肯迪Al-Kindi

肯迪在库法出生并长大，库法在9世纪是阿拉伯文化和学术的中心。对于肯迪来说，这无疑是当时获得最好教育的合适地方。尽管各种资料中给出了肯迪生平的不少细节（以及传说），但这些并不全都一致。下面我们将尽量给出相当有根据的细节。

根据[3]，肯迪的父亲是库法的总督，就像他的祖父之前一样。当然，所有人都同意肯迪是皇家金达部落的后裔，该部落起源于阿拉伯南部。这个部落联合了许多部落，在5世纪和6世纪达到了显赫的地位，但从6世纪中叶开始失去了权力。然而，皇家金达的后裔在穆斯林时代继续担任显赫的宫廷职位。

在库法开始接受教育后，肯迪迁至巴格达完成学业，并很快因其学识而声名鹊起。他引起了哈里发al-Ma'mun的注意，当时al-Ma'mun正在巴格达建立“智慧宫”。al-Ma'mun在813年赢得对其兄弟的武装斗争，并于同年成为哈里发。他统治其帝国，最初从梅尔夫，然后在818年后，他从巴格达统治，他不得不前往那里镇压一次未遂政变。

Al-Ma'mun是学术的赞助人，他创立了一所名为智慧宫的学院，希腊哲学和科学著作在那里被翻译。肯迪被al-Ma'mun任命到智慧宫，与花拉子米和巴努·穆萨一起。肯迪及其同事在智慧宫承担的主要任务涉及翻译希腊科学手稿。Al-Ma'mun建立了一个手稿图书馆，这是自亚历山大图书馆以来建立的第一个大型图书馆，从费隆收集重要著作。除了智慧宫，al-Ma'mun还建立了天文台，穆斯林天文学家可以在其中以早期民族获得的知识为基础继续发展。

833年，al-Ma'mun去世，其弟al-Mu'tasim继位。肯迪继续受到恩宠，al-Mu'tasim雇用肯迪辅导其子Ahmad。al-Mu'tasim于842年去世，al-Wathiq继位，后者又于847年由al-Mutawakkil继任哈里发。在这两位哈里发统治下，肯迪的境遇较差。尚不完全清楚这是因为他的宗教观点，还是因为智慧宫学者之间的内部争论和竞争。当然，al-Mutawakkil迫害所有非正统和非穆斯林群体，同时摧毁了巴格达的犹太会堂和教堂。然而，肯迪的[6]：-

……对宗教争论缺乏兴趣可以从他写作的主题中看出。……他似乎与正统伊斯兰教的世界观共存。

事实上，肯迪的大部分哲学著作似乎旨在表明他相信追求哲学与正统伊斯兰教是相容的。这似乎表明，更可能的是肯迪成为了[1]：-

……他是数学家巴努·穆萨和占星家肯迪Ma'shar这类对手的受害者。

据称，巴努·穆萨使肯迪失去了al-Mutawakkil的宠信，以至于他命人鞭打肯迪，并将肯迪的藏书交给了巴努·穆萨。

肯迪最为人所知的身份是哲学家，但他也是一位重要的数学家和科学家[3]：-

在他的族人中，他被称为……阿拉伯人的哲学家。他是唯一一位纯阿拉伯血统的著名哲学家，也是伊斯兰教中的第一位。肯迪“是他那个时代最博学的人，在同代人中独树一帜，通晓古代科学家的全部知识，涵盖逻辑学、哲学、几何学、数学、音乐和占星术。

对于一个如此博学、受雇翻译希腊文本的人来说，也许相当令人惊讶的是，肯迪的希腊语似乎并不足以流利到亲自翻译。相反，他润色他人所作的翻译，并撰写了许多希腊著作的评注。显然，他受亚里士多德著作的影响最为强烈，但柏拉图、波菲利和普罗克洛的影响也能在肯迪的思想中看到。我们当然不应给人这样的印象，即肯迪仅仅借用了这些早期作者的东西，因为他将他们的思想构建成了一个整体体系，而这无疑是他自己的发明。

