Frank Plumpton Ramsey (; 22 February 1903 – 19 January 1930) was a
British
British may refer to:
Peoples, culture, and language
* British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies.
** Britishness, the British identity and common culture
* British English, ...
philosopher,
mathematician, and
economist
An economist is a professional and practitioner in the social science discipline of economics.
The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this field there are ...
who made major contributions to all three fields before his death at the age of 26. He was a close friend of
Ludwig Wittgenstein and, as an undergraduate, translated Wittgenstein's ''
Tractatus Logico-Philosophicus'' into English. He was also influential in persuading Wittgenstein to return to
philosophy and Cambridge. Like Wittgenstein, he was a member of the
Cambridge Apostles
The Cambridge Apostles (also known as '' Conversazione Society'') is an intellectual society at the University of Cambridge founded in 1820 by George Tomlinson, a Cambridge student who became the first Bishop of Gibraltar.W. C. Lubenow, ''The C ...
, the secret intellectual society, from 1921.
Life
Ramsey was born on 22 February 1903 in
Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge becam ...
where his father
Arthur Stanley Ramsey
Arthur Stanley Ramsey (9 September 1867 – 31 December 1954) was a British mathematician and author of mathematics and physics textbooks. He was Fellow of Magdalene College, Cambridge, and its President from 1915–52.
Biography
The son of Rev ...
(1867–1954), also a mathematician, was President of
Magdalene College. His mother was Mary Agnes Stanley (1875–1927). He was the eldest of two brothers and two sisters, and his brother
Michael Ramsey, the only one of the four siblings who was to remain Christian, later became
Archbishop of Canterbury
The archbishop of Canterbury is the senior bishop and a principal leader of the Church of England, the ceremonial head of the worldwide Anglican Communion and the diocesan bishop of the Diocese of Canterbury. The current archbishop is Jus ...
. He entered
Winchester College in 1915 and later returned to Cambridge to study mathematics at
Trinity College Trinity College may refer to:
Australia
* Trinity Anglican College, an Anglican coeducational primary and secondary school in , New South Wales
* Trinity Catholic College, Auburn, a coeducational school in the inner-western suburbs of Sydney, New ...
. There he became a student of
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...
, and an active member in the Apostles. In 1923, he received his bachelor's degree in mathematics, passing his examinations with the result of
first class with distinction, and was named
Senior Wrangler (top of his class). 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:
In 1923, Ramsey was befriended by
Geoffrey and
Margaret Pyke
Margaret Amy Pyke (née Chubb; 1893–1966) was a British family planning activist and pioneer. A founding member of the British National Birth Control Committee (NBCC), later known as the Family Planning Association (FPA), she succeeded Lady Ge ...
, then on the point of founding the
Malting 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 on Lake Orta
Lake Orta (Italian: ''Lago d’Orta'') is a lake in northern Italy, west of Lake Maggiore.
It has been so named since the 16th century, but was previously called Lago di San Giulio, after Saint Julius (4th century), the patron saint of the r ...
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 the Burne Jones style) ‘Margaret will you fuck with me?’
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 for
psychoanalysis. Like many of his contemporaries, including his Viennese flatmate and fellow Apostle
Lionel Penrose
Lionel Sharples Penrose, FRS (11 June 1898 – 12 May 1972) was an English psychiatrist, medical geneticist, paediatrician, mathematician and chess theorist, who carried out pioneering work on the genetics of intellectual disability. Penr ...
(also in analysis with
Siegfried Bernfeld
Siegfried Bernfeld (May 7, 1892, Lemberg, Galicia, Austria-Hungary (today Ukraine) – April 2, 1953, San Francisco) was an Austrian psychologist and educator who was a native of Lemberg (now Lviv, Ukraine). Etchegoyen, R. Horacio. "Siegfried ...
