One of the epistemological results emerging from this initial study is that the different forms of co-relational inference, known in the Islamic jurisprudence as qiyās, represent an innovative and sophisticated form of reasoning that not only provides new epistemological insights into legal reasoning in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical argumentation studied in contemporary philosophy of science. However, in the present paper we will only discuss the case of so-called co-relational inferences of the occasioning factor and only in the context of Islamic jurisprudence.

In the absence of the Arabic text of al-Khwārizmī's Arithmetic (ca. 825), which has not yet been found, the oldest Latin adaptations from the twelfth century are the only evidence documenting the genesis and the first spreading of a decimal arithmetic that uses nine figures and zero, i.e. the Indian reckoning known in the Middle Ages as algorismus. This paper studies these texts, their content, their sources, and identifies their authors and the milieus in which they were written.

In this paper, I raise the following problem: what propositions have an import in Avicenna's modal logic? Which ones do not? Starting from the assumption that the singular and quantified propositions have an import if they require the existence of their subject's referent(s) to be true, I first discuss the import of the absolute propositions then I analyze the import of the modal propositions by considering Avicenna's definitions and the relations between these propositions. This leads to the following results: Avicenna's general opinion is that the affirmatives, be they assertoric or modal, have an import while the negatives do not. The possible affirmative propositions are given an import both in the externalist and the internalist post-Avicennan readings, provided that the subject is not impossible. However, the theory is not always clear, for the propositions containing ‘sometimes not’ are given an import, together with the negative necessaries containing ‘as long as it is P’, despite their negative character; the necessary affirmative propositions containing ‘as long as it is P’ are given an import, although they do not require it. In addition, Avicenna's analysis of the special assertorics E and O (containing the internal conditions ‘at some times but not always’) and their contradictories is erroneous, which does not help determine their import. But when correctly analyzed, these special E and O do not have an import, while their contradictories – I and A special assertorics respectively – have an import.

This paper examines the history of glass colouring. It reviews Kitāb al-Durra al-maknūna of Jābir ibn Ḥayyān, which deals with the subject. The manuscript of this practical treatise was discovered recently. Part one of the paper deals with Jābir as a philosopher and chemist. The art of lustre-painting on glass originated in Syria during the Umayyad Caliphate in the eighth century and was soon practised in the neighbouring area. The paper reviews Arabic literature that deals with the colouring of glass until the 13th century, and with pre-Islamic and Latin books of recipes that deal with glass colouring. Recipes for cast coloured glass are very few and scant in non-Arabic literature, and lustre-painting on glass was not mentioned in any treatise outside Arabic, even in the works of Theophilus and Neri. The colouring of glass gemstones by colour diffusion is not mentioned also. The paper compares the recipes of Kitāb al-Durra with the results of modern analysis of existing Islamic stained glass objects. There is a close correspondence, and the main indispensable ingredients in both cases are silver and copper compounds. Part one ends with an account of lāzaward as cobalt oxide in glass colouring. Part two of the paper gives a representative selection of recipes from Kitāb al-Durra for the three methods of glass colouring.

There are three principal philosophical-scientific encyclopaedias written in Hebrew during the Middle Ages: Yehudah ha-Cohen's Midrash ha-Ḥokmah (1245–1247), Shem Tov ibn Falaquera's De'ot ha-Filosofim (ca. 1270) and Gershon ben Shlomoh's Sha'ar ha-Shamayin (end of the 13th century). All three include detailed treatments of zoology, and the last two of botany and mineralogy as well. The principal feature of their treatments is their “theoretical” – not merely “descriptive” – approach: these encyclopaedias do not contain only lists of stones, plants and animals (such as other Arabic and Latin Medieval encyclopaedias), but also attempts at systematization and philosophical arrangement of the various available theories in the fields of mineralogy, botany and zoology qua sciences. An examination of the doctrines and the sources of these texts shows that, while the treatment of zoology relies upon Aristotle's zoological works and, above all, their Compendia by Averroes, the treatment of mineralogy and botany reflects the non-Aristotelian theories of the Brethren of Purity (Iḫwān al-Ṣafā'), rather than such texts as pseudo-Aristotle's De lapidibus and Nicolaus Damascenus' De plantis. In particular, Falaquera's encyclopaedia represents the most convincing effort to provide a truly scientific discussion of mineralogy and botany, comparable to that of his contemporary Albert the Great, and based upon the Brethren, Avicenna and, maybe, some lost works by Averroes.

