数学家传记
尼古拉是一位德国哲学家和主教。他对几何学和逻辑学以及哲学和天文学感兴趣。
尼古拉 Kryffs 或 Krebs 是摩泽尔河畔富有的船商 Johan Krebs（或 Cryfts）与 Catharina Roemers 的儿子。尼古拉 是他父母四个孩子之一。他出生在库斯，即现在的贝恩卡斯特尔-库斯，距特里尔约30公里，这是普法尔茨地区一座由罗马人建立的古老城镇。按照拉丁语教会环境中的惯常做法，他的名字常以 Nikolaus Cusanus 出现，源自该镇的拉丁语名称。他离开家，被曼德沙伊德的狄奥多里克伯爵送到荷兰的代芬特尔。据称他离家的原因是为了逃避父亲的虐待（故事说 尼古拉 只对书感兴趣，因不会划桨而惹恼了父亲）。尽管这出现在 尼古拉 的古代传记中，但几乎没有证据支持。在代芬特尔，他早期教育是在共同生活兄弟会接受的。共同生活兄弟会是由 Gerard Groote 在14世纪创立的一个罗马天主教宗教团体，其神秘主义与理性的混合无疑会强烈影响年轻的 尼古拉。
关于尼古拉受教育情况的第一个确切信息是在1416年，当时他在海德堡大学注册入学。正如人们所料，记录中列明他来自特里尔教区。在海德堡，尼古拉学习了一年的自由技艺，尤其是哲学，之后于1417年前往帕多瓦大学。在帕多瓦，他师从Giuliano Cesarini学习教会法，后者仅比尼古拉大三岁，刚在帕多瓦完成自己的教会法博士学位。在帕多瓦，他与同学Paolo dal Pozzo Toscanelli成为朋友，后者正在学习数学和医学。Toscanelli后来成为重要的数学家和天文学家，与尼古拉终生保持友谊。这是两位极具才智之人之间的友谊，他们强烈地相互影响。正是在帕多瓦，尼古拉了解到数学和天文学的最新发展，二十年后，尼古拉将他的两部数学著作献给了Toscanelli。Giovanni Andrea Bussi（1417-1475），人文主义者，自1469年起任阿莱里亚主教，后来成为尼古拉的朋友，并撰写了关于尼古拉在帕多瓦学生时代的文字：-
尼古拉学习了拉丁语、希腊语、希伯来语，晚年还学习了阿拉伯语，尽管他并不喜爱修辞学和诗歌。
尼古拉于1423年在帕多瓦获得教会法博士学位，在罗马逗留一段时间后，于1425年春季在科隆大学注册入学，学习神学。他在特里尔大主教的支持下进行这些学业。朋友再次对尼古拉产生了强烈影响，在科隆，他与Heimericus de Campo成为朋友，后者向他介绍了伪狄奥尼修斯、艾尔伯图斯·麦格努斯和拉蒙的思想。科隆是特里尔教区的一部分，自1418年起任特里尔大主教的Otto of Ziegenhain通过提供来自科布伦茨、Oberwesel、Münstermaifeld、Dypurgh、St Wendel和列日等地圣职俸禄的收入来支持尼古拉。到1427年9月，尼古拉成为Otto of Ziegenhain的秘书，但Otto——一位坚定的教会改革倡导者——于1430年去世，关于谁应接替他发生了严重争执。Otto去世后，尼古拉成为Ulrich of Manderscheid的秘书，后者是科隆会议上支持接替Otto的选帝侯之一。然而，教皇希望Raban von Helmsted接替Otto。1431年，巴塞尔会议成立，旨在尝试改革教会并结束对立教皇的局面。尼古拉以前的老师Cesarini于9月成为会议主席，但教皇试图在三个月后解散会议。会议拒绝服从教皇的命令，1432年，Ulrich与Raban之间的争端被提交给会议。尼古拉向会议陈述了Ulrich的理由，反对教皇有权任命其候选人的主张。尽管会议与教皇存在争端，尼古拉输掉了他的案件，但他成为会议的重要成员。他于1433年撰写了De concordantia catholica Ⓣ（天主教会的权威），主张会议的权威优先于教皇的权威。在这部著作中，他写道：-
既然从本性上说所有人都是自由的，那么一切政府——无论是基于成文法，还是基于通过其治理使臣民被约束远离恶行、其自由为着良好目的而受惩罚之恐惧所规范的、体现于统治者身上的法律——都仅仅源自臣民的同意与认可。
他于1436年就历法改革向会议提出建议，到1436年12月，他在会议观点是否优先于教皇（此时为Eugenius IV）观点的争论中改变了立场，站到了教皇一边。这使尼古拉在会议上处于少数派，但在教皇同意下，他成为1437年派往君士坦丁堡的三人代表团成员之一。代表团的目的是启动一个导致东西方教会重新统一的进程，尼古拉在君士坦丁堡的两个月里取得了很大成就。他的外交活动带来了暂时的成功，但始于1439年7月的重新统一进程很快瓦解。同样在君士坦丁堡期间，他发现了一些重要的希腊手稿。
1428年，鲁汶大学曾向尼古拉提供教会法讲席；他拒绝了。1435年他们再次提出同样的邀请，他再次拒绝。1438年至1448年间，尼古拉作为教皇使节参加了数次前往德国的使命，特别是在美因茨帝国议会（1441年）、法兰克福（1442年）、纽伦堡（1444年）和法兰克福（1446年）代表教皇。他在1430年至1440年间的某个时候被授予圣职，并于1446年被教皇Eugenius IV任命为枢机，以表彰他作为教皇使节的工作。然而，Eugenius IV在任命正式生效前去世，因此尼古拉不得不等到1448年12月，教皇尼古拉五世任命他为枢机。随后他于1450年成为布里克森（今布雷萨诺内）主教。（注意“枢机”是头衔，而“主教”是职务。）由于奥地利公爵的反对，他两年内无法在布里克森履职，因此教皇派他作为教皇使节前往北德意志和尼德兰。他被赋予了一些极其困难的任务，即[15]：-
