数学家传记
亚伯拉罕·阿德里安·艾伯特(或艾尔伯图斯·麦格努斯)是一位德国多明我会修士,他撰写了关于欧几里得的《几何原本》的评注。他于1931年被封为圣徒,并于1941年被立为自然科学家的主保圣人。
亚伯拉罕·阿德里安·艾伯特(或麦格努斯)出生于巴伐利亚富裕的博尔施泰特伯爵家族,是家中的长子。他后来被授予“麦格努斯”(艾尔伯图斯·麦格努斯)以及“Doctor Universalis”的称号,以表明同时代人对他的尊敬。他早年在劳因根度过,一定是在家里或离家很近的学校接受教育。他的叔叔住在帕多瓦,由于那里的大学以文科闻名,自然是他学习的地方。在帕多瓦大学学习文科后,他于1223年在帕多瓦加入了多明我会,被当时修会领袖萨克森的乔丹的教导所吸引。这意味着他不受教区或修道院的束缚,因此可以在广阔的地区学习和教学。
加入多明我会后,他在帕多瓦、博洛尼亚、科隆以及希尔德斯海姆、弗赖堡、雷根斯堡、斯特拉斯堡和科隆的其他德国修道院学习和教学。大约1241年,他被派往巴黎大学圣雅各多明我会修道院,在那里他阅读了亚里士多德阿拉伯语和希腊语文本的新译本及注释。这是一个阿拉伯学者的著作,以及通过他们传播的古希腊哲学家文本,在整个基督教欧洲逐渐为人所知的时期,欧洲不得不接受这些新知识。麦格努斯以其涵盖几乎全部知识的广泛学识,在接受这些新学问进入欧洲方面发挥了重要作用。
他在圣雅各学院任教四年,讲授圣经和彼得·隆巴德所著的神学教科书The Book of the Sentences。1245年,他从巴黎大学获得神学硕士学位,获得该学位后,他最早教授的学生之一是托马斯·阿奎那。在巴黎期间,麦格努斯开始了呈现整个知识体系的任务,包括自然科学、逻辑学、修辞学、数学、天文学、伦理学、经济学、政治学和形而上学。他撰写了关于圣经、彼得·隆巴德的Book of the Sentences以及亚里士多德全部著作的注释。这些注释包含了他自己的观察和实验。所谓‘实验’,麦格努斯指的是‘观察、描述和分类’。例如,在De MineralibusⓉ(论矿物)中,麦格努斯写道:-
自然科学的目的是不仅仅接受他人的陈述,而是探究自然界中起作用的原因。
我们不应低估这些观念的重要性,因为当时大多数学者认为知识只能从研读经文中获得。在13世纪,很少有人准备甚至考虑科学研究的可能性,大多数人认为知识都来自上帝,通过古代神圣启示的著作。麦格努斯不仅倡导我们今天所谓的科学研究真实世界的方法,而且他以一种使他的观念被教会接受的方式这样做。再次在一部关于植物的著作中,麦格努斯写道:-
在研究自然时,我们不必探究造物主上帝如何可能如他自由意志所愿,利用他的造物来施行奇迹,从而彰显他的力量:我们更应探究自然及其内在原因能自然地产生什么。
这些引文表明,尽管他在收集和传播早期科学家思想方面做了大量有价值的工作,通过他众多而广泛的著作,他也看到了通过实验进行新研究的价值。然而,并非每个人都高度评价麦格努斯。罗吉尔·培根是同时代人,在许多方面是麦格努斯的竞争对手,他高度批评(尽管可以感觉到他是在攻击一个他认为不配获得比他更多成就的人)。罗吉尔·培根写道,麦格努斯:-
……是一个极有耐心的人,积累了麦格努斯的资料,但他的著作有四个缺点。第一是无限而幼稚的虚荣;第二是难以言喻的虚假;第三是篇幅冗赘;第四是他对哲学中最有用、最美好的部分一无所知。
必须明白,罗吉尔·培根本人比麦格努斯更坚决地拥护实验科学,但他虽然是个虔诚的基督徒,却与麦格努斯不同,逾越了教会可能接受的范围。罗吉尔·培根也正确地看出麦格努斯著作中的错误,因为罗吉尔·培根对科学的理解比麦格努斯更深。
1248年,麦格努斯离开巴黎,建立新的Studium Generale,这实质上是一所位于科隆的多明我会大学。他从建立该机构起至1254年担任Studium Generale的摄政,在此期间他讲课、撰写重要著作,并与他的学生托马斯·阿奎那密切合作,后者被任命为学生导师(至少直到1252年阿奎那返回巴黎)。1254年,麦格努斯成为条顿尼亚(德国)多明我会省会的会长。他现在有沉重的行政负担,但仍抽出时间继续他的科学工作。然而,希望花更多时间在科学工作上,他于1257年辞去省会长职务,返回科隆。
1260年,他被任命为拉蒂斯邦主教,尽管多明我会会长亨伯特·德·罗曼尼斯努力将麦格努斯留在修会内。两年后,他辞去主教职务,回到科隆的Studium Generale担任教授。1274年,教皇格里高利十世要求麦格努斯参加第二次里昂会议。在这次罗马天主教会议上,麦格努斯全面参与了关于教义、管理、纪律和其他事项的讨论。托马斯·阿奎那于1274年去世(实际上是在前往里昂会议的路上),三年后,教会内的某些派别试图谴责他的教导,理由是他对非基督教哲学家(阿拉伯和希腊的)过于好感。此时麦格努斯已是老人,但他前往巴黎为托马斯·阿奎那辩护,后者的思想当然虽与自己的不完全相同,但在支持亚里士多德的教导方面是相似的。
然而我们应当注意,麦格努斯并未把亚里士多德的著作视为绝对且必然正确。他说:——
在Summa theologiae中,他主张将亚里士多德的教导与基督教思想调和,但仍用一章来讨论他所谓的“亚里士多德的错误”。
麦格努斯对数学的贡献如何?在[6]中,Anthony Lo Bello给出了:——
……一篇英文译文,附有数学与哲学注释,内容为麦格努斯对欧几里得《几何原本》所作评注的三个部分:(1) 序言,(2) “角是一种量吗?”这一问题,以及 (3) 第一卷命题11。
在[7]中,J E Hofmann考察了维也纳多明我会图书馆的一份手稿,其中包含麦格努斯用拉丁文对欧几里得的Elements第一卷至第四卷的处理。该文本表明,麦格努斯熟悉波爱修斯和巴斯的巴斯的阿德拉德从阿拉伯文翻译的欧几里得的Elements拉丁译本。既然麦格努斯显然没有读过诺瓦拉的坎帕努斯的译本,那么考虑到麦格努斯的学术范围,人们可以合理地假定麦格努斯撰写其对欧几里得的评注早于诺瓦拉的坎帕努斯的评注。
在Super Dionysii epistulasⓉ(《论狄奥尼修斯的书信》)中,麦格努斯考察了“恒星天球”的运动,目的是确定拿撒勒的耶稣受难时的日食是自然的还是奇迹的。他追溯太阳和月亮位置的方法很有趣。麦格努斯所使用的方法在[9]中得到了详细考察。
在他的其他著作中,有De natura locorum(论场所的性质),这是一部地理学著作,其中麦格努斯提供了关于地点和特征的数据,并强调了地理学在理解世界中的重要性。
