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.

Contemporary natural sciences succeed remarkably well in ensuring a relatively continuous transmission of their cognitively relevant traditions and in creating a widely shared background consensus among their practitioners – hermeneutical ends seemingly achieved without hermeneutical awareness or explicitly acquired hermeneutical skills.

It is a historically specific – emerging only in the nineteenth century – cultural organization of the Author-Text-Reader relation which endows them with such an ease of hermeneutical achievements: an institutionally fixed form of textual and intertextual practices, normatively posited ways of adequate reception and criticism, etc. The same organization also explains a number of their often-discussed epistemic and cultural characteristics: their depersonalized objectivity, the social closure of their discourse and their reduced cultural significance, the shallow historical depth of their activated traditions, etc.

The cognitive structure and the social function of contemporary natural sciences are intimately interwoven with a set of sui generis cultural relations that are partially fixed in the textual characteristics of their literary objectivations. A comparative hermeneutical analysis of natural sciences as a specifically constituted and institutionalized cultural genre or discourse-type brings into relief those contingent cultural conditions and relations to which some of their fundamental epistemological characteristics are bound, or at least with which they are historically closely associated.

Recent historiography of the Scientific Revolution has challenged the assumption that the achievements of seventeenth-century natural philosophy can easily be described as the ‘mechanization of the world-picture.’ That assumption licensed a story which took mechanization as self-evidently progressive and so in no need of further historical analysis. The clock-work world was triumphant and inevitably so. However, a close examination of one key group of natural philosophers working in England during the 1670s shows that their program necessarily incorporated souls and spirits, attractions and congruities, within both their ontology and their epistemology. Any natural philosophical strategy which excluded spirits and sympathies from its world was condemned as tending to subversion and irreligion. This examination shows that the term ‘mechanical philosophy’ was a category given its meanings within local contexts and carries no universal sense separate from that accomplished by these natural philosophers. It also shows how the experimental praxis was compelled to treat souls and spirits, to produce them through experimental labor, and then to extend these experimentally developed entities throughout the cosmos, both social and natural. The development of mechanical philosophy cannot be used to explain the cognitive and social structure of this program, nor its success: instead, the historical setting of experimental work shows how a philosophy of matter and spirit was deliberately constructed by the end of the seventeenth century.

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.

The inclusion of an item within a theory may be essential or accidental, and if the former then the explanation of its meaning and of its inclusion in the theory cannot be by accidental events and circumstances. Since all events and circumstances – be they social, political, religious, psychological, etc. – are accidental vis-à-vis the ideas they occasion, they cannot serve as explanation of these ideas. The only way to explain the ideas is by showing their essentiality to the theory rather than their importance to the people. Thus, the place of spirits and souls within seventeenth-century science is explained by Platonic ideology.

This demands a concept of nature which is thoroughly efficient causative, and a concept of explanation which is thoroughly informative. This means that theories must explain any given effect by a cause which is separable from it and is conceptually heterogeneous to it. Such a nature and such an explanation are inherently paradoxical and irrational, which explains the preponderance of these traits in seventeenth-century science as created by Kepler, through Galileo and Descartes to Newton.

The primary efficient-causal and explanatory agency is force, which is ontically distinct from matter and from the motion it causes in matter. Soul, spirit and active principle are mere variants of force. Thus, their presence in seventeenth-century science is explained only by their being conceptually essential to any Platonic philosophy of nature.

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.

From about 1620 on a profound revolution occurred in the thought of the most developed European nations (France, Italy, Holland, and England), which found its most pregnant expression in the birth of the new philosophical schools of Descartes, Gassendi, and Hobbes. The renewal of philosophy at this juncture in the history of thought, however, does not signify above all a change in the specific, metaphysical content of thought about God, the soul, and immortality, although the revolution in thought does concern these themes as well. Central to the whole “modern” school of philosophers of this period is the constitution of a new conception of nature and – directly for some of them, implicitly for all – of human society as well.

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.

Franz Borkenau's book, The Transition from Feudal to Modern Thought (Der Übergang vom feudalen zum bürgerlichen Weltbild [literally: The Transition from the Feudal to the Bourgeois World-Picture]), serves as background for Grossmann's study. The objective of this book was to trace the sociological origins of the mechanistic categories of modern thought as developed in the philosophy of Descartes and his successors. In the beginning of the seventeenth century, according to Borkenau, mechanistic thinking triumphed over medieval philosophy which emphasized qualitative, not quantitative considerations. This transition from medieval and feudal methods of thought to modern principles is the general theme of Borkenau's book, and is traced to the social changes of this time. According to this work, the essential economic change that marked the transition from medieval to modern times was the destruction of the handicraft system and the organization of labor under one roof and under one management. The roots of the change in thought are to be sought here. With the dismemberment of the handicraft system and the division of labor into relatively unskilled, uniform, and therefore comparable activities, the conception of abstract homogeneous social labor arises. The division of the labor process into simple repeated movements permits a comparison of hours of labor. Calculation with such abstract social unities, according to Borkenau, was the source from which modern mechanistic thinking in general derived its origin.

Grossmann, although he considers Borkenau's work a valuable and important contribution, does not believe that the author has achieved his purpose. First of all, he contends that the period that Borkenau describes as the period of the triumph of modern thought over medieval should not be placed at the beginning of the seventeenth century, but in the Renaissance, and that not Descartes and Hobbes but Leonardo da Vinci was the initiator of modern thought. Leonardo's theories, evolved from a study of machines, were the source of the mechanistic categories that culminated in modern thought.

If Borkenau's conception as to the historical origin of these categories is incorrect in regard to time, Grossmann claims it follows that it is incorrect also in regard to the social sources to which it is ascribed. In the beginning, the factory system did not involve a division of labor into comparable homogeneous processes, but in general only united skilled handicraftsmen under one roof. The development of machinery, not the calculation with abstract hours of labor, is the immediate source of modern scientific mechanics. This goes back to the Renaissance and has relatively little to do with the original factory system that was finally superseded by the Industrial Revolution.

While Borkenau, in tracing the social background of the thought of the period, relies chiefly on the conflicts and strife of political parties, Grossmann regards this as one element only in the formation of the general social situation, which in its entirety and in the interaction of its elements explains the development of modern thought.

In the following pages I will outline the main biographical data and the intellectual activity of two of the major protagonists of the debate on the mechanistisches Weltbild within the Frankfurt “Institut fur Sozialforschung” in the thirties. I have included a selected bibliography of Grossmann's and Borkenau's works, and refer to titles with abbreviations [H.G.…] and [F.B.…].

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.