……宣讲禧年大赦，并推动对土耳其人的十字军；巡视、改革和整顿堂区、修院、医院；努力使胡斯派与教会重新合一；结束克莱沃公爵与科隆大主教之间的纷争；并与勃艮第公爵谈判，以期英法之间实现和平。
Jasper Hopkins在17中写到尼古拉于1452年在布里克斯恩开始的工作：-
他试图改革教区并使其摆脱奥地利公爵兼蒂罗尔伯爵西吉斯蒙德的控制，这招致威胁和冲突，两次迫使他前往罗马寻求慰藉和庇护。
尼古拉首次出版的著作是De docta ignorantia Ⓣ（论有学问的无知），于1440年出版，这部论著的思想是他在1437年出使君士坦丁堡归来途中形成的。在这部或许是他最著名的哲学著作中，他论证了人类对宇宙的认识是不完整的。他声称，寻求真理等同于化圆为方。Dermot Moran写道[22]：-
他的目标始终是揭示单纯人类知识的局限，并在我们的无知中教导我们。这就是“无知的教导”（doctrina ignorantiae）。库萨努斯强调人类心智的有限性，以及绝对科学知识这一普罗米修斯式计划的最终失败。但在他所有的表述中，他都极为忠实地遵循柏拉图传统……
在他关于数学的著作中，我们提及：De geometricis transmutationibus Ⓣ（论几何变换）（1445年）、De arithmeticis complementis Ⓣ（论算术补数）（1445年）、De circuli quadratura Ⓣ（圆的求积）（1450年）、Quadratura circuli Ⓣ（圆的求积）（1450年）、De mathematicis complementis Ⓣ（论数学补数）（1453年）、Dialogus de circuli quadratura Ⓣ（关于圆求积的对话）（1457年）、De caesarea circuli quadratura Ⓣ（凯撒圆的求积）（1457年）、De mathematica perfectione Ⓣ（论数学的完善）（1458年）、Aurea propositio in mathematicis Ⓣ（数学中的黄金命题）（1459年）。他还写了Declaratio rectilineationis curvae Ⓣ（关于一条直线曲线的声明）和De una recti curvique mensura Ⓣ（论直线或曲线度量），但它们的日期不详。他对几何学和逻辑学感兴趣，并且显然至少研究过欧几里得的Elements的部分内容以及托马斯·布拉德华和诺瓦拉的坎帕努斯的著作。他对无穷的研究作出了贡献，研究了无穷大和无穷小。他把圆视为正多边形的极限，并在他的宗教教导中用它来说明人如何能够接近真理，却永远无法完全达到真理。他写道：-
无限与有限之间不存在可比关系，这是不言自明的。……因此，有限理智不可能借助相似性精确地获得关于事物的真理。……因为真理不是多些或少些的东西，而是不可分割的东西。凡不是真理的东西都不能精确地衡量真理。……因为理智之于真理，正如内接多边形之于外接圆。
1444年，他对天文学产生了兴趣，购买了十六本天文学书籍、一个木制天球仪、一个铜制天球仪以及各种天文仪器，其中包括一个星盘。（他的天文仪器如今保存在库斯的图书馆中。）他对天文学的兴趣无疑使他得出了一些正确的理论，以及其他一些可能仍将被证明为正确的理论。例如，他声称地球绕太阳运动。他还声称恒星是其他的太阳，空间是无限的。他还相信恒星有其他世界环绕它们运行，而这些世界上有人居住。他正确的地方如此之多，也许有一天这些也会被证明是正确的！Volker Bialas写道[12]：-
在其主要致力于形而上学问题的哲学和科学著作中，库萨的尼古拉……超越了有限与无限之间的界限。这一点在他关于展开的宇宙的观念中表现得最为明显。库萨努斯虽然对他那个时代的天文学问题感兴趣，但他构建了一种——可以这么说——基于三条原则的思辨宇宙论：对立面的重合、世界首要基础的原则以及一切存在者的三位一体原则。通过假定一个无限的宇宙，库萨努斯提出了影响随后几个世纪宇宙论思考的新问题，例如焦尔达诺·布鲁诺和约翰内斯·开普勒的那些问题。
据说焦尔达诺·布鲁诺曾写道：-
如果[尼古拉]没有受到其神父法衣的阻碍，他甚至会比毕达哥拉斯更伟大！
尼古拉发表了《阿方索星表》的改进版，该表利用克劳狄乌斯·托勒密的模型给出了一种确定太阳、月亮和行星位置的实用方法。这些星表最初是在1272年得到卡斯蒂利亚国王阿方索十世的支持下编纂的。像他那个时代的许多博学之士一样，尼古拉也撰写了关于历法改革的文章，但尽管他关于闰年提出了合理的建议，教会并没有实施他的想法。
在他的哲学著作中，尼古拉对“知识论”特别感兴趣，并在诸如De conjecturis（1440-44）和Compendium（1464）等著作中就此主题进行了写作。尼古拉认为，知识通过感官获得，但理解是对多样感官形象的抽象。所有人类知识都只能是猜测，而智慧只有通过理解自己无知的程度才能获得。在Compendium中，尼古拉写道：-
