The present study seeks to lay out the most basic elements of the ontology of classical Aš‘arite theology. In several cases this requires a careful examination of the traditional and the formal lexicography of certain key expressions. The topics primarily treated are: (1) how they understood “Being/ existence” and “being/existent” and essential natures; the systematic exploitation of the equivocities of certain expressions (e.g., ḫaqīqa, ḫadd, ma‘na) within a general context in which other than words there are no universals proves to be elegant as well as insightful; (2) the basic categories of primary entities: independant beings and nonindependant beings, (a) created and (b) uncreated, the equivocity of “being/existent” as predicated of contingent entities on the one hand and of God and His attributes on the other, and certain problems that arise because of the rigid application of the system's underlying analytic principles.

R. Saadia Ga'on (882–942) of Baghdad sought to avoid anthropomorphism by arguing that scriptural phrases which seem to ascribe materiality to the Deity in fact refer not to God Himself, but rather to a created entity, God's Glory, which he described as a very tenuous “air.” This paper argues that Saadia's conception of a quasi-divine “air” through which God accomplishes His acts in the material world is heavily indebted to the Stoic theory of pneuma. It follows that the immanentist theology of Ḥasidey Ashkenaz (German Pietists), which is known to have been substantially influenced by Saadia, in fine is also indebted to Stoic philosophy and physics.

The author examines the relationship between mathematics and philosophy in the works of al-Kindī, and suggests that the real character of his contribution will become clear only when we restore to mathematics their proper role in his philosophy. The recently discovered treatise of al-Kindī on the approximation of π, of which the author gives the editio princeps here, throws important new light on al-Kindī's knowledge of mathematics, and on the history of the transmission of The Measurement of the Circle of Archimedes. The author shows that al-Kindī's commentary on the third proposition of the Measurement of the Circle was written before 857, at the same time if not before that of the Banū Mūsā, and that it was one of the sources of the Florence Versions, the Latin commentary on the same proposition.

The perfect compass, used by al-Qūhī, al-Sijzī and his successors for the continuous drawing of conic sections, reappeared after a long eclipse in the works of Renaissance mathematicians like Francesco Barozzi in Venice. The resurgence of this instrument seems to have depended on its interest to solve new optico-perspective problems. Having reviewed the various instruments designed for the drawing of conic sections, the article is focused on the sole conic compass. Theoretical and empirical applications are detailed. Contrarily to the common thesis of an independant discovery, various elements suggest a direct descent between the birkār al-tāmm of the Arabic mathematical tradition and the Italian conic compass. Then we present the most probable transmission hypothesis involving: 1° Ibn Yūnus and his disciples of Mosul, 2° Sultan Malik al-Kāmil in Damas, 3° Master Theodore and Frederick II at the court of Sicily, 4° Andalò di Negro and Robert of Anjou in Naples, 5° Lorenzo della Volpaia, Vinci, Sangallo and Michelangelo in Florence, 6° Ausonio, Contarini, Thiene and Francesco Barozzi in Venice.

The theological foundations of Ghazali's causal theory are fully expressed in the chapter on the attribute of divine power in his al-Iqtiṣād fi al-I'tiqād (Moderation in Belief). The basic doctrine which he proclaims and argues for is that divine power, an attribute additional to the divine essence, is one and pervasive. It does not consist of a multiplicity of powers that produce a multiplicity of effects, but is a unitary direct cause of each and every created existent. In a defense of the doctrine of kasb (acquisition), Ghazali argues (a) that power in all animate creatures is created directly (i.e. without intermediaries) by God and (b) that there is created with it the object of power, normally, but erroneously regarded as its effect: the object of power is in fact directly created by God. It exists with the created power, but not by it. In his critique of the Mu'tazilite theory of the generated act he again denies that created power has any causal efficacy and denies that inanimate things have any causal efficacy. What one normally regards as the effects of inanimate causes are in reality their concomitants, directly caused by divine power.

The discussion of kasb, the longest in the chapter, includes Ghazali's spirited defense of it against possible objections. The defense, however, as will be shown, is not immune against criticism. At the same time, the discussion of kasb, central as it is, has to be understood in the context of the chapter as a whole, whose intricate arguments remain integrated and unified. Hence a brief exposition of the chapter's arguments will first be given, followed by a critical comment on some aspects of Ghazali's defense of kasb. This is then followed by an annotated translation of the entire chapter, a chapter so very basic for the study of Ghazali's position on causality.