Ibn Rušd devoted a certain number of works to Aristotle's Prior Analytics. In a series of opuscules written over a period of twenty years and following upon his Middle Commentary on Aristotle's Prior Analytics, he faced a problem particular to the modal syllogism – that of the mood of the conclusion in mixed syllogisms.

The problem can be stated as follows: At the beginning of the Prior Analytics, Aristotle established a formal deductive principle – that of universal attribution (Pr. An. I.1.24b26–30). Applied to the modal syllogism, this principle is inadequate as stated. It is too general to be applied in a univocal manner in all modal syllogisms. To preserve a sense of coherence in Aristotle's declarations, the commentators had to interpret it. Presenting the interpretations of the commentators, primarily al-Fārābī and Alexander, on the basis of al-Fārābī's Large Commentary on Aristotle's Prior Analytics, Averroes criticizes them. Applied according to Alexander's interpretation, the principle of universal attribution is valid only for modal syllogisms one of whose premises is necessary and the other assertoric; according to al-Fārābī's interpretation, it is verified only when the minor premise is possible. Averroes proposes two preliminary solutions. Either this formal deductive principle must be applied differently according to the modal differences of the minor premises in mixed syllogisms (first solution) or would be used in two ways, generally or in keeping with each mood (second solution). These solutions are not satisfactory, for they call into question the unity and universality of the principle of universal attribution as established by Aristotle. What is the utility, Averroes asks, of a principle which does not hold for all modalities or does not apply to all the premises when the Pr. An. ought to furnish formal and universal principles of deduction? And why did Aristotle define the principle of universal attribution without distinguishing its application according to each of the three modal premises? Returning at the end of his career to a literal exegesis of Aristotle's propositions and without harkening back to the earlier solutions, he proposes a theory of making the terms modal (fourth solution) in order to save Aristotle's declarations with respect to the principle of universal attribution and the mood of the conclusion of mixed syllogisms (Pr. An. I. 9.30al5–20). Though formally inadequate, this solution, which had a continued history, proposes a new way of looking at the classification of modal propositions.

Written by the 11th-century Spanish Arab, Abū ʿAbd Allāh Muhammad ibn Mucādh al-Jayyānī, “On Twilight and the Rising of Clouds” represents a unique attempt to determine the height of the atmosphere on the basis of the first tinging of its upper reaches by dawn light. In fact, Ibn Mucādh's value of around 52 miles remained standard until the 17th century, when it was revised sharply downward in consideration of atmospheric refraction and barometric studies. The treatise itself survives in a single Hebrew exemplar, 25 Latin exemplars, and an Italian exemplar derived from the Latin. At the heart of this present study is a critical text based on a fullscale comparative transcription of 22 of the Latin manuscripts, ranging in date from the 13th to the 17th century.

The starting-point and, at the same time, the foundation of recent scholarship on the Arabic translations of Aristotle's Metaphysics are Maurice Bouyges' excellent critical edition of the work in which the extant translations of the Metaphysics are preserved – i.e. Averroes' Tafsīr (the so-called “Long Commentary”) of the Metaphysics – and his comprehensive account of the Arabic translations and translators of the Metaphysics in the introductory volume. Relying on the texts made available by Bouyges and the impressive amount of philological information conveyed in his edition, subsequent scholars have been able to select and focus on more specific topics, providing, for example, a closer inspection of the Arabic translations of the single books of the Metaphysics (books A, α, and Λ in particular), or a detailed comparison of some of these translations with the original text of the Metaphysics. A new trend of research in recent times has been the study of these versions as part of the wider context of the Graeco-Arabic translation movement.

Galen’s Commentaries on the Hippocratic Epidemics constitute one of the most detailed studies of Hippocratic medicine from Antiquity. The Arabic translation of the Commentaries by Ḥunayn ibn Isḥāq (d. c. 873) is of crucial importance because it preserves large sections now lost in Greek, and because it helped to establish an Arabic clinical literature. The present contribution investigate the translation of this seminal work into Syriac and Arabic. It provides a first survey of the manuscript tradition, and explores how physicians in the medieval Muslim world drew on it both to teach medicine to students, and to develop a framework for their own clinical research.