尽管麦格努斯在1277年能够为托马斯·阿奎那进行有说服力的辩护,但到了第二年,他的记忆力开始衰退。在接下来的三年里,他的精神和身体都迅速衰退。
麦格努斯于1931年12月16日被册封为圣徒并被宣布为教会的圣师,他的纪念日是每年的11月15日。1941年,教皇庇护十二世册封麦格努斯为自然科学家的主保圣人。
Albert (or Albertus) was born into the wealthy Bavarian family of the Count of Bollstädt, being the eldest son in the family. He was later given the name "Magnus" (The Great) and also "Doctor Universalis" to indicate the esteem that he was held in by his contemporaries. He spent his early years in Lauingen and must have been educated at home or at a school close to his home. His uncle lived in Padua so, since the university there was famous for liberal arts, it was a natural place for his studies. After studying liberal arts at the University of Padua he joined the Dominican Order at Padua in 1223 being attracted by the teachings of Jordan of Saxony who was the head of the Order. This meant that he was not tied to a parish or a monastery, so could study and teach over a wide area.
After joining the Dominican Order, he studied and taught at Padua, Bologna, Cologne and other German convents in Hildesheim, Freiburg, Ratisbon, Strasbourg, and Cologne. He was sent to the Dominican convent of Saint-Jacques at the University of Paris in about 1241 where he read the new translations, with commentaries, of the Arabic and Greek texts of Aristotle. This was a period when the writings of Arabic scholars, and through them the texts of ancient Greek philosophers, was becoming known throughout Christian Europe and it was having to come to terms with this new knowledge. Albertus would play a major role in accepting this new learning into Europe with his wide ranging scholarship over essentially the whole of knowledge.
He taught for four years at Saint-Jacques, giving courses on the Bible and on the theological textbook The Book of the Sentences which had been written by Peter Lombard. In 1245 he received the degree of Master of Theology from the University of Paris and, after receiving this degree, one of the first students he taught was Thomas Aquinas. While in Paris Albertus began the task of presenting the entire body of knowledge, natural science, logic, rhetoric, mathematics, astronomy, ethics, economics, politics and metaphysics. He wrote commentaries on the Bible, Peter Lombard's Book of the Sentences, and all of Aristotle's works. These commentaries contained his own observations and experiments. By 'experiment' Albertus meant 'observing, describing and classifying'. For example, in De Mineralibus Ⓣ Albertus wrote:-
The aim of natural science is not simply to accept the statements of others, but to investigate the causes that are at work in nature.
