尼古拉·德·孔多塞Jean-Antoine-Nicolas de Caritat de Condorcet

孔多塞-Jean-路易·安托万-Nicolas de 孔多塞从多菲内的孔多塞镇获得了世袭头衔Marquis 孔多塞。他的父母是Jean Pierre Antoine 尼古拉·德·孔多塞（1702-1743）和孔多塞 Madeleine Catherine Gaudry（1710-1784）。安托万 孔多塞是一名军人，是Barbançon团的队长。他于1740年3月12日在Ribemont与Madeleine Gaudry结婚。Madeleine于1710年1月30日出生在Ribemont，并于1731年1月3日与她的第一任丈夫Fulcrand Philippe Etienne de Saint Félixon结婚。他于1734年9月19日在意大利的Gastalla战役中阵亡。安托万随后成为Madeleine的第二任丈夫，但不幸的是，他于1743年10月22日在法国Neuf Brisach附近演习时阵亡，仅在他们唯一的孩子孔多塞 Jean Antoine Nicolas de 孔多塞出生五周后，后者是本传记的主题。贵族孔多塞家族经历了被迫的宗教变革，这些变革值得提及，因为它们几乎肯定对年幼的孩子产生了影响。Henri de 孔多塞，他的高祖父的祖父的祖父的祖父，早在1561年就采纳了归正信仰，但当法国转而反对胡格诺派时，孔多塞家族的一些成员逃离法国，而留下的那些人则重新皈依罗马天主教。孔多塞，我们将以此指代本传记的主题，来自重新皈依天主教的分支，如果他遵循家族传统，他会加入军队或教会，这是唯一两个被认为适合贵族的职业。

孔多塞的母亲是一位虔诚的宗教女性，她将儿子奉献给圣母玛利亚，并以极其保护的方式对待他，这在失去两任丈夫之后是可以理解的。她一直给孔多塞穿白色连衣裙，直到他八岁。他与他人隔离，被剥夺了小男孩会享受的运动和户外玩耍。直到八岁，他从母亲那里接受了一些教育，但他的叔叔雅克-孔多塞 孔多塞主教担心这个小男孩没有得到适当的教育，安排了一位耶稣会家庭教师从九岁到十一岁在家中教他。1754年，孔多塞进入兰斯的耶稣会学院，在那里度过了四年。他在这所学院的表现非常好，但鉴于他后来的天才，并不像人们可能预期的那样出类拔萃；他在十三岁时获得了二等奖。他关于教育的想法，如On the Nature and Purpose of Public Instruction（1791）中所述，与他在学校的表现有关（例如见[5]：-

人生不是一场对手争夺奖品的斗争。它是一次兄弟们共同进行的航行：每个人为所有人的利益贡献自己的力量，并以相互善意的甜蜜、因感到赢得他人的感激或尊重而带来的愉悦作为回报……相比之下，我们学院授予的桂冠——使学童相信自己已经是一个伟大的人——只会激起一种幼稚的虚荣心，一种明智的教育体系会设法使我们避免这种虚荣心，如果不幸的是，它的根源在于我们的本性，而不是我们错误百出的制度。追求第一名的习惯，对于被灌输这种习惯的个人来说，要么是荒谬的，要么是不幸的。

与他这些年的教育相关的还有一点，他在晚年强烈反对由教会管理教育。

1758年，孔多塞进入巴黎的纳瓦拉学院，该学院享有很高的学术声誉。最近的一项发展是在1753年，孔多塞-安托万 Nollet（1700-1770）被任命为第一位实验物理学教授，并在一个专门建造的能容纳600名学生的演讲厅授课。打破所有教学都用拉丁语的传统，Nollet坚持用法语教授物理学。Georges Girault de Kéroudou在纳瓦拉学院教授数学和哲学，他使孔多塞对数学产生了热情，因此，当他在1760年从纳瓦拉学院毕业时，他决心从事数学职业。然而，他的家人非常强烈地反对这样的职业，觉得这完全违背了“孔多塞”贵族地位的世袭性质的精神。他回到Ribemont的家中自学数学两年，争取被允许从事数学和科学职业，最终，他成功了。

1762年，孔多塞离开位于里贝蒙的家前往巴黎，在那里他与Georges Girault de Kéroudou同住，后者曾在纳瓦拉学院教他数学。孔多塞住在Girault de Kéroudou位于巴黎市中心雅各街住所上方的一间小阁楼里，靠近大学。Jeanne Julie Éléonore de Lespinasse（1732-1776）在巴黎经营一家沙龙，并以书信作家闻名，她是让·勒朗·达朗贝尔的密友，此时与孔多塞熟识。她这样描述他[3]：-

