest in Duhem. Over the past ten years, attention has been focused on Duhem's life (Jaki 1984), his physics (Jaki 1984; Nye 1986, 208–23), his philosophy of science (Jaki 1984, chap. 9; Paul 1979, chap. 5; Ariew 1984),' and his history of science (Jaki 1984, chap. 10; Martin 1976). But the significance of this translation is that - leaving aside To Save the Phenomena – for the first time we have a partial translation into English of one of the two great historical works that revitalized the study of medieval science.