查尔斯·桑德斯·皮尔士Charles Sanders Peirce

查尔斯·桑德斯·皮尔士是本杰明·皮尔斯和萨拉·亨特·米尔斯的儿子，萨拉是参议员伊莱贾·亨特·米尔斯的女儿。我们注意到这个姓氏发音为“Purse”。皮尔士是他父母五个孩子中的第二个。他的哥哥是詹姆斯·米尔斯·皮尔士，后来成为哈佛数学系的数学家，然后从1890年到1895年担任哈佛研究生院院长，之后担任文理学院院长。皮尔士的两个弟弟也享有成功的职业生涯，本杰明·米尔斯·皮尔士作为采矿工程师，赫伯特·亨利·戴维斯·皮尔士作为外交官。

皮尔士出生在一个领先的美国家庭。他的父亲也许是美国领先的科学家，他邀请学者、政治家、诗人、科学家和数学家到家中。作为一个神童，皮尔士在知识氛围中茁壮成长。本杰明·皮尔斯发现很难找到足够聪明的学生来受益于他的教学，但在自己的孩子中，他找到了其他地方似乎缺乏的才能。他用自己教育理念教皮尔士和其他孩子，在许多方面这确实为他们从事研究做好了准备。然而，意识到最伟大的思想家享有思想独立，他拒绝管教孩子，以免破坏这种独创性。在许多方面，这种教养产生了皮尔士所展现的天才，但也给皮尔士带来了适应问题，这意味着他的生活很艰难。到十二岁时，皮尔士正在阅读大学水平的逻辑标准文本，次年他开始阅读伊曼努尔·康德的Critique of Pure Reason。他一生都深受康德影响。

人们或许会期望这位才华横溢的年轻人皮尔士在教育体系中崭露头角，但正是在这个阶段，他父亲如此精心培养的独立思考却对他不利[13]：-

在大学里，他已显露出后来与人相处困难的迹象：他在课业上并不出众，更喜欢阅读自己挑选的著作。

他于1855年进入哈佛学院，四年后毕业获得A.B.学位，并继续在那里攻读研究生一年。到这时，他的父亲本杰明·皮尔斯正在为美国海岸调查局工作，皮尔士也开始偶尔为海岸调查局承担工作。特别是他从1859年7月1日起为他们工作。1861年，他进入哈佛的劳伦斯科学学校，在那里他父亲再次发挥了重要作用，而他在那里似乎比本科时期出色得多。他于1862年从哈佛获得硕士学位，随后于1863年以优异成绩从劳伦斯科学学校获得Sc.B.学位。同年10月16日，他与Harriet Melusina Fay结婚，她来自剑桥的一个显赫家庭，是一位活跃的女权运动者。

皮尔士现在从事了一系列不同的科学研究。他曾跟随哈佛动物学家路易斯·阿加西学习物种分类。1865年春季，他讲授了关于The Logic of Science的哈佛讲座，1866年下半年讲授了关于The Logic of Science; or Induction and Hypothesis的洛厄尔研究所讲座。他于1867年1月30日当选为美国艺术与科学院，然后从1869年10月到1872年12月，他作为哈佛天文台的助理从事天文学研究。在此期间，他继续为美国海岸调查局进行大地测量学研究，并于1870年6月至次年3月被调查局派往欧洲。他在美国海岸调查局不断晋升，1872年11月被任命负责摆实验，同年12月晋升为助理。皮尔士在美国海岸调查局的大地测量工作中所执行的主要任务，是测量美国国内外各个地点的重力。他的另一项任务是利用实验结果的数据来确定地球的形状。作为这项工作的一部分，他进一步前往欧洲，从1875年4月到1876年8月，以及从1877年9月起又去了三个月。在这两次旅行之间，他于1876年10月与妻子梅卢西娜分居，这标志着一个将极大影响他职业生涯的问题的开始。