……一个高大笨拙的年轻人，举止羞怯尴尬，走路弯腰驼背，咬指甲，别人跟他说话就脸红，要么什么都不回答，要么低声快速地说几句。

我们让读者来判断，他当时的举止有多少是他那种极为保护性教养的结果。孔多塞此时正在研究积分，他完成了一篇论文，由亚历克西斯·克劳德·克莱罗和Alexis Fontaine审阅。他们在年轻的孔多塞身上看到了很大潜力，但拒绝了这篇论文，不过同时给予鼓励并建议他应如何继续。

1765年，孔多塞的论文Essai sur le calcul intégralⓉ（积分论）提交给Académie des Sciences，由让·勒朗·达朗贝尔和艾蒂安·贝祖审阅，他们于1765年5月22日给出了正面报告。他们写道：-

孔多塞……完全解决了这个一般问题：“给定一个给定阶的微分方程，其中包含任意多个变量，判定这个方程在它所被提出的状态下，是否容许一个低一阶的积分。”他对这个问题的解答，除了具有实用价值外，还具有优雅性和一般性。……这项工作显示出最伟大的才能，也最值得受到科学院认可的激励。

孔多塞为这部著作写了如下前言：-

我在这项工作中提出一种确定给定微分方程的有限积分的一般方法。我将其分为两部分。在第一部分中，我将以足够的篇幅处理常微分方程：在第二部分中，我将给出一些原则，用于将第一部分中阐述的理论应用于有限差分方程，以及那些其中同一个变量等于其他几个变量的函数、并已依次假定随其中每一个变量而变化的方程。

在致谢中，他感谢Alexis Fontaine的“好意，在我印刷其Recherches sur Differens Points Importans du Systeme du Monde之前，将其中第24页所载的基本定理告知我。”他还指出，他关于差分方程的工作与让·勒朗·达朗贝尔在其Recherches sur Differens Points Importans du Systeme du MondeⓉ（《关于世界体系不同重要点的研究》）（1754—56）中的结果，以及与莱昂哈德·欧拉在其Institutions Calculi DifferentialisⓉ（《微分学方法》）（1755）中的结果有联系。他补充道：-

我给出一些原则的那些偏差分方程，最初是在M 让·勒朗·达朗贝尔的学位论文《关于风的普遍原因的思考》（1747）中从一种不同的观点加以处理的。在那里，其中几个方程通过一种非常巧妙的方法被积分，这种方法兼具优雅与简洁。M M 莱昂哈德·欧拉和约瑟夫·拉格朗日此后用其他方法解出了其中一些。后者的那些方法具有极大的普遍性，其作者已将它们应用于非常复杂的方程。

由于这篇论文以及他此时发表的一系列其他数学论文，孔多塞于1769年当选为Académie des Sciences院士。大约在这段时间，他经常造访朱莉·德·莱斯皮纳斯于1764年在贝勒沙斯街开设的沙龙。这个沙龙被恰如其分地描述为“百科全书的实验室”，因为在这里贵族、外交官、哲学家、数学家和政治家相聚。孔多塞会与住在朱莉·德·莱斯皮纳斯沙龙里的让·勒朗·达朗贝尔进行深入的数学讨论。他产生了若干重要著作，其中包括1772年的一部关于积分学的著作，约瑟夫·拉格朗日将其描述为[见弗朗索瓦·阿拉戈在Académie des Sciences中的《孔多塞传》]：-

……充满崇高而富有成果的思想，这些思想本可为若干部著作提供材料。最后一篇文章尤其令我满意，因为它的优雅和实用。……循环级数已经被处理得如此频繁，以至于人们会说这个题材已经被穷尽了。然而，这里是这些级数的一个新应用，在我看来，比我们此前所作的任何应用都更重要。可以说，它为‘积分学’的完善开辟了一个新领域。

在他1772年著作出版后不久，孔多塞在朱莉·德·莱斯皮纳斯的沙龙里遇见了安·罗伯特·雅克·杜尔哥（1727—1781），一位法国经济学家。杜尔哥在路易十五治下成为一名行政官员，并于1774年8月在路易十六治下被任命为财政总监。在他被任命的那一年，他任命孔多塞为造币厂总监。这标志着孔多塞职业生涯方向的重大变化。直到那时，他一直完全致力于数学，但从那时起，尽管他继续作出数学贡献，他却忙于其他角色和各种其他学术兴趣[49]：-

在孔多塞于1774-76年担任大臣期间，他发表了一系列关于经济主题的著作，包括谷物贸易（1774年）、徭役税（1775年）、垄断（1775年）、放松管制（1775年），以及再次关于谷物贸易（1776年）。