La diffusion d'Alexandre d'Aphrodise, en raison de la qualité inégalée de son exégèse d'Aristote, est celle des textes vivants. Simplicius est plus érudit, Philopon plus critique, Averroès plus savant. Mais Alexandre possédait un art de la synthèse entre l'analyse philologique de la lettre et la saisie de l'orientation générale d'un texte, qui fait de lui l'Exégète par excellence. On comprend, dans ces conditions, que sa transmission ne soit pas le relais linéaire d'un ‘‘témoin” figé. Citons aussi bien le recours extensif de Simplicius, au VIe siècle, à ses commentaires physiques que la renaissance philosophique des IXe–Xe siècles en terre d’Islam, qui s'accompagne d'un mouvement massif de traduction de textes alexandriques. Or s'il apparaît de plus en plus clairement que c'est la nécessité de bâtir une ontologie du sensible aristotélicienne, subordonnée à l'ontologie platonicienne des Formes divines, qui a poussé le ‘‘platonicien” Simplicius à puiser dans les commentaires de son prédécesseur, on ne s’est pas encore assez interrogé sur le sens de l'intérêt aigu des philosophes islamiques pour Alexandre. Pourquoi, par exemple, alors que les Byzantins, quand ils ont eu le choix entre Alexandre et Simplicius, ont choisi Simplicius, les Arabes se sont-ils systématiquement décidés pour Alexandre?

In this article the author analyzes a fifteenth-century Arabic reform of the Ptolemaic model for Mercury. The author of the reform was the Central Asian – Ottoman astronomer ‘Alā” al-Dīn al-Qushjī (d. 1474 A.D.) who, in his youth, had been instructed in the mathematical sciences by none other than the famous Central Asian monarch Ulugh Beg (1394–1449). Although the astronomers of Ulugh Beg's circle are known to have produced extensive astronomical Persian tables, no one other than Qushjī has been yet identified to have produced a theoretical text devoted to the criticism, let alone the reform, of the Ptolemaic mathematical planetary models. The present article on Qushji's reform of the Ptolemaic model for Mercury includes a critical first edition of Qushji's Arabic text, an English translation, and a historical and technical commentary.

How do the variegated forms of sublunar substances (the elements, homoeomerous substances, plants, animals) arise in prime matter? Averroes throughout his life believed that “a principle from without” was involved, but changed his mind over its identity. While in an early period of his life he maintained that all forms emanate from the active intellect, he later discarded that metaphysical notion and sought to develop a more naturalistic, astrologically inspired account, which identified the heavenly bodies as the source of sublunar forms. Comparing different versions of Averroean texts, this paper seeks to spell out how, in Averroes' view, the heavenly bodies generate forms in matter. Averroes claims that this is brought about by means of their “heats,” an answer that is however problematic seeing that in the Aristotelian cosmology the celestial realm is quality-less. The paper examines Averroes' ideas on the relationship between light and heat, concluding that the Commentator was unable to integrate the postulate that the heavenly bodies inform matter within his Aristotelian theory of matter.

The purpose of the article is to present further information about Avicenna's work on Eastern philosophy, supplementing what was written in the author's Avicenna and the Aristotelian Tradition (Leiden, 1988), pp. 115-30. In view of the prevalent but unfounded notions among some students of Avicenna that the Eastern philosophy is mystical or illuminationist, an initial section traces the history of the development of these tendentious ideas first to Ibn T[dotu]ufayl and then to the followers of his interpretation in the West in the nineteenth and twentieth centuries. Further sections discuss the title of the book, list its contents insofar as they can be reconstructed from Avicenna's statements and the extant portions, and provide additional information about its manuscripts and transmission. The style of the work is then analyzed and compared with that of the šifā' in order to verify Avicenna's claim in the Preface to the latter work that the difference between the two was merely stylistic. A final section gives a table of concordance between the contents of the extant part on physics and the corresponding sections in the šifā', establishing the direct relationship and verbal congruity between the two works.

At the basis of Ghazali's criticisms of Ash'arite kalām is the thesis that its primary function is the defence of traditional Islamic belief, the 'aqida, against the distortions of heretical innovations (al-bida'). Kalām is not an end in itself and it is error to think that the mere engagement in it constitutes the experientially religious. In the I[hdotu]yā' he maintains in effect that when it is pursued as an end in itself, its dogmas can constitute a veil preventive of the attainment of gnosis (ma'rifa). On the other hand, Ash'arite kalām when not pursued as an end in itself can be an aid in the quest after gnosis. This is implicit in his reference (in Kitāb al-Arba'īn) to his own major work of Ash'arite kalām, the Iqti[sdotu]ād fī al-i'tiqād, where he states that “it goes deeper in ascertaining [the truth] and is closer to knocking at the doors of gnosis than the official discourse encountered in the books of the mutakallimīn.” The I[hdotu]yā' abounds with homilies, guides for the pious, particularly for those seeking mystical knowledge. Ash'arism pervades such homilies. Thus in Kitāb al-Tawba, Ghazali formulates, analyzes and defends the concept of human choice in Ash'arite terms. He thus argues that each of the ingredients of this concept - knowledge, power, the decisive will, as well as the ensuing choice - is individually the direct creation of God. Not that the argument for this concept yields experiential knowledge of its meaning within the cosmic scheme of things. For Ghazali such knowledge is only attained through mystical vision. But the Ash'arite argument, when not pursued as an end in itself, can be an aid to the seekers of gnosis. It can bring them closer to knocking at its doors.