完美的有生命存在是拥有感觉和理智的存在。这个存在应被视为一位宇宙志学者，他有一座拥有五座城门的城市，这五座城门就是五种感官。通过这些城门，来自世界各地的信使进入，宣告整个世界的状况……宇宙志学者应坐下来，记录下所有与他相关的事物，以便在自己的城市中拥有一幅整个可感知世界的描述……因此，宇宙志学者尽其所能保持所有城门敞开，不断倾听新信使的报告，并使他的描述越来越接近真理。最后，当他在自己的城市中完整地呈现了可感知世界之后，他将其编纂成一幅秩序井然、比例适度的地图，以免遗失。
也许对他宗教观点最好的总结见于他的著作De visione dei（1453）：-
如今我仿佛对着镜子观看，如同猜谜，看见永生，因为那无非是那蒙福的注视，你以最慈爱的方式永不停止地注视我，甚至我灵魂的隐秘之处。对你而言，看见就是赐予生命；就是不断分赐对你最甜蜜的爱；就是通过分赐爱而点燃我对你的爱，并通过点燃来喂养我，通过喂养来激起我的渴望，通过激起使我饮于喜乐，通过饮于在我里面注入生命之泉，通过注入使其增长并持续。就是使我分享你的不朽……因为这是每一个理性欲望的绝对最大者，比它更大的不可能存在。
尼古拉于1460年被西吉斯蒙德囚禁，遭受虐待，健康从未完全恢复。教皇庇护二世于1464年派他前往里窝那，鼓励十字军更快准备对土耳其人的行动。然而，尼古拉的健康在旅途中恶化，他在托迪去世，朋友保罗·达尔·波佐·托斯卡内利在场。
让我们以[5]出版商描述中给出的总结作为结束：-
神学、数学、哲学、科学、艺术、医学——人文主义者尼古拉的探究触及了所有这些领域……然而，他本人将学者定义为“意识到自己无知的人”（《论有学识的无知》）……尼古拉思想的哪些方面在今天仍然切题？他对人类知识界限的敏锐意识，使他成为……关于有限性问题及其与普遍者之关系这一现代进路的前驱。他对数学的偏爱：尼古拉实际上并不以亚里士多德哲学基础的矛盾原则为出发点，而是偏好柏拉图对辩证法和数学的阐述，借此可以将上帝的无限想象为“对立面的重合”，这是他哲学中的另一个关键概念。然而，数学只能让我们接近上帝以及反映上帝的事物，而不能完全把握上帝。但这种否定神学并不归结为对神学的否定；相反，它从上帝所 encompassed 的有限者之存在中的过剩出发，设想上帝的绝对他异性。
Nicholas Kryffs or Krebs was the son of Johan Krebs (or Cryfts), a wealthy shipper on the river Moselle, and Catharina Roemers. Nicholas was one of his parents' four children. He was born in Kues, now Bernkastel-Kues, about 30 km from Trier, an old town in the Palatinate, founded by the Romans. His name often appears as Nikolaus Cusanus, following the usual practice in the Latin speaking church environment, from the Latin name of the town. He left his home and was sent to Deventer, in the Netherlands, by Count Theodoric von Manderscheid. It is claimed that the reason he left home was to escape from ill-treatment by his father (the story being that Nicholas was only interested in books and annoyed his father by being unable to handle an oar). Although this appears in ancient biographies of Nicholas, there is little evidence to support it. In Deventer, his early education took place at the Brothers of the Common Life. Certainly the Brothers of the Common Life, a Roman Catholic religious community founded by Gerard Groote in the 14th century, would have strongly influenced the young Nicholas with their mixture of mysticism and reason.