肯迪写了许多关于算术的著作，其中包括关于印度数字、数的和谐、线与数的乘法、相对量、测量比例与时间，以及数值程序和消去法的手稿。他还写了关于空间和时间的著作，他相信两者都是有限的，并用一个关于无限的悖论来“证明”他的断言。Garro给出了肯迪的“证明”，即实际无限物体或大小的存在会导致[7]中的矛盾。在Garro较近期的论文[8]中，他以现代术语表述了肯迪无限悖论的非形式公理化，并从数学和哲学两个角度讨论了这一悖论。

在几何学中，肯迪写了关于平行线理论等著作。他给出了一个引理，探讨在平面中展示同时非平行且不相交的线对的可能性。同样与几何相关的是他写的两本关于光学的著作，尽管他遵循了当时的惯例，混淆了光的理论和视觉理论。

也许肯迪自己的话最能说明他在全部工作中试图做什么。在他的一本书的导言中，他写道（例如见[1]）：-

我们在本书中努力做到，正如我们在所有学科中的习惯那样，回顾古人过去已经说尽的一切，这对后来者来说是最容易、最简捷的采纳方式，并在他们尚未说尽的领域更进一步，这是很好的……

当然，肯迪努力遵循这条道路。例如，在他关于光学的著作中，他批评了特拉勒斯的安提莫斯对战斗中如何用镜子点燃船只的希腊描述。肯迪采用了更科学的方法（例如见[1]）：-

安特米乌斯不应未经证明就接受信息……他告诉我们如何构造一面镜子，使二十四条光线反射到一个点上，却没有说明如何确定光线在距镜面中心给定距离处汇聚的那个点。另一方面，我们已在我们能力允许的范围内尽可能多地用证据描述了这一点，补足了缺失的内容，因为他没有提到一个确定的距离。

肯迪的许多工作仍有待仔细研究，或者直到最近才受到学术研究。例如，肯迪对阿基米德的The measurement of the circle的评注直到1993年Rashed的出版物[10]才受到仔细关注。

Al-Kindi was born and brought up in Kufa, which was a centre for Arab culture and learning in the 9th century. This was certainly the right place for al-Kindi to get the best education possible at this time. Although quite a few details (and legends) of al-Kindi's life are given in various sources, these are not all consistent. We shall try to give below details which are fairly well substantiated.

According to [3], al-Kindi's father was the governor of Kufah, as his grandfather had been before him. Certainly all agree that al-Kindi was descended from the Royal Kindah tribe which had originated in southern Arabia. This tribe had united a number of tribes and reached a position of prominence in the 5th and 6th centuries but then lost power from the middle of the 6th century. However, descendants of the Royal Kindah continued to hold prominent court positions in Muslim times.

After beginning his education in Kufah, al-Kindi moved to Baghdad to complete his studies and there he quickly achieved fame for his scholarship. He came to the attention of the Caliph al-Ma'mun who was at that time setting up the "House of Wisdom" in Baghdad. Al-Ma'mun had won an armed struggle against his brother in 813 and became Caliph in that year. He ruled his empire, first from Merv then, after 818, he ruled from Baghdad where he had to go to put down an attempted coup.

Al-Ma'mun was a patron of learning and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. Al-Kindi was appointed by al-Ma'mun to the House of Wisdom together with al-Khwarizmi and the Banu Musa brothers. The main task that al-Kindi and his colleagues undertook in the House of Wisdom involved the translation of Greek scientific manuscripts. Al-Ma'mun had built up a library of manuscripts, the first major library to be set up since that at Alexandria, collecting important works from Byzantium. In addition to the House of Wisdom, al-Ma'mun set up observatories in which Muslim astronomers could build on the knowledge acquired by earlier peoples.

