阿尔贝特Albertus de Saxonia

阿尔贝特以几个不同的名字为人所知。其他版本包括赫尔姆施泰特的亚伯拉罕·阿德里安·艾伯特、里克斯多夫的艾伯特以及绰号Albertucius，意为“小艾伯特”，以区别于大艾伯特。我们所知的第一个确切日期是艾伯特于1351年3月在巴黎大学获得文学硕士学位。这仍然给他的出生日期留下了相当宽泛的可能范围，大多数学者认为他一定出生于1316年至1320年之间。相当确定的是，艾伯特在赫尔姆施泰特地区长大，在巴黎学习之前，他访问了许多其他地方。据信他访问过埃尔福特，也许还有哈尔伯施塔特和马格德堡。他从1351年到1362年在巴黎任教，从1353年6月开始担任校长一职，任期六个月。

巴黎大学的校长是教学的首脑；这是一个经选举产生的短期职位。此时的大学分为四个同乡会：法兰西同乡会面向来自包括法国（北部除外）、西班牙和意大利地区的学生；英格兰同乡会涵盖英格兰、苏格兰和德国；诺曼同乡会涵盖法国北部一小块诺曼地区；皮卡第同乡会涵盖诺曼地区以东的一块区域。尽管此时被称为英格兰同乡会，但该同乡会的大多数学生来自苏格兰或德国（事实上，它的名字后来改为德国同乡会）。艾伯特出生于下阿尔贝特，属于英格兰同乡会：事实上，他在1352年至1362年间多次代表英格兰同乡会。1358年，他带领英格兰同乡会与皮卡第同乡会就两个同乡会之间的边界位置进行谈判。

在1352年至1362年这十年间，艾伯特在巴黎任教，讲授亚里士多德的Physics以及其他自然哲学著作。他受到著名同事让·布里丹（约1300年—1358年后）的影响。布里丹在艾伯特在巴黎大学的前半段时间里教授自然哲学和逻辑学。艾伯特似乎在这些年里学习了神学，在索邦大学听课，但从未获得该学科的学位。他于1362年11月离开巴黎，被任命为美因茨大教堂的受俸牧师。这个职位使艾伯特从大教堂的产业中获得收入。1363年7月访问阿维尼翁时，他会见了奥地利公爵鲁道夫四世，似乎作为大使承担了与公爵的外交角色。1364年4月和5月，他随公爵访问布拉格，同年9月，他作为奥地利大使回到阿维尼翁，试图说服教皇乌尔班五世同意创建维也纳大学。他的使命只取得了部分成功，因为尽管教皇乌尔班五世同意创建大学，但他不同意创建神学院，因为这将与1347年创建的布拉格查理大学形成竞争。然而，艾伯特确实获得了教皇诏书，以建立文学院、法学院和医学院。

维也纳大学由鲁道夫四世和他的两个兄弟于1365年3月12日创建，但鲁道夫几个月后于7月去世。艾伯特留下来组织大学的建立，他做到了，文学院仿照巴黎模式。他像巴黎一样设立了四个同乡会：奥地利、波希米亚、阿尔贝特和匈牙利。他成为大学的第一任校长，为教职员工和学生赢得了某些特权，如免税和免服兵役。大学有自己的着装规范，其成员受大学法律而非国家法律约束，这些法律由校长执行。艾伯特担任这一职位的时间不长，因为1366年10月21日，他被任命为哈尔伯施塔特主教，并于次年2月就职。到他离开维也纳时，大学的文学院是唯一已经建立的学院。

也许有人会认为，被任命为哈尔伯施塔特主教意味着从此他的人生将转向精神事务，但恰恰相反，此时它转向了政治。1367年，艾伯特与不伦瑞克-吕讷堡公爵马格努斯、马格德堡大主教迪特里希、安哈尔特亲王瓦尔德马等人一起，参与了对希尔德斯海姆主教贝格的格哈德的征讨。1367年9月3日，他们在希尔德斯海姆附近的丁克拉尔的一场战斗中战败。这次军事行动失败后，艾伯特努力促成地区和平联盟。教皇乌尔班五世于1370年去世，由教皇格列高利十一世继任，他是最后一位阿维尼翁教皇。教皇格列高利十一世对异端采取强硬措施，尤其是在德国，他于1372年联系德国宗教裁判官，要求他们调查对艾伯特提出的决定论指控（即认为人没有自由意志，因此不对自己的行为负责）。然而，没有对艾伯特提出任何指控，他一直担任哈尔伯施塔特主教，直到1390年去世。

