From Antiquity until recently, philosophers and mathematicians have continually discussed the concept of angle and its relation to archimedean and non-archimedean theories of measurement. For the first time, this book traces the history of these discussions in Greek and Arabic, from Euclid to Kamāl al-Dīn al-Fārisī, after whom the discussion was not resumed until Newton and Euler. The volume presents first editions of over twenty texts, either in Arabic or Greek and translated into Arabic, of the greatest mathematicians and philosophers (...) of the time. The texts are here translated into French and supplemented with extensive commentary. The book begins with the definitions and propositions of Euclid on angles and measurement, followed by the Greek commentary tradition represented by Proclus and Simplicius (only extant in Arabic) and the writings of the Arabic mathematicians and philosophers from the 9th through 14th century, placing the fundamental contributions by Avicenna and Ibn al-Haytham into their historical context and showing how numerous successors produced new syntheses of their work. (shrink)

Philosophy; mathematics; Avicenna, 980-1037; Fārisī, Kamāl al-Dīn Abū al-Ḥasan, active 1300.

The "Text" and the "Commentary" mentioned in the title of this essay are, respectively, the "Kitāb al-Manāẓir", or "Optics", of al-Ḥasan ibn al-Haytham, composed in the first half of the fifth/eleventh century, and the "Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir", written by Abū l-Ḥasan (or al-Ḥasan) Kamāl al-Dīn al-Fārisī in the second half of the seventh/thirteenth century. It is known that, so far, only the first five of the seven "maqālāt"/Books that make up the Arabic text of IH's "Optics" have (...) been published, and that the "Tanqīḥ" was published in two volumes. I shall be concerned with certain episodes in the lives of these two works, my aim being to shed light on their transmission within the Islamic Arabic and Persian worlds. -/- . (shrink)

The mutakallimūn, who began to take care of nature as a result of their metaphysical concerns from the early period and with the influence of the dualist and materialist groups, suggested various theories that attempt to explain the structure and functioning of the universe. Over time, many subjects of physics became an indispensable part of Kalām and were used in the proof of the fundamental principles. Thus, in addition to the definition of body (jism), Kalām books began to contain detailed (...) topics such as time, space, movement and distance. After summarizing the definitions of body, which were made by the mutakallimūn, this article will examine the contents of Ibn Kamāl's epistle on ṭafra (leaping), which has many copies with various titles in the Turkish Libraries. In the beginning of the epistle, Ibn Kamāl mentions the descriptions of body suggested by the prominent mutakallimūn, and then, he compares the views of al-Naẓẓām, who believes in the finite division, with atomist mutakallimūn who accept the infinite division. He criticizes the idea of ṭafra with regard to the notion of body in Kalām. After explaining the arguments of both groups with their justifications, he points out the weaknesses of the arguments of each group, as well. In this connection, he revisits the theory of ṭafra, which is, he argues, a mandatory consequence of al-Naẓẓām’s definition of object, as he also reviews the opinions of Quṭb al-Din al-Rāzī in this direction. (shrink)

Introduces young readers to Ibn Sina, telling his story as he might tell it himself. It provides a fascinating glimpse into the life of this philosopher, scientist and physician who was one of the greatest thinkers of his time.

We argue that there is an incompatibility between the two basic principles of Molinism, i.e., God’s middle knowledge of counterfactuals of creaturely freedom, and divine immutability. To this end, firstly, we set out the difference between strong and weak immutability: according to the latter only God’s essential attributes remain unchanged, while the former affirms that God cannot change in any way. Our next step is to argue that Molinism ascribes strong immutability to God. However, according to Molinism, some counterfactuals of (...) freedom need to be actualized by divine will. We argue that this claim does entail a change in God because it attributes a knowledge to God that involves moving from possibility to actuality through divine will. Therefore, claiming God knows counterfactuals of freedom leads us to reject the strong sense of divine immutability. Further, we argue that assuming God’s knowledge encompasses counterfactuals of freedom cannot be consistent even with weak immutability because, according to Molinism, a change in God’s knowledge requires a change in His essence. We conclude that Molinism is incoherent. (shrink)

This is a major work of Islamic mysticism by the great thirteenth-century Persian poet, Farid al-Din Attar. Translated by A J Arberry, Attar’s work and thought is set in perspective in a substantial introduction.