), Ramsey was intellectually interested in psychoanalysis. Ramsey's analyst was
Theodor Reik
Theodor Reik (; 12 May 1888, in Vienna, Austria – 31 December 1969, in New York) was a psychoanalyst who trained as one of Freud's first students in Vienna, Austria, and was a pioneer of lay analysis in the United States.
Education and career
...
, a disciple of
Freud
Sigmund Freud ( , ; born Sigismund Schlomo Freud; 6 May 1856 – 23 September 1939) was an Austrian neurologist and the founder of psychoanalysis, a clinical method for evaluating and treating pathologies explained as originating in conflicts in ...
. 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 to
Puchberg in order to visit Wittgenstein, was befriended by the Wittgenstein family and visited
A.S. Neill
Alexander Sutherland Neill (17 October 1883 – 23 September 1973) was a Scottish educator and author known for his school, Summerhill, and its philosophy of freedom from adult coercion and community self-governance. Raised in Scotland, Neill ...
's experimental school four hours from Vienna at Sonntagsberg. In the summer of 1924, he continued his analysis by joining Reik at Dobbiaco (in
South Tyrol), where a fellow analysand was
Lewis Namier. Ramsey returned to England in October 1924; with
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...
's support he became a fellow of
King's College, Cambridge
King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the cit ...
. He joined a Psychoanalysis Group in Cambridge with fellow members
Arthur Tansley
Sir Arthur George Tansley FLS, FRS (15 August 1871 – 25 November 1955) was an English botanist
Botany, also called , plant biology or phytology, is the science of plant life and a branch of biology. A botanist, plant scientist or phy ...
,
Lionel Penrose
Lionel Sharples Penrose, FRS (11 June 1898 – 12 May 1972) was an English psychiatrist, medical geneticist, paediatrician, mathematician and chess theorist, who carried out pioneering work on the genetics of intellectual disability. Penr ...
,
Harold Jeffreys,
John Rickman and
James Strachey
James Beaumont Strachey (; 26 September 1887, London25 April 1967, High Wycombe) was a British psychoanalyst, and, with his wife Alix, a translator of Sigmund Freud into English. He is perhaps best known as the general editor of '' The Standa ...
, the qualification for membership of which was a completed psychoanalysis.
Ramsey married Lettice Baker in September 1925, the wedding taking place in a Register Office since Ramsey was, as his wife described him, a 'militant
atheist
Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no d ...
'. The marriage produced two daughters. After Ramsey's death,
Lettice Ramsey opened a photography studio in Cambridge with photographer
Helen Muspratt. Despite his
atheism
Atheism, in the broadest sense, is an absence of belief in the existence of Deity, deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that ther ...
, Ramsey was "quite tolerant" towards his brother when the latter decided to become a priest in the
Church of England.
In 1926 he became a university lecturer in mathematics and later a Director of Studies in Mathematics at King's College.
The
Vienna Circle manifesto (1929) lists three of his publications in a bibliography of closely related authors.
Ramsey and Wittgenstein
When
I. A. Richards and
C. K. Ogden
Charles Kay Ogden (; 1 June 1889 – 20 March 1957) was an English linguist, philosopher, and writer. Described as a polymath but also an eccentric and outsider, he took part in many ventures related to literature, politics, the arts, and phil ...
, both Fellows of
Magdalene, first met Ramsey, he expressed his interest in learning German. According to Richards, he mastered the language "in almost hardly over a week", although other sources show he had taken one year of German in school. Ramsey was then able, at the age of 19, to make the first draft of the translation of the German text of
Ludwig Wittgenstein's ''
Tractatus Logico-Philosophicus''. Ramsey was impressed by Wittgenstein's work and after graduating as
Senior Wrangler in the Mathematical
Tripos of 1923 he made a journey to
Austria
Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous c ...
to 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 ''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.
Ramsey and
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...
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 the ''Tractatus Logico-Philosophicus'' as his doctoral thesis.
