弗兰克·普伦普顿·拉姆齐Frank P. Ramsey

弗兰克·普伦普顿·拉姆齐的父母是Arthur Stanley Ramsey和Agnes Mary Wilson。Arthur Ramsey是剑桥大学莫德林学院院长，也是那里的数学导师。拉姆齐是他父母四个孩子中最大的。他有一个兄弟和两个姐妹，他的兄弟Michael Ramsey后来成为坎特伯雷大主教。

拉姆齐于1915年进入温切斯特公学，并从那里获得奖学金进入剑桥大学三一学院。他于1920年在温切斯特完成中学教育，随后进入剑桥大学三一学院学习数学。在剑桥，拉姆齐于1921年成为高级学者，并在1923年的数学荣誉学位考试中以数学荣誉学位考试一等及格者（Wrangler）身份毕业。

毕业后，拉姆齐曾短暂前往维也纳，之后返回剑桥，于1924年被选为剑桥大学国王学院的研究员。值得注意的是，这是极为罕见的情况，事实上拉姆齐是历史上第二位未曾在国王学院学习过却被选为该学院研究员的人。

1925年，拉姆齐与Lettice C Baker结婚，他们有两个女儿。1926年，他被任命为大学数学讲师，后来成为国王学院数学研究主任。这是一个短暂的职业生涯，因为令人悲伤的是，拉姆齐于1930年初去世。然而，在他在剑桥讲课的短时间内，他已经确立了自己作为杰出讲师的地位。Broadbent在[1]中写道：-

他关于数学基础的讲座以其非凡的清晰和热情给年轻学生留下了深刻印象……

拉姆齐 是数学讲师，他在短时间内产出了涵盖广泛主题的工作。除了开创了现在被称为“拉姆齐论”的数学新领域（我们将在下文进一步讨论）之外，他还撰写了关于数学基础、经济学和哲学的作品。

他于1925年出版了他的第一部主要著作The Foundations of Mathematics。在这部著作中，他接受了伯特兰·罗素和阿尔弗雷德·诺思·怀特海在Principia Mathematica中提出的数学是逻辑的一部分的主张。然而，拉姆齐在这篇论文中的目的是改进Principia Mathematica，他通过两种方式做到了这一点。首先，他提议放弃可化归性公理，他写道，该公理：-

……肯定不是自明的，也没有理由假设它是真的；如果它是真的，那将是一个幸运的偶然，而不是逻辑必然性，因为它不是重言式。

他的第二个简化是建议通过将某些语义悖论视为语言学的来简化伯特兰·罗素的类型论。他接受了伯特兰·罗素的解决方案，以消除集合论中由例如“所有不属于自身的集合的集合”引起的逻辑悖论。然而，拉姆齐声称，诸如“这句话是谎话”这样的语义悖论是完全不同的，并且取决于“谎话”一词的含义。他通过重新解释消除了这些悖论，从而去掉了可化归性公理。

拉姆齐于1926年在Mathematical Gazette上发表了Mathematical Logic。在这篇文章中，他抨击了：-

……勒伊岑·布劳威尔和赫尔曼·外尔的布尔什维克威胁……

因为他否认命题非真即假。他写道：

勒伊岑·布劳威尔会拒绝同意要么下雨要么不下雨，除非他亲自去看过。

他还在Mathematical Logic中批评大卫·希尔伯特，说后者曾试图把数学归结为：

……一种在纸上做记号的毫无意义的游戏。

他关于数学的第二篇论文On a problem of formal logic于1928年12月13日在伦敦数学会上宣读，并于1930年发表在Proceedings of the London Mathematical Society上。该文考察了判定一个逻辑公式一致性的方法，并包含了一些组合数学方面的定理，这些定理引出了对整个一个被称为拉姆齐理论的新数学领域的研究。Harary在[8]中描述了拉姆齐理论的这一诞生，他在其中写道：

拉姆齐[1930年]那篇著名论文，极大地推动了图论……以及数学其他分支……中的大量研究。如今，“拉姆齐理论”无疑已是组合数学中一个确立且不断发展的分支。它的结果往往容易陈述（在被发现之后）却难以证明；精确时优美，且丰富多彩。未解决的问题比比皆是，而新的有趣开放问题出现的速度，快于现有问题的解决。

组合学是由拉姆齐引入的，用以解决一阶谓词演算判定问题的一个特例。然而，正如Mellor在[9]中指出的，现在已知存在一个比拉姆齐所给出的更为直接的证明，而判定问题的一般情形则无法解决。因此Mellor指出[9]：-

拉姆齐在数学中持久的名声……建立在一个他并不需要的定理之上，该定理是在试图做一件我们现在知道不可能做到的事情的过程中证明的！

拉姆齐进行了一次系统的尝试，将数学theory of probability建立在部分信念的概念之上。这项关于概率的工作，以及经济学方面的重要工作，主要源于拉姆齐是约翰·梅纳德·凯恩斯的密友。然而，作为约翰·梅纳德·凯恩斯的朋友，当然并未阻止拉姆齐攻击约翰·梅纳德·凯恩斯的工作，在拉姆齐于1926年发表的Truth and probability中，他反对约翰·梅纳德·凯恩斯关于先验归纳逻辑的思想。拉姆齐的论证说服了约翰·梅纳德·凯恩斯，后者随后放弃了自己的想法。拉姆齐提出了一种基于信念强度的概率测度，[11]：-