有一段时间，皮尔士的职业生涯继续向前发展。他于1877年4月当选为国家科学院（美国），并在一本书Photometric Researches（1878年）中发表了他早期天文学研究的成果。尽管他的工作在科学领域范围广泛，但他一直对哲学和逻辑感兴趣，并于1879年被任命为约翰威廉·霍普金斯大学数学系的逻辑学讲师。詹姆斯·约瑟夫·西尔维斯特当时是约翰霍普金斯大学的数学系主任，有一段时间皮尔士的事情进展顺利。他对Four Colour Problem以及阿尔弗雷德·布雷·肯普所研究的knots和连杆问题产生了兴趣。随后，他扩展了他父亲在结合代数方面的工作，并研究数学逻辑、拓扑学和集合论。然而此时，皮尔士正与朱丽叶·弗鲁瓦西·普塔莱斯同居，她是一位法国吉普赛人。他于1883年4月24日与第一任妻子梅卢西娜离婚，六天后与朱丽叶结婚。1884年，刚被任命为约翰霍普金斯大学数学和天文学教授的西蒙·纽康向大学董事会报告说，皮尔士在与梅卢西娜仍保持婚姻关系期间一直与一位法国吉普赛人同居。董事会不愿卷入丑闻，选择不再续签皮尔士的合同。皮尔士再也不会担任任何学术职位。

皮尔士现在唯一稳定的工作是为海岸和大地测量局工作。他前往华盛顿特区，处理从北极返回的重力测量数据。1886年，他搬到纽约市，继续为测量局工作，但他与上级越来越不合，越来越孤立地工作。海岸测量局也因政府缺乏资金而面临越来越大的压力。皮尔士于1887年4月搬进宾夕法尼亚州米尔福德的一所租来的房子，但那年10月12日他母亲去世后，他继承了一笔遗产，足以购买土地并开始在米尔福德附近建造一个他称之为阿里斯贝的庄园。1888年，他从一位未婚姑妈那里得到一小笔遗产后，又购买了更多的土地和一个农场。当他在1890年最终向美国海岸测量局提交关于重力的主要报告时，该报告被拒绝出版，除非他进行重大修改。到1891年底，他再也没有收到任何东西，测量局要求他辞职。皮尔士现在完全没有收入。

在他生命中这段困难时期，他的妻子健康状况不佳。她在1889年中被诊断出患有肺结核，并在那年年底前前往欧洲试图康复。1890年春天返回美国时，她仍然没有好转，1891年1月她接受了手术。尽管有这些健康问题，与皮尔士在美国海岸测量局的困难同时发生，朱丽叶还是比她的丈夫活得长。

汤马斯·费斯克在[29]中写到New York Mathematical Society（在它成为美国数学会之前）时，描述了19世纪90年代初的皮尔士：-

在九十年代初参加每月会议的人中，引人注目的是著名的逻辑学家皮尔士 S 皮尔士。他戏剧性的举止，对他所谓的“不重要细节”的准确性的轻率漠视，他描述我们年轻学会会议的巧妙报纸文章，都让我们所有人感到有趣和好笑。……他总是手头拮据，部分靠向朋友借钱生活，部分靠写书评等零工所得……无论是否在酒精影响下，他都同样才华横溢，他所属的各种组织都珍视他的陪伴；即使他无力支付会费，他也从未被任何组织除名。他激怒了Charlotte Angas Scott，因为他向《纽约晚邮报》投稿了一篇未署名的阿瑟·凯莱讣告，其中他毫无根据地声称，仅因为阿瑟·凯莱的父亲曾在俄罗斯居住过一段时间，阿瑟·凯莱就从其父亲在圣彼得堡娶的一位俄罗斯人那里继承了天才。不久之后，Scott小姐向《公报》投稿了一篇关于阿瑟·凯莱生平和工作的更符合事实、更为冷静的文章……

从这时起，皮尔士所写的许多东西要么被拒绝发表，要么他未能完成项目。属于第一类的有How to Reason（1894年被两家出版商拒绝）和New Elements of Mathematics（1895年被拒绝）。属于第二类的有Search for a Method（1893年宣布但未完成）、The Principles of Philosophy（1894年宣布十二卷但未完成）和The History of Science（1898年宣布但未完成）。

