数学家传记
萨缪尔·克拉克是一位英国牧师,他撰写了关于力学以及哲学和形而上学的著作。
萨缪尔·克拉克的父母是汉娜·帕门特和Edward Clarke。汉娜是诺里奇一位商人的女儿,而爱德华则是一位布料制造商。皮埃尔·萨米埃尔在诺里奇接受教育,1685年至1690年就读于诺里奇免费文法学校,随后于1691年进入剑桥大学凯厄斯学院。在剑桥,他[2]:-
……以其兴趣之广泛以及试图在一个科学与学术日益成为专家领域的时代涵盖所有知识领域的努力而闻名。
他研究了艾萨克·牛顿的著作,深入钻研了其中的数学和物理学,但他也研习了神学和古典学。他于1695年毕业,在毕业考试中提交了艾萨克·牛顿的Principia的部分内容。由于在一场辩论中为艾萨克·牛顿的Principia中的一个命题进行辩护时的表现,他成为剑桥大学凯厄斯学院的研究员。他从1696年到1700年担任这一研究员职位。在此期间,他承担的任务之一是将罗奥的Traité de physiqueⓉ(物理学论著)从拉丁文翻译过来,这是一部基于勒内·笛卡儿物理学的物理学教材。克拉克添加了注释,赋予文本以牛顿主义的视角,该书于1697年出版。当他在1702年和1710年推出更多版本时,克拉克更进一步,编写了一部基于牛顿物理学的文本。
在诺里奇的一家咖啡馆里,他与当时担任诺里奇主教座堂牧师的威廉·惠斯顿偶然相遇,这导致他们讨论了艾萨克·牛顿的工作。威廉·惠斯顿将克拉克引荐给诺里奇主教,而当威廉·惠斯顿于1698年离开(三年后最终成为剑桥艾萨克·牛顿的助手)时,克拉克接替他担任诺里奇主教的牧师。主教将诺里奇附近的德雷顿教区交给克拉克管理,大约此时克拉克与凯瑟琳·洛克伍德结婚,她是诺福克郡小马宁厄姆教区长的女儿。他们有七个孩子,其中五个活到成年。
1704年洛克去世时,克拉克被认为是英格兰最伟大的metaphysician。1706年,艾萨克·牛顿请克拉克将他的Opticks译成拉丁文。克拉克因其宗教观点而引发巨大争议,支持者寥寥无几。然而,他于1706年成为圣贝尼特保罗码头教堂的教区长,随后于1709年成为威斯敏斯特圣詹姆斯教堂的教区长。进一步的宗教争议接踵而至,克拉克不得不作出各种正统信仰的声明,这些声明似乎刚好足以使他免于灾祸,尽管有人注意到他并未公开认错。让我们给出一些关于他宗教信仰的细节,同时展示数学如何成为他提出论点的方式的一部分。
克拉克早期的宗教著作中没有任何引起争议的内容。第一部是1699年的Three practical essays on baptism, confirmation, and repentance。他反对高教会仪式,但他也反对加尔文的观点,从而使自己处于各种观点的中间位置。1704年他发表波义耳讲座时,作为哲学家获得了相当大的声誉,并且由于以下原因,他史无前例地被要求在随后几年再次发表波义耳讲座:-
……在神学、哲学和数学方面具有如此才能的人,并不常见。
他1704年的讲座为自然宗教提出了强有力的论据,而1705年的讲座则涉及宗教启示。他认为,首先必须证明宗教信仰的逻辑有效性,然后才能在此基础上建立关于基督的基督教信仰。这种将关于上帝和基督的论证分开的做法,导致他采取了与官方基督教教义相悖的观点。克拉克本人相信数学论证是逻辑推理的最高形式,他在Demonstration of the being and attributes of God(1705)的序言中解释说,他将论证:-
……尽可能接近数学,只要这种论述的性质允许。
在这部著作中,克拉克还使用了基于艾萨克·牛顿的Principia的论证,作为试图证明一位有智慧的设计者对于创造和维持宇宙都是必要的这一证明的基础。
1709年,克拉克前往剑桥进行获得神学博士学位所必需的公开辩论。在这场辩论中,他再次证明了自己非凡的造诣,但有些人仍然怀疑他关于三位一体的观点是否与主流观点一致。在The scripture-doctrine of the Trinity: wherein every text in the New Testament relating to that doctrine is distinctly considered(1712)中,他不再让任何人怀疑,并论证说:-
……唯有圣父是自存的、非派生的、无本源的、独立的……[然而]圣子不是自存的;而是从圣父那里获得他的存在和所有属性……
这些观点当然与艾萨克·牛顿所持的观点接近,尽管他一直谨慎地不公开表达这些观点。克拉克在明确表达自己的立场后,实际上已使自己在教会内进一步晋升变得不可能,因为他会被要求再次签署《三十九条信纲》,这要求他宣誓信仰三位一体。因此,他余生将留在威斯敏斯特的圣詹姆斯。
1714年安妮女王去世后,他成为威尔士王妃的亲密顾问,后者后来成为卡罗琳王后。他每周与她见面,并应她的要求,与哥特弗里德·威廉·莱布尼茨就空间和时间的本质展开争论。克拉克捍卫牛顿理论,并与哥特弗里德·威廉·莱布尼茨通信,在通信期间对力学做出了重要贡献。让我们简要看看哥特弗里德·威廉·莱布尼茨提出的论点以及克拉克的答复(参见[6]、[9]、[11]和[13]中的有趣讨论)。
首先哥特弗里德·威廉·莱布尼茨论证说,艾萨克·牛顿对空间的描述使上帝成为他自己创造物的一部分。克拉克回答说:-
无限空间是广大,但广大不是上帝,因此无限空间不是上帝。
哥特弗里德·威廉·莱布尼茨还论证说,艾萨克·牛顿把上帝描绘成创造了一个不完美的宇宙,因为按照艾萨克·牛顿,上帝不得不持续调整行星的轨道。但是,克拉克论证说,如果宇宙无需上帝干预就能永远运行下去,那就不需要上帝了:-
[W]hosever contends that the course of the world can go on without the continual direction of God, the Supreme Governor; his doctrine does in effect tend to exclude God out of the world.