G.E. Moore
George Edward Moore (4 November 1873 – 24 October 1958) was an English philosopher, who with Bertrand Russell, Ludwig Wittgenstein and earlier Gottlob Frege was among the founders of analytic philosophy. He and Russell led the turn from ideal ...
and
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
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 with
Piero Sraffa, an
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional It ...
economist who had been brought to Cambridge by Keynes after Sraffa had aroused
Benito Mussolini
Benito Amilcare Andrea Mussolini (; 29 July 188328 April 1945) was an Italian politician and journalist who founded and led the National Fascist Party. He was Prime Minister of Italy from the March on Rome in 1922 until his deposition in 194 ...
's ire by publishing an article critical of the Fascist regime in the ''
Manchester Guardian
''The Guardian'' is a British daily newspaper. It was founded in 1821 as ''The Manchester Guardian'', and changed its name in 1959. Along with its sister papers ''The Observer'' and '' The Guardian Weekly'', ''The Guardian'' is part of the G ...
''. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work, the latter mentioning him in the introduction to his ''
Philosophical Investigations'' as an influence.
Early death
Suffering chronic
liver problems, Ramsey developed
jaundice
Jaundice, also known as icterus, is a yellowish or greenish pigmentation of the skin and sclera due to high bilirubin levels. Jaundice in adults is typically a sign indicating the presence of underlying diseases involving abnormal heme meta ...
after an abdominal operation and died on 19 January 1930 at
Guy's Hospital
Guy's Hospital is an NHS hospital in the borough of Southwark in central London. It is part of Guy's and St Thomas' NHS Foundation Trust and one of the institutions that comprise the King's Health Partners, an academic health science centre.
...
in London at the age of 26. There is a suspicion that the cause of his death might be an undiagnosed
leptospirosis with which Ramsey, an avid swimmer, could have become infected while swimming in the
Cam
Calmodulin (CaM) (an abbreviation for calcium-modulated protein) is a multifunctional intermediate calcium-binding messenger protein expressed in all eukaryotic cells. It is an intracellular target of the secondary messenger Ca2+, and the bin ...
.
He is buried in the
Parish of the Ascension Burial Ground in Cambridge; his parents are buried in the same plot.
Ramsey's notes and manuscripts were acquired by
Nicholas Rescher for the Archives of Scientific Philosophy at the
University of Pittsburgh. 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 widow Lettice Ramsey and his father, are held in the Modern Archives, King's College, Cambridge.
Work
Mathematical logic
One of the
theorems proved by Ramsey in his 1928 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 proved it only in passing, as a minor
lemma
Lemma may refer to:
Language and linguistics
* Lemma (morphology), the canonical, dictionary or citation form of a word
* Lemma (psycholinguistics), a mental abstraction of a word about to be uttered
Science and mathematics
* Lemma (botany), ...
along the way to his true goal in the paper, solving a special case of the
decision problem for first-order logic, namely the
decidability of what is now called the
Bernays–Schönfinkel–Ramsey class of
first-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifi ...
, as well as a characterisation of the spectrum of sentences in this fragment of logic.
Alonzo Church
Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scien ...
would go on to show that the general case of the decision problem for first-order logic is
unsolvable and that first-order logic is undecidable (see
Church's theorem
In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the stat ...
). 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 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.
In 1926, Ramsey proposed a simplification of the
Theory of Types developed by
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
and
Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...
in their ''
Principia Mathematica
The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...
''. The resulting theory is known today as
Theory of Simple Type (TST) or Simple Type Theory. Ramsey observed that a hierarchy of types was sufficient to deal with mathematical
paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
es, so removed Russell's and Whitehead's ramified hierarchy, which was meant to elude semantic paradoxes. Ramsey's version of the theory is the one considered by
Kurt Gödel in the original proof of his
First incompleteness theorem. Ramsey's Theory of Simple Types was further simplified by
Willard van Orman Quine in his
New Foundations set theory, in which any explicit reference to types is eliminated from the language of the theory.