孔多塞于1776年被免职，孔多塞为表示支持而提出辞职。然而，孔多塞的辞职被拒绝，他继续担任此职位直到1791年。

1777年，孔多塞被任命为Académie des Sciences的秘书。伏尔泰和让·勒朗·达朗贝尔曾建议他成为撰写讣告的专家，以提高获得该职位的机会。这当然是好建议，他撰写的大量讣告受到高度赞扬，但尽管如此，这严重削减了他的数学产出。

他最重要的著作是关于概率和数学哲学的，特别是他的论著Essay on the Application of Analysis to the Probability of Majority Decisions（1785年）。这是概率论发展中的一部极其重要的著作[49]：-

孔多塞1785年的《随笔》献给了Turgot。他将其呈现为试图证明计算适用于“具有普遍效用的问题”。正如孔多塞在引言开头所解释的，它明确关注的是自古以来就广泛存在的将所有人服从于最大多数人意志的做法。它还关注古代与现代宪法的差异，孔多塞在其余生中一直回到这个问题……孔多塞在《随笔》中写道，古代宪法中多数投票的正当性与“自由”和“效用”这两个词相关，而不是与“真理”和“正义”相关。……

孔多塞在《随笔》的引言中明确指出，现代宪法中要做的决定是关于重要社会问题的，包括经济政策。他给出了四个例子来说明民主程序中的困难，这现在被称为他的不可能性结果，或者他对不可能找到一个“孔多塞赢家”的证明（在某些偏好分布下，多数选举中的每个候选人都会被其他某个候选人击败。）

孔多塞的最后一个例子今天被称为“孔多塞悖论”。它指出，可能多数人偏好选项A胜过选项B，多数人偏好选项B胜过选项C，然而多数人偏好选项C胜过选项A。（因此，“多数人偏好”不具有传递性。）

孔多塞出版了Vie de M TurgotⓉ（杜尔哥传）（1786）和Vie de VoltaireⓉ（伏尔泰传）（1789）。在这些传记中，他表明自己赞同杜尔哥的经济理论，并同意伏尔泰对教会的反对。同样在1786年，他再次研究了自己关于微分和积分的想法，对无穷小给出了新的处理。然而他的论著从未付印。

1786年12月28日，孔多塞与孔多塞 Louise Sophie de Grouchy在法兰西岛大区孔代库尔的维莱特城堡礼拜堂结婚。Sophie de Grouchy（1764-1822）是François Jacques de Grouchy（1715-1808）和孔多塞 Gilberte Henriette Freteau de Peny（约1740-1793）的女儿。Joan Landes写道[41]：-

与她的丈夫一样，de Grouchy致力于在法国实现重大的司法和政治改革；她自己在修道院的经历使她对教会产生了同样强烈的厌恶，并致力于世俗价值观。两人因共同关注为三名司法错误和法律滥用的农民受害者辩护而相识……这一事业由de Grouchy的叔叔、波尔多议会主席、法官Charles Dupaty接手。……孔多塞夫人本人是一位有成就的翻译家和作家；她与丈夫一样持有自由主义和共和主义观点，尤其是在刑事司法、政治改革以及少数群体和妇女权利问题上。

1790年4月24日，安托万和Sophie 孔多塞唯一的孩子Alexandrine-Louise-Sophie 孔多塞（1790-1859）出生于巴黎孔蒂码头11号的货币酒店。这是巴黎铸币厂的所在地。她被称为Élisa，次日受洗，教父为Louis Alexandre，罗什富科公爵，教母为孔多塞 Henriette Gilberte Freteau，由其女儿Charlotte Félicité de Grouchy代表。十七岁时，Élisa于1807年7月4日在巴黎与Arthur O'Connor（1763-1852）结婚。他出生于爱尔兰科克，曾前往法国寻求对爱尔兰革命的支持，并被拿破仑任命为法国军队成员。

1789年见证了法国大革命的爆发，同年5月法国成为君主立宪制国家，随后7月14日攻占巴士底狱。孔多塞支持自由主义事业，他当选为立法议会的巴黎代表，并成为议会秘书。他起草了国家教育体系的计划，但由于当时法国的政治局势，这些计划只得到了很少的关注。在这份报告中，他写道（见[33]）：-

为人类的所有个体提供满足其需求、确保其福祉、了解和行使权利、理解和履行义务的手段，确保每个人有能力完善自己的行业，使自己能够胜任有权被召唤的社会职能，发展自然赋予他的全部才能，并以此在所有公民之间建立事实上的平等，实现法律承认的政治平等——这必须是国家教育体系的首要目标。

他于1790年，即他女儿出生那年，出版了Sur l'admission des femmes au droit de cité Ⓣ（论妇女获得公民权利）。Guillaume Ansart在[20]中写道关于这部作品：-

