威廉·休厄尔William Whewell

威廉·休厄尔的父母是John Whewell，一位木匠大师，和Elizabeth Bennison。这是一个大家庭，休厄尔是父母七个孩子中的长子。他就读于兰开斯特的蓝学校，他的父亲打算让他从那里继续成为木匠学徒。然而，兰开斯特文法学校校长兼教区牧师Revd Joseph Rowley认识到了休厄尔的才能，并为他提供了在兰开斯特文法学校的免费教育。几年后，他说服弗瑞兹·约翰让休厄尔就读于威斯特摩兰的Heversham文法学校，该学校位于他家乡以北约20公里处，在那里他将接受指导，以便竞争剑桥大学三一学院的奖学金。1810年，休厄尔去了Heversham，在那里度过了两年。他还从肯德尔的盲人数学家约翰 Gough那里接受了一些私人数学辅导，在：-

……圆锥曲线、流数术和力学。

他赢得了三一学院的一个展览奖学金，但这不足以支持他的学业，因此通过私人订阅筹集了进一步支持他的资金。

休厄尔于1812年10月进入剑桥，但此时家庭已经遭受了一系列悲剧，他的母亲于1807年去世，他的三个弟弟在休厄尔开始大学学习之前去世。他自己的健康状况一直不佳，但在剑桥开始学习一个月后，他写信给他的父亲：-

我离开兰开斯特以来身体一直很好。

他的母亲曾是一位诗人，在当地报纸上发表过诗作，休厄尔一定继承了他母亲的诗歌天赋，因为1814年，他凭借一首题为Boadicea的史诗赢得了校长奖。他开始融入大学生活，尽管鉴于他的背景，这并不容易。他在1815年将自己的社交活动描述为[1]：-

……射燕子，成群结队地洗澡，航行到切斯特顿，在乡村集市上跳舞，打台球，把烧杯变成音乐玻璃杯，制作火箭，成群骑马外出……

他还在数学荣誉学位考试中表现出色，于1816年1月以第二名数学荣誉学位考试一等及格者（Wrangler）毕业，随后成为第二名史密斯奖获得者。这是休厄尔第一次没有在班级中取得第一名，但他坦然接受，在给家人的信中解释说，他写得不够快。1816年7月，他的父亲在他毕业前去世。1817年10月，他被选为三一学院的 fellowship，并写信给他的姐妹们说，他收到了[1]：-

……你曾与我一同欢庆的最实质性的好处。它确保了我一生舒适的地位，至少只要我的生活简单。

在这个阶段，我们应该注意到，休厄尔在剑桥大学本科期间结交了许多顶尖学者，包括约翰·赫歇尔、查尔斯·巴贝奇、乔治·皮科克以及分析学会的其他成员。休厄尔于1818年被任命为剑桥大学的数学讲师和助理导师。他是1819年剑桥哲学学会的创始成员之一。

在剑桥仍在接受欧洲大陆优越数学方法的时代，休厄尔通过他的教科书An Elementary Treatise on Mechanics（1819年）和A Treatise on Dynamics（1823年）在现代化他们的方法方面发挥了重要作用。他1819年的文本是第一部采用欧洲大陆数学符号的英语应用数学著作，而他的第二部著作是一部使用法国分析技巧的优美文本。他的成就很快得到认可，于1820年当选为伦敦皇家学会。此时他正在与年轻的剑桥人如奥古斯塔斯·德摩根和威廉·哈密顿交朋友。尽管他在上述两部著作的第一版中表现出对法国分析方法的极大热情，但我们应该说，多年来休厄尔开始担心缺乏几何方法会损害学生的直觉理解，因此他减少了分析工具，在后来版本的书中增加了几何方法。他还出版了The Mechanical Euclid, containing the Elements of Mechanics and Hydrostatics demonstrated after the Manner of the Elements of Geometry （1837年），其中他采用了完全几何的方法。