The first certain information about Nicholas's education is in 1416 when he matriculated at the University of Heidelberg. The record, as one would expect, lists him as from the diocese of Trier. In Heidelberg Nicholas studied liberal arts, particularly philosophy, for a year before going to the University of Padua in 1417. At Padua he studied canon law under Giuliano Cesarini, who was only three years older than Nicholas, having just completed his own doctorate in canon law at Padua. At Padua he became friends with fellow student Paolo dal Pozzo Toscanelli, who was studying mathematics and medicine. Toscanelli became an important mathematician and astronomer, remaining friends with Nicholas throughout his life. It was a friendship between two highly intelligent men who strongly influenced each other. It was in Padua that Nicholas learnt about the latest developments in mathematics and astronomy and, twenty years later, Nicholas dedicated two of his mathematical works to Toscanelli. Giovanni Andrea Bussi (1417-1475), humanist and Bishop of Aleria from 1469, later became a friend of Nicholas and wrote about Nicholas's student days at Padua:-
Nicholas studied Latin, Greek, Hebrew, and, in later years, Arabic, though he was not a lover of rhetoric and poetry.
Nicholas graduated with a doctorate in canon law from Padua in 1423 and, after spending some time in Rome, he matriculated at the University of Cologne in the spring of 1425 to study divinity. He undertook these studies with the support of the Archbishop of Trier. Again friends would influence Nicholas strongly and, at Cologne, he became friends with Heimericus de Campo who introduced him to the ideas of Pseudo-Dionysius, Albertus Magnus and Ramon Llull. Cologne was part of the diocese of Trier and Otto of Ziegenhain, archbishop of Trier from 1418, supported Nicholas by providing him with an income from benefices at Coblenz, Oberwesel, Münstermaifeld, Dypurgh, St Wendel, and Liège. By September 1427 Nicholas was Otto of Ziegenhain's secretary but Otto, a strong advocate for Church reform, died in 1430 and there was a serious dispute over whom should replace him. Following Otto's death, Nicholas became secretary to Ulrich of Manderscheid, one of the electors at the assembly in Cologne who was favoured by the electors to replace Otto. However, the pope wanted Raban von Helmsted to succeed Otto. In 1431 the Council of Basel had been set up to try to reform the Church and end the situation of rival popes. Cesarini, Nicholas's former teacher, became president of the Council in September but the pope tried to dissolve the three months later. The Council refused to follow the pope's order and, in 1432, the dispute between Ulrich and Raban was referred to the Council. Nicholas put the case for Ulrich to the Council, arguing against the pope's right make the appointment of his candidate. Despite the Council being in dispute with the pope, Nicholas lost his case but he became an important member of the Council. He wrote De concordantia catholica Ⓣ in 1433, arguing that the Council's authority took precedence over that of the pope. In this work he wrote:-
Since by nature all men are free, all government - whether based on written law or on law embodied in a ruler through whose government the subjects are restrained from evil deeds and their liberty regulated, for a good end by fear of punishment - arises solely from agreement and consent of the subjects.