In this work the Persian and English texts are edited and published together for the first time. This is Tusi’s major Ismaili work and the most important primary source on Ismaili doctrines during the Alamut period.

The article covers main features of Early Modern Sufi Philosophy in Crimea. Based on the new discoveries of Arabic manuscripts in Turkey (libraries in Istanbul and Corum) and Germany (Berlin library), the study provides analysis of the Sufi approach towards human onthology, developed by Crimean thinkers Ibrahim al-Qirimi, Abu Bakr al-Kafawi and finally Hussam al-Din al-Qirimi. Apart from the classical Sufi rethinking of a human being as the body-soul entity making spiritual journey towards final Perfect Man (al-insan al-kamal) and approaching (...) ultimate revival, Crimean thinkers also paid great attention to the issue of human freedom, naming it by special term (Arabic al-istiqlal, literary meaning “independence”). In contrast to rather conservative background of Islamic discursive theology (kalam) and other schools of Islamic philosophical thought of the Post-Classical period, special attention to this concept can be regarded as evidence of some "humanistic" tendencies among thinkers of the Crimean Khanate. The article also notes that this concept of freedom was considered by Crimean thinkers as one of the important conditions for the manifestation of Divine Attributes in human existence; that is, the anthropologic measurement of the pantheistic idea of "unity of being", widely poplular among Sufis of those times. Taking into account the fact that the modern notion of "freedom" in the Arabic philosophical thought is based predominantly on Western concepts, the new reading of Sufi Post-Classical manuscripts reveals autochthonous cultural potential of this tradition. (shrink)

The appearance of nonlinear equations in science, engineering, economics, and medicine cannot be denied. Solving such equations requires numerical methods having higher-order convergence with cost-effectiveness, for the equations do not have exact solutions. In the pursuit of efficient numerical methods, an attempt is made to devise a modified strategy for approximating the solution of nonlinear models in either scalar or vector versions. Two numerical methods of second-and sixth-order convergence are carefully merged to obtain a hybrid multi-step numerical method with twelfth-order (...) convergence while using seven function evaluations per iteration, resulting in the efficiency index of about 1.4262. The convergence is also ascertained theoretically, and the asymptotic error constant is computed. Furthermore, various numerical methods of varying orders are used to compare the numerical results obtained with the proposed hybrid method in approximate solution, number of iterations, absolute error, absolute functional value, and the machine time measured in seconds. The obtained results outperformed the chosen methods when applied models arising from physical and natural fields were solved. Finally, to observe the convergence graphically, some complex polynomials are plotted as polynomiographs, wherein the rapid convergence of the proposed method is guaranteed. (shrink)

The central issue in this work is self-knowledge. The human soul is created in the Image of God with a purpose.

Quʹest-ce que lʹêre? Cette question passe pour fonder la philosophie. Encore faut-il s'entendre sur le sens du mot "être ". L'essence des choses détermine-t-elle leur existence? Devons-nous affirmer, au contraire, que l'existence conditionne l'intensité d'être qui qualifie une certaine réalité? Molla Sadr Shirazi, dans ce traité écrit en Iran au siècle de Descartes et de Leibniz, médite ces questions qui sont encore les nôtres. Mais les solutions qu'il propose s'évadent hors de nos perspectives, après avoir opéré une révolution décisive dans (...) la métaphysique des Orientaux. Penseur shi'ite en butte à la persécution, Molla Sadra est la plus haute figure de la philosophie iranienne islamique au temps splendide de la cour safavide d'Ispahan. Sa doctrine du primat de l'existence, que le présent ouvrage expose complètement, ouvre sur une interprétation spirituelle de la résurrection des corps. Cette traduction par Henry Corbin, qui fut aussi l'éditeur du texte original, a fait événement : par son ample introduction, il situe la question de l'être et déploie une explication comparée de ce que l'Occident grec puis médiéval en ont fait, avec la tradition shi'iite. -- Back cover. (shrink)

El presente artículo ofrece una traducción anotada del _Tratado acerca de las reglas del arte de los poetas_ (_Qawānīn fī ṣināʿat al-šuʿarāʾ_) de Abū Naṣr al-Fārābī. Acompañamos esta traducción de una introducción dividida en tres partes. En primer lugar, se ofrece un contexto general acerca del lugar del Qawānīn en la obra de al-Fārābī y en la tradición filosófica árabe. En segundo, se plantea una posible división temática del texto. Y finalmente, en tercer lugar, se especifican las peculiaridades de la (...) traducción, referente al texto tomado como base y las principales decisiones de traducción. (shrink)