直到19世纪20年代中期，休厄尔一直教授、写作和研究数学。然而，这种情况发生了变化，他转向更广泛的科学兴趣，出版了诸如Essay on Mineralogical Classification and Nomenclature（1828年）、Architectural Notes on German Churches, with Remarks on the Origin of Gothic Architecture （1830年）、Astronomy and General Physics（1833年）、History of the Inductive Sciences（3卷）（1837年）和The Philosophy of the Inductive Sciences（2卷）（1840年）等书籍。正如人们所料，这导致他在剑桥的角色发生变化，他于1828年被任命为矿物学教授，然后于1838年被任命为道德哲学教授。1841年6月，他与Cordelia Marshall订婚，他们于1841年10月12日在Cumberland结婚。五天后，休厄尔收到首相Robert Peel爵士的一封信，说女王已接受他的推荐，任命休厄尔为三一学院院长。他于1842年和1855年担任剑桥大学副校长，那一年他的妻子Cordelia去世。

休厄尔的贡献之广列于[3]中：-

除了在教育改革中的作用外，休厄尔还证明自己是一位热忱而多产的研究者。他在实验物理学、晶体学、矿物学、物理天文学、科学教育、建筑学、诗歌和宗教方面发表了重要著作，此外还有数量多得令人眼花缭乱的更通俗的评论、讲座和布道。他是自记风速计的发明者，也是许多新科学术语的创造者，包括“ion”“cathode”“Eocene”“Miocene”“physicist”和“scientist”。

事实上，其中许多词是由休厄尔应朋友之请创造的，例如“anode”、“cathode”和“ion”这些术语是为麦可·法拉第创造的，而“scientist”则是应诗人皮埃尔·萨米埃尔 Taylor Coleridge之请产生的。然而，不应给人留下休厄尔远离应用数学的印象，相反，他在继续研究应用数学领域的同时，将许多其他领域纳入其广泛的兴趣范围。例如，他在1833年至1850年间发表了十四篇关于潮汐研究的重要论文。事实上，他因这项关于潮汐的杰出工作而获得了皇家学会的皇家奖章。

另一项重要贡献是他对英国协会 for the Advancement of Science的支持和为之所做的工作。他大力支持该协会于1831年成立；尽管他没有出席该协会当年在约克举行的第一次会议，但正是他建议他们征求各门科学的年度报告。他为1832年的会议撰写了矿物学报告，为1835年的会议撰写了电学和磁学报告。他在1832年牛津会议上担任英国协会副主席，1835年又在都柏林担任此职；1833年协会在剑桥开会时，他是当地秘书；后来他在1841年于普利茅斯担任主席。事实上，正是在他向1833年英国协会会议所作的演讲中，他第一次使用了“scientist”一词，并解释说他是类比“artist”创造了这个词。他后来写道[10]：-

……正如Artist是Musician、Painter或Poet，Scientist是Mathematician、Physicist或Naturalist。

请注意，休厄尔在这段引文中使用的“Physicist”一词也是他创造的。

今天休厄尔最为人所知的领域是科学哲学、科学史和道德哲学。他考察了“知识”，并声称[10]：-

……在每一次认识活动中……都有两个对立的要素，我们可以称之为观念和知觉。

他声称基本观念[10]：-

……不是经验的产物，而是心灵特定构造与活动的结果，其起源独立于一切经验，尽管在运用中始终与经验相结合。

作为基本观念的例子，他给出了时间、数、原因、实体和相似性。他写道[10]：-

没有空间的观念，我们就不能看见一个对象；没有相似或差异的观念，我们就不能看见两个对象。

他发展了一种归纳理论，试图解释物理定律是如何被发现的。他认为，除了考察定律实例的过程之外[10]：-

……正是通过将它们组合起来的思维活动本身，一个新的元素被添加到了[实例的]组合之中。

在通过归纳产生一条定律之后，休厄尔认为接下来需要一个确认阶段。他还主张一个他称之为必然真理的概念。他举了7 + 8 = 15这个真理作为例子[10]：-

……我们参照我们对七、八和加法的概念，一旦我们清晰地拥有这些概念，我们就看到和必定是15。也就是说，仅仅通过知道“七”、“八”和“加法”的含义，我们就看到“7 + 8 = 15”必然成立。