从政治角度来看，孔多塞坚持认为，两性之间没有根本差异。性别差异要么是教育和社会化的产物——因而可以改变——要么与自然权利的讨论根本无关。第一类包括男女传统上运用其智力的不同活动领域（公共领域与私人领域），以及据称不同的道德感或正义感。据说，女性受情感而非理性或良知的引导。但孔多塞断言，这些差异是由纯粹的社会因素造成的：女性通常被排除在公共生活之外，因此将她们的智力导向不同的对象，从而可能发展出例如与男性不同的正义感……[孔多塞写道]“如果诸如此类的理由被用来反对女性，那么也必须剥夺那部分人的公民权利，他们因为忙于不断的劳动，既无法获得知识，也无法运用其理性。很快，渐渐地，只有修过公法课程的人才能被允许成为公民。”

到1792年，孔多塞已成为共和派事业的领导人之一。他加入了温和的吉伦特派，并强烈主张应保全国王的性命。当吉伦特派失势，由罗伯斯庇尔领导的更激进的政治团体雅各宾派接管后，孔多塞强烈反对新匆忙写就的宪法，该宪法旨在取代他本人曾主要负责起草的那部宪法。这表明他缺乏常识，当逮捕令发出时，他为此付出了代价。

在他被捕前的那段时期，他写了Tableau généralⓉ（总表）。[32]的作者们写道：-

孔多塞在1793年春夏（可能是六月，也可能是七月初）的几天里匆忙写下了《总表》，就在他被捕之前。他没有足够的时间完成或润色它。这就是为什么许多段落仍然省略甚至含糊不清，以及为什么文章结构不平衡的原因。但这些并不是《总表》Ⓣ（总表）难以阅读的唯一原因：编辑上的瑕疵被添加到手稿中已有的瑕疵之上，尤其是在第一版中。

Pierre Crépel和孔多塞-Nicolas Rieucau以以下结论结束了他们有趣的文章[32]：-

孔多塞将微积分应用于政治和道德科学的计划的种子早在1770年代初就已存在，当时孔多塞将“道德或政治关系的科学”置于“物理数学”的分支内。他在整个1780年代以各种方式发展了这一计划，最著名的是他在选举方面的工作。在这方面，尽管《总表》确实是未来工作的蓝图，但它也构成了早期研究的方法论综合。但它最具体的特征却在别处。它同时是一部成熟的文本，而且主要由于写作时的政治环境，也是一部相当混乱的文本，其结构本可以改进。……回顾过去，人们可以想象，如果孔多塞有足够的时间，他会多么用心地校正和完成《总表》。在即将被流放的威胁下，在政治不稳定的高潮中，孔多塞选择写一部相当抽象的文本，几乎是他署名的最后一部。在任何情况下，都不能将其视为他会“轻率对待”的偶然作品。他为什么决定在那个特定时间写它？通过呈现他所认为的真正的公共幸福科学，他的目标可能是“超越政治辩论”……人们还可以推测，已经半地下生活的孔多塞，意在留下遗产，意图推广一个探究主题，正如他几个月后所写，“尽管一些数学家的成功尝试，它仍然可以说处于早期阶段，并且……[它]必须为下一代开启一个真正无限的启蒙源泉。”人们可以猜到，孔多塞将自己视为这些“数学家”之一。

孔多塞躲藏起来，写了一部非常有趣的哲学著作Esquisse d'un tableau historique des progrès de l'esprit humainⓉ（人类精神进步史表纲要）（1795年）。Oliver H Prior在1938年编辑了一版EsquisseⓉ（纲要），在导言中写道（见[39]）：-

孔多塞在法国思想史上占有特殊地位。他是最后一位“哲学家”，也是唯一一位积极参与大革命的人。他并未构想出一个完全原创的体系，但他确实综合了所有前人的理论。在他的著作中，我们可以找到伏尔泰、卢梭、杜尔哥、爱尔维修、孔狄亚克的思想，这些思想一点一点地被塑造成一个和谐的整体，其最终表达就是《纲要》，一种十八世纪哲学的概要。

我们在THIS LINK呈现孔多塞为EsquisseⓉ（纲要）所写导言的一个版本。

1794年3月，他认为他在巴黎藏身的房子正被敌人监视，他不再感到安全。他逃离巴黎，三天后于1794年3月27日被捕入狱。两天后，他被发现死在牢房里，不知道他是自然死亡，还是被谋杀或自杀。

John Herivel对孔多塞的描述如下[12]：-

……孔多塞不是政治家。他毫不妥协的直率态度和无法沉默忍受不合逻辑的空谈家，使他树敌众多而朋友寥寥。他声音微弱，缺乏演说才能，且因论点过于高深而常令国民公会感到厌烦，这是大革命的悲剧之一。

