In the last few decades, a critical mass of excellent studies by competent historians of Islamic science has led to a qualitative shift in our understanding of this history. Yet despite this shift, an integrated approach to the study of the history of science in Muslim societies still needs to overcome some real hurdles. To start with, such an undertaking calls for an examination of wide-ranging cultural activities, in a vast geographical area, under different historical conditions, and for a period of at least seven centuries. Moreover, the sources for the study of this subject are daunting, and they include, in addition to material evidence, thousands of scientific manuscripts, most of which remain unexamined. The abundance of evidence also gives rise to a number of methodological difficulties: earlier surveys of the history of Islamic science were based on a handful of random studies of scientific treatises. Some of the actual studies were of a high quality; yet ironically, the paucity of hard evidence available to early scholars often enabled them to cover all the fields of science in all-inclusive, and often reductive, narratives. In the last few decades, many more scientific treatises have been critically examined, with the dual effect of providing detailed information about the various scientific disciplines, and highlighting the peculiarity of the history of each separate discipline or even fields within disciplines.

In the absence of thorough and exhaustive accounts for developments in the various scientific disciplines as well as accounts for the epistemological foundations of these sciences, it only stands to reason that attempts to provide general characterizations of science in Muslim societies and its relation to religion can only be provisional and subject to scrutiny. Even such seemingly straight forward characterizations of the scientific activity in Muslim societies as Islamic or Arabic cannot be taken for granted, and the same applies to the assertion that Islam has either a positive or a negative attitude towards science. I do not mean here to deny the validity of using terms such as "Islamic science", but simply to stress the importance of addressing the question of methodology before venturing such general characterizations.

Due to the extent of the scientific enterprise in classical Muslim societies, the question of the relationship between science and religion in Islam can be approached from many different perspectives, and may vary according to, and within, the region, period, or discipline under consideration. For example, one may look at standard discussions among religious scholars and theologians. Alternatively, the classifications of the sciences provide an epistemological perspective which pertains to theories of knowledge. One can also examine and attempt to classify the manifold views of scientists as well as religious scholars on the relationship between science and religion. In this essay, I will restrict myself to the field of astronomy; in particular, I will compare two important trends of research in theoretical astronomy. Astronomy, I should add, is especially relevant to the question of the relationship between science and religion because of its cosmological dimension and the relative ease with which it can be invoked in connection with metaphysical questions. The main focus in this paper is on the way communities of scientific knowledge conceived of their profession and research within the larger context of religion. However, I will first say a few words about religious scholars who discussed science and proposed "Islamic" assessments of the various sciences.

Almost invariably, discussions of the Islamic attitude toward science invoke the works of al-Ghazali (d. 505/111). I will not attempt to summarize Ghazališs views on the various sciences; these views have received more scholarly attention than those of any other Muslim scholar who had written on the subject. It is important to note, however, that the debate regarding Ghazališs true attitudes and views continues among contemporary scholars, and there seems to be no consensus even over the interpretation of his most obvious work, Tahafut al-Falasifa (The Incoherence of the Philosophers), let alone an integrated assessment of his whole oeuvre, including such relevant works to our subject as al-Iqtisad fi al-IŒtqad, MiŒyar al-ŒIlm, al-Qustas al-Mustaqim, Maqasid al-Falasifa, and al-Mustasfa min ŒIlm al-Usul.

Aside from al-Ghazali and whether he actually condoned, neglected, or opposed the sciences, there are, to be sure, some radical and credible traditionalists, such as Ibn Taymiyya (d. 1328), who attacked some of the fields of knowledge that Ghazali condoned, but in the face of these there are equally radical and popular traditionalists, such as Ibn Hazm (11th century), who defended logic and argued for the interconnection between the various sciences. What is more important about the provocative writings of Ibn Taymiyya with such titles as "The Rebuttal of Logic" and "The attack on Logicians" is that Ibn Taymiyya employed the discourse of formal logic, and rather than deny the validity of logic, he only denies the claim by a professional group of logicians to have an exclusive monopoly over methods of arriving at Truth. Moreover, Ibn Taymiyya questioned the validity of some of the propositions and syllogisms of certain kinds of formal logic, and not all kinds of logic. Furthermore, Ibn Taymiyya criticized Ghazališs denial of causality and was a strong believer in physics and the natural laws. Again, the purpose of citing these authors here is not to provide an exhaustive analysis of their views, but simply to point out the diversity as well as complexity of the views of traditional Muslim scholars on science and scientific knowledge.