这本传记的读者现在可能会想，为什么艾伯特会被收录在这个档案中，因为除了提到他在巴黎期间教授自然哲学外，我们还没有提到任何其他数学专长。事实上，艾伯特主要是优秀数学思想的传播者，但他本人也对其中许多思想做出了大量贡献。他撰写了关于托马斯·布拉德华、奥卡姆的威廉、尼克尔·奥里斯姆等人思想的著作。他总共出版了大约30部文本，大多是在巴黎任教期间完成的，其中许多是对亚里士多德著作的评注。[5]的作者写道：-

……艾伯特是一位相当独立的思想家，有时会综合前人的理论（尤其是布里丹、尼克尔·奥里斯姆以及英国和巴黎大师们的理论），或者选择以教学方式呈现问题。

他的逻辑学著作最为出色，尤其是他考察逻辑悖论的时候。他在这一领域的三大主要著作是Questiones logicalesⓉ（逻辑探究）、Perutilis LogicaⓉ（实用逻辑）和SophismtaⓉ（诡辩术）。Perutilis LogicaⓉ（逻辑探究）是一部逻辑手册，由六个部分组成：命题；词项的性质；命题的类型；推论与三段论；谬误；以及不可解命题与义务。尽管这部著作显示出奥卡姆的威廉和布里丹的影响，但必须始终强调，艾伯特是一位原创思想家，在许多地方提出了与这两位学者都相当不同的思想。让我们举一个他对悖论贡献的例子。让·布里丹曾制造了一个逻辑谬误，他制作了一页纸，上面只写了这样一句话：“这页纸上的所有陈述都是假的。”许多人认为这个悖论是自指的结果，但艾伯特表明情况并非如此。他给出了以下没有自指的例子：“下面这句话是真的。上面那句话是假的。”他还指出，这可以轻易扩展到任意数量的句子。

他的自然哲学著作主要包含在他对亚里士多德的Physica、对De Caelo、对De generatione、对De Anima、对Meteora、对Parva Naturalia以及对约翰尼斯·德·萨克罗博斯科的De Sphaera的评注中。艾伯特还写了一部自己的著作，即Tractatus proportionum。他关于抛射体的著作，正如当时所有著作一样，是错误的。艾伯特认为，水平发射的抛射体会水平飞行一段距离，然后沿曲线路径飞行一段时间，最后垂直下落。在这三个阶段中的第一阶段，物体靠自身的冲力运动；在第二阶段，重力开始起作用；在最后阶段，由于冲力已经耗尽，只有重力在起作用。这也许相当错误，但至少比更早的理论更接近抛射体的实际路径。他喜欢做思想实验。例如，他考虑如果在地球上打一个洞并让一块石头掉下去会发生什么。他得出结论，石头会穿过地球中心，然后朝中心落回，围绕中心继续振荡，振荡幅度逐渐减小，直到石头中的冲力耗尽。在考察他的抛射体理论时，有趣的是他还声称，空气可以像水支撑船只一样支撑一台构造合理的机器。尽管他没有主张地球绕太阳运动，但他至少表明，那些被提出来证明地球必定静止的论据是谬误的。当然，艾伯特相信许多现象可以用数学来解释，他用自己的动力学理论试图解释地震、潮汐和地质学等自然现象。皮埃尔·杜埃姆写道[9]：-

地球与海洋的平衡是艾伯特所钟爱的一个理论的主题。当整个陆地元素的重心与世界的中心重合时，它就处于平衡状态。此外，陆地物质并非处处具有相同的密度，因此其重心并不与其形状的中心重合。这样，地球最轻的部分比最重的部分离地球的重心更远。河流造成的侵蚀不断将陆地颗粒从大陆带入海洋的怀抱。这种侵蚀，通过挖出山谷，塑造了山脉，不断移动陆地物质的重心，而这一物质处于运动之中，以使地球的重心回到其形状的中心。通过这种运动，地球被淹没的部分不断向上推挤露出的部分，而露出的部分不断被侵蚀，随后又被淹没的部分所取代。在十六世纪初，艾伯特的这一理论强烈吸引了列奥纳多·达·芬奇的注意，正是为了证实它，他致力于对化石的众多观察。此外，阿尔贝特将岁差归因于陆地元素类似的非常缓慢的运动。

艾伯特在物理学方面的工作使他产生了一个相当精妙的数学极限概念。这发生在他考虑一个困扰学者们数个世纪的问题时，即苏格拉底所能承载的最大重量是否存在。他论证说，对于任何小于这个最大重量的重量，必定存在一个苏格拉底也能承载的更大重量。

最后让我们注意到，他还写了道德哲学方面的著作，例如对亚里士多德的Nicomachean Ethics和对他自己的Oeconomica的评注。

艾伯特对后来学者的影响由Joél Biard描述[6]：-

阿尔贝特关于逻辑和形而上学的教导极具影响力。尽管布里丹仍然是逻辑学中的主要人物，但艾伯特的《Perutilis logica》注定要成为一部流行的教材，因为它具有系统性的特点，也因为它采纳并发展了奥卡姆立场的重要方面。但尤其被广泛阅读的是他对亚里士多德《物理学》的评注。其许多手稿可以在法国和意大利，在埃尔福特和布拉格找到。多亏了阿尔贝特，中世纪后期在巴黎物理学和宇宙学中提出的许多新思想在中欧传播开来。

