理查德·普莱斯Richard Price

理查德·普莱斯的父亲是Rice 普莱斯，一位公理会牧师。在相当年轻的时候，普莱斯似乎已经采纳了与父亲有些不同的宗教观点，被更自由的基督教观点所吸引。他接受私人教育，然后在1739年父亲去世后，进入伦敦Tenter Alley的Fund Academy，这是由非国教徒独立建立的一所异议学院之一。我们注意到，他的宗教观点会使他不可能进入牛津或剑桥大学，而异议学院为那些希望在英格兰学习但观点与英格兰教会标准信仰不一致的人提供了大学教育的替代方案。

普莱斯 于1744年离开基金学院，搬到斯托克纽因顿，在那里他担任乔治·斯特里特菲尔德的家庭牧师。他时常为各个会众服务，其中一个职位是协助 皮埃尔·萨米埃尔 钱德勒在旧犹太区长老会教堂的工作。1756年，乔治·斯特里特菲尔德和 普莱斯 的一位叔叔去世，由于留给他的钱，普莱斯 的经济状况大大改善。到1757年，他的经济状况已足够强大，得以与来自莱斯特郡贝尔格雷夫的莎拉·布伦德尔结婚，次年他们搬到了哈克尼附近的小村庄纽因顿格林。普莱斯 于1757年出版了 Review of the Principal Questions in Morals，其中包含他的伦理学理论。他提出了基于个人良心和理性的道德决策的理性案例。他不认同基督教的原罪和永恒惩罚教义。普莱斯 在引言中写道：-

事实上，没有人具备那种冷静而公正的性情，那种摆脱一切错误偏见的自由，那种专注和耐心思考的习惯，以及那种敏锐和睿智的心灵，这些才是防止错误的适当保障。那么，谦逊和谨慎对我们来说是多么必要？我们应当多么乐于接受说服，并对那些持不同观点的人多么宽容？

当然，到目前为止，我们提到的关于普莱斯的任何内容都不会表明他应该在这个档案中，但我们收录他的原因是他对统计学的贡献。这似乎是通过他与托马斯·贝叶斯的友谊而产生的。William Morgan在他为其叔叔普莱斯写的传记中写道[2]：-

1761年，他的朋友、来自坦布里奇韦尔斯的托马斯·贝叶斯去世后，普莱斯应这位真正富有独创性的人的亲属请求，检查他关于不同主题所写的论文……

因此，托马斯·贝叶斯的几篇论文被交给了普莱斯。一篇由托马斯·贝叶斯撰写的Notebook至今仍保存在公平人寿保险协会的档案室中，人们不得不假设它被存放在那里是因为普莱斯对该协会的工作感兴趣并参与其中。普莱斯负责将托马斯·贝叶斯的Essay towards solving a problem in the doctrine of chances传达给皇家学会。普莱斯在附信中写道：-

我现在寄给你一篇我在我们已故朋友托马斯·贝叶斯先生的论文中找到的文章，在我看来，它很有价值，很值得保存。

Some of the calculations, particularly in the appendix, no one can make without a good deal of labour. I have taken so much care about them, that I believe there can be no material error in any of them; but should there be any such errors, I am the only person who ought to be considered as answerable for them。

有时很难分辨普莱斯对托马斯·贝叶斯的工作做出了哪些贡献，但可以清楚看出，普莱斯是一个谦逊的人，并不为自己的贡献谋求赞誉。他无疑显示出自己是一位极为称职的数学家。在[4]中，Zabell指出，普莱斯曾陈述：-

如果一个事件已经发生了$n$次，那么它在进一步试验中发生的几率大于均等的机会为$2^{n+1} - 1$比一。

Zabell [4]指出：-

这不是皮埃尔·西蒙·拉普拉斯的继任规则，而是基于托马斯·贝叶斯关于x的所有值先验等可能的假设，计算事件未知概率x超过$\large\frac{1}{2}\normalsize$的后验概率。

Royal Society于1765年因普莱斯对probability的贡献而选举其为会士。D O Thomas认为，正是他出版了托马斯·贝叶斯的论文，开启了普莱斯的：-

……对保险、人口学以及财政和政治改革的日益深入的参与。

1769年，在写给本杰明·富兰克林的一封信中，普莱斯评论了寿命预期、人口增长以及伦敦的人口。他的观察结果于同年晚些时候发表在Philosophical Transactions of the Royal Society上。1770年5月，普莱斯写信给皇家学会，解释了如何计算或有复归年金的价值。普莱斯似乎很清楚，新近建立的保险和福利社团在计算其保单时依据的是错误的理论。

我们知道普莱斯的科学兴趣非常广泛。他对电学也感兴趣，这一点可以从Joseph Priestley在History and present state of electricity的引言中感谢他这一事实得到证明：-