The differences between these traditional religious scholars highlight the difficulty of identifying a unified, traditional Islamic attitude toward science. It is clear, however, that the overall outcome of the religious debates over scientific knowledge was to naturalize some of the exact sciences and to provide Islamic justifications for certain kinds of scientific knowledge. Such was the assessment of the famous 14th century historian Ibn Khaldun who remarks in his Muqaddima that after Ghazali all religious scholars studied logic, but they studied it from new sources, such as the works of Ibn al-Khatib and al-Khunji (13th century), and that people stopped using the books of the ancients; "the books and the methods of the ancients", says Ibn Khaldun, "are avoided, as if they had never been". Later, he adds (p. 143) "It should be known that the early Muslims and the early speculative theologians greatly disapproved of the study of this discipline [logic]. They vehemently attacked it and warned against it... Later on, ever since al-Ghazzali and the imam Ibn al-Khatib, scholars have been somewhat more lenient in this respect. Since that time, they have gone on studying (logic)..."

Generally speaking, therefore, religious assessments of the epistemic value of various kinds of scientific knowledge were nuanced and diverse. And although one cannot adduce a direct and mechanical correlation between the religious arguments and the ways in which scientists perceived of and theorized their own scientific disciplines, it is abundantly clear that the views of scientists were also manifold. Furthermore, since they were inspired by a variety of cultural factors, these articulations by scientists are obvious and tangible expressions of what "Islamic" science meant in actual history, and are as indicative of the Islamic dimension as the views expressed by religious scholars. In what follows, I will approach the question of the relationshipbetween science and religion by focusing on two particular traditions of astronomical research, one in the Muslim east and the other in the Muslim west. My interest is in charting out the peculiar modes of thinking that provided the epistemological and methodological conditions for the formation of these two traditions, and the diverse conceptual frameworks that informed the different planetary theories proposed in each.

Ever since Sartonšs attempt to write a universal history of science, the Islamic sciences have had a considerable presence in various accounts of this history. Despite their large quantitative presence, however, Islamic sciences are all too often absent from grand, integrative narratives of the history of science. When historians offer conceptual analysis of epochal changes in the history of science (which is something they often do), the cumulative legacy of the Islamic sciences is simply overlooked. Conceptually, the Islamic scientific legacy is seen as a rather mechanical continuation of the Greek one: the Islamic sciences expanded and refined the Greek sciences without departing from them conceptually. A justification of this oversight is seldom provided, but when it is, it usually has to do with the role of philosophy or theory in science. In the field of astronomy in particular, theoretical considerations were often overlooked on the basis of a widely held assumption that Islamic science was practical and hence theoretically or philosophically shallow. The decline of Islamic science, according to this view, was a result of the lack of theoretical rigor. In the last few decades, however, an alternative view has been proposed, often by competent historians of science. In contrast to the notion that the Islamic sciences declined because of their feeble philosophical foundations, historians of astronomy now argued that the motivation for the most important tradition of astronomical reform in the Muslim world was philosophical. Despite its different understanding of the role of philosophy in connection with the science of astronomy, this thesis often served to undermine the "scientific" value of these astronomical reforms.

In a sense, the two different views regarding the role of philosophy in Islamic science echo a fundamental debate over the function of scientific theory. Simply put, scientist and philosophers (as well as historians of science) differ over whether the primary role of scientific theory is to explain nature as it exists in reality or simply describe and predict its appearance as we perceive it. In the latter case (description and prediction), the quest of science is to "save the phenomena," whereas in the former case, science goes beyond appearance to explore causal connections or, in the language of philosophers, "first causes." This philosophical controversy, and many variations of it, is at the roots of the emergence of what is commonly called "modern science", and it continues to inform modern and postmodern debates on the relationship between scientific knowledge and others forms of knowledge. This controversy has also influenced readings of the history of "non-western" science. Before examining the question of the role of theory in science as reflected in the two Islamic traditions of astronomical reform, a few words on the early developments in Islamic astronomy that provided the background for the latter reform traditions.