皮尔士今天最为著名的是作为哲学家，尽管可以说这种名声来得较晚。1877年和1878年，皮尔士在Popular Science Monthly上发表了六篇关于Illustrations of the Logic of Science的文章。这些文章的前两篇是The Fixation of Belief和How to Make Our Ideas Clear。正是在第二篇文章中，他阐述了他今天最为人所知的实用主义哲学。他写道：-

考虑我们设想我们概念的对象可能具有的效果，这些效果可能具有实际影响。那么，我们对这些效果的概念就是我们对该对象概念的全部。

Burch在19中写道：-

也许在理解皮尔士的哲学时，最需要记住的一个最重要的事实是，皮尔士一生都是一位从事实际工作的物理科学家……当他说一个（清晰的）概念的全部意义在于其实际后果的整个集合时，他心里想的是一个有意义的概念必须具有某种经验性的“现金价值”，能够被具体化为在可指定条件下可能经验观察的某种集合。皮尔士坚持认为，一个有意义的概念的全部意义就在于对可能观察的这种具体化的总体。

事实上，在他发表这些关于实用主义的思想二十年之后，通过William James的工作，皮尔士才开始因其思想而获得赞誉。皮尔士于1903年3月至5月在哈佛就Pragmatism进行讲座，并于1905年在The Monist上发表了一系列解释其思想的文章。

在这篇文章中不可能公正地评价皮尔士哲学工作的广度。我们只需注意一些进一步的例子。他写了关于无限集合和无穷小的文章，并论证了将无穷小引入数系统的一致性。他写了关于probability的文章，反对De Morgan关于概率是置信度的度量的观点，也反对托马斯·贝叶斯的观点。相反，对于皮尔士来说，概率是观察到的发生次数与可能发生次数之比的极限，而观察次数趋于无穷。他还研究了普遍范畴，对他来说几乎一切都分为三个范畴或三元组。在数学方面，从他为海岸调查所做的工作中，我们提到他对conformal map投影感兴趣，在那里他使用椭圆函数发明了一种梅花形地图投影。

我们已经指出，皮尔士是一个有些不同寻常的人物。以下是皮尔士于1879年5月21日向哈佛哲学俱乐部所作讲座的一份报告，摘自Thomas Davidson写的一封信：-

皮尔士的论文吹毛求疵、聪明但质量差。结束后，我与Benjamin Peirce教授进行了长谈，他试图用数学向我证明空间有四个维度。我认为皮尔士一家人都有点疯狂。

皮尔士在宾夕法尼亚州米尔福德阿里斯贝的家中死于癌症。

Charles S Peirce was the son of Benjamin Peirce and Sarah Hunt Mills, the daughter of Senator Elijah Hunt Mills. We note that this surname is pronounced "Purse". Charles was the second of his parents five children. His older brother was James Mills Peirce who became a mathematician in the Mathematics Department at Harvard, and then from 1890 to 1895 served as Dean of the Graduate School at Harvard and, after that, as Dean of the Faculty of Arts and Sciences. Charles' two younger brothers also enjoyed successful careers, Benjamin Mills Peirce as a mining engineer and Herbert Henry Davis Peirce as a diplomat.

Charles was born into a leading American household. His father was perhaps the leading scientist in America and he invited academics, politicians, poets, scientists, and mathematicians into his home. A child prodigy, Charles thrived in the intellectual atmosphere. Benjamin Peirce found it difficult to find students who were bright enough to benefit from his teaching, but in his own children he found the talent that seemed to be lacking elsewhere. He used his own educational ideas in teaching Charles and his other children, and in many ways this did set them up to undertake research. However, realising that the greatest thinkers enjoyed an independence of thought, he refused to discipline his children in case he destroyed this originality. In many ways this upbringing produced the genius that Charles displayed but it also gave Charles problems of fitting in, which meant that his life was a difficult one. By the age of twelve Charles was reading standard university level texts on logic, and in the following year he began reading Immanuel Kant's Critique of Pure Reason. He remained greatly influenced by Kant throughout his life.