We should not underestimate the importance of such ideas, for most scholars at that time believed that knowledge could only be obtained from a study of the scriptures. In the 13th century few were prepared to even consider the possibility of scientific research, and most considered that knowledge all came from God through ancient divinely inspired writings. Not only did Albertus advocate what we would call today the scientific approach to studying the real world, but he did so in such a way that his ideas were accepted by the Church. Again in a work on plants Albertus wrote:-
In studying nature we have not to inquire how God the Creator may, as He freely wills, use His creatures to work miracles and thereby show forth His power: we have rather to inquire what Nature with its immanent causes can naturally bring to pass.
These quotes show that, although he did an immense amount of valuable work in collecting and propagating the ideas of earlier scientists in his numerous and wide ranging writings, he also saw the value of new research by experiment. Not everyone held Albertus in high esteem, however. Bacon, who was a contemporary, and in many ways a rival of Albertus, was highly critical (although one can sense that he is attacking someone whom he considers to have undeservedly achieved more than he has). Bacon writes that Albertus:-
... is a man of infinite patience and has amassed great information, but his works have four faults. The first is boundless, puerile vanity; the second in ineffable falsity; the third is superfluity of bulk; and the fourth is his ignorance of the most useful and the most beautiful parts of philosophy.
One has to understand that Bacon was himself an even stronger advocate of experimental science than was Albertus but, although himself a devote Christian, unlike Albertus he overstepped what the Church might accept. Bacon was also correct to see errors in Albertus's writings for Bacon had a deeper understanding of science than had Albertus.
In 1248 Albertus left Paris to set up the new Studium Generale which was essentially a Dominican university in Cologne. He was Regent of the Studium Generale from the time that he set it up until 1254 and during this time he lectured, wrote important works, and worked closely with his student Thomas Aquinas who was appointed Master of Students (at least until 1252 when Aquinas returned to Paris). In 1254 Albertus became superior of the Dominican province of Teutonia (Germany). He now had a heavy administrative load but still found time to continue his scientific work. However, wishing to spend still more time on scientific work, he resigned from his role of Provincial in 1257 and returned to Cologne.
In 1260 he was appointed Bishop of Ratisbon despite the efforts of Humbert de Romanis, the Head of the Dominican Order, to keep Magnus within the Order. After two years he resigned as bishop and returned to his position as professor at the Studium Generale in Cologne. In 1274 Pope Gregory X required Albertus to attend the Second Council of Lyon. At this Roman Catholic Council Albertus took a full part in discussing questions of doctrine, administration, discipline, and other matters. Thomas Aquinas died in 1274 (actually on his way to the Council in Lyon) and three years later certain factions within the Church tried to condemn his teachings on the grounds that he was too favourably disposed to non-Christian philosophers, both Arabic and Greek. By this time Albertus was an old man, but he travelled to Paris to argue in favour of Thomas Aquinas, whose ideas of course, although not identical to his own, were similar in their support for the teachings of Aristotle.
We should note, however, that Albertus did not treat Aristotle's writings as absolutely and necessarily correct. He stated:-
Whoever believes that Aristotle was a god, must also believe that he never erred. But if one believes that Aristotle was a man, then doubtless he was liable to error just as we are.
In Summa theologiae he argues for reconciling the teachings of Aristotle with Christian thinking, but nevertheless, devotes a chapter to what he calls "the errors of Aristotle".
What of Albertus's contributions to mathematics? In [6] Anthony Lo Bello gives:-
... an English translation, with mathematical and philosophical notes, of three sections of the commentary by Albertus Magnus on Euclid's Elements : (1) the prologue, (2) the question "Is an angle a quantity?" and (3) Book I, Proposition 11.
In [7] J E Hofmann examines a manuscript in the Dominikaner-Bibliothek Vienna which contains a treatment of the books I to IV of Euclid's Elements in Latin by Albertus. The text shows that Albertus was familiar with the Latin translations from Arabic of Euclid's Elements by Boethius and Adelard of Bath. Since Albertus has clearly not read the translation by Campanus then, given the range of Albertus's scholarship, one can reasonably assume that Albertus wrote his commentary on Euclid before that of Campanus.
In Super Dionysii epistulas Ⓣ Albertus considers the motion of the "Sphere of Stars" with the aim of determining whether the eclipse at the crucifixion of Jesus of Nazareth was natural or miraculous. His methods of tracing back the positions of the sun and moon is interesting. The methods used by Albertus are examined in detail in [9].
Among his other works is De natura locorum (on the nature of places) which is a work on geography in which Albertus presents data on locations and features and emphasises the importance of geography in understanding the world.
Although Albertus was able to argue convincingly for Thomas Aquinas in 1277, by the following year his memory was beginning to fail him. Over the next three years he rapidly declined both mentally and physically
Albertus was made a Saint and declared a Holy Doctor of the Church on 16 December 1931 and his feast day is 15 November in each year. In 1941 Albertus was made patron of natural scientists by Pope Pius XII.
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