Astronomy was one of the oldest, most developed and most esteemed exact sciences of antiquity. (Many of the mathematical sciences were originally developed to facilitate astronomical research. Various disciplines and belief systems intersected and interacted in astronomy, including physics and metaphysics, as well as mathematics and religion. Islamic/Arabic astronomy was also culturally hybrid (Babylonian, Indian, Persian, and Greek), and intimately connected to politics (astrology, dynastic legitimization). Finally, practical considerations such as finding one's direction during night travel, and the correlation between the seasons of the year and the positions of the planets provided additional incentives for the study of astronomy. For all of these reasons, astronomical research was hybrid and spirited, and the field of astronomy provided fertile grounds for questioning old conceptions and developing and testing new ones.

The first astronomical texts that were translated into Arabic in the eighth century were of Indian and Persian origin. The real emergence of Arabic astronomy, however, occurred in the ninth century at which time the major Greek astronomical texts were translated. Right from its very beginnings in the ninth and all the way till the sixteenth century, astronomical activity was wide-spread and intensive. This activity is reflected in the large number of scientists working in practical and theoretical astronomy, the number of books written, the active observatories, and the new observations.

Arabic astronomy was first exposed to Persian and Indian astronomy, and it continued to use some of the parameters and methods of these two traditions, yet the greatest formative influence on Arabic astronomy is undoubtedly Greek. Early in the ninth century, astronomers realized that the Greek astronomical tradition was far superior to the other two, both in its comprehensiveness and its use of effective geometrical representations. One particular Greek author, and more specifically one work by this author, exerted a disproportionate influence on all of medieval astronomy through the whole of the Arabic period and until the eventual demise of the geocentric astronomical system. This is the Almagest of Ptolemy (second century AD). That this text should exert so much influence is neither accidental nor surprising, for it is the highest achievement in Hellenistic mathematical astronomy, and one of the greatest achievements of all of Hellenistic science.

The Almagest was rightly considered the main authoritative work of antiquity on Astronomy. In this book, Ptolemy synthesizes the earlier knowledge of Hellenistic astronomy in light of his own new observations. The main purpose of the book is to establish the geometric models which would accurately account for observational phenomena. A large part of the book is dedicated to the methods for constructing various models and for calculating the parameters of these models. Ptolemy also provides tables for planetary motions to be used in conjunction with his models. Of all the books of antiquity, the Almagest represents the most successful work of mathematical astronomy: its geometric representations of the universe provided the most accurate and best predictive accounts for the celestial phenomena. A Greek tradition of physical astronomy is also reflected in the Almagest and in Ptolemy's other influential work, the Planetary Hypothesis. According to this predominantly Aristotelian tradition, the universe is organized into a set of concentric spheres, each carrying a star and rotating around the stationary earth at the center of the universe. In contrast to sublunary rectilinear motion, the heavenly bodies move in perfect uniform circular motions. Ptolemy adopted, at least in theory, the two basic Aristotelian principles: that the earth is stationary at the center of the universe, and that the motion of heavenly bodies ought to be represented by a set of uniform circular motions. In practice, mathematical considerations often forced Ptolemy to disregard the second of these principles. However, against his better "mathematical" judgement, the only physical theory or cosmology available to Ptolemy was that of Aristotle. Ptolemy thus had no other option but to profess his adherence to this cosmology, an adherence which gave rise, in the Islamic period and later in Europe, to a long and fruitful tradition of astronomical reform.

Astronomical reform in the Islamic period took different forms. Under the Caliph al-Mašmun, a program of astronomical observations was organized in Baghdad and Damascus. Like any organized research project, this program endowed astronomical activity in the Islamic world with formal prestige. The professed purpose of this program was to verify the Ptolemaic observations by comparing the results derived by calculation, based on the Ptolemaic models, with actual observations conducted in Baghdad and Damascus some 700 years after Ptolemy. The results were compiled in al-Zij al-Mumtahan (The verified tables), which is no longer extant in its entirety, but is widely quoted by later astronomers. The most important correction introduced was to show that the apogee of the solar orb moves with the precession of the fixed stars. On a more general note, this program stressed the need for continuing verification of astronomical observations, and for the use of more precise instruments.

Thus, right from its beginnings, Arabic astronomy set out to rectify and complement Ptolemaic astronomy. Having noted several discrepancies between new observations and Ptolemaic calculations, astronomers then proceeded to reexamine the theoretical basis of Ptolemy's results. This critical reexamination took several forms. Although the general astronomical research of this period (ninth century) is conducted within the framework of Ptolemaic astronomy, this research reworked and critically examined the observations and the computational methods of this astronomy and, in a limited way, was able to explore problems outside its set frame. The application of diverse mathematical disciplines to each other also had the immediate effect of expanding the frontiers of disciplines and introducing new scientific concepts and ideas. The use of systematic mathematization transformed the methods of reasoning and enabled, in turn, further creative developments in the branches of science.