Harry Burrows Acton（1908-1974）在[2]中对他的生平总结如下：-

作为一个完全的启蒙运动者，一个经济自由、宗教宽容、法律和教育改革以及废除奴隶制的倡导者，孔多塞试图将理性的帝国扩展到社会事务。他并非像迄今为止那样，通过求助于道德科学或物理科学来阐明人类行为，而是试图通过将这两种科学融合在一起来解释它，这种融合最终演变成了社会学学科。

Marie-Jean-Antoine-Nicolas de Caritat took his hereditary title Marquis de Condorcet from the town of Condorcet in Dauphiné. His parents were Jean Pierre Antoine Caritat de Condorcet (1702-1743) and Marie Madeleine Catherine Gaudry (1710-1784). Antoine Caritat de Condorcet was a military man and was captain of the Barbançon regiment. He married Madeleine Gaudry on 12 March 1740 in Ribemont. Madeleine had been born in Ribemont on 30 January 1710 and had married her first husband Fulcrand Philippe Etienne de Saint Félixon on 3 January 1731. He had been killed at the Battle of Gastalla, in Italy, on 19 September 1734. Antoine was then Madeleine's second husband but, sadly, he was killed on manoeuvres near Neuf Brisach, France, on 22 October 1743, only five weeks after the birth of their only child Marie Jean Antoine Nicolas de Caritat, the subject of this biography. The noble Condorcet family had undergone forced religious changes which are worth mentioning since they almost certainly had an impact on the young child. Henri de Caritat, his great-great-great-great grandfather, had adopted the Reformed faith as early as 1561 but when France turned against the Huguenots some members of the Condorcet family fled France while those was remained converted back to Roman Catholicism. Condorcet, as we will refer to the subject of this biography, came from the branch re-converted to Catholicism and, had he followed the family tradition, he would have joined the military or the Church, the only two occupations deemed suitable to the nobility.

Condorcet's mother was a deeply religious woman and she dedicated her son to the Virgin Mary and treated him in an extremely protective manner, understandable after the loss of two husbands. She continued to dress Condorcet as a baby in white dresses until he was eight years old. He was kept away from others and denied the exercise and open air play that young boys would enjoy. Up to the age of eight he received some instruction from his mother but his uncle, Bishop Jacques-Marie de Caritat de Condorcet, worried that the young boy was not getting a proper education, arranged for a Jesuit tutor to teach the boy at his home from the age of nine to eleven. In 1754 Condorcet entered the Jesuit College in Reims where he spent four years. His achievements at this College were very good but not quite as exceptional as one might have expected given his later genius; he gained a second prize at the age of thirteen. His ideas about education, as given in On the Nature and Purpose of Public Instruction (1791), are relevant to his performance at school (see for example [5]:-

Human life is not a struggle in which rivals contend for prizes. It is a voyage that brothers make together: where each employs his forces for the good of all and is rewarded by the sweetness of mutual benevolence, by the pleasure that comes with the sentiment of having earned the gratitude or the esteem of others ... By contrast, the crowns bestowed in our colleges - which induce the schoolboy to believe himself already a great man - only arouse a childish vanity from which a wise system of instruction would seek to preserve us if, by misfortune, its origin lay in our nature and not in our blundering institutions. The habit of striving for first place is either ridiculous or unfortunate for the individual in whom it has been inculcated.

Also relevant to these years of his education is the fact that, in later life, he argued strongly against education being run by the Church.

In 1758 Condorcet entered the Collège de Navarre in Paris which had a high academic reputation. A recent development had been in 1753 when Jean-Antoine Nollet (1700-1770) had been appointed as the first professor of experimental physics and had taught in a specially constructed lecture theatre for 600 students. Breaking with the tradition that all teaching had been in Latin, Nollet insisted that physics be taught in French. Georges Girault de Kéroudou taught mathematics and philosophy at the Collège de Navarre and he gave Condorcet a passion for mathematics so, when he graduated from the Collège de Navarre in 1760, he was determined to pursue a career in mathematics. His family, however, were very strongly opposed to such a career feeling that this was totally against the spirit of the hereditary nature of the noble standing of "de Condorcet." He spent two years back at his home in Ribemont studying mathematics on his own, arguing to be allowed to pursue a career in mathematics and science and, eventually, he prevailed.

In 1762 Condorcet left his home in Ribemont and went to Paris where he lived with Georges Girault de Kéroudou who had taught him mathematics at the Collège de Navarre. Condorcet lived in a small attic above Girault de Kéroudou's home on the rue de Jacob in central Paris, close to the University. Jeanne Julie Éléonore de Lespinasse (1732-1776), who ran a salon in Paris and became famed as a letter writer, was a close friend of Jean le Rond d'Alembert and she got to know Condorcet well at this time. She described him as [3]:-

... a great hulking gawky youth, shy and embarrassed in manner, who walked stooping, bit his nails, blushed when spoken to, and either said nothing in reply or else spoke low and fast.