In 833 al-Ma'mun died and was succeeded by his brother al-Mu'tasim. Al-Kindi continued to be in favour and al-Mu'tasim employed al-Kindi to tutor his son Ahmad. Al-Mu'tasim died in 842 and was succeeded by al-Wathiq who, in turn, was succeeded as Caliph in 847 by al-Mutawakkil. Under both these Caliphs al-Kindi fared less well. It is not entirely clear whether this was because of his religious views or because of internal arguments and rivalry between the scholars in the House of Wisdom. Certainly al-Mutawakkil persecuted all non-orthodox and non-Muslim groups while he had synagogues and churches in Baghdad destroyed. However, al-Kindi's [6]:-

... lack of interest in religious argument can be seen in the topics on which he wrote. ... he appears to coexist with the world view of orthodox Islam.

In fact most of al-Kindi's philosophical writings seem designed to show that he believed that the pursuit of philosophy is compatible with orthodox Islam. This would seem to indicate that it is more probably that al-Kindi became [1]:-

... the victim of such rivals as the mathematicians Banu Musa and the astrologer Abu Ma'shar.

It is claimed that the Banu Musa brothers caused al-Kindi to lose favour with al-Mutawakkil to the extent that he had him beaten and gave al-Kindi's library to the Banu Musa brothers.

Al-Kindi was best known as a philosopher but he was also a mathematician and scientist of importance [3]:-

To his people he became known as ... the philosopher of the Arabs. He was the only notable philosopher of pure Arabian blood and the first one in Islam. Al-Kindi "was the most leaned of his age, unique among his contemporaries in the knowledge of the totality of ancient scientists, embracing logic, philosophy, geometry, mathematics, music and astrology.

Perhaps, rather surprisingly for a man of such learning whose was employed to translate Greek texts, al-Kindi does not appear to have been fluent enough in Greek to do the translation himself. Rather he polished the translations made by others and wrote commentaries on many Greek works. Clearly he was most influenced most strongly by the writings of Aristotle but the influence of Plato, Porphyry and Proclus can also be seen in al-Kindi's ideas. We should certainly not give the impression that al-Kindi merely borrowed from these earlier writer, for he built their ideas into an overall scheme which was certainly his own invention.

Al-Kindi wrote many works on arithmetic which included manuscripts on Indian numbers, the harmony of numbers, lines and multiplication with numbers, relative quantities, measuring proportion and time, and numerical procedures and cancellation. He also wrote on space and time, both of which he believed were finite, 'proving' his assertion with a paradox of the infinite. Garro gives al-Kindi's 'proof' that the existence of an actual infinite body or magnitude leads to a contradiction in [7]. In his more recent paper [8], Garro formulates the informal axiomatics of al-Kindi's paradox of the infinite in modern terms and discusses the paradox both from a mathematical and philosophical point of view.

In geometry al-Kindi wrote, among other works, on the theory of parallels. He gave a lemma investigating the possibility of exhibiting pairs of lines in the plane which are simultaneously non-parallel and non-intersecting. Also related to geometry was the two works he wrote on optics, although he followed the usual practice of the time and confused the theory of light and the theory of vision.

Perhaps al-Kindi's own words give the best indication of what he attempted to do in all his work. In the introduction to one of his books he wrote (see for example [1]):-

It is good ... that we endeavour in this book, as is our habit in all subjects, to recall that concerning which the Ancients have said everything in the past, that is the easiest and shortest to adopt for those who follow them, and to go further in those areas where they have not said everything ...

Certainly al-Kindi tried hard to follow this path. For example in his work on optics he is critical of a Greek description by Anthemius of how a mirror was used to set a ship on fire during a battle. Al-Kindi adopts a more scientific approach (see for example [1]):-

Anthemius should not have accepted information without proof ... He tells us how to construct a mirror from which twenty-four rays are reflected on a single point, without showing how to establish the point where the rays unite at a given distance from the middle of the mirror's surface. We, on the other hand, have described this with as much evidence as our ability permits, furnishing what was missing, for he has not mentioned a definite distance.

Much of al-Kindi's work remains to be studied closely or has only recently been subjected to scholarly research. For example al-Kindi's commentary on Archimedes' The measurement of the circle has only received careful attention as recently as the 1993 publication [10] by Rashed.