In the tenth and eleventh centuries, the earlier examinations of Ptolemaic astronomy led to systematic projects which, rather than addressing the field in its totality, focused on specific aspects of astronomy. One of the main characteristics of this period was the tendency to provide exhaustive synthesizing works on particular astronomical topics, culminating in Birunišs (973-c. 1048) al-Qanun al-MasŒudi, a synthesis of the Greek, Indian, and Arabic astronomical traditions. It is with Biruni that we have the first systematic discussion, by a scientist (astronomer), of the relationship between science and philosophy. A book entitled al-Asšila wal-Ajwiba (questions and answers) preserves an exchange between Biruni and his contemporary Ibn Sina, the most celebrated Muslim philosopher of all time. Biruni presents Ibn Sina with a set of questions in which he criticizes Aristotle's physical theory, especially as it pertains to astronomy. Ibn Sina then responds, and a lively debate ensues. In the course of this exchange, Biruni questions almost all of the fundamental Aristotelian physical axioms: he rejects the notion that heavenly bodies have an inherent nature, and asserts that their motion could very well be compulsory; he maintains that there is no observable evidence that rules out the possibility of vacuum; he further asserts that, although observation corroborates Aristotle's claim that the motion of heavenly bodies is circular, there is no inherent "natural" reason why this motion cannot be, among other things, elliptical. What is more significant than the actual objections raised by Biruni is the argument he employs in the course of the debate. Biruni draws a distinction between his vocation and that of Aristotle and Ibn Sina. He seems to argues that the metaphysical axioms on which philosophers build their physical theories do not constitute valid evidence for the mathematical astronomer. In other words, Biruni clearly distinguishes between the philosopher and the mathematician, the metaphysician and the scientist. He conceives of himself as a mathematical astronomer for whom the only valid evidence is observational or mathematical. Biruni's example illustrates how the systematic application of rigorous mathematical reasoning led to the mathematization of astronomy and, by extension, to the mathematization of nature. Rather than subsuming the various sciences under the all-encompassing umbrella of philosophy, many scientists considered their professions as autonomous mathematical enterprises, separate from, and on par with philosophy.

As I noted earlier, Ptolemy had taken the liberty to propose models that did not conform to Aristotelian cosmology; so how does Birunišs example differ from that of Ptolemy? Put differently, can we think of both Ptolemy and Biruni as prototypes for scientists that are interested in the descriptive functions of science, in "saving the phenomena," as opposed to scientists seeking to explain and not just describe? I will try to answer this question by comparing two traditions of astronomical reform in the Muslim east and west.

Traditions of astronomical reform in the Islamic period

Building on the cumulative achievements of Arabic astronomy, the eleventh century witnessed the emergence of a new tradition of astronomical research. After the eleventh century, the efforts of most theoretical astronomers were directed towards providing a thorough evaluation of the physical and philosophical underpinnings of Ptolemaic astronomy, and proposing alternatives to it. It should be noted here that the emergence of this tendency in astronomical research does not represent a move away from the thorough mathematical examination of astronomy, but is an outcome of this increasing mathematization. This line of research was pursued by several eleventh-century scientists. In a book entitled Tarkib al-Aflak, Abu ŒUbayd al-Juzjani (d. c. 1070) indicates that both he and his teacher, Ibn Sina, were aware of the o-called equant problem of the Ptolemaic model. Juzjani even proposes a solution for this problem. The author of an anonymous Andalusian astronomical manuscript refers to another work which he composed under the title al-Istidrak Œala Batlamyus (recapitulation regarding Ptolemy), and indicates that he included in this book a list of objections to Ptolemaic astronomy. The most important work of this genre, however, was written in the same period by Ibn al-Haytham (d. 1039). In his celebrated work Al-Shukuk Œala Batlamyus (doubts on Ptolemy), Ibn al-Haytham sums up the physical and philosophical problems inherent in the Greek astronomical system, and provides an inventory of the theoretical inconsistencies of the Ptolemaic models. The tradition of astronomical reform thrived in the thirteenth century, climaxed in the fourteenth, and continued well into the fifteenth and sixteenth centuries. Most astronomers of this period took up the theoretical challenge outlined by Ibn al-Haytham, attempted to rework the models of Ptolemaic astronomy and to provide, with varying degrees of success, alternatives to these models. The list of astronomers working within this tradition comprises some of the greatest and most original Muslim scientists. The astronomers who have received modern scholarly attention include: Mušayyad al-Din al-ŒUrdi (d. 1266), Nasir al-Din al-Tusi (d. 1274), Qutb al-Din al-Shirazi (d. 1311), Sadr al-ShariŒa al-Bukhari (d. 1347), Ibn al-Shatir (d. 1375), and ŒAlaš al-Din al-Qushji (d. 1474).