We leave the reader to judge how much of his manner at the time was a result of his very protective upbringing. Condorcet was now undertaking research on the integral calculus and he produced a memoir which was refereed by Alexis Claude Clairaut and Alexis Fontaine. They saw much potential in the young Condorcet, but rejected the paper with, however, encouragement and advice on how he should proceed.

In 1765 Condorcet's memoir Essai sur le calcul intégral Ⓣ was submitted to the Académie des Sciences and refereed by d'Alembert and Étienne Bézout who reported positively on 22 May 1765. They write:-

M de Condorcet ... fully resolves this general problem: "Given a differential equation of a given order, which contains as many variables as one wishes, determine whether this equation, in the state in which it is proposed, admits, or does not admit, an integral of an immediately lower degree." The solution he gives of this problem, in addition to having the merit of utility, has the merit of elegance and of generality. ... The work announces the greatest talents, and those most worthy of being stimulated by the approval of the Academy.

Condorcet gives the following Preface to the work:-

I propose in this work to give a general method of determining the finite integral of a given differential equation. I divide it into two parts. I will deal in the first, with sufficient scope, with ordinary differential equations: in the second I will give some principles for applying the theory explained in the first part to finite difference equations, and to those where the same variable, equal to a function of several others, has been successively assumed to vary with each of them.

In the acknowledgements he thanks Alexis Fontaine for his "kindness to communicate to me, before the printing of his Memoirs, the fundamental Theorem which is found there on page 24." He also notes connections of his work on difference equations to results of d'Alembert in his memoir Recherches sur Differens Points Importans du Systeme du Monde Ⓣ (1754-56) and to Euler in his Institutions Calculi Differentialis Ⓣ (1755). He adds:-

The partial difference equations for which I give some principles, were first treated from a different point of view in the dissertation 'Reflexions sur la Cause Generale des Vents' (1747) of M d'Alembert. There several of these equations are integrated by a very ingenious method, which combines elegance with simplicity. M M Euler and Lagrange have since solved some by other methods. Those of the latter have a very great generality, and its author has applied them to very complicated equations.

As a result of this memoir and a series of other mathematics papers he published at this time, Condorcet was elected to the Académie des Sciences in 1769. Around this time he was a frequent visitor to Julie de Lespinasse's salon which she had opened on the rue de Belle Chasse in 1764. This salon was justly described as the "laboratory of the Encyclopaedia" for here aristocrats, diplomats, philosophers, mathematicians and politicians met. Condorcet would have deep mathematical discussions with d'Alembert who was living in Julie de Lespinasse's salon. He produced several important works, including one in 1772 on the integral calculus which was described by Lagrange as [see Arago's 'Biographie de Condorcet' in the Académie des Sciences]:-

... filled with sublime and fruitful ideas which could have furnished material for several works. The last article particularly pleased me for its elegance and its utility. ... The recurring series had already been treated so often that one would have said that this matter had been exhausted. However, here is a new application of these series, more important, in my opinion, than any that we have already made. It opens up, so to speak, a new field for the perfection of 'Integral Calculus'.

Soon after the publication of his 1772 work, Condorcet met Anne Robert Jacques Turgot (1727-1781), a French economist, in Julie de Lespinasse's salon. Turgot had become an administrator under Louis XV and was appointed Controller General of Finances in August 1774 under Louis XVI. In the year he was appointed, he had Condorcet appointed Inspector General of the Mint. This marks a major change in direction in Condorcet's career. Up to that time he had devoted himself entirely to mathematics, but from then on, although he continued to make mathematical contributions, he was occupied with other roles and a variety of other academic interests [49]:-

At the time of Turgot's ministry of 1774-76, [Condorcet] published a sequence of works on economic subjects, including the grain trade (1774), the corvée tax (1775), monopoly (1775), deregulation (1775), and, again, the grain trade (1776).

Turgot was dismissed from his post in 1776 and Condorcet tended his resignation in support. Condorcet's resignation, however, was refused and he continued to fill this post until 1791.

In 1777 Condorcet was appointed Secretary of the Académie des Sciences. He had been advised by Voltaire and by d'Alembert to become an expert in writing obituaries in order to improve his chances of getting the post. It certainly was good advice and the large number of obituaries he wrote were highly praised, but nevertheless it severely curtailed his mathematical output.

