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Frank Ramsey | |
|---|---|
 Ramsey,c. 1921 | |
| Born | Frank Plumpton Ramsey (1903-02-22)22 February 1903 |
| Died | 19 January 1930(1930-01-19) (aged 26) |
| Education | Trinity College, Cambridge (BA, 1923) |
| Spouse | |
| Children | 2 |
| Era | 20th-century philosophy |
| Region | Western philosophy |
| School | Analytic philosophy |
| Institutions | King's College, Cambridge |
Main interests | |
Notable ideas | |
Frank Plumpton Ramsey (/ˈræmzi/; 22 February 1903 – 19 January 1930) was aBritishphilosopher,mathematician, andeconomist who made major contributions to all three fields before his death at the age of 26. He was a close friend ofLudwig Wittgenstein and, as an undergraduate, translated Wittgenstein'sTractatus Logico-Philosophicus into English. He was also influential in persuading Wittgenstein to return tophilosophy and Cambridge. Like Wittgenstein, he was a member of theCambridge Apostles, the secret intellectual society, from 1921.
Ramsey was born on 22 February 1903 inCambridge where his fatherArthur Stanley Ramsey (1867–1954), also a mathematician, was President ofMagdalene College. His mother was Mary Agnes Stanley (1875–1927). He was the eldest of two brothers and two sisters, and his brotherMichael Ramsey, the only one of the four siblings who was to remain Christian, later becameArchbishop of Canterbury. He enteredWinchester College in 1915 and later returned to Cambridge to study mathematics atTrinity College. There he became a student ofJohn Maynard Keynes and an active member in the Apostles. In 1923, he received his bachelor's degree in mathematics, passing his examinations with the result offirst class with distinction, and was namedSenior Wrangler (top of his class).[2] Easy-going, simple and modest, Ramsey had many interests besides his mathematical and scientific studies. Even as a teenager, Ramsey exhibited both a profound ability and, as attested by his brother, an extremely diverse range of interests:
He was interested in almost everything. He was immensely widely read inEnglish literature; he was enjoyingclassics though he was on the verge of plunging into being a mathematical specialist; he was very interested in politics, and well-informed; he had got a political concern and a sort of left-wing caring-for-the-underdog kind of outlook about politics.
— Michael Ramsey, Quoted in Mellor
In 1923, Ramsey was befriended byGeoffrey andMargaret Pyke, then on the point of founding theMalting House School in Cambridge; the Pykes took Ramsey into their family, taking him on holiday and asking him to be the godfather of their young son. Margaret found herself to be the object of his affection, Ramsey recording in his diary:
One afternoon I went out alone with her onLake Orta and became filled with desire and we came back and lay on two beds side by side she reading, I pretending to, but with an awful conflict in my mind. After about an hour I said (she was wearing her horn spectacles and looking superlatively beautiful in theBurne Jones style) 'Margaret will you fuck with me?'[3]
Margaret wanted time to consider his proposition and thus began an uncomfortable dance between them, which contributed to Ramsey's depressive moods in early 1924; as a result, he travelled to Vienna forpsychoanalysis. Like many of his contemporaries, including his Viennese flatmate and fellow ApostleLionel Penrose (also in analysis withSiegfried Bernfeld), Ramsey was intellectually interested in psychoanalysis. Ramsey's analyst wasTheodor Reik, a disciple ofFreud. As one of the justifications for undertaking the therapy, he asserted in a letter to his mother that unconscious impulses might affect even a mathematician's work. While in Vienna, he made a trip toPuchberg in order to visit Wittgenstein, was befriended by the Wittgenstein family and visitedA.S. Neill's experimental school four hours from Vienna at Sonntagsberg. In the summer of 1924, he continued his analysis by joining Reik atDobbiaco (inSouth Tyrol), where a fellow analysand wasLewis Namier. Ramsey returned to England in October 1924; withJohn Maynard Keynes's support, he became a fellow ofKing's College, Cambridge. He joined a Psychoanalysis Group in Cambridge with fellow membersArthur Tansley,Lionel Penrose,Harold Jeffreys,John Rickman andJames Strachey, the qualification for membership of which was a completed psychoanalysis.