……感谢[他]对这项工作给予的关注，以及[他]在这方面为我提供的许多重要帮助。

事实上，氧气的发现者约瑟夫·普里斯特利是 普莱斯 的朋友。他们都被任命为非国教牧师，普里斯特利经常拜访纽因顿格林的 普莱斯。其他拜访纽因顿格林的朋友包括 弗瑞兹·约翰 霍华德、约翰 昆西·亚当斯、本杰明·富兰克林 和亚当·斯密。

1776年，普莱斯出版了一本小册子Observations on Civil Liberty and the War with America。据说1776年7月4日的Declaration of Independence of the Thirteen Colonies受到了普莱斯小册子的影响。1777年春天的第二本小册子再次讨论了与美国的战争，但也讨论了国家债务和其他财政事务。1778年冬天，他被大陆会议邀请前往美国协助财政管理，但他拒绝了。

普莱斯于1786年去世，此时普莱斯的健康状况正在恶化。然而，他仍有精力在1789年宣讲了一篇极具争议的布道：-

11月4日[1789年]上午，著名的不信奉国教派牧师普莱斯博士在老犹太会堂的不信奉国教派聚会所，向他的俱乐部或社团宣讲了一篇非常特别的杂糅布道，其中有一些良好的道德和宗教情感，表达得也不算差，混杂在各种政治观点和反思的糊状物中；但法国大革命是这口大锅中的主要成分。

这篇布道文出版后引起了极大争议，Edmund Burke在Reflections on the Revolution in France中写了一篇有力的答复，强烈主张世袭君主制。在其出版布道文的第四版中，普莱斯写了一篇导言：-

自从以下论述的前几版问世以来，已有许多批评文章发表。面对其中一些文章所伴随的辱骂，我因发现自己与巴黎市和法国国民议会站在一起而感到安慰。我不考虑花时间作任何答复。我知道我一生的工作一直是促进自由、和平与美德这些我认为人类最大利益的事业，并且相信我的努力并非完全徒劳，我感到一种满足，任何反对都无法夺走，我将默默接受公众的评判，除了提及以下这一辱骂实例外，不对我所遭遇的辱骂作任何其他关注。

一位论派协会成立于1791年，就在普莱斯去世前不久，他成为创始成员。普莱斯于1791年4月26日被安葬在Bunhill约翰·查尔斯·菲尔兹，在葬礼上Joseph Priestley作了葬礼布道。Bunhill菲尔兹是一个不信国教者的墓地，用于安葬那些信仰使他们脱离英格兰教会的人。

普莱斯在他那个时代很有名，尽管他的观点极具争议，许多人前来听他布道。他获得了伦敦市的自由，并被耶鲁学院授予D.D.学位。

Richard Price's father was Rice Price, a Congregational minister. At quite a young age Richard seems to have adopted somewhat different religious opinions from those of his father, being attracted towards more liberal Christian views. He was educated privately then, after the death of his father in 1739, he entered Fund Academy in Tenter Alley, London, one of the Dissenting academies that had been established independently by Nonconformists. We note that his religious views would have made it impossible for him to attend Oxford or Cambridge university, and the Dissenting academy provided an alternative to a university education for those wishing to study in England but who had views at odds with the standard beliefs of the Church of England.

Price left Fund Academy in 1744 and moved to Stoke Newington where he was family chaplain to George Streatfield. He ministered from time to time to various congregations, one of these posts having him assist Samuel Chandler at the Presbyterian Chapel at Old Jewry. In 1756 George Streatfield and an uncle of Price died, and as a result of money left to him Price's financial circumstances improved greatly. By 1757 he was in a strong enough financial position to marry Sarah Blundell, originally of Belgrave in Leicestershire, and in the following year they moved to Newington Green, a small village near Hackney. Price published Review of the Principal Questions in Morals in 1757 which contains his theory of ethics. He presented a rational case for moral decisions based on individual conscience and reason. He did not subscribe to the Christian doctrines of original sin and eternal punishment. Price wrote in the introduction:-

There are in truth none who are possessed of that cool and dispassionate temper, that freedom from all wrong biases, that habit of attention and patience of thought, and, also, that penetration and sagacity of mind, which are the proper securities against error. How much then do modesty and diffidence become us? How ought we to be to conviction, and candid to those of different sentiments?

Certainly up to this point nothing we have mentioned about Price would suggest that he should be in this archive, but the reason that we have included him is his contributions to statistics. This seems to have come about through his friendship with Bayes. William Morgan, in his biography of Price, his uncle, wrote [2]:-

On the death of his friend Mr Bayes of Tunbridge Wells in the year 1761 Price was requested by the relatives of that truly ingenious man, to examine the papers which he had written on different subjects ...