His most important work was on probability and the philosophy of mathematics, especially his treatise Essay on the Application of Analysis to the Probability of Majority Decisions (1785). This is an extremely important work in the development of the theory of probability [49]:-

Condorcet's 'Essai' of 1785 was dedicated to Turgot. and he presented it as an attempt to demonstrate the applicability of calculation to "questions of interest for common utility". It was concerned explicitly, as Condorcet explains at the beginning of the introduction, with the practice, widespread since antiquity, of submitting all individuals to the will of the greatest number. It was also concerned with the differences between ancient and modern constitutions to which Condorcet returned throughout the rest of his life ... The justification for majority voting in the ancient constitutions, Condorcet wrote in the 'Essai', was associated with "the words 'freedom' and 'utility'," more than with '''truth' and 'justice'." ...

Condorcet makes clear, in the introduction to the 'Essai', that the decisions to be made in modern constitutions are about important social questions, including economic policy. He gives four examples of the difficulty in democratic procedures that is now known as his impossibility result, or his demonstration of the impossibility of finding a "Condorcet winner" (under certain distributions of preferences, in which every candidate in a majority election will be defeated by some other candidate.)

The final of Condorcet's examples is today known as the 'Condorcet Paradox'. It points out that it is possible that a majority prefers option A over option B, a majority prefers option B over option C, and yet a majority prefers option C over option A. (Thus, "majority prefers" is not transitive.)

Condorcet published Vie de M Turgot Ⓣ (1786) and Vie de Voltaire Ⓣ (1789). In these biographies he showed that he favoured Turgot's economic theories and agreed with Voltaire in his opposition to the Church. Also in 1786 he again worked on his ideas for the differential and integral calculus, giving a new treatment of infinitesimals. However his treatise was never printed.

On 28 December 1786, Condorcet married Marie Louise Sophie de Grouchy in the Chapelle du Château de Villette, Condécourt, Île-de-France. Sophie de Grouchy (1764-1822) was the daughter of François Jacques de Grouchy (1715-1808) and Marie Gilberte Henriette Freteau de Peny (about 1740-1793). Joan Landes writes [41]:-

Like her husband, de Grouchy was committed to bringing about major judicial and political reforms in France; and her own experiences at a convent left her with a similarly fierce dislike of the Church and a commitment to secular values. The two met through their common interest in the defence of three peasant victims of judicial error and legal abuse ... whose cause had been taken up by de Grouchy's uncle, the magistrate Charles Dupaty, president of the parliament of Bordeaux. ... Mme de Condorcet was an accomplished translator and author, in her own right; and she shared her husband's liberal and republican views, especially on matters of criminal justice, political reform, and minority and women's rights.

On the 24 April 1790 Antoine and Sophie de Caritat de Condorcet's only child, Alexandrine-Louise-Sophie de Caritat de Condorcet (1790-1859), was born at the Hôtel des Monnaies at 11 Quai de Conti, Paris. This was the building housing the Paris Mint. Known as Élisa, she was baptised on the following day with Louis Alexandre, Duke of Rochefoucauld, as her godfather, and Marie Henriette Gilberte Freteau, represented by her daughter, Charlotte Félicité de Grouchy, as godmother. When she was seventeen years old, Élisa married Arthur O'Connor (1763-1852) in Paris on 4 July 1807. He was born in Cork, Ireland, had gone to France to seek support for an Irish revolution and had been appointed to the French army by Napoleon.

The year 1789 saw the outbreak of the French Revolution when in May of that year France became a constitutional monarchy followed by the storming of the Bastille on 14 July. Condorcet championed the liberal cause, he was elected as the Paris representative in the Legislative Assembly and he became the secretary of the Assembly. He drew up plans for a state education system which were given only a little attention due to the political situation of France at the time. In this report he writes (see [33]):-

To offer all individuals of the human race the means to provide for their needs, to ensure their well-being, to know and exercise their rights, to understand and fulfil their duties, to ensure for each one the faculty of perfecting his industry, to render himself capable of the social functions to which he has the right to be called, to develop the whole range of talents with which nature has endowed him, and by this means to establish between all citizens an equality of fact and to realise the political equality recognised by the law - this must be the first goal of national educational system.

He published Sur l'admission des femmes au droit de cité Ⓣ in 1790, the year his daughter was born. Guillaume Ansart writes about this work in [20]:-

From a political perspective, Condorcet insists, there are no fundamental differences between the sexes. Sexual and gender differences are either the product of education and socialisation - and therefore subject to change - or they are simply irrelevant to a discussion of natural rights. The first category includes the different spheres of activity (public versus private) to which men and women have traditionally applied their intellect, as well as their allegedly different senses of morality or justice. Women, it has been said, are guided by their feelings rather than by their reason or conscience. But such differences, Condorcet asserts, are caused by purely social factors: generally excluded from public life, women have directed their intelligence toward different objects and therefore may have developed, for instance, a different sense of justice from that of me ...[Condorcet writes] "if reasons such as these were admitted against women, it would also be necessary to deprive of the rights of citizenship that portion of the people who, because they are occupied in constant labour, can neither acquire knowledge nor exercise their reason. Soon, little by little, only persons who had taken a course in public law would be permitted to be citizens."