Euclid's Elements were translated into Hebrew from Arabic in the 13th century; but precious few of the Arabic commentaries have come down to us in a Hebrew version (al-Fārābī, Ibn al-Hayṯam). Nonetheless, a study of several texts dealing with the Fifth Postulate (the Parallel Postulate) of Book I reveals that the Hebrew authors are greatly indebted to Arabic sources.

We shall examine three attempted proofs of the Parallel Postulate. The two attempts by Moses ha-Levi of Seville (13th century) and Alfonso of Valladolid (14th century) are mathematically unconvincing. Nevertheless they are interesting historically: Moses ha-Levi exploits the movement of lines which are infinite in actu; and Alfonso, starting from a critique of Ibn al-Hayṯam and al-Nayrīzī, claims to innovate in the use of the method of superposition.

In contrast, Gersonides' attempt (14th century) is a well-articulated series of premises and proofs, including several arguments which we have traced back to the Taḥrīr Uṣūl Uqlīdis of Pseudo-Ṭūsī. We feel it is important to emphasize this relationship, even though it is impossible to establish the route by which these arguments found their way to Gersonides.

“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena (1604), “henceforth the [visible] representations of objects should be considered as paintings [picturae] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization (“up to now” having surely been meant within the narrow context of the treatise itself), this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot.

This paper is devoted to Ibn Sinān's treatise on analysis and synthesis. Ibn Sinān's text deals with two distinct, though closely related, subjects. First he considers the classification of problems, founded on the logical criteria which are the number and degree of indetermination of the solutions and (though in a less relevant way) the number of hypotheses and their possible independence. This classification does not replace the Hellenistic one, which remains relevant insofar as it purports to solve geometrical problems, but complements it and has a different frame of reference, applying principally to algebra, that new born science. Ibn Sinān's classification will be taken up and used by algebraists. Secondly, the text presents a new way of setting out analysis and synthesis, so that they become exactly reciprocal. This leads Ibn Sinān to bestow more importance on the role played by analysis in the course of the proof, the only role left to synthesis being to check that all implications involved in the course of analysis are in fact equivalences. This method will prove to be productive in algebra too, so much so that some algebraists will explicitly identify algebra with analysis.

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.

Al-Fārābī's lost commentary on Aristotle's Ethica Nicomachea is without doubt one of the most sorely missed lost works of the Islamic falāsifa. In part, this is because the commentary was in some respects a scandal, and scholars accordingly believe it may hold the key to resolving present-day disagreements on how to interpret al-Fārābī's views as expressed in his independent treatises. Perhaps al-Fārābī's most shocking or scandalous statement is that preserved by the Hispano-Muslim philosophers Ibn Bājja, Ibn Ṭufayl, and Ibn Rushd. According to them al-Fārābī says in his commentary on Aristotle's Ethica Nicomachea that happiness is to be achieved only in this life, not in the afterlife; that there is no happiness but political happiness; and that union with the active intellect – generally considered the highest goal of human existence by the philosophers – is impossible. This paper addresses the following questions: What exactly is the debate about? Why is the question of immortality or conjunction related to Aristotle's Ethica Nicomachea? And why was it so controversial to say, in the context of the Ethica Nicomachea, that there is no happiness but political happiness? Although the bulk of al-Fārābī's commentary is still lost, I have discovered two quotations of it in Hebrew manuscripts. As I will argue in this paper, these newly-discovered quotations – which are included with an English translation in the appendix – can shed light on the mysteries concerning al-Fārābī's commentary.

Sa‘d ibn Mansūr Ibn Kammūna was a Jewish physician-philosopher of Iraqi origin who flourished in the thirteenth century (d. 1284). Best known for his original and comparative inquiry into the three monotheistic faiths, whose publication nearly cost him his life, he was, in fact, a very productive thinker, and a scholar well in tune with developments in the philosophy and science of his day. He had personal contact with some leading intellectuals, and he played an important role in the diffusion of some new trends of thought. His legacy, in the form of commentaries, correspondence, and original works, is now being studied in earnest.