He advised the Council on calendar reform in 1436 and by December 1436 had changed sides in the argument as to whether the Council's views took precedence over those of the pope (at this time Eugenius IV), taking the pope's side. This put Nicholas in a minority on the Council but, with the pope's agreement, he was part of a three-man delegation sent to Constantinople in 1437. The aim of the delegation was to set up a process leading to the eastern and western Churches reuniting and Nicholas achieved much during two months in Constantinople. His diplomacy led to temporary success, but the moves towards reunification, begun in July 1439, soon fell apart. Also while in Constantinople, he discovered some important Greek manuscripts.
In 1428 the University of Louvain had offered Nicholas its chair of canon law; he had declined. Again in 1435 they made the same offer which again he declined. Nicholas took part in several missions to Germany as papal envoy between 1438 and 1448, in particular representing the pope at the Diets of Mainz (1441), Frankfort (1442), Nuremberg (1444), and Frankfort (1446). He was ordained sometime between 1430 and 1440 and was named cardinal by pope Eugenius IV in 1446 in recognition of his work as a papal envoy. However, Eugenius IV died before the appointment became official so Nicholas had to wait till December 1448 when pope Nicholas V made him a cardinal. Then he became the bishop of Brixon (now Bressanone) in 1450. (Note that 'cardinal' was a title, while 'bishop' was an office.) Because of opposition by the Duke of Austria, he could not take up his duties in Brixon for two years so the pope sent him as papal legate to North Germany and the Netherlands. He was given some seriously difficult tasks, namely [15]:-
... to preach the Jubilee indulgence and to promote the crusade against the Turks; to visit, reform, and correct parishes, monasteries, hospitals; to endeavour to reunite the Hussites with the Church; to end the dissensions between the Duke of Cleve and the Archbishop of Cologne; and to treat with the Duke of Burgundy with a view to peace between England and France.
Jasper Hopkins writes of Nicholas's work in Brixon which he took up in 1452 [17]:-
His attempts to reform the diocese and to free it from domination by Sigismund, duke of Austria and count of Tirol, led to threats and clashes that twice caused him to seek consolation and refuge in Rome.
Nicholas's first published work was De docta ignorantia Ⓣ which was published in 1440, a treatise whose ideas came to him on the return voyage from the 1437 mission to Constantinople. In this treatise, perhaps his best known philosophical work, he argued the incomplete nature of man's knowledge of the universe. He claimed that the search for truth was equal to the task of squaring the circle. Dermot Moran writes [22]:-
His aim is always to show the limitations on merely human knowledge, and to instruct us in our ignorance. This is the 'instruction of ignorance' (doctrina ignorantiae). Cusanus is stressing the finitude of the human mind and the ultimate failure of the promethean project of absolute scientific knowledge. But in all his formulations he remains remarkably faithful to the Platonic tradition ...
Among his writings on mathematics we mention: De geometricis transmutationibus Ⓣ (1445), De arithmeticis complementis Ⓣ (1445), De circuli quadratura Ⓣ (1450), Quadratura circuli Ⓣ (1450), De mathematicis complementis Ⓣ (1453) Dialogus de circuli quadratura Ⓣ (1457), De caesarea circuli quadratura Ⓣ (1457), De mathematica perfectione Ⓣ (1458), Aurea propositio in mathematicis Ⓣ (1459). He also wrote Declaratio rectilineationis curvae Ⓣ and De una recti curvique mensura Ⓣ but their dates are unknown. He was interested in geometry and logic and had clearly made a study of at least parts of Euclid's Elements and works of Thomas Bradwardine and Campanus of Novara. He contributed to the study of infinity, studying the infinitely large and the infinitely small. He looked at the circle as the limit of regular polygons and used it in his religious teaching to show how one can approach truth but never reach it completely. He wrote:-
It is self-evident that there is no comparative relation of the infinite to the finite. ... Therefore, it is not the case that by means of likeness a finite intellect can precisely attain the truth about things. ... For truth is not something more or something less but is something indivisible. Whatever is not truth cannot measure truth precisely. ... For the intellect is to truth as an inscribed polygon is to the inscribing circle.