Ramsey marriedLettice Baker in August 1925, the wedding taking place in a Register Office since Ramsey was, as his wife described him, a 'militantatheist'. The marriage produced two daughters. After Ramsey's death,Lettice Ramsey opened a photography studio in Cambridge with photographerHelen Muspratt.[4] Despite hisatheism, Ramsey was "quite tolerant" towards his brother when the latter decided to become a priest in theChurch of England.[5]
In 1926 he became a university lecturer in mathematics and later a Director of Studies in Mathematics at King's College. TheVienna Circle manifesto (1929) lists three of his publications[6][7][8] in a bibliography of closely related authors.
WhenI. A. Richards andC. K. Ogden, both Fellows ofMagdalene, first met Ramsey, he expressed his interest in learning German. According to Richards, he mastered the language "in almost hardly over a week",[9] although other sources show he had taken one year of German in school.[10] Ramsey was then able, at the age of 19, to make the first draft of the translation of the German text ofLudwig Wittgenstein'sTractatus Logico-Philosophicus. Ramsey was impressed by Wittgenstein's work and after graduating asSenior Wrangler in the MathematicalTripos of 1923 he made a journey toAustria to visit Wittgenstein, at that time teaching in a primary school in the small community ofPuchberg am Schneeberg. For two weeks Ramsey discussed the difficulties he was facing in understanding theTractatus. 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.
Ramsey andJohn Maynard Keynes cooperated to try to bring Wittgenstein back to Cambridge (he had been a student there before World War I). Once Wittgenstein had returned to Cambridge, Ramsey became his nominal supervisor. Wittgenstein submitted theTractatus Logico-Philosophicus as his doctoral thesis.G.E. Moore andBertrand Russell acted as examiners. Later, 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 mathematics and philosophy withPiero Sraffa, anItalian economist who had been brought to Cambridge by Keynes after Sraffa had arousedBenito Mussolini's ire by publishing an article critical of the Fascist regime in theManchester Guardian. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work.
In the introduction toPhilosophical Investigations Wittgenstein credits Ramsey's criticism of theTractatus in the "interminable conversations" they had as having helped him realise "grave mistakes" within the work.[11]
Suffering chronicliver problems, Ramsey developedjaundice after an abdominal operation and died on 19 January 1930 atGuy's Hospital in London at the age of 26. There is a suspicion that the cause of his death might be an undiagnosedleptospirosis with which Ramsey, an avid swimmer, could have become infected while swimming in theCam.[12]
He is buried in theParish of the Ascension Burial Ground in Cambridge; his parents are buried in the same plot.[13]
Ramsey's notes and manuscripts were acquired byNicholas Rescher for the Archives of Scientific Philosophy at theUniversity of Pittsburgh.[14][15] This collection contains only a few letters but a great many drafts of papers and book chapters, some still unpublished. Other papers, including his diary and letters and memoirs by his widowLettice Ramsey and his father, are held in the Modern Archives, King's College, Cambridge.
One of thetheorems proved by Ramsey in his 1928 paperOn 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 proved it only in passing, as a minorlemma along the way to his true goal in the paper, solving a special case of thedecision problem for first-order logic, namely thedecidability of what is now called theBernays–Schönfinkel–Ramsey class offirst-order logic, as well as a characterisation of the spectrum of sentences in this fragment of logic.Alonzo Church would go on to show that the general case of the decision problem for first-order logic isunsolvable and that first-order logic is undecidable (seeChurch's theorem). A great amount of later work in mathematics was fruitfully developed out of the ostensibly minor lemma used by Ramsey in his decidability proof: this lemma turned out to be an important early result incombinatorics, 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 asRamsey theory, which is dedicated to studying similar results.
In 1926,[16] Ramsey proposed a simplification of theTheory of Types developed byBertrand Russell andAlfred North Whitehead in theirPrincipia Mathematica. The resulting theory is known today asTheory of Simple Type (TST) or Simple Type Theory. Ramsey observed that a hierarchy of types was sufficient to deal with mathematicalparadoxes, so removed Russell's and Whitehead's ramified hierarchy, which was meant to elude semantic paradoxes.[17] Ramsey's version of the theory is the one considered byKurt Gödel in the original proof of hisfirst incompleteness theorem.[18] Ramsey's Theory of Simple Types was further simplified byWillard van Orman Quine in hisNew Foundations forset theory, in which any explicit reference to types is eliminated from the language of the theory.[19]
His main philosophical works includedUniversals (1925),Facts and Propositions (1927) (which proposed aredundancy theory of truth),Universals of Law and of Fact (1928),Knowledge (1929),Theories (1929),On Truth (1929),Causal Qualities (1929), andGeneral Propositions and Causality (1929). Ramsey was perhaps the first to propose areliabilist theory of knowledge.[20] He also produced what philosopher Alan Hájek has described as an "enormously influential version of the subjective interpretation of probability".[21] His thought in this area was outlined in the paperTruth and Probability (discussed below) which was written in 1926 but first published posthumously in 1931.[22]
Keynes and Pigou encouraged Ramsey to work on economics as "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 onsubjective probability andutility (1926),optimal taxation (1927) andoptimal growth in a one-sector economy (1928). The economistPaul Samuelson described 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."[23]
Ramsey's economic views weresocialist.[24]
InA Treatise on Probability (1921), Keynes argued against the subjective approach inepistemic probabilities. For Keynes, the subjectivity of probabilities does not matter as much, as for him there is an objective relationship between knowledge and probabilities, as knowledge is disembodied and not personal.