By 1792 Condorcet had become one of the leaders of the Republican cause. He joined the moderate Girondists and argued strongly that the King's life should be spared. When the Girondists fell from favour and the Jacobins, a more radical political group led by Robespierre, took over, Condorcet argued strongly against the new, hurriedly written, constitution which was drawn up to replace the one which he himself had been chiefly responsible for drawing up. This showed a lack of common sense and he paid for it when a warrant was issued for his arrest.

In the period to the run-up to his arrest he wrote Tableau général Ⓣ. The authors of [32] write:-

Condorcet wrote 'Tableau général' in haste during a few days in spring-summer 1793 (probably in June, and possibly in early July), just before he was put under arrest. He did not have enough time to finish or polish it. That is the reason why many passages remain elliptical or even equivocal, and why the structure of the essay is unbalanced. But these are not the only reasons why the 'Tableau général' Ⓣ is difficult to read: editorial blemishes were added to those contained in the manuscript, especially in the first edition.

Pierre Crépel and Jean-Nicolas Rieucau end their interesting article with the following conclusion [32]:-

The seeds of Condorcet's plan of applying calculus to political and moral sciences were already present in the early 1770s, when Condorcet located the "science of moral or political relations" within the branch of "physical mathematics." He developed it in various ways throughout the 1780s, most famously with his work on elections. In that respect, although the 'Tableau général' is indeed a blueprint for future work, it also constitutes a methodological synthesis of earlier researches. But its most specific features lie elsewhere. It is at the same time a mature text and, mostly because of the political circumstances in which it was written, quite a confused one, whose structure could have been improved. ... Retrospectively, one can imagine how much care Condorcet would have given to correcting and completing the 'Tableau général' had he had sufficient time for it. Under threat of impending banishment, at the climax of political instability, Condorcet chose to write quite an abstract text, almost the last which bore his signature. In no case can it be considered as a contingent work which he would have "taken lightly." Why did he decide to write it at that specific time? By presenting what he believed to be the true science of public happiness, his goal might have been "to rise above political debates," ... One can also suggest that Condorcet, who was already living half-clandestinely, meant to leave behind a legacy, with the intention of promoting a subject of enquiry which, as he wrote a few months later, "despite the successful attempts of some mathematicians, remains, as it were, in its early stages and ... [which] must open for the next generations a truly infinite source of enlightenment." One can guess that Condorcet considered himself as one of these "mathematicians."

Condorcet went into hiding and wrote a very interesting philosophical work Esquisse d'un tableau historique des progrès de l'esprit humain Ⓣ (1795). Oliver H Prior, who edited an edition of the Esquisse Ⓣ in 1938, writes in the Introduction (see [39]):-

Condorcet occupies a special place in the history of French thought. He is the last of the 'philosophes', and the only one who took an active part in the Revolution. He did not conceive a completely original system, but he did create a synthesis of all the theories of his predecessors. We can find in his writings the ideas of Voltaire, of Rousseau, of Turgot, of Helvetius, of Condillac, moulded bit by bit into a harmonious whole whose final expression is the 'Esquisse', a sort of philosophic résumé of the XVIII th century.

We present a version of Condorcet's Introduction to the Esquisse Ⓣ at THIS LINK.

In March 1794 he thought that the house in which he was hiding in Paris was being watched by his enemies and he no longer felt safe. He fled from Paris and after three days he was arrested and imprisoned on 27 March 1794. Two days later he was found dead in his prison cell and it is not known if he died from natural causes or whether he was murdered or took his own life.

John Herivel described Condorcet as follows [12]:-

... Condorcet was no politician. His uncompromising directness of manner and inability to suffer illogical windbags in silence made him many enemies and few friends. His weak voice, lack of oratorical powers, and tendency to bore the Convention by the excessive height of his arguments was one of the tragedies of the Revolution.

His life is summed up by Harry Burrows Acton (1908-1974) in [2] as follows:-

Wholly a man of the Enlightenment, an advocate of economic freedom, religious toleration, legal and educational reform, and the abolition of slavery, Condorcet sought to extend the empire of reason to social affairs. Rather than elucidate human behaviour, as had been done thus far, by recourse to either the moral or physical sciences, he sought to explain it by a merger of the two sciences that eventually became transmuted into the discipline of sociology.