In 1444 he became interested in astronomy and purchased sixteen books on astronomy, a wooden celestial globe, a copper celestial globe and various astronomical instruments including an astrolabe. (His astronomical instruments are today preserved in the library at Kues.) His interest in astronomy certainly led him to certain theories which were true and others which may still prove to be true. For example he claimed that the Earth moved round the Sun. He also claimed that the stars were other suns and that space was infinite. He also believed that the stars had other worlds orbiting them which were inhabited. He got so much right that perhaps this will also be found to be true one day! Volker Bialas writes [12]:-
In his philosophical and scientific writings, mainly devoted to metaphysical questions, Nicolas of Cues ... transcended the bounds between the finite and the infinite. Nowhere more than in his idea of the unfolding universe has this crossing of the bounds become more obvious. Cusanus, although interested in the astronomical problems of his time, constructed a - so to speak - speculative cosmology based on three principles: the coincidence of opposites, the principle of the primary basis of the world and the principle of Trinity of all the being. By postulating an unlimited universe Cusanus asked new questions which influenced cosmological considerations in the following centuries, such as for example those of Giordano Bruno and Johannes Kepler.
Giordano Bruno is said to have written:-
If [Nicholas of Cusa] had not been hindered by his priest's vestment, he would have even been greater than Pythagoras!
Nicholas published improvements to the Alfonsine Tables which gave a practical method to find the position of the Sun, Moon and planets using Ptolemy's model. These tables had originally been compiled in 1272 with the support of King Alfonso X of Castile. Like many learned men of his time, Nicholas also wrote on calendar reform but, despite his sensible suggestions about leap years, the Church did not implement his ideas.
In his philosophical works Nicholas was particularly interested in the 'Theory of Knowledge', writing on this topic in works such as De conjecturis (1440-44) and Compendium (1464). Knowledge, Nicholas believed, is derived through the senses but understanding is an abstraction of diverse sensory images. All human knowledge must be mere conjecture, and wisdom is attained only through understanding the extent of one's ignorance. In Compendium, Nicholas writes:-
The perfect animate being is one possessing sense and intellect. This being should be thought of as a cosmographer who has a city with five gates, which are the five senses. Through these gates messengers enter from all over the world, announcing the disposition of the entire world ... The cosmographer should sit and note down all things that are related to him, in order to have a description of the entire perceptible world represented in his own city. ... The cosmographer therefore tries as hard as he can to keep all the gates open, to listen constantly for the reports of new messengers, and to bring his description ever closer to the truth. Finally, when he has made a complete representation of the perceptible world in his own city, he compiles it into a well-ordered and proportionately measured map lest it be lost.
Perhaps the best summary of his religious views is given in his book De visione dei (1453):-
Now I behold as in a mirror, in an icon, in a riddle, life eternal, for that is naught other than that blessed regard wherewith Thou never ceasest most lovingly to behold me, yea, even the secret places of my soul. With Thee, to behold is to give life; 'tis unceasingly to impart sweetest love of Thee; 'tis to inflame me to love of Thee by love's imparting, and to feed me by inflaming, and by feeding to kindle my yearning, and by kindling to make me drink of gladness, and by drinking to infuse in me a fountain of life, and by infusing to make it increase and endure. 'Tis to cause me to share Thine immortality. . . . For it is the absolute maximum of every rational desire, than which a greater cannot be.
Nicholas was imprisoned by Sigmund in 1460 and suffered ill-treatment from which his health never completely recovered. Pope Pius II sent him to Livorno in 1464 to encourage the Crusaders to prepare more rapidly for action against the Turks. However, Nicholas's poor health deteriorated on the journey and he died in Todi in the presence of his friend Paolo dal Pozzo Toscanelli.
Let us end with the summary given in the publisher's description of [5]:-
Theology, mathematics, philosophy, science, art, medicine - no avenue of inquiry escaped the attention of the humanist Nicholas of Cusa ... He himself, however, defined the scholar as one who 'is aware of his own ignorance' (De docta ignorantia)... What aspects of Nicholas of Cusa's thought are still pertinent today? His acute sense of the limits of human knowledge, which makes him ... a precursor of the modern approach to the problem of finiteness and its relation with the universal. His predilection for mathematics: instead of the principle of contradiction, which was the basis of Aristotelian philosophy, Nicholas of Cusa in fact preferred the Platonic articulation of dialectics and mathematics, by which one can imagine the infinity of God as a 'coincidence of opposites', another key notion in his philosophy. However, mathematics allows us only to approach God and that which reflects Him, not to fully apprehend Him. But this negative theology does not reduce to a negation of theology; rather, it envisions the absolute otherness of God in terms of superabundance in the existence given to the finite that is encompassed by God.
正文里的方括号编号指向这里，悬停即可直接看到条目。书目保留原文——译了书名反而查不到文献。
原站列出的延伸阅读与外部数据库，照原样保留，目标多为英文页面。
关于尼古拉的其它页面：
原站的交叉引用。指向本站已镜像专题的留在站内，其余仍指回原站。