他选择不使用艾萨克·牛顿本人提出的那个风险更大的论证,即:-
[I]f the world could go on to all eternity, then it might have gone on from all eternity, and that is all that the atheists contend for.
我们考虑的最后论点是哥特弗里德·威廉·莱布尼茨提出的,即艾萨克·牛顿的超距作用观念,没有任何力学解释,是对神秘力量的诉求。克拉克在回复中设法利用超距作用观念来支持对人类自由和道德选择的信念。哥特弗里德·威廉·莱布尼茨于1716年11月14日在通信中途去世,这反倒把胜利拱手让给了克拉克。他当然选择这样来利用它,出版了通信并附上自己的最后回复,总结了自己的立场并让他说了最后一句话。
1727年艾萨克·牛顿去世时,克拉克被提供皇家铸币厂厂长的职位,但他拒绝了, stating that it was not consistent with his role as a clergyman. 尽管他的大部分出版物都是关于宗教和形而上学的,但他最后一部作品之一是On the proportion of force to velocity in bodies in motion,于他去世前一年出版。他在威斯敏斯特圣詹姆斯教堂的牧师住宅中去世,五天后被安葬在教堂的圣坛内。
Samuel Clarke's parents were Hannah Parmenter and Edward Clarke. Hannah was the daughter of a Norwich merchant while Edward was a cloth manufacturer. Samuel was educated in Norwich, attending the Norwich Free Grammar School from 1685 to 1690, then entering Caius College, Cambridge in 1691. At Cambridge he [2]:-
... was noted for the range of his interests and his attempt to span all fields of knowledge in an age when science, and learning more generally, were increasingly becoming the province of the expert.
He studied Newton's works, going deeply into both the mathematics and physics, but he also studied divinity and classical studies. He graduated in 1695 offering parts of Newton's Principia for his final examinations. He became a Fellow of Caius College, Cambridge, as a result of his performance in defending a proposition from Newton's Principia in a disputation. He held this fellowship from 1696 to 1700. One of the tasks he undertook at this time was a Latin translation of Rohault's Traité de physique Ⓣ which was a physics text based on the physics of Descartes. Clarke added notes giving a Newtonian perspective to the text which was published in 1697. When he produced further editions in 1702 and 1710, Clarke went even further in producing a text based on Newtonian physics.
A chance meeting with Whiston, at that time chaplain to the Bishop of Norwich, in a Norwich coffee house led to their discussing Newton's work. Whiston introduced Clarke to the Bishop of Norwich and, when Whiston moved on in 1698 (eventually becoming Newton's assistant at Cambridge three years later), Clarke replaced him as chaplain to the Bishop of Norwich. The Bishop gave Clarke the charge of Drayton, near Norwich, and around this time Clarke married Katherine Lockwood, daughter of the rector of Little Maningham in Norfolk. They had seven children, five of whom reached adulthood.