To appreciate the technical aspects of these astronomical reforms, a quick overview of some aspects of Ptolemaic astronomy is in order. In his Almagest, Ptolemy used the results of earlier Hellenistic astronomy and incorporated them into one great synthesis. Of particular geometrical utility was the concept of eccentrics and epicycles developed by Hipparchus (second century BC) and adopted by Ptolemy. In an astronomical representation employing the eccentric model (Figure 1), a planet is carried on the circumference of an eccentric circle which rotates uniformly around its own center G. This center, however, does not coincide with the location O of an observer on the earth. As a result, the speed of the planet appears to vary with respect to the observer at O. In an epicyclic model, the planet P is carried on the circumference of an epicycle, whose center is in turn carried on a circle called the deferent, which rotates uniformly around the center of the universe, the earth. Viewed by an observer at point O, the combination of the two uniform motions of the deferent and the epicycle produces a non-uniform motion which is mathematically equivalent to the motion of the eccentric model.

(Not Shown)
Figure 1

The Ptolemaic model for the motion of the sun utilized either a simple eccentric or the equivalent combination of a deferent and an epicycle. All the other Ptolemaic models for planetary motions were considerably more complex. For example, in the model for the longitudinal motion of the upper planets Mars, Jupiter and Saturn (Figure 2), the center G of the deferent circle no longer coincides with the earth O; moreover, the uniform motion of the center of the epicycle on the circumference of the deferent is measured around the point E, called the equant center, rather than the center G of the deferent. Ptolemy proposed this model because it allowed for fairly accurate predictions of planetary positions. However, circle G in this model is made to rotate uniformly around the equant E which is not its center. This represented a violation of the Aristotelian principle, adopted by Ptolemy, of uniform circular motion around the Earth, the stationary center of the universe. In other words, for the sake of observation, Ptolemy was forced to breach the physical and philosophical principles on which he built his astronomical theory. Other Ptolemaic models were even more complex, and with each additional level of complexity new objections were raised against Ptolemaic astronomy.

(Not Shown)
Figure 2

Other objections raised by Ibn al-Haytham and taken up by later astronomers include the problem of the prosneusis point in the model for the longitudinal motion of the moon; the problem of the inclination and deviation of the spheres of Mercury and Venus; the problem of planetary distances, and so on. In the case of the moon, additional difficulties arise because Ptolemy's model has a deferent center which is itself moving; moreover, the motion of the center of the epicycle on this deferent is not uniform around the deferent's center; rather, it rotates uniformly around the center of the world. To complicate matters further, the anomalistic motion on the epicycle is measured away from the mean epicyclic apogee, that is aligned with a movable point called the prosneusis point, rather than being measured from the true apogee, that is aligned with the center of the world. This prosneusis point is the point diametrically opposite to the center of the deferent on the other side of the center of the world. The model for the longitudinal motion of Mercury contained complex mechanisms that were equally objectionable. Additional complications also resulted from the motion of the planets in latitude: the motion in longitude is measured on the plane of the ecliptic which is the great circle of the celestial sphere that traces the apparent yearly path of the sun as seen from the earth. The deferents of the Ptolemaic models, however, did not coincide with this plane. The least problematic is the case of the lunar model, where the deferent has a fixed inclination with respect to the ecliptic, and the epicycle lies in the plane of the deferent. However, the epicycles of the upper planets do not lie in the plane of the deferent, and they have a variable deviation with respect to it. In the case of the lower planets, both the inclination of the deferent with respect to the ecliptic and that of the epicycle with respect to the deferent are variable. Without getting into details, one can easily imagine the complexity and potential problems of the Ptolemaic models which attempted to account for these see-saw and oscillation motions.