One might have expected the brilliant young man Charles to make his mark in the education system, but it was at this stage that the independence of thought which his father has so carefully cultivated worked to his disadvantage [13]:-

In college he showed signs of his later difficulties in getting along with people: he did not excel in classwork, preferring to read works of his own choosing.

He entered Harvard College in 1855 and graduated four years later with an A.B., continuing to study there at graduate level for a year. By this stage his father, Benjamin Peirce, was working for the United States Coast Survey and Charles began to undertake occasional work for the Coast Survey. In particular he worked for them beginning on 1 July 1859. In 1861 he entered the Lawrence Scientific School at Harvard, where again his father played an important role, and here he seems to have shone much more than in his undergraduate years. He received a Master's degree from Harvard in 1862 and then a Sc.B. with distinction from the Lawrence Scientific School in 1863. On 16 October of that year he married Harriet Melusina Fay who came from a leading Cambridge family and was an active feminist campaigner.

Peirce now undertook a range of different scientific studies. He had studied species classification with Louis Agassiz, a Harvard zoologist. He gave the Harvard lectures on The Logic of Science in the spring of 1865 and the Lowell Institute lectures on The Logic of Science; or Induction and Hypothesis in the latter part of 1866. He was elected to the American Academy of Arts and Sciences on 30 January 1867, then from October 1869 to December 1872 he conducted research in astronomy as an assistant at Harvard Observatory. Throughout this time he continued research in geodesy for the U.S. Coast Survey, and he was sent to Europe by the Survey from June 1870 to March on the following year. He continued to progress through the ranks at the U.S. Coast Survey being put in charge of pendulum experiments in November 1872, then promoted to assistant in December of that year. The main task that Peirce carried out in his geodetic work for the U.S. Coast Survey was to measure the force of gravity at various sites both in the United States and abroad. His other task was to use the data from the results of his experiments to determine the shape of the earth. As part of this work he made further trips to Europe, from April 1875 to August 1876, and again for three months from September 1877. Between these two trips he separated from his wife Melusina in October 1876 and this marked the beginning of a problem which would greatly affect his career.

For a while Peirce's career continued to move forward. He was elected to the National Academy of Sciences (United States) in April 1877 and published the results of his earlier research in astronomy in a book Photometric Researches (1878). Although his work had been wide ranging in the sciences, he had always been interested in philosophy and logic and, in 1879, he was appointed as Lecturer in Logic in the Department of Mathematics at Johns Hopkins University. Sylvester was Head of Mathematics at Johns Hopkins University at this time and for a while things went well for Peirce. He became interested in the Four Colour Problem, and problems of knots and linkages studied by Kempe. He then extended his father's work on associative algebras and worked on mathematical logic, topology and set theory. However by now Peirce was living with Juliette Froissy Pourtalès, a French gypsy. He was divorced from his first wife Melusina on 24 April 1883 and married Juliette six days later. In 1884 Simon Newcomb, who had just been appointed professor of mathematics and astronomy at Johns Hopkins University, reported to the trustees of the university that Peirce had been living with a French gypsy while still married to Melusina. Not wishing to be involved in a scandal, the trustees chose not to renew Peirce's contract. Peirce would never hold another academic post.

Peirce's only steady work was now for the Coast and Geodetic Survey. He went to Washington, D.C. to work on data on gravity measurements which had been returned from the Artic. He moved to New York City in 1886 and continued on his work for the Survey but he became increasingly at odds with his superiors and worked more and more in isolation. The Coast Survey also came under increasing pressure through lack of funding by the government. Peirce moved into a rented house in Milford, Pennsylvania, in April 1887 but after his mother died on 12 October of that year he inherited enough to purchase land and begin building an estate he called Arisbe near Milford. He purchased further land and a farm after he received a small inheritance from a maiden aunt in 1888. When he finally submitted his major report on gravity to the U.S. Coastal Survey in 1890 it was rejected for publication unless he made major revisions. When nothing further was received from him by the end of 1891 the Survey asked for his resignation. Peirce now had no income at all.