The reception of Avicenna by medieval Jewish readers presents an underappreciated enigma. Despite the philosophical and scientific stature of Avicenna, his philosophical writings were relatively little studied in Jewish milieus, be it in Arabic or in Hebrew. In particular, Avicenna's philosophical writings are not among the “Hebräische Übersetzungen des Mittelalters” – only very few of them were translated into Hebrew. As an author associated with a definite corpus of writings, Avicenna hardly existed in Jewish philosophy in Hebrew (contrary to Averroes). Paradoxically, however, some of Avicenna's most distinctive ideas were widely known and embraced by Jewish philosophers. This is the phenomenon that we dub Avicennian knowledge without Avicenna. In contrast with the philosophical treatises, Avicenna's medical writings were widely and intensively studied by Jews, especially in Hebrew, and remained influential until at least the seventeenth century. The present article presents a comprehensive picture of Avicenna's reception within medieval Jewish cultures in both Arabic and Hebrew and tries to explain the Jews’ complex attitude to Avicenna.

The present article aims to show that the treatise On the Harmonization of the Opinions of the Two Sages the Divine Plato and Aristotle cannot have been written by al-Fārābī. It considers to this end four crucial issues treated in this work, concerning (1) divine Providence and the particulars, (2) Platonic Ideas and the divine Intellect, (3) creation ex nihilo and (4) the divine attribute of ‘will’. It establishes in each case that the thesis defended by the author is contrary to al-Fārābī’s doctrine and akin to that of Yaḥyā ibn ‘Adī. This twofold result prompts us to suggest that the author should be associated with Ibn ‘Adī and his milieu; it also suggests a new periodization of 10th century Arabic philosophy. Rather than imagining a Kindian phase followed by a ‘‘school of Baghdad’’ extending from al-Fārābī’s masters to the age of Avicenna, we should postulate that some of al-Fārābī’s followers returned to al-Kindī in the field of cosmology, for theological reasons.

This study examines a number of different answers to the question: where does Avicenna demonstrate the existence of God within the Metaphysics of the Healing? Many interpreters have contended that there is an argument for God's existence in Metaphysics of the Healing I.6–7. In this study I show that such views are incorrect and that the only argument for God's existence in the Metaphysics of the Healing is found in VIII.1–3. My own interpretation relies upon a careful consideration of the scientific order and first principles of the Metaphysics of the Healing, paying attention to Avicenna's own explicit statements concerning the goals and intentions of different books and chapters, and a close analysis of the structure of the different arguments found in the relevant texts of the Metaphysics of the Healing. I conclude that Avicenna's explicit goal in I.6–7 is to establish the properties that belong to necessary existence and possible existence, which consists, not in a demonstration of God's existence, but in a dialectical treatment of the first principles of metaphysics.

Islamic polities of the classical period recognized the importance of seaweeds in their daily life. Their men of science, craftsmen, and navigators used them for medicinal purposes, manufacturing, and navigation. The agar components were used in treating pathological conditions such jaundice, spleen, kidney and skin ailments, and malignancies. As food, we stress that our conclusions derive from Qur'ān-based commentaries and Muslim religious law that encouraged seafaring and exploiting the resources of the sea. Concerning navigation, sailors could identify coastal trunk routes, shallows, and various marine phenomena; shipwrights used agar compounds as a protective coating against the Greek Fire. Like their Greco-Roman counterparts, Muslim physicians, chemists, botanists, and professional sailors of this period were acquainted with numerous species of seaweeds and could appreciate the actual scientific importance of each type as well as the aquatic environment where these species lived and developed. Their scholarly literature consists of several generic Arabic and Arabicized terms to denote seaweeds and the terms variations appeared to be physical rather than linguistic.

Averroes defended philosophy by returning to the true Aristotle. For this purpose, Aristotle's book “On the Heaven,” in which he explained the eternity, uniqueness and movement of the universe, occupied a place of special importance. But the Aristotelian philosopher had a hard time holding his own in the face of contradictions within the book and with respect to Aristotle's later works. In his early Compendium, later Paraphrase, and final Long Commentary of De Caelo, Ibn Rushd continued the efforts of the Hellenistic commentators in order to integrate all the elements of his doctrine into a unified system, to harmonize his early cosmology with his later Metaphysics – the early doctrine of natural movement of the elements, and of the self-moving star-souls (a Platonic element), with the doctrine of potency and actuality and the theory of the First Mover – and to uphold his models of homocentric planetary spheres against the mathematical paradigm of Ptolemaic astronomy. By insisting throughout on demonstrative arguments based on rational principles, he asserted the philosophers' claim to irrefutable truth.