Ramsey disagreed with this approach. In his article "Truth and Probability" (1926), he argued that there is a difference between the notions ofprobability inphysics and inlogic.[22] 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 notions ofsubjective probability andBayesian 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 whatodds the individual would accept whenbetting 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,[25] although Ramsey later noted that "taking the whole field of chance events no generalizations about them are possible (consider e.g. infectious diseases, dactyls in hexameters, deaths from horse kicks, births of great men)."[26]
Despite the fact that Ramsey's work on probabilities was of great importance, no one paid any attention to it until the publication ofTheory of Games and Economic Behavior byJohn von Neumann andOskar Morgenstern in 1944 (1947 2nd ed.)[citation needed], although after Ramsey's death, an approach to probability similar to his was developed independently by the ItalianmathematicianBruno de Finetti.[27]
This paper, first published in 1927 has been described byJoseph E. Stiglitz as "a landmark in the economics of public finance"[28][29] In the same, Ramsey contributed toeconomic theory the elegant concept ofRamsey pricing. This is applicable in situations where a (regulated)monopolist wants to maximiseconsumer surplus whilst at the same time ensuring that its costs are adequately covered. This is achieved by setting the price such that the markup overmarginal cost is inversely proportional to theprice elasticity of demand for that good. 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 the decrement of utility may be a minimum?"[29] The problem was suggested to him by the economistArthur Pigou and the paper was Ramsey's answer to the problem.[citation needed]
Described byPartha Dasgupta, in aStanford Encyclopedia of Philosophy entry devoted to it, as "one of the dozen or so most influential papers of the 20th century" in the field of academic economics, "A Mathematical Theory of Saving" was originally published inThe Economic Journal in 1928.[30][31] It employed, asPaul Samuelson described it, "a strategically beautiful application of thecalculus of variations"[23] to determine the optimal amount an economy should invest rather than consume so as to maximise futureutility, or as Ramsey put it, "How much of its income should a nation save?"[31]
Keynes described the article as "one of the most remarkable contributions tomathematical 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 its 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."[32] The Ramsey model is today acknowledged as the starting point foroptimal accumulation theory although its importance was not recognised 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 maximisation (optimisation) of collective or individual utility by applying techniques of dynamic optimisation.Tjalling C. Koopmans andDavid Cass modified the Ramsey model incorporating the dynamic features ofpopulation growth at a steady rate and of Harrod-neutral technical progress again at a steady rate, giving birth to a model named theRamsey–Cass–Koopmans model where the objective now is to maximise household'sutility function.[citation needed]
The Decision Analysis Society[33] annually awards the Frank P. Ramsey Medal[34] to recognise substantial contributions todecision theory and its application to important classes of real decision problems.
Howard Raiffa was made the first Frank P. Ramsey Professor (of Managerial Economics) at Harvard University.Richard Zeckhauser was made the Frank P. Ramsey Professor of Political Economy atHarvard University in 1971. Raiffa's chair was joint between theHarvard Business andKennedy Schools. Zeckhauser's chair is in the Kennedy School.Partha Dasgupta was made the Frank Ramsey Professor of Economics in 1994 and Frank Ramsey Professor Emeritus of Economics in 2010 at theUniversity of Cambridge.[35]
In 1999, the philosopherDonald Davidson gave the name "Ramsey Effect" to anyone's realisation that their splendid new philosophical discovery already existed within Frank Ramsey's body of work.[36]
Perhaps the first formulation of a reliability account of knowing appeared in a brief discussion byF.P. Ramsey (1931), who said that a belief is knowledge if it is true, certain and obtained by a reliable process. This attracted no attention at the time and apparently did not influence reliability theories of the 1960s, 70s, or 80s.
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