Philosophy
His main philosophical works included ''Universals'' (1925), ''Facts and propositions'' (1927) (which proposed a
redundancy theory of truth), ''Universals of law and of fact'' (1928), ''Knowledge'' (1929), ''Theories'' (1929), ''On Truth'' (1929), ''Causal Qualities'' (1929), and ''General propositions and causality'' (1929). Ramsey was perhaps the first to propose a
reliablist theory of knowledge. He also produced what philosopher Alan Hájek has described as an "enormously influential version of the subjective interpretation of probability." His thought in this area was outlined in the paper ''
Truth and Probability'' (discussed below) which was written in 1926 but first published posthumously in 1931.
Economics
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 on
subjective probability
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification o ...
and
utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophe ...
(1926),
optimal
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
taxation (1927) and optimal growth with one-sector
economic growth
Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of ...
(1928). The economist
Paul 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."
''A Mathematical Theory of Saving''
Described by
Partha Dasgupta, in a ''
Stanford 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 in ''
The Economic Journal'' in 1928.
It employed, as
Paul Samuelson described it, "a strategically beautiful application of the
calculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
"
to determine the optimal amount an economy should invest rather than consume so as to maximise future
utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophe ...
, or as Ramsey put it, "how much of its income should a nation save?"
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 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." The Ramsey model is today acknowledged as the starting point for
optimal 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 and
David Cass
David Cass (January 19, 1937 – April 15, 2008) was a professor of economics at the University of Pennsylvania, mostly known for his contributions to general equilibrium theory. His most famous work was on the Ramsey–Cass–Koopmans model of ...
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 maximise household's
utility function
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...
.
''A Contribution to the Theory of Taxation''
This paper, first published in 1927 has been described by
Joseph E. Stiglitz
Joseph Eugene Stiglitz (; born February 9, 1943) is an American New Keynesian economist, a public policy analyst, and a full professor at Columbia University. He is a recipient of the Nobel Memorial Prize in Economic Sciences (2001) and the J ...
as "a landmark in the economics of public finance"
In the same, Ramsey contributed to
economic theory
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyze ...
the elegant concept of
Ramsey pricing. This is applicable in situations where a (regulated)
monopolist
A monopoly (from Greek el, μόνος, mónos, single, alone, label=none and el, πωλεῖν, pōleîn, to sell, label=none), as described by Irving Fisher, is a market with the "absence of competition", creating a situation where a speci ...
wants to maximise
consumer surplus
In mainstream economics, economic surplus, also known as total welfare or total social welfare or Marshallian surplus (after Alfred Marshall), is either of two related quantities:
* Consumer surplus, or consumers' surplus, is the monetary gain ...
whilst at the same time ensuring that its costs are adequately covered. This is achieved by setting the price such that the markup over
marginal cost is inversely proportional to the
price elasticity
A good's price elasticity of demand (E_d, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elastici ...
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?"
The problem was suggested to him by the economist
Arthur Pigou
Arthur Cecil Pigou (; 18 November 1877 – 7 March 1959) was an English economist. As a teacher and builder of the School of Economics at the University of Cambridge, he trained and influenced many Cambridge economists who went on to take chair ...
and the paper was Ramsey's answer to the problem.
''Truth and Probability''
In ''
A Treatise on Probability
''A Treatise on Probability'' is a book published by John Maynard Keynes while at Cambridge University in 1921. The ''Treatise'' attacked the classical theory of probability and proposed a "logical-relationist" theory instead. In a 1922 review, ...
'' (1921), Keynes had argued against the subjective approach in
epistemic probabilities. For Keynes, 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 of
probability in
physics and in
logic.
[F.P. Ramsey (1926) "Truth and Probability", in Ramsey, 1931, '' The Foundations of Mathematics and other Logical Essays'', Ch. VII, p.156-198, edited by R.B. Braithwaite, London: Kegan, Paul, Trench, Trubner & Co., New York: Harcourt, Brace and Company ']
1999 electronic edition
'' 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 of
subjective probability
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification o ...
and
Bayesian probability
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification o ...