This paper presents an edition of al-Hasan ibn al-Ḥasan ibn al-Haytham's (d. 1040) treatise, Qawl fi samt al-qibla bi-al-ḥisāb (on finding the azimuth of the Qibla by calculation) with translation and commentary. In it Ibn al-Haytham provides a universal method for finding the direction of the qibla at any location on the surface of the earth by using spherical trigonometry and accurate calculation. Ibn al-Haytham's computational solution has not been studied before, and it has often been confused with another work of his in which he uses an analemma construction to solve the problem of the qibla graphically. As a result of this confusion, contemporary scholars have mistakenly attributed the first universal solution of the qibla problem to Jamshīd al-Kāshī (15th century), some four centuries after the introduction of this method by Ibn al-Haytham. The present treatise represents an important juncture in the history of the development of mathematics of the qibla, and sheds more light on the contributions of one of the most important scientists of medieval Islam.

This is the first paper in a series in which we provide critical editions of four texts written between the eleventh and the thirteenth century concerning Proposition III.5 of Menelaus' Spherics. The first paper contains introductory material on the work of Ibn ʿIrāq on spherical geometry and a critical edition of his two texts on the rectification of Proposition III.5, together with translations and historical and mathematical commentaries. The second paper contains critical editions of the texts by Naṣīr al-Dīn al-Ṭūsī and Ibn Abī Jarrāda on the same subject, again with translations and historical and mathematical commentaries.

My aim here is to present an editio princeps of a newly discovered Arabic translation of a very important passage from Plato's Republic (Book VI, 506d3–509b10) found in the work entitled Kitāb fī Masā'il al-umūr al-ilāhiyya (hereafter Masā'il), penned by the somewhat obscure Neoplatonist Abū Hāmid al-Isfizārī (fl. mid-fourth / tenth c.). While an edition of al-Isfizārī's work has been published by Daniel Gimaret, the manuscript he used (Ragıp Paşa 1463) lacked the literal translation of the Republic passage. The one other known exemplar of the work, MS Zāhiriyya 4871, dated slightly later than the first, appears to be closer to the author's original unedited version; it contains the Republic passage. I am currently preparing a new edition of the work on the basis of the Zāhiriyya manuscript, but it seemed worthwhile to bring the Republic passage to immediate attention. I do not attempt here a thorough evaluation of al-Isfizārī's philosophy as presented in the Masā'il; this can be done successfully only upon completion of the edition. However, to place the work in its proper context, I do provide a brief overview of the transmission of Plato's Republic in Arabic; a discussion of new information on al-Isfizārī's Nachlass, and a description of the two exemplars of his Masā'il. The edited text of the passage from the Republic is accompanied by a provisional translation.

Scholars working in the field of Graeco-Arabic Neoplatonism often discuss the role Porphyry, the editor of Plotinus, must be credited with in the formation of the Arabic Plotinian corpus. A note in this corpus apparently suggests that Porphyry provided a commentary to the so-called Theology of Aristotle, i.e., parts of some treatises of Enneads IV-VI. Consequently, Porphyry has been considered as responsible for the (sometimes relevant) doctrinal shifts which affect the Arabic Plotinian paraphrase with respect to the original text. This article aims at submitting this hypothesis to trial on a specific doctrinal point where Porphyry parts company with Plotinus: the relationship between the Demiurgic Intellect and World Soul. The ancient doxographical sources testify that Porphyry, in his conviction to be in agreement with Plotinus, in fact parted company with him in so far as he merged the World Soul into the Demiurgic Intellect, while Plotinus always kept them apart. There are in the Enneads some baffling passages where the role of Intellect as the Demiurge of the sensible world is not clearly distinguishable from the role of World Soul. Notwithstanding that, these passages in the Arabic paraphrase do not bear any trace of the characteristically Porphyrian merging of World Soul into Intellect. The Arabic paraphrase of Plotinus’ writings never confuses Intellect and World Soul, as Porphyry did. This fact seems to disprove, at least on this point, the hypothesis of Porphyry's intervention as the explanation for the doctrinal differences between the original Plotinus’ text and its Arabic tradition.

Our aim here is to show that an enigmatic text of Avicenna's Glosses, devoted to the problem of evil, takes on its full meaning in the light of the last chapter of the šifā' on De generatione et corruptione. We will see how Avicenna, deepening and developing a cosmological argument already present in the commentary of Alexander of Aphrodisias on the De generatione, ends up building most of his theodicy on the relative incommensurability of the different celestial periods. All the problem of divine Justice is thus reinterpreted in terms of opposition between discrete and continuous. Finally we will show the importance that this development of Avicenna had in Western Christendom in the 14th century, and the complex relationship which Leibniz has with it in his recently edited reflections on the Great Year.