Albert of Saxony is known under several different names. Others versions include Albert of Helmstedt, Albert of Rickmersdorf and the nickname Albertucius, meaning 'little Albert', to distinguish him from Albert the Great. The first definite date that we know is Albert's degree of Master of Arts from the University of Paris in March 1351. This still leaves a fairly wide range of possible dates for his birth, with most scholars arguing that he must have been born between 1316 and 1320. It is fairly certain that Albert grew up in the Helmstedt district and, before studying in Paris, he visited a number of other places. It is believed that he visited Erfurt and perhaps Halberstadt and Magdeburg. He taught at Paris from 1351 to 1362 becoming rector there for a term of six months beginning in June 1353.

The rector of the University of Paris was head the teaching; it was an elected position of short duration. The University at this time was divided into four Nations: the French Nation was for students from a region including France (except the North), Spain and Italy; the English Nation covered England, Scotland and Germany; the Norman Nation covered a small Norman region in the North of France; and the Piccardian Nation covered a region to the east of the Norman one. Despite being called the English Nation at this time, most of the students in this Nation were from Scotland or Germany (in fact its name was later changed to the German Nation). Albert, being born in Lower Saxony, was in the English Nation: in fact he represented the English Nation on a number of occasions between 1352 and 1362. In 1358 he led the English Nation in negotiating with the Piccardian Nation the concerning the position of the border between the two Nations.

During the ten years, 1352-62, that Albert spent teaching in Paris he lectured on Aristotle's Physics and other works on natural philosophy. He was influenced by his famous colleague Jean Buridan (about 1300- after 1358). Buridan taught natural philosophy and logic at the University of Paris during the first half of Albert's time there. Albert seems to have studied theology during these years, taking courses at the Sorbonne, but never took a degree in the subject. He left Paris in November 1362 being named prebend of the cathedral in Mainz. This position gave Albert an income from the cathedral estates. While visiting Avignon in July 1363 he met with Rudolf IV, Duke of Austria, and seems to have taken on a diplomatic role with the Duke as an ambassador. He was with the Duke on a visit to Prague in April and May of 1364 and in September of the same year, he went back to Avignon as Austrian ambassador to try to persuade Pope Urban V to agree to the founding of the University of Vienna. He was only partially successful in his mission for, although Pope Urban V agreed to the founding of the University, he did not agree to the founding of a Theology Faculty since this would have provided competition with the Charles University of Prague which had been founded in 1347. However, Albert did secure a papal bull to establish the faculties of Arts, Law and Medicine.

The University of Vienna was founded by Rudolf IV and his two brothers on 12 March 1365 but Rudolf died a few months later in July. Albert was left to organise the setting up of the University which he did, modelling the Arts Faculty on the Paris model. He set up, like Paris, four Nations: Austria, Bohemia, Saxony and Hungary. He became the first rector of the University having won certain privileges for the staff and students such as exemption from taxes and military service. The University had its own dress code and its members were subject to University laws, rather than those of the state, which were carried out by the rector. Albert did not hold this position for very long for, on 21 October 1366, he was appointed Bishop of Halberstadt, taking up this appointment in February of the following year. By the time he left Vienna, the Arts Faculty of the University was the only Faculty which had been set up.

Perhaps one might think that an appointment as Bishop of Halberstadt would mean that from then on his life was directed towards spiritual matters but, rather the contrary, it now became directed towards politics. In 1367 Albert joined Magnus the Duke of Brunswick-Lüneburg, Dietrich the Archbishop of Magdeburg, Valdemar the Prince of Anhalt, and others in a campaign against Gerhard of Berg the Bishop of Hildesheim. They were defeated in a battle at Dinklar, near Hildesheim, on 3 September 1367. After this unsuccessful military venture, Albert worked hard to form regional peace alliances. Pope Urban V died in 1370 and was succeeded by Pope Gregory XI, the last of the Avignon popes. Pope Gregory XI took vigorous measures against heresies, particularly in Germany, and he contacted the German Inquisitors in 1372 asking that they investigate a charge of determinism (a belief that man has no free will and therefore is not responsible for his actions) which had been made against Albert. No charges were brought against Albert, however, who remained as Bishop of Halberstadt until his death in 1390.