Several of Bayes's papers were therefore given to Price. A Notebook written by Bayes is still preserved in the muniment room of the Equitable Life Assurance Society and one has to assume that it was deposited there because Price was interested in the work of that Society, and involved with it. Price was responsible for the communication of Bayes's Essay towards solving a problem in the doctrine of chances to the Royal Society. Price wrote in the covering letter:-

I now send you an essay which I have found among the papers of our deceased friend Mr Bayes, and which, in my opinion, has great merit, and well deserves to be preserved.

Some of the calculations, particularly in the appendix, no one can make without a good deal of labour. I have taken so much care about them, that I believe there can be no material error in any of them; but should there be any such errors, I am the only person who ought to be considered as answerable for them.

At times it is hard to tell which contributions Price made to Bayes's work, but it is clear that Price was a modest man who did not seek credit for his contributions. He certainly shows himself to be a highly competent mathematician. In [4] Zabell notes that Price stated:-

If an event has happened $n$ times, there will be an odds of $2^{n+1} - 1$ to one, for more than an equal chance that it will on further trials.

Zabell [4] notes that:-

This is not Laplace's rule of succession, but rather a calculation of the posterior probability that the unknown chance x of the event exceeds $\large\frac{1}{2}\normalsize$, based on Bayes's assumption that all values of x are a priori equally likely.

The Royal Society elected Price a fellow in 1765 on the strength of his contributions to probability. D O Thomas suggests that it was his publication of Bayes's papers which started Price's:-

... increasing involvement in insurance, demography, and financial and political reform.

It was in 1769, in a letter to Benjamin Franklin, that Price commented on the expectation of lives, the increase of mankind, and the population of London. His observations were published in the Philosophical Transactions of the Royal Society later the same year. In May 1770 Price wrote to the Royal Society explaining how to calculate the values of contingent reversions. Price seemed to be well aware that the recently established insurance and benefit societies were basing the calculations of their policies on erroneous theory.

We know that Price's scientific interests were very broad. That he was also interested in electricity is demonstrated by the fact that Joseph Priestley thanks him in the introduction to History and present state of electricity :-

... for the attention [he] has given to the work, and for the many important services [he has] rendered me with respect to it.

In fact Joseph Priestley, the discoverer of oxygen, was a friend of Price. They were both ordained to the Dissenting ministry and Priestley frequently visited Price in Newington Green. Other friends who visited Newington Green included John Howard, John Quincy Adams, Benjamin Franklin and Adam Smith.

in 1776 Price published a pamphlet Observations on Civil Liberty and the War with America. It is said that the Declaration of Independence of the Thirteen Colonies made on 4 July 1776 was influenced by Price's pamphlet. A second pamphlet in the spring of 1777 again discussed the war with America but also discussed national debts and other financial matters. In the winter of 1778 he was invited by Congress to go to America to assist in financial administration but he declined.

Sarah Price died in 1786 and by this time Price's health was deteriorating. However he still had the energy to preach a highly controversial sermon in 1789:-

On the forenoon of the 4th of November [1789], Doctor Richard Price, a non-conforming minister of eminence, preached at the dissenting meeting-house of the Old Jewry, to his club or society, a very extraordinary miscellaneous sermon, in which there are some good moral and religious sentiments, and not ill expressed, mixed up in a sort of porridge of various political opinions and reflections; but the Revolution in France is the grand ingredient in the cauldron.

The sermon, which was published, was highly controversial and Edmund Burke wrote a vigorous reply in Reflections on the Revolution in France arguing strongly in favour of an inherited monarchy. In the fourth edition of his published sermon Price wrote an introduction:-

Since the former editions of the following discourse, many animadversions upon it have been published. Under the abuse with which some of them are accompanied, I have been comforted by finding myself joined to the City of Paris, and the National Assembly of France. I cannot think of employing my time in making any replies. Knowing that it has been the labour of my life to promote those interests of liberty, peace, and virtue, which I reckon the best interests of mankind, and believing that I have not laboured quite in vain, I feel a satisfaction that no opposition can take from me, and shall submit myself in silence to the judgment of the public without taking any other notice of the abuse I have met with than by mentioning the following instance of it.

The Unitarian Society was established in 1791, shortly before Price's death, and he became a founder member. Price was buried in Bunhill Fields on 26 April 1791 and at the service Joseph Priestley gave the funeral sermon. Bunhill Fields was a dissenters' cemetery for those whose beliefs took them outside the Church of England.

Price was famous in his day, although his views were highly controversial, and many came to hear him preach. He received the freedom of the City of London and was honoured with the award of the degree of D.D. from Yale College.