After having reformulated optics, Ibn al-Haytham conceived of an analogous project for astronomy. This has just been revealed by an important book by the mathematician which has never been studied until now. Ibn al-Haytham's reform consists in excluding all cosmology, and in developing a systematic study of a celestial kinematics that has been completely geometrized. In turn, the realization of such a reform demanded innovative research in infinitesimal geometry. In this article, an attempt is made to present this new geometry, as well as the mathematical means invented to elaborate it.

Abraham ibn Ezra's (ca 1089-ca 1167) scientific corpus represented an exceptional case: instead of the common Latin model embodied by the scholar coming from the Christian North to the Iberian Peninsula to initiate a translation enterprise, we have in Ibn Ezra the contrary case of an intellectual imbued with the Arabic culture, who abandons al-Andalus, roams around the Christian countries and delivers in his wandering through Italy, France and England, the scientific and cultural cargo that he amassed during his youth in al-Andalus. The main purpose of this article is to provide a picture of Ibn Ezra's scientific corpus as comprehensive and detailed as possible given the present state of research. The paper will fall into two main parts: (a) Ibn Ezra's scientific work will be broken up into three main genres: (1) Mathematics, Astronomy, Scientific Instruments and Tools; (2) The astrological encyclopaedia; (3) Translations from Arabic into Hebrew. (b) In the second part, Ibn Ezra's scientific corpus will be reassembled as a whole in order to provide a global characterization, trying to point out its general organization and shape, and to indicate its main aims and special traits revealing Ibn Ezra personal contribution.

The Hebrew text On the Heavens and the World, ascribed to Ibn Sīnā, is an interesting and intriguing composition. It dates from the 13th century and was quite influential. It is not a translation of any text of Ibn Sīnā known to us, but is related to the (pseudo-Avicennian) Latin De celo et mundo, which appears in the 1508 Venice edition of translations of Ibn Sīnā. The Latin and Hebrew texts differ widely and the relation between them is far from being clear. Both are in sixteen chapters, the titles of the chapters are the same, but the texts are only roughly similar. The Hebrew text often offers short, incomplete summaries of the Latin arguments. On the other hand it includes many passages which have no parallel in the Latin. There are two possible explanations of the perplexing relationship between the two texts: either that there was more than one version of the Latin (or of the original Arabic) text, or that the translator, Shlomo ben Moshe of Laguiri wrote a kind of paraphrase. The paper shows that the second explanation is correct and offers a preliminary study of the sources and the aims of the Hebrew text.

How do the heavenly bodies physically affect the sublunary world? On this topic, the few fragmentary statements by Aristotle were refined and expanded by his Greek commentator Alexander of Aphrodisias. In the Kindī-circle, particular attention was paid to Alexander's treatises on this very topic. They were not simply translated but were rather reworked in terms of an astrological interpretation. Typically, such reworking was attributed directly to Aristotle by the addition of a number of references and pseudo-references to Aristotle's genuine and spurious works. The article demonstrates this phenomenon, and examines the circular relationship between the Kindī-circle adaptations of Alexander and al-Kindī's own works. The Kindī-circle's Alexander was closely followed by al-Kindī on certain points, while al-Kindī himself exerted a reciprocal influence on the Arabic Alexander, who was largely the product of his own group of translators. The appendix contains English translations from Arabic of two adapted Alexander's treatises.

The problem of the Qibla was one of the central issues in the scientific culture of Medieval Islam, and to solve it properly, one needed mathematics and observation. The mathematics consisted of two parts: plane trigonometry (to construct the trigonometric tables) and spherical trigonometry (as the problem belongs to spherical astronomy). Observation and its instruments were needed to find the geographical coordinates of Mecca and the given location; these coordinates (latitude, longitude) will be the input data in the formulas of the Qibla. In his Almagest, Abū al-Wafāʾ produced a brilliant work to solve the problem. He worked on both mathematics and observation, and reached accurate and easy “modern” solutions. In plane trigonometry, he introduced the trigonometric functions with new definitions, proved the formulas for sines, approximated the sine of degree one, and thus constructed the tables of sines and tangents with high accuracy. In spherical trigonometry, he proved four new spherical theorems, including the tangent rule (which was based on the new definitions and this rule allowed him to work out the easiest solution, as will be shown). In observation, he described three instruments which he used over several years in Baghdad. This paper is a detailed technical and analytical description of Abū al-Wafāʾ's mathematical methods and the Qibla determinations, supplemented with many important original Arabic texts with translation and commentary.