休厄尔他在科学史方面的工作是科学哲学工作不可分割的一部分，两者都对知识有所贡献。他感到科学史极其重要[10]：-

……当今一代发现自己是一笔巨大科学遗产的继承人；我们必须关心这些财产是通过哪些步骤获得的，以及通过哪些文献它们被确保为我们和我们的后代永远所有。

休厄尔晚年的生活充满悲伤。他的妻子科迪莉亚在长期患病后于1855年12月18日去世。随后，他于1858年7月1日与吉尔伯特·阿弗莱克爵士的遗孀埃弗琳娜·弗朗西丝·阿弗莱克夫人结婚。她于1865年4月1日去世。1866年2月24日，休厄尔在剑桥郊外骑马时，因马匹受惊而坠落。他被用马车送回三一学院，但发现已瘫痪。他于3月6日在三一学院的房间内去世，最后的请求是拉开窗帘，以便他能最后一次眺望三一学院的大庭院。

关于他的性格，莱斯利·斯蒂芬在其1899年的传记中写道[24]：-

他喜欢争论，而作为小圈子里的伟人，他的地位往往使争论变得片面。他作为导师很受欢迎；但有一段时间，他作为院长招致了不少敌意。早年他几乎没有机会获得社交上的优雅；尽管他渴望好客，但他对自己地位尊严的意识导致了一种拘谨，使得院长住所的客厅绝不是一个轻松社交的场所。晚年，年龄和悲伤使他明显变得温和，不仅成为大学的骄傲，也成为大学热爱的对象。尽管有时粗鲁，但他从一开始就宽宏大量；他从不怀恨在心，坦率承认失败，并以非凡的礼貌接受年轻和微不足道的人的意见。也很少有人拥有更多的朋友或更小心地保持友谊。他有许多争论，但没有个人恩怨。

在如此多不同领域取得如此多成就，显然我们在本文中未能提及他贡献的许多重要方面。也许我们应该提到最后一个至今未提及的事实，即他作为牧师的角色。他于1825年三一主日被任命为牧师，这是三一学院会士的要求，次年被任命为执事。他定期在大学布道，特别是他在1837年布道了四次On the Foundation of Morals，并于当年出版。十年后，他出版了Sermons preached in the Chapel of Trinity College, Cambridge，其中包含他的二十二篇布道。

让我们引用他多年的朋友约翰·赫歇尔的话来结束这篇休厄尔的传记[3]：-

……在人类探究的几乎每一个领域，如此奇妙多样的知识量，或许从未有人在同样的时间间隔内积累过。

William Whewell's parents were John Whewell, a master carpenter, and Elizabeth Bennison. It was a large family, and William was the eldest of his parents' seven children. He attended Blue School in Lancaster and his father intended that his son should proceed from there to become an apprentice carpenter. However, the Revd Joseph Rowley, headmaster of Lancaster grammar school and the parish priest, recognised William's talents and offered free education for him at Lancaster grammar school. Several years later he persuaded John to let William attend Heversham Grammar School in Westmorland, about 20 kilometres north of his native town, where he would receive instruction to allow him to compete for a scholarship at Trinity College, Cambridge. In 1810 William went to Heversham where he spent two years. He also received some private coaching in mathematics from John Gough, a blind mathematician from Kendal, in:-

... conic sections, fluxions, and mechanics.

He won an exhibition to Trinity College, but this was not sufficient to support him during his studies so further funds to support him were raised by private subscription.

Whewell entered Cambridge in October 1812, but by this time the family had suffered a series of tragedies with his mother dying in 1807 and three of his younger brothers dying before William began his university studies. His own health had been poor but a month after starting his studies at Cambridge he wrote to his father:-

I have enjoyed very good health since I left Lancaster.

His mother had been a poet who had published poems in local papers and Whewell must have inherited his mother's poetic gifts since, in 1814, he won the Chancellor's prize for an epic poem he wrote entitled Boadicea. He began to fit into the university life although given his background this did not come easily. He described his social activities in 1815 as [1]:-

... shooting swallows, bathing by half dozens, sailing to Chesterton, dancing at country fairs, playing billiards, turning beakers into musical glasses, making rockets, riding out in bodies ...