……推导出欲望的测度（主观效用）和信念的测度（主观概率），从而奠定了这些概念如今的标准用法。

在经济学中，拉姆齐写了两篇论文A contribution to the theory of taxation和A mathematical theory of saving。这些论文将引领该学科进入重要的新领域。

然而，哲学才是拉姆齐真正的挚爱。他写了许多著作，如Universals（1925年）、Facts and propositions（1927年）、Universals of law an of fact（1928年）、Knowledge（1929年）、Theories（1929年）和General propositions and causality（1929年）。Braithwaite在[6]中写道：-

……总的来说，哲学越来越占据他的注意力。对于这个最困难领域中有益的思考，拉姆齐具备极高的素养，毫无疑问，他的早逝使世界失去了一位最有前途的哲学家。

然而，人们不得不说，拉姆齐在哲学方面的工作在某种程度上被路德维希·维特根斯坦的工作所掩盖。不过，最近拉姆齐在哲学方面的工作似乎受到了更多关注。

参考文献中引用的几篇文章生动地描绘了拉姆齐的性格。例如，Braithwaite在[6]中写道：-

作为一个人，不亚于作为一个思想家，拉姆齐是剑桥的荣耀。从本科时代起，他就被公认为任何抽象主题的权威，他直截了当的处事方式和坦率激励着他的同伴。他巨大的体格与他智力的广度相称，他极具摧毁力的笑声与他幽默地摒弃无关紧要之事的能力相称，这种能力使他能够在最高程度上既精妙又深刻。

Mellor在[10]中描绘了类似的画面：-

他是一个安静、谦逊的人，随和而不拘束，笑声洪亮而富有感染力，他的宽容和好脾气使他能够强烈地表示异议而不冒犯他人或感到被冒犯；正如他的兄弟Michael……其授圣职……拉姆齐作为一名战斗的无神论者对此感到遗憾。

他身高六英尺三英寸，体格魁梧，近视，戴着钢边眼镜，看上去笨手笨脚，但实际上是一名优秀的网球手。他每天上午用四个小时完成其非凡的成果——他觉得再多做就过于费力——下午和晚上则常常散步或听唱片。他大量聆听古典音乐，既有现场演奏也有录音，并且热衷于山间徒步。

在2中，他的潜力得到了强调：-

在剑桥的年轻人中，没有人在思维的力量与品质上，以及在这门最困难学科之一中构想的胆识与独创性上，被认为能与他匹敌。

拉姆齐患了黄疸，被送往伦敦的盖伊医院接受手术。他在手术后去世。

一篇关于他去世的文章在THIS LINK。

Frank Ramsey's parents were Arthur Stanley Ramsey and Agnes Mary Wilson. Arthur Ramsey was President of Magdalene College, Cambridge, and a tutor in mathematics there. Frank was the oldest of his parents four children. He had one brother and two sisters and his brother Michael Ramsey went on to become Archbishop of Canterbury.

Ramsey entered Winchester College in 1915 and from there he won a scholarship to Trinity College, Cambridge. He completed his secondary school education at Winchester in 1920 and he entered Trinity College, Cambridge, to study mathematics. At Cambridge, Ramsey became a senior scholar in 1921 and graduated as a Wrangler in the Mathematical Tripos of 1923.

After graduating, Ramsey went to Vienna for a short while, returning to Cambridge where he was elected a fellow of King's College Cambridge in 1924. It is worth noting that this was a most unusual occurrence, and in fact Ramsey was only the second person ever to be elected to a fellowship at King's College, not having previously studied at King's.

In 1925 Ramsey married Lettice C Baker and they had two daughters. In 1926 he was appointed as a university lecturer in mathematics and he later became a Director of Studies in Mathematics at King's College. It was a short career, for sadly Ramsey died at the beginning of 1930. However, in the short time during which he lectured at Cambridge he had already established himself as an outstanding lecturer. Broadbent writes in [1]:-

His lectures on the foundations of mathematics impressed young students by their remarkable clarity and enthusiasm ...

Although Ramsey was a lecturer in mathematics, he produced work in a remarkable range of topics over a short period. As well as starting up the new area of mathematics now called 'Ramsey theory', which we say more about below, he wrote on the foundations of mathematics, economics and philosophy.

He published his first major work The Foundations of Mathematics in 1925. In this work he accepted the claim by Russell and Whitehead made in the Principia Mathematica that mathematics is a part of logic. Ramsey's aim in this paper, however, was to improve on the Principia Mathematica and he did so in two ways. Firstly he proposed dropping the axiom of reducibility which, he writes, is:-

... certainly not self-evident and there is no reason to suppose it true; and if it were true, this would be a happy accident and not a logical necessity, for it is not a tautology.

