- Frank P. Ramsey
era = 20th century
color = #B0C4DE
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name = Frank P. Ramsey
birth = 22 February 1903
death = 19 January 1930
Philosophy of Mathematics, Logic, Metaphysics, Epistemology
Frank Plumpton Ramsey (
February 22, 1903– January 19, 1930) was a British mathematicianwho, in addition to mathematics, made significant contributions in philosophyand economics.
He was born on 22 February 1903 in
Cambridgewhere his father, also a mathematician, was President of Magdalene College. He was the eldest of one brother and two sisters, and his brother Michael Ramseylater became Archbishopof Canterbury. He entered Winchester Collegein 1915 and later returned to Cambridge to study mathematics at Trinity College. Easy-going, simple and modest, Ramsey had many interests besides his scientific work. Even as a teenager Ramsey showed both his profound abilities and the heterogeneity of the issues that concerned him. His brother Lord Ramsey was well aware of both these facts:
In September 1925 he married Lettice Baker, the wedding taking place in a Registry Office since Ramsey was, as his wife described him, a ‘militant
atheist’. The marriage subsequently produced two daughters. Despite his atheism, Ramsey showed great tolerance towards his brother when the latter decided to become a priest in the Church of England.
He returned to England in 1924, and with
Keynes's support he became a fellow of King's College, Cambridge, being the second person ever to be elected without having previously studied at King's College.
In 1926 he became a university lecturer in mathematics and later a Director of Studies in Mathematics at King's College. When Wittgenstein submitted the
Tractatus Logico-Philosophicusas his doctoral thesisat Cambridge, Ramsey was Wittgenstein’s supervisor and G.E. Mooreand Bertrand Russellwere the examiners. Later on the three of them arranged financial aid for Wittgenstein to help him continue his research work.
In 1929 Ramsey and Wittgenstein regularly discussed issues in
mathematicsand philosophywith Piero Sraffa, an Italian economist who had been brought to Cambridge by Keynes after Sraffa had aroused Mussolini’s ire by publishing an article critical of the Fascistregime in the Manchester Guardian. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work.
Ramsey and Wittgenstein
The manner in which Ramsey familiarized himself with German demonstrates his great intellectual facility. When
I.A. Richardsand C. K. Ogden, both Fellows of Magdalene, first met Ramsey, he expressed his interest in learning German. And, according to Richards, he mastered the language "in almost hardly over a week". [Quoted in Mellor, "Ramsey", p. 245.] Ramsey was then able, at the age of 19, to make the first draft of the translation of the German text of Wittgenstein’s " Tractatus Logico Philosophicus". Ramsey was impressed by Wittgenstein’s work and after graduating as a Wrangler in the Mathematical Triposof 1923 he made a journey to Austriato visit Wittgenstein, at that time teaching in a primary school in the small community of Puchberg am Schneeberg. For two weeks Ramsey discussed the difficulties he was facing in understanding the extremely difficult "Tractatus". Wittgenstein made some corrections to the English translation in Ramsey’s copy and some annotations and changes to the German text that subsequently appeared in the second edition in 1933.
In 1927 Ramsey published the influential article "Facts and Propositions", in which he proposed what is sometimes described as a "
redundancy theory of truth".
One of the
theorems proved by Ramsey in his 1930 paper "On a problem of formal logic" now bears his name ( Ramsey's theorem). While this theorem is the work Ramsey is probably best remembered for, he only proved it in passing, as a minor lemma along the way to his true goal in the paper, solving a special case of the decision problem for first-order logic. As it happened, the lemma was not actually necessary for the results he obtained from it. However, Alonzo Churchwould go on to show that the general case of the problem Ramsey was tackling is unsolvable (see Church's theorem), while, ironically, a great amount of later work in mathematics was fruitfully developed out of the ostensibly minor lemma, which turned out to be an important early result in combinatorics, supporting the idea that within some sufficiently large systems, however disordered, there must be some order. So fruitful, in fact, was Ramsey's theorem that today there is an entire branch of mathematics, known as Ramsey theory, which is dedicated to studying similar results.
His philosophical works included "Universals" (1925), "Facts and propositions" (1927), "Universals of law and of fact" (1928), "Knowledge" (1929), "Theories" (1929), and "General propositions and causality" (1929). A few philosophers consider him to have been, or at least to have had the potential to be, an even greater philosopher than Wittgenstein Fact|date=April 2007. Wittgenstein mentions him in the introduction to his "
Philosophical Investigations" as an influence (but not as great an influence as Piero Sraffa).
Work in economics
Keynesencouraged Ramsey to work on economicsas ‘"From a very early age, about sixteen I think, his precocious mind was intensely interested in economic problems’" (Keynes, 1933). Ramsey responded to Keynes's urging by writing three papers in economic theory all of which were of fundamental importance, though it was many years before they received their proper recognition by the community of economists.
Ramsey’s three papers, described below in detail, were on
subjective probabilityand utility(1926), optimal taxation(1927) and optimal one-sector economic growth (1928). The economist Paul Samuelsondescribed them in 1970 as " 'three great legacies - legacies that were for the most part mere by-products of his major interest in the foundations of mathematics and knowledge.' "
A mathematical theory of saving
This significant paper was published in The Economic Journal, and involved "a strategically beautiful application of the
calculus of variations" (Paul Samuelson) in order to determine the optimal amount an economy should invest (save) rather than consume so as to maximize future utility, or in Ramsey’s words "how much of its income should a nation save"? (Ramsey, 1928).