The astronomers who attempted to solve the above problems can be classified into two general schools: a mathematically oriented school which was predominantly in the eastern parts of the Muslim world, and a philosophically oriented school based in the western regions of the empire. The name "Maragha school" is often given to the eastern reformers in recognition of the achievements of a number of astronomers working in an observatory established at Maragha. Whereas the contributions of these astronomers are no doubt monumental, it should be noted that the reform of Ptolemaic astronomy started before the establishment of the Maragha observatory in the thirteenth century, and reached its highest point in the fourteenth. In fact, some of the astronomers of the Maragha group seem to have started their reform projects even before they joined this observatory; they were perhaps invited to join the observatory team because they were already engaged in such research. The eastern reform tradition, then, was too diffused to be associated with any one geographical area or period; rather, it characterizes several centuries of Arabic astronomical research throughout the Eastern domains of the Muslim world.

Astronomers of the eastern reform tradition adopted several mathematical strategies in their attempts to solve the theoretical problems of the Ptolemaic models. One of their main objectives was to come up with models in which the motions of the planets could be generated as a result of combinations of uniform circular motions, while at the same time conforming to the accurate Ptolemaic observations. Two useful and extremely influential mathematical tools were invented by Tusi and ŒUrdi. The first tool, known in modern scholarship as the Tusi couple, in effect produces linear oscillation as a result of a combination of two uniform circular motions. The tool was used in various ways by many astronomers including Copernicus. The ŒUrdi lemma is an equally versatile mathematical tool used by ŒUrdi and his successors. To produce optimal representations that are physically and mathematically sound, other astronomers used various combinations of these two tools, and devised additional tools of their own invention. In addition, other mathematical solutions were proposed to resolve the contradictions inherent in the Ptolemaic models. For example, ŒUrdi reversed the direction and tripled the magnitude of motion of the inclined sphere in the Ptolemaic lunar model; he was thus able to produce uniform motion around the geometric center of the sphere, while at the same time reproducing the uniform motion around the old Ptolemaic center. The most comprehensive and successful models were introduced in the fourteenth century by the Damascene astronomer Ibn al-Shatir; his models for all the planets utilize combinations of perfect circular motions where each circle rotates uniformly around its center. Ibn al-Shatir was also able to solve problems of planetary distances, and to provide more accurate accounts for observations.

The development of Arabic astronomy in al-Andalus and North Africa followed different routes. The beginnings of significant scientific activity in al-Andalus started in the ninth century; yet this activity was almost completely dependent upon and lagging behind the sciences of the eastern part of the Muslim world. Between the ninth and eleventh centuries, however, a full-fledged scientific tradition emerged. Many scientists traveled east to study science; scientific books were systematically acquired and large private and public libraries were established. A solid familiarity with the eastern astronomical tradition led, in the eleventh century, to an intensive and at times original astronomical activity. The emphasis of the activity of these and other astronomers was focused on the compilation of tables and on spherical astronomy. Their primary original contributions were limited to some new observations, but mostly to the mathematics of the trepidation movement of the stars, as well as to the invention of highly sophisticated astronomical instruments. During this entire period, however, little work of significance was devoted to planetary theory.

In contrast to the earlier period, the focus of astronomical research in al-Andalus and North Africa in the twelfth century shifted to planetary theory. The names associated with this research tradition include Ibn Baja (d. 1138), Jabir Ibn Aflah (fl. 1120), Ibn Tufayl (d. 1185), Averroes (d. 1198), and Al-Bitruji (fl. 1200). Of these, Al-Bitruji was the only one to formulate an alternative to Ptolemaic astronomy, while the others produced philosophical discussions of this astronomy. Both the discourses on Ptolemaic astronomy, as well as the actual proposed model of al-Bitruji, conceived of astronomical reform in reactionary terms-that is, in terms of adopting older and mathematically inferior models in place of the ones used since Ptolemy. The aim of the western school was to reinstate Aristotelian homocentric spheres, and to completely eliminate any use of eccentrics and epicycles. In accordance with the most stringent and literal interpretations of Aristotelian principles, the western researchers demanded that the heavens be represented exclusively by nested homocentric spheres and perfect uniform circular motions. Even epicycles and deferents that rotated uniformly around their centers were not tolerated, because their use entailed an attribution of compoundednesss to heavenly phenomena; according to Aristotelian principles, the heavens are perfectly simple. However, since the predictive power of the Ptolemaic models and their ability to account for the observed phenomena relied on the use of epicycles and eccentrics, the western models were strictly qualitative and philosophical, and were completely useless from a mathematical point of view. These models were neither numerically verifiable, nor could they be used for predicting planetary positions. It is no wonder, therefore, that all but one of the western philosophers did not bother to produce actual geometrical models.