His second simplification is to suggest simplifying Russell's theory of types by regarding certain semantic paradoxes as linguistic. He accepted Russell's solution to remove the logical paradoxes of set theory arising from, for example, "the set of all sets which are not members of themselves". However, the semantic paradoxes such as "this is a lie" are, Ramsey claims, quite different and depend on the meaning of the word "lie". These he removed with his reinterpretation that removed the axiom of reducibility.

Ramsey published Mathematical Logic in the Mathematical Gazette in 1926. In this he attacks the:-

... Bolshevik menace of Brouwer and Weyl ...

for denying that propositions are either true of false. He writes:-

Brouwer would refuse to agree that either it was raining or it was not raining, unless he had looked to see.

He also criticises Hilbert in Mathematical Logic saying that he had attempted to reduce mathematics to:-

... a meaningless game with marks on paper.

His second paper on mathematics On a problem of formal logic was read to the London Mathematical Society on 13 December 1928 and published in the Proceedings of the London Mathematical Society in 1930. This examines methods for determining the consistency of a logical formula and it includes some theorems on combinatorics which have led to the study of a whole new area of mathematics called Ramsey theory. Harary describes this birth of Ramsey theory in [8] where he writes the following:-

The celebrated paper of Ramsey [in 1930] has stimulated an enormous study in both graph theory ..., and in other branches of mathematics .... Most certainly 'Ramsey theory' is now an established and growing branch of combinatorics. Its results are often easy to state (after they have been found) and difficult to prove; they are beautiful when exact, and colourful. Unsolved problems abound, and additional interesting open questions arise faster than solutions to the existing problems.

The combinatorics was introduced by Ramsey to solve a special case of the decision problem for the first-order predicate calculus. However, as Mellor points out in [9], it is now known that there is a more direct proof than that given by Ramsey, while the general case of the decision problem cannot be solved. So Mellor points out that [9]:-

Ramsey's enduring fame in mathematics ... rests on a theorem he didn't need, proved in the course of trying to do something we now know can't be done!

Ramsey made a systematic attempt to base the mathematical theory of probability on the notion of partial belief. This work on probability, and also important work on economics, came about mainly because Ramsey was a close friend of Keynes. Being a friend of Keynes certainly did not stop Ramsey attacking Keynes' work, however, and in Truth and probability , which Ramsey published in 1926, he argues against Keynes' ideas of an a priori inductive logic. Ramsey's arguments convinced Keynes who then abandoned his own ideas. Ramsey, proposing a probability measure based on strength of belief, [11]:-

... derives measures both of desires (subjective utilities) and of beliefs (subjective probabilities), thereby founding the now standard use of these concepts.

In economics, Ramsey wrote two papers A contribution to the theory of taxation and A mathematical theory of saving. These would lead to important new areas in the subject.

It was philosophy, however, that was Ramsey's real love. He wrote a number of works such as Universals (1925), Facts and propositions (1927), Universals of law an of fact (1928), Knowledge (1929), Theories (1929), and General propositions and causality (1929). Braithwaite writes in [6]:-

... in general philosophy took more and more of his attention. For profitable thought in this most difficult field Ramsey was superbly equipped, and there is no doubt that his early death has deprived the world of one of its most promising philosophers.

One would have to say, however, that Ramsey's work in philosophy has been somewhat overshadowed by that of Wittgenstein. Recently, however, Ramsey's work in philosophy seems to be receiving more attention.

Several of the articles cited in the references paint vivid pictures of Ramsey's character. For example Braithwaite writes in [6]:-

As a person, no less than as a thinker, Ramsey was an ornament to Cambridge. From his undergraduate days he had been recognised as an authority on any abstract subject, and his directness of approach and candour were an inspiration to his associates. His enormous physical size fitted well the range of his intellect, and his devastating laugh suited his power of humorously discarding irrelevancies, which power enabled him to be both subtle and profound in the highest degree.

Mellor, in [10], paints a similar picture:-

He was a quiet, modest man, easy going and uninhibited, with a loud infectious laugh, his tolerance and good humour enabling him to disagree strongly without giving or taking offence; as with his brother Michael ... whose ordination ... Frank, as a militant atheist, regretted.

He was tall (six feet three inches) and bulky, short-sighted, wore steel-rimmed spectacles and appeared clumsy but was in fact a good tennis player. He produced his remarkable output in four hours a day - he found it too exacting to do more - in the mornings, with afternoons and evenings often spent walking or listening to records. He listened a lot to classical music, both live and recorded, and was a keen hill-walker.

In [2] his potential is emphasised:-

There was no one in Cambridge among the younger men who would be considered his equal for power and quality of mind, and also for the boldness and originality of conception in one of the most difficult subjects of study.

Ramsey suffered an attack of jaundice and was taken to Guy's Hospital in London for an operation. He died following the operation.

An article about his death is at THIS LINK.