Keynes described the article as " 'one of the most remarkable contributions to mathematical economics ever made, both in respect of the intrinsic importance and difficulty of its subject, the power and elegance of the technical methods employed, and the clear purity of illumination with which the writer's mind is felt by the reader to play about it subject. The article is terribly difficult reading for an economist, but it is not difficult to appreciate how scientific and aesthetic qualities are combined in it together' " (Keynes 1933). The Ramsey model is today acknowledged as the starting point for optimal accumulation theory although its importance was not recognized until many years after its first publication.
The main contributions of the model were firstly the initial question Ramsey posed on how much savings should be and secondly the method of analysis, the intertemporal maximization (optimization) of collective or individual utility by applying techniques of dynamic optimization. Tjalling C. Koopmans and David Cass modified the Ramsey model incorporating the dynamic features of population growth at a steady rate and of Harrod-neutral technical progress again at a steady rate, giving birth to a model named the Ramsey-Cass-Koopmans model where the objective now is to maximize household’s utility function
A contribution to the theory of taxation
In this paper Ramsey's contribution to
economic theorywas the elegant conceptof Ramsey pricing. This is applicable in situations where a (regulated) "monopolist" wants to maximise consumer surpluswhilst at the same time ensuring that its costs are adequately covered. This is achieved by setting the price such that the markup over marginal costis inversely proportional to the price elasticityof demand for that good. Like its predecessor this paper was published in The Economic Journal in 1927. Ramsey poses the question that is to be solved at the beginning of the article: " 'a given revenue is to be raised by proportionate taxes on some or all uses of income, the taxes on different uses being possibly at different rates; how much should these rates be adjusted in order that that the decrement of utility may be a minimum?' " (Ramsey 1927). The problem was suggested to him by the economist Arthur Pigouand the paper was Ramsey’s answer to the problem.
Truth and probability
Keynes in his
Treatise on Probability(1921) argued against the subjective approach in epistemic probabilities. For Keynes, subjectivity of probabilities doesn’t matter as much, as for him there is an objective relationship between knowledge and probabilities, as knowledge is disembodied and not personal.
Ramsey in his article disagrees with Keynes’s approach as for him there is a difference between the notions of probability in physics and in logic. For Ramsey probability is not related to a disembodied body of knowledge but is related to the knowledge that each individual possesses alone. Thus personal beliefs that are formulated by this individual knowledge govern probabilities leading to the notion of subjective probability. Consequently, subjective probabilities can be inferred by observing actions that reflect individuals' personal beliefs. Ramsey argued that the degree of probability that an individual attaches to a particular outcome can be measured by finding what
oddsthe individual would accept when betting on that outcome. Ramsey suggested a way of deriving a consistent theory of choice under uncertainty that could isolate beliefs from preferences while still maintaining subjective probabilities.
Despite the fact that Ramsey’s work on probabilities was of great importance again no one paid any attention to it until the publication of
Theory of Games and Economic Behaviorof John von Neumannand Oskar Morgensternin 1944 (1947 2nd ed.).
Suffering from chronic
liverproblems, Ramsey contracted jaundiceafter an abdominal operation and died on 19 January 1930 at Guy’s Hospitalin London at the age of 26.
Decision Analysis Societyannually awards the Frank P. Ramsey Medalto recognise substantial contributions to decision theoryand its application to important classes of real decision problems. He is buried at the Parish of the Ascension Burial Ground in Cambridge.
Ramsey growth model
*Arrow K. (1980), "Review: Foundations: Essays in Philosophy, Logic, Mathematics and Economics," "Journal of Political Economy", Vol. 88, No. 3. pp. 636-638
* Grattan-Guinness, Ivor (2000), "The Search for Mathematical Roots 1870–1940", Princeton University Press, Princeton, NJ.
* Keynes, John Maynard (1933), "Frank Plumpton Ramsey," in "Essays in Biography", New York, NY.
*Mellor D.H. (1995), "Cambridge Philosophers I: F. P. Ramsey," "Philosophy" 70, pp. 243-262
*Newbery D., "Ramsey model," "The ", v. 4, pp.46-48
*Newman P. (1987)., "Ramsey, Frank Plumpton," "The New Palgrave: A Dictionary of Economics", v. 4, pp.41-46
* Ramsey, F.P. (1927), "Facts and Propositions," "Aristotelian Society Supplementary Volume 7", 153–170. Reprinted, pp. 34–51 in
*Ramsey F.P. (1928), "A Mathematical Theory of Saving," "Economic Journal", Vol. 38, No 152, pp.543-559
*Ramsey F.P. (1927), "A Contribution to the Theory of Taxation," "Economic Journal", Vol. 37, No 145, pp.47-61
*Samuelson P. (1970), "What Makes for a Beautiful Problem in Science?" "Journal of Political Economy", Vol. 78, No. 6. pp. 1372-1377
* [http://www.algana.co.uk/Societies/RamseySociety/FrankRamseyAppreciationSociety.htm Appreciation of Frank]
* [http://www.fil.lu.se/sahlin/ramsey/ Comprehensive resource on Ramsey]
* [http://cepa.newschool.edu/het/profiles/ramsey.htm Short Ramsey biography]
* [http://www.dspace.cam.ac.uk/handle/1810/3484 Realaudio BBC profile of Ramsey from 1978, & transcript]
* [http://plato.stanford.edu/entries/probability-interpret/ Stanford Encyclopedia of Philosophy: Interpretations of Probability.] See 3.5 (3.2) for Ramsey's (Keynes's) views on probability.
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