In Islamic thought, the accumulation regarding Tafsir appears in various ways. One of them is the type of work called Anmudhaj that contains chapters about Tafsīr. In the An-mudhaj type of works, the determination of the sciences to investigate may occur according to different criteria. These criteria may occur as a classification of science and they also can be limited to a few sciences. In this article, we will examine the Tafsīr chapter from the work of Sipāhīzādah who took charge (...) as a teacher and judge in the Ottoman Empire. That part cons-titutes the first chapter of the work called Anmūdhaju’l-Funūn which he symbolically limited the investigated sciences to seven. The other investigated sciences in the work are Ḥadīth, Kalām, the methodology of Islamic Law, Fiqh, Bayân, and Medical Science. In the Tafsīr chap-ter of the work of Sipāhīzādah called Anmūdhaju’l-Funūn, seven different issues are investi-gated in total. Those questions are “Does Bismillah count as a vow?” and “What is the order of the creation of the earth and the heavens in the light of the verse al-Baqarah 2/29?” and “Do the names of the numbers imply limitation (hasr)?” and “What is the reason behind the borrowing of Israelites the jewels of the Egyptians in the light of the verse al-Baqarah 2/50?” and “The entry order to the city was given to Israelites in the verses al-Baqara 2/58-59, was this order given to them before or after their deviation?” and “Where is the prostrated door which is mentioned in the verse?” and “How can we assess Fakhr al-Dīn al-Rāzī’s questions and answers regarding the narrative differences between the verses al-Baqarah (2/58-59) and al-A‘râf (7/161-162)?” Sipāhīzādah examined the issues of Tafsīr through a historical which makes him the participant of the debate and allows him to the continue the present discourse through a critical reading. This makes the subject of work quite important. Because thanks to the work, it will be possible to catch some clues about the progress of the accumu-lation regarding Tafsīr in the era the author lived.Summary: In Islamic thought, the accumulation regarding Tafsīr appears in various ways. One of them is the type of work called Anmudhaj that contains chapters about Tafsīr. In Anmudhaj type of works, the determination of the sciences to investigate may occur according to diffe-rent criteria. These criteria may occur as a classification of science and they also can be limi-ted to a few sciences. In this article, we will examine the Tafsīr chapter from the work of Sipāhīzādah who took charge as a teacher and judge in the Ottoman Empire. That part cons-titutes the first chapter of the work called Anmūdhaju’l-Funūn which he symbolically limited the investigated sciences to seven. The other investigated sciences in the work are Ḥadīth, Kalām, the methodology of Islamic Law, Fiqh, Bayân, and Medical Science.The work of Sipāhīzādah, Anmūdhaju’l-Funūn consists of seven chapters and also seven is-sues are investigated in the Tafsīr part of the work. The first investigated issue in the Tafsīr part is the issue of Basmalah and in our opinion, it would not be surprising to accept that in one dimension it is a conscious choice aimed at the beginning of the work. His general attitude is presenting the issues firstly. He constituted all of the issues through the trio of al-Zamakhs-harī, al-Rāzī, and al-Bayḍāwī either one or two of them. Another remarkable point in the de-velopment of the issues is Sipāhīzādah begins with Basmalah according to the Mushaf com-position and proceeds to al-Baqarah verse 59 in a particular order. According to this, the aut-hor takes the problems he detected in the relevant parts as a subject.The issues that are investigated in the Tafsīr chapter can be listed as follows:1. Can Bismillah be used as a vow? According to Sipāhīzādah, al-Bayḍāwī, al-Jurjānī and Mollā Khusraw claim that there is a difference between vowing in the name of God and starting something with Bismillah and this difference should be rejected through the work of al-Mergīnānī that is called Hidâye and Ibn al-Humām’s Sharh. Thus, according to him one of the differences between Billah and Bismillah is not that they count as a vow.2. What is the order of the creation of the earth and the heavens in the light of the verse al-Baqarah 2/29? Sipāhīzādah mentions that the creation and the arrangement of the earth did not happen at the same time.3. Do the names of the numbers imply limitation (hasr)? Regarding this issue, Sipāhīzādah took the verse that says “…and made them seven heavens” as the focal point and claimed that the mentioned number in this verse indicated limitation and gave examples from verses, hadith, linguists