The significance of the difference between the eastern and western reform traditions of Arabic astronomy cannot be overemphasized. The prevalent view in contemporary scholarship attributes the steady decline of the intellectual sciences in al-Andalus and North Africa to the rise of the so-called "fundamentalist" states of the Almoravids (1091-1144) and Almohads (1147-1232). It was precisely during this period, however, that the greatest Andalusian philosophers worked under the patronage of the rulers of these two states. What we have, therefore, is not a steady decline of the intellectual disciplines, but the rise of some at the expense of others. The decline of mathematical astronomy has nothing to do with the Almoravids or the Almohads, nor with an alleged theological counter-revolution. Rather, the decline is a result of the adoption of a specific research program of astronomical research, a program which is driven by the untenable, and by then outdated, Aristotelian philosophical concerns that proved incompatible with the advanced mathematical and scientific aspects of astronomy.

In sharp contrast with the western school, the eastern school of Arabic astronomy did not favor philosophy at the expense of mathematics. The objections of this school were mathematical and physical and, as the comparison with their western counterpart clearly illustrates, these objections were certainly not philosophical. A common view which is prevalent in earlier studies maintains that the eastern reform tradition of Arabic astronomy was driven by philosophical considerations, a notion which is often used to undermine the mathematical and scientific significance of this tradition. Given the overwhelming evidence of detailed research on this tradition, such a view is no longer tenable. The alternative solar model proposed by Ibn al-Shatir is an example in which reform was motivated by purely observational considerations, even though the Ptolemaic model was completely unobjectionable from a physical or philosophical point of view. More generally, the eastern tradition of astronomical reform has its roots in the systematic mathematization of astronomy and, to some extent, even of nature itself. A recent study of the al-Takmila fi Sharh al-Tadhkira of al-Khafri (d. 1525) clearly illustrates one of the main characteristics of this tradition. Al-Khafri was primarily a religious scholar who wrote a highly sophisticated commentary on the Tadhkira of Nasir al-Din al-Tusi, one of the classics of the eastern reform tradition. Al-Khafri presents in this work thorough accounts for the various alternative models proposed by arlier astronomers. The purpose of this presentation, however, is not to look for a correct model, nor to decide which one conforms with an ideal or preferred cosmology, but to establish the mathematical equivalence of all of these models.

Now to go back to the question I raised earlier, namely whether we can think of this tradition of astronomical research as an expansion of the descriptive tendency started by Ptolemy himself. The answer, in my view, is no. To start with, it would be inaccurate to talk of a mathematical school and a philosophical school in Greek astronomy, since the astronomers who provided mathematical models in violation of Aristotelian physics did not theorize the superiority of mathematical principles over philosophical ones. Moreover, this supposed school of mathematical astronomy culminated in Ptolemy, who considered his models defective because they did not conform fully with Aristotelian cosmology. In contrast, in the case of the eastern Islamic astronomical tradition, the proposed mathematical models were deliberate theoretical and epistemological choices that were conceived as alternatives to the philosophical choice. This reform tradition thus shifted the understanding of physics from metaphysics to mathematics. In turn, this shift laid the foundation for the demise of Aristotelian physics and for the emergence of the new sciences. Despite the diversity of their proposed solutions, a shared, fundamental change introduced by the astronomers of the Muslim east is in the understanding of what constitutes a principle. The principles employed by these astronomers did not derive from philosophical speculation about the nature of heavenly bodies (as in the case of the principles adopted by Ptolemy), but from mathematics. Such is, for example, the principle that the uniform motion of a sphere can only be around an axis passing through its center, since any other rotation is, by definition, non-uniform. At the same time, ŒUrdi, for example, does not hesitate to reverse the direction of the motion in his proposed model, simply because he can reproduce the Ptolemaic observations while employing spheres that rotate uniformly around their own centers; ŒUrdi could not have possibly conceived of this reversed motion as one that corresponds to reality, but only as one that allows accurate predictions of planetary positions. Likewise, Tusišs couple and ŒUrdišs lemma were pure mathematical tools that had no physical counterpart. While the objective of the western Islamic astronomical tradition was to save the (meta)-physical theory, that of the eastern tradition was to save the phenomena as well as the newly constituted physics. In this physics, mathematical principles were not just tools or a vehicles for studying nature but also for conceptualizing it.