Clarke was considered the greatest metaphysician in England when Locke died in 1704. In 1706 Newton asked Clarke to translate his Opticks into Latin. Clarke attracted great controversy with his religious views having few supporters. However he became rector of St Benet Paul's Wharf in 1706 and then of St James's, Westminster in 1709. Further religious controversy followed and Clarke had to make various declarations of orthodox belief which seemed to be just enough to save him, although it was noted that he had not recanted. Let us give a few details on his religious beliefs and at the same time show how mathematics became part of the way that he put forward his arguments.
In Clarke's early religious writings there was nothing to arouse controversy. The first was Three practical essays on baptism, confirmation, and repentance of 1699. He opposed high church ritual but he put himself somewhere in the middle of the range of views by also opposing the views of Calvin. He gained considerable fame as a philosopher when he delivered the Boyle lectures in 1704 and in an unprecedented move he was asked to give the Boyle lectures again in the following years since:-
... persons of such abilities in theology, philosophy, and mathematics, are not to be commonly found.
His lectures of 1704 put strong arguments for natural religion while those of 1705 dealt with religious revelation. He believed that one first had to demonstrate the logical validity of religious belief before building on top of that the Christian beliefs concerning Christ. This separation in arguments concerning God and Christ led to him taking views which were at odds with official Christian doctrine. Clarke himself believed that mathematical argument was the supreme form of logical reasoning and he explained in the preface of Demonstration of the being and attributes of God (1705) that he would argue:-
... as near to mathematical as the nature of such a discourse would allow.
In this work Clarke also used arguments based on Newton's Principia as the basis of an attempted proof that an intelligent designer was necessary both to create and to maintain the universe.
In 1709 Clarke went to Cambridge to undertake the public dispute necessary to receive the degree of doctor of divinity. In this disputation he again proved himself to be remarkably accomplished but some were left doubting that his views on the Trinity conformed with those of the mainstream. In The scripture-doctrine of the Trinity: wherein every text in the New Testament relating to that doctrine is distinctly considered (1712) he left nobody in doubt and argued that:-
... the Father alone is self-existent, underived, unoriginated, independent ... [However] the Son is not self-existent; but derives his Being and all his attributes from the Father ...
These views of course were close to those held by Newton, although he had been careful not to express them publicly. In making his position clear, Clarke had now made further advancement within the Church virtually impossible since he would have been asked to again subscribe to the Thirty-Nine Articles which required him to swear belief in the Trinity. As a consequence to would remain at St James's, Westminster, for the rest of his life.
After the death of Queen Anne in 1714, he became a close advisor to the Princess of Wales, who was to become Queen Caroline. He had weekly meetings with her and at her request he entered into dispute with Leibniz over the nature of space and time. Clarke defended Newtonian theory and corresponded with Leibniz making significant contributions to mechanics during the correspondence. Let us look briefly at the arguments put forward by Leibniz and at Clarke's reply (see [6], [9], [11] and [13] for interesting discusssions).
First Leibniz argued that Newton's description of space made God part of his own creation. Clarke replied:-
Infinite space is immensity but immensity is not God and therefore infinite space is not God.
Leibniz also argued that Newton portrayed God as having made an imperfect universe since, according to Newton, God had to continually adjust the planets in their orbits. But, argued Clarke, if the universe ran forever without God's intervention there would be no need for God:-
[W]hosever contends that the course of the world can go on without the continual direction of God, the Supreme Governor; his doctrine does in effect tend to exclude God out of the world.
He chose not to use the rather more risky argument put forward by Newton himself, namely:-
[I]f the world could go on to all eternity, then it might have gone on from all eternity, and that is all that the atheists contend for.
The final argument by Leibniz that we consider is that Newton's idea of action at a distance, without any mechanical explanation, was an appeal to the occult. Clarke, in his reply, managed to use the idea of action at a distance to support a belief in human freedom and moral choice. The death of Leibniz on 14 November 1716 in the middle of the correspondence rather handed victory to Clarke. He certainly chose to play it in that way, publishing the correspondence with a final reply of his own which summed up his position and gave him the final word.
When Newton died in 1727, Clarke was offered the position as master of the Royal Mint but he turned it down, stating that it was not consistent with his role as a clergyman. Although most of his publications were on religion and metaphysics, one of his last works was On the proportion of force to velocity in bodies in motion published a year before his death. He died in the rectory of his church of St James's, Westminster, and was buried five days later in the chancel of the church.
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