and scholars of the methodology.4. What is the reason behind the borrowing of Israelites the jewels of the Egyptians in the light of the verse al-Baqarah 2/50? Sipāhīzādah criticized the two arguments of Fakhr al-Dīn al-Rāzī. Sipāhīzādah criticized the assessments that Ancient Egyptians pursued those properties which they lent before and Israelites kept those jewels and he rejected them.5. The entry order to the city was given to Israelites in the verses al-Baqara 2/58-59, was this order given to them before or after their deviation? He criticized the argu-ments of al-Zamakhsharī and al-Bayḍāwī which they have given to prove that this order was given to them after their deviation. He offered arguments and emphasi-zed that the entry order to the city was given before their deviation.6. Where is the prostrated door which is mentioned in the verse al-Baqara 2/58? It is controversial if it is Jerusalem or the door of the Mosque in which they were perfor-ming the prayer. al-Zamakhsharī and al-Bayḍāwī claim that it is Jerusalem. Was this order given before or after the death of the prophet Moses? Sipāhīzādah thinks that it has to be the door of Jerusalem.7. How can we assess Fakhr al-Dīn al-Rāzī’s questions and answers regarding the nar-rative differences between the verses al-Baqarah (2/58-59) and al-A‘râf (7/161-162)? Sipāhīzādah criticized the responses which are given by al-Rāzī and gives contrary responses.It is obvious that the author is Hanafi in the matters of Islamic Law. Besides this, we can say that Sipāhīzādah did not examine the issues of Tafsīr through a sense of belonging, he emp-hasized the opinions of people which he found compatible with his beliefs. Hence, He someti-mes comes to an agreement with al-Bayḍāwī who is a Shaffi in the matters of Islamic Law and from time to time he affirms al-Zamakhsharī who is a Mutazilite in the matters of faith. Sipāhīzādah examined the issues of Tafsīr through a historical depth and this both makes him a participant of the debate and allows the continuation of the present discourse through a critical reading. Thus, an attitude of critical consistency is prominent in his works. In our opi-nion, this attitude of critical consistency is an action of consolidation for the maintenance of the power of the relevant text-centered linguistic system. In this regard, we can say that Tafsīr remained its liveliness in the geography in which the author lived. So, the founders of the system which we can list as al-Zamakhsharī, Fakhr al-Dīn al-Rāzī, and al-Bayḍāwī and the ones who caused it to continue which we can list as Sayyid Sharif al-Jurjānī, Mollā Khusraw, and Ibn Kamāl Pasha have been read critically by the author. This makes the subject of work quite important. Because thanks to the work, it will be possible to catch some clues about the progress of the accumulation regarding Tafsir in the era the author lived. Even though it was negative in the issues that are investigated by the author, the fact that the Fakhr al-Dīn al-Rāzī is a prominent figure is an indicator of the maintenance of the dominance of Rāzī. It would be more appropriate to link this with his effectiveness rather than the Kalāmī power of his Tafsir. For Rāzī is not taken as the focal point by Sipāhīzādah only in issues of Kalām. Besides that, he renders Rāzī as a participant of the subject in linguistic issues too such as whether if the name of the numbers implies limitation or not and the usage of varied phrases in verses. (shrink)

Sad al-Din Dashtaki, and following him, Mulla Sadra Shirazi maintains that all real compositions are unified. After a short review of Dashtaki’s thesis, we concentrate on Mulla Sadra’s version. Mulla Sadra believes that Dashtaki’s version is not coherent and he declines the existence of real parts. We will argue that Mulla Sadra’s objections do not work and furthermore, all things said and done there is no difference between these two versions of the thesis of unified composition. If there is any (...) difference, it is about their theory of existence, not about their theory of composition. Sad al-Din Dashtaki, and following him, Mulla Sadra Shirazi maintains that all real compositions are unified. After a short review of Dashtaki’s thesis, we concentrate on Mulla Sadra’s version. Mulla Sadra believes that Dashtaki’s version is not coherent and he declines the existence of real parts. We will argue that Mulla Sadra’s objections do not work and furthermore, all things said and done there is no difference between these two versions of the thesis of unified composition. If there is any difference, it is about their theory of existence, not about their theory of composition. (shrink)