He also excelled in the Mathematical Tripos graduating as second wrangler in January 1816 and then becoming second Smith's Prizeman. It was the first time that Whewell had not achieved the top place in a class but he took it in good part explaining in a letter to his family that he had not been able to write quickly enough. In July 1816 his father died before his son had graduated. In October 1817 he was elected to a fellowship at Trinity and wrote to his sisters saying that he had received [1]:-

... the most substantial benefit at which you ever had to rejoice with me. It secures me a comfortable establishment for life at least so long as my life is a simple one.

We should note at this stage that Whewell had made a number of friends among top academics during his undergraduate years at Cambridge including John Herschel, Charles Babbage, George Peacock and other members of the Analytical Society. Whewell was appointed as a mathematics lecturer and assistant tutor at Cambridge in 1818. He was one of the founder members of the Cambridge Philosophical Society in 1819.

At a time when Cambridge was still finding acceptance of the superior Continental approach to mathematics, Whewell played a major role in modernising their approach with his textbooks An Elementary Treatise on Mechanics (1819) and A Treatise on Dynamics (1823). His 1819 text was the first applied mathematics work in English to adopt continental mathematical symbolism, while his second work was a beautiful text using French analytic techniques. His achievements were quickly recognised with election to the Royal Society of London in 1820. He was by now making friends with younger Cambridge men such as Augustus De Morgan and William Rowan Hamilton. Although he showed himself a great enthusiast for the French analytical methods in the first editions of the above two works, we should say that over the years Whewell became worried that the lack of geometric methods would damage students' intuitive understanding and as a result he reduced the analytical tools, increasing the geometrical methods in the later editions of his books. He also published The Mechanical Euclid, containing the Elements of Mechanics and Hydrostatics demonstrated after the Manner of the Elements of Geometry (1837) where he took a completely geometrical approach.

Up to the mid 1820s Whewell had taught, written and researched mathematics. However this changed and he moved towards broader scientific interests with publications of books such as Essay on Mineralogical Classification and Nomenclature (1828), Architectural Notes on German Churches, with Remarks on the Origin of Gothic Architecture (1830), Astronomy and General Physics (1833), History of the Inductive Sciences (3 vols.) (1837), and The Philosophy of the Inductive Sciences (2 vols.) (1840). As one might expect this led to his role changing at Cambridge and he was appointed professor of Mineralogy in 1828, then professor of Moral Philosophy in 1838. In June 1841 he became engaged to be married to Cordelia Marshall and they married on 12 October 1841 in Cumberland. Five days later Whewell received a letter from Sir Robert Peel, the prime minister, saying that the Queen had accepted his recommendation that Whewell should be appointed master of Trinity. He was Vice-Chancellor of Cambridge University in 1842 and again in 1855, the year in which his wife Cordelia died.

The breadth of Whewell's contributions are listed in [3]:-

Along with his role in educational reform, Whewell also proved a zealous and prolific researcher. He published significant works in experimental physics, crystallography, mineralogy, physical astronomy, science education, architecture, poetry, and religion, along with a bewildering number of more popular reviews, lectures, and sermons. He is the inventor of the self-registering anemometer, and the originator of many new scientific terms, including "ion," "cathode," "Eocene," "Miocene," "physicist," and "scientist."

In fact many of these words were coined by Whewell at the request of friends, for example terms "anode", "cathode" and "ion" were for Faraday, while "scientist" was produced at the request of the poet Samuel Taylor Coleridge. One should not get the impression that Whewell moved away from applied mathematics, however, rather he included many other areas in his wide range of interests while continuing to research applied mathematical fields. For example he published fourteen major papers on the study of the tides between 1833 and 1850. In fact he won the Royal Medal from the Royal Society for this outstanding work on tides.