The reader of this biography might well be wondering by now why Albert is included in this archive for, except for mentioning that he taught natural philosophy while in Paris, we have not mentioned any other mathematical expertise. In fact Albert was mainly a transmitter of good mathematical ideas but he did contribute a great deal of his own to these. He wrote about the ideas of Bradwardine, Ockham, Oresme and others. In all he published around 30 texts, mostly produced during his years teaching in Paris, many of these being commentaries on the works of Aristotle. The authors of [5] write:-

... Albert was quite an independent thinker who sometimes combined the theories of his predecessors (especially those of Buridan, Oresme, and the English and Parisian masters) or chose to present problems in a didactic manner.

His books on logic are his best, particularly when he examined logical paradoxes. His three main works in this area are Questiones logicales Ⓣ, Perutilis Logica Ⓣ and Sophismta Ⓣ. The Perutilis Logica Ⓣ is a logic handbook consisting of six parts: Propositions; Properties of Terms; Type of Propositions; Consequences and Syllogisms; Fallacies; and Insolubles and Obligations. Although the work shows influences from Ockham and Buridan but one must always stress that Albert was an original thinker and in many places proposes ideas which are quite different from those of either of these two scholars. Let us give one example of his contributions to paradoxes. Jean Buridan had produced a logical fallacy by producing a folio on which the only words written were "All statements on this folio are false." Many argued that the paradox was the result of self-reference but Albert showed that this was not the case. He gave the following example where there was no self-reference: "The following sentence is true. The previous sentence is false." He also states that this can easily be extended to any number of sentences.

His work on natural philosophy is mostly contained in his commentaries on Aristotle's Physica, on his De Caelo, on his De generatione, on his De Anima, on his Meteora, on his Parva Naturalia, and on Sacrobosco's De Sphaera. Albert also wrote a work of his own, the Tractatus proportionum. His work on projectiles is, as all work was at that time, incorrect. Albert believed that a projectile fired horizontally will travel horizontally for a certain distance, then follow a curved path for a while, then fall vertically. During the first of these three phases the body moved by its own impetus, during the second phase gravity began to take effect, and in the final stage gravity only acted since impetus had died. This may be quite false but at least it approximates the path of a projectile more closely than do earlier theories. He was fond of making thought experiments. For example, he considered what would happen if a hole could be made though the Earth and a stone dropped down it. He concluded that the stone would pass the centre of the Earth then fall back towards the centre, continuing to oscillate about the centre in decreasing oscillations until the impetus in the stone was exhausted. While looking at his theory of projectiles, it is interesting to note that he also claimed that air could support a reasonably constructed machine in the same way as water can support a ship. Although not advocating that the Earth moved round the sun, he did at least show that the arguments that he been put forward to prove that the Earth must be stationary were fallacious. Certainly Albert believed that much could be explained by mathematics and he used his dynamical theory to attempt to explain natural phenomena such as earthquakes, tides and geology. Pierre Duhem writes [9]:-

The equilibrium of the earth and seas is the subject of a favourite theory of Albert's. The entire terrestrial element is in equilibrium when its centre of gravity coincides with the centre of the world. Moreover, the terrestrial mass has not everywhere the same density, so that its centre of gravity does not coincide with the centre of its figure. Thus the lightest part of the earth is more distant from the centre of gravity of the earth than the heaviest part. The erosion produced by rivers constantly draws terrestrial particles from the continents to the bosom of the sea. This erosion, which, by scooping out the valleys, has shaped the mountains, constantly displaces the centre of gravity of the terrestrial mass, and this mass is in motion to bring back the centre of gravity of the earth to the centre of its figure. Through this motion the submerged portions of the earth constantly push upwards the emerged parts, which are incessantly being eaten away and afterwards replaced by the submerged parts. At the beginning of the sixteenth century this theory of Albert's strongly attracted the attention of Leonardo da Vinci, and it was to confirm it that he devoted himself to numerous observations of fossils. Albert of Saxony, moreover, ascribed the precession of the equinoxes to the similar very slow movement of the terrestrial element.

Albert's work on physics led him to a quite sophisticated idea of a mathematical limit. This occurs when he considered the question, which had worried scholars for centuries, of whether there is a maximum weight that Socrates can carry. He argued that for any weight less than this maximum weight, there must be a greater weight that Socrates could also carry.

Finally let us note that he also wrote works on moral philosophy such as commentaries on Aristotle's Nicomachean Ethics and on his Oeconomica.

Albert's influence on later scholars is described by Joél Biard [6]:-

Albert of Saxony's teachings on logic and metaphysics were extremely influential. Although Buridan remained the predominant figure in logic, Albert's 'Perutilis logica' was destined to serve as a popular text because of its systematic nature and also because it takes up and develops essential aspects of the Ockhamist position. But it was his commentary on Aristotle's 'Physics' that was especially widely read. Many manuscripts of it can be found in France and Italy, in Erfurt and Prague. Thanks to Albert of Saxony, many new ideas raised in Parisian physics and cosmology in the later Middle Ages became widespread in Central Europe.