During this difficult period in his life his wife was suffering from poor health. She was diagnosed as having tuberculosis in the middle of 1889 and before the end of the year she travelled to Europe in an attempt to recover. Returning to the United States in the spring of 1890, she still was not well and in January of 1891 she underwent surgery. Despite these health problems, which coincided with Peirce's difficulties with the U.S. Coastal Survey, Juliette outlived her husband.

T S Fiske, writing about the New York Mathematical Society (before it became the American Mathematical Society) in [29], describes Charles Peirce in the early 1890s:-

Conspicuous among those who in the early nineties attended the monthly meetings ... was the famous logician, Charles S Peirce. His dramatic manner, his reckless disregard of accuracy in what he termed 'unimportant details', his clever newspaper articles describing the meetings of our young Society interested and amused us all. ... He was always hard up, living partly on what he could borrow from friends, and partly on what he got from odd jobs such as writing book reviews ... He was equally brilliant, whether under the influence of liquor or otherwise, and his company was prized by the various organisations to which he belonged; and he was never dropped from any of them even though he was unable to pay his dues. He infuriated Charlotte Angas Scott by contributing to the New York Evening Post an unsigned obituary of Arthur Cayley in which he stated upon no grounds, except that Cayley's father had for a time resided in Russia, that Cayley had inherited his genius from a Russian whom his father had married in St Petersburg. Shortly afterwards Miss Scott contributed to the Bulletin a more factual, sober article upon Cayley's life and work ...

Much of what Peirce wrote from this time onwards was either rejected for publication, or he failed to complete the project. In the first category there is How to Reason (rejected by two publishers in 1894), and New Elements of Mathematics (rejected in 1895). In the second category is Search for a Method (announced in 1893 but not completed), The Principles of Philosophy (twelve volumes announced in 1894 but not completed), and The History of Science (announced in 1898 but not completed).

Peirce today is most famous as a philosopher although it is fair to say that this fame only came late. In 1877 and 1878 Peirce published six essays on Illustrations of the Logic of Science in the Popular Science Monthly. The first two of these essays were The Fixation of Belief and How to Make Our Ideas Clear. It was in the second of these that he set out his pragmatic philosophy for which he is best known today. He wrote:-

Consider what effects, which might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.

Burch writes in [19]:-

Perhaps the single most important fact to keep in mind in understanding Peirce's philosophy is that Peirce was a practicing physical scientist all his life ... When he said that the whole meaning of a (clear) conception consists in the entire set of its practical consequences, he had in mind that a meaningful conception must have some experiential "cash value," capable of being specified as some sort of collection of possible empirical observations under specifiable conditions. Peirce insisted that the entire meaning of a meaningful conception consisted in the totality of such specifications of possible observations.

In fact it was twenty years after he published these ideas on pragmatism that, through the work of William James, Peirce began to gain the credit for his ideas. Peirce lectured on Pragmatism at Harvard in March to May of 1903 and published a series of essays explaining his ideas in The Monist in 1905.

It is impossible to do justice to the breadth of Peirce's philosophical work in this article. Let us just note some further examples. He wrote on infinite sets and infinitesimals and argued for the consistency of introducing infinitesimals into the number system. He wrote on probability arguing against De Morgan's ideas that probability is a measure of confidence and also arguing against the ideas of Bayes. Rather for Peirce probability is the limit of the ratio of observed occurrences over the possible occurrences and the number of observations tend to infinity. He also studied universal categories and for him almost everything split into three categories or triads. On the mathematical side, coming out of his work for the Coast Survey, we mention that he was interested in conformal map projections where he invented a quincuncial map projection using elliptic functions.

We have already indicated that Peirce was a somewhat unusual character. Here is a report of a lecture that Peirce gave to the Harvard Philosophy Club on 21 May 1879 extracted from a letter written by Thomas Davidson:-

Peirce's paper was captious, bright, and poor. After it was over, I had a long talk with Professor Benjamin Peirce, who undertook to prove to me mathematically that space has four dimensions. The Peirce's are all a little crazy, I think.

Peirce died of cancer at his home at Arisbe, Milford, Pennsylvania.