Another important contribution was his support of, and work for, the British Association for the Advancement of Science. He strongly supported the founding of the Association in 1831 and, although he did not attend the first meeting of the Association in York in that year, it was his suggestion that they seek annual reports on the various sciences. He wrote the report on mineralogy for the meeting in 1832 and that on electricity and magnetism for the meeting of 1835. He served the British Association as vice-president at the Oxford meeting in 1832 and again at Dublin in 1835, he was the local secretary in 1833 when the Association met in Cambridge, then he was president at Plymouth in 1841. In fact it was in his address to the 1833 British Association meeting that he used the word 'scientist' for the first time, explaining that he coined the word in analogy to 'artist'. He later wrote [10]:-

... as an Artist is a Musician, Painter, or Poet, a Scientist is a Mathematician, Physicist, or Naturalist.

Note that the word 'Physicist' used in this quote by Whewell is also a word coined by him.

The areas for which Whewell is most famous today are philosophy of science, history of science, and moral philosophy. He examined 'knowledge' and claimed that [10]:-

... in every act of knowledge ... there are two opposite elements, which we may call Ideas and Perceptions.

He claimed that Fundamental Ideas were [10]:-

... not a consequence of experience, but a result of the particular constitution and activity of the mind, which is independent of all experience in its origin, though constantly combined with experience in its exercise.

As examples of Fundamental Ideas he gave time, number, cause, substance, and likeness. He wrote [10]:-

We cannot see one object without the idea of space; we cannot see two without the idea of resemblance or difference.

He developed a theory of induction, attempting to explain how physical laws are discovered. He argued that as well as the process of examining instances of a law [10]:-

... there is a New Element added to the combination [of instances] by the very act of thought by which they were combined.

After a law is produced by induction, Whewell argued that next is required a confirmation stage. He also argued for a concept he called Necessary Truth. He gave as an example the truth 7 + 8 = 15 [10]:-

... we refer to our conceptions of seven, of eight, and of addition, and as soon as we possess the conceptions distinctly, we see that the sum must be 15. That is, merely by knowing the meanings of "seven," and "eight," and "addition," we see that it follows necessarily that "7 + 8 = 15".

For Whewell his work on the history of science was an integral part of that on the philosophy of science, both contributing to knowledge. He felt that the history of science was extremely important [10]:-

... the present generation finds itself the heir of a vast patrimony of science; and it must needs concern us to know the steps by which these possessions were acquired, and the documents by which they are secured to us and our heirs for ever.

The last years of Whewell's life were filled with sadness. His wife Cordelia died on 18 December 1855 after a long illness. He then married Lady Everina Frances Affleck, widow of Sir Gilbert Affleck, on 1 July 1858. She died on 1 April 1865. On 24 February 1866 Whewell fell from his horse while riding outside Cambridge after the animal bolted. He was brought back to Trinity in a carriage but found to be paralysed. He died in his room in Trinity on 6 March, his last request being that the curtains be drawn back so that he could look at the great court of Trinity for the last time.

As to his character Leslie Stephen in his 1899 biography writes [24]:-

He loved an argument, and his position as a great man in a small circle tended to make argument one-sided. He was popular as a tutor; but for some time he provoked a good deal of hostility as master. In early days he had little chance of acquiring social refinement; and, though he was anxious to be hospitable, his sense of the dignity of his position led to a formality which made the drawing-room of the lodge anything but a place of easy sociability. In later years age and sorrow made him conspicuously milder, and the object not only of the pride but of the warm affection of the university. Though rough at times, he was from the first magnanimous; he never cherished resentment and admitted defeat frankly, and received the opinions of young and insignificant persons with remarkable courtesy. Few men, too, have had more friends or retained their friendships more carefully. He had many controversies, but no personal quarrels.

With so many achievements in so many different areas it is clear that we must have failed to mention many important aspects of his contributions in this article. Perhaps we should mention one final fact which we have failed to mention until now, namely his role as a priest. He was ordained a priest on Trinity Sunday 1825, which was a requirement of Fellows of Trinity, then ordained as a deacon in the following year. He preached in the university on a regular basis, in particular he preached four sermons On the Foundation of Morals in 1837 which were published in that year. Ten years later he published Sermons preached in the Chapel of Trinity College, Cambridge containing twenty-two of his sermons.

Let us end this biography of Whewell by quoting John Herschel, his friend for many years [3]:-

... a more wonderful variety and amount of knowledge in almost every department of human inquiry was perhaps never in the same interval of time accumulated by any man.