. 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
odds the individual would accept when
betting on that outcome. After Ramsey's death, an approach to probability similar to his was developed independently by the Italian
mathematician Bruno de Finetti
Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 "La prévision: ...
.
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, no one paid any attention to it until the publication of ''
Theory of Games and Economic Behavior'' of
John von Neumann and
Oskar Morgenstern
Oskar Morgenstern (January 24, 1902 – July 26, 1977) was an Austrian-American economist. In collaboration with mathematician John von Neumann, he founded the mathematical field of game theory as applied to the social sciences and strategic decis ...
in 1944 (1947 2nd ed.).
Legacy
Frank P. Ramsey Medal
The Decision Analysis Society annually awards the Frank P. Ramsey Medal to recognise substantial contributions to
decision theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
and its application to important classes of real decision problems.
Frank Ramsey Professorships
Howard Raiffa
Howard Raiffa (; January 24, 1924 – July 8, 2016) was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and Harvard Kennedy School at Harvard University. He ...
was made the first Frank P. Ramsey Professor (of Managerial Economics) at Harvard University.
Richard Zeckhauser
Richard Jay Zeckhauser (born 1940) is an American economist and the Frank P. Ramsey Professor of Political Economy at the Kennedy School of Government at Harvard University.
He holds a BA (''summa cum laude'') and a PhD in economics from Harvard ...
was made the Frank P. Ramsey Professor of Political Economy at
Harvard University in 1971. Raiffa's chair was joint between the
Harvard Business and
Kennedy 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 the
University of Cambridge.
Ramsey Effect
In 1999, the philosopher
Donald Davidson gave the name "the Ramsey Effect" to anyone's realisation that their splendid new philosophical discovery already existed within Frank Ramsey's body of work.
See also
*
Clique game
*
Expected utility hypothesis
*
Money pump
*
Ramsey cardinal In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by and named after Frank P. Ramsey, whose theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize to the uncountable case.
Le ...
*
Structural Ramsey theory In mathematics, structural Ramsey theory is a categorical generalisation of Ramsey theory, rooted in the idea that many important results of Ramsey theory have "similar" logical structure. The key observation is noting that these Ramsey-type theore ...
*
Quantum Bayesianism
In physics and the philosophy of physics, quantum Bayesianism is a collection of related approaches to the interpretation of quantum mechanics, of which the most prominent is QBism (pronounced "cubism"). QBism is an interpretation that takes an a ...
*
Theorem on friends and strangers
The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory.
Statement
Suppose a party has six people. Consider any two of them. They might be meeting for the first time—in which case we will ...
*
Type theory
*
History of type theory The type theory was initially created to avoid paradoxes in a variety of formal logics and rewrite systems. Later, type theory referred to a class of formal systems, some of which can serve as alternatives to naive set theory as a foundation for ...
*
Frederick Rowbottom
*
Bayesian epistemology
Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory. One advantage of its formal method in contrast to traditional epistemology is that its conc ...
Notes
References
*
*
*
*
*
*Galavotti, M. C. (Ed.) (2006), ''
Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle'', Dordrecht, The Netherlands: Springer.
*
Grattan-Guinness, Ivor (2000), ''The Search for Mathematical Roots 1870–1940'', Princeton University Press, Princeton, NJ.
*
Keynes, John Maynard (1933),
F. P. Ramsey, in ''Essays in Biography'', New York, NY.
*
*
*
*
*
*
*
*Ramsey, F.P. (1931),
''The Foundations of Mathematics, and other Essays'', (ed.)
R. B. Braithwaite
Richard Bevan Braithwaite (15 January 1900 – 21 April 1990) was an English philosopher who specialized in the philosophy of science, ethics, and the philosophy of religion.
Life
Braithwaite was born in Banbury, Oxfordshire, son of the ...
**Ramsey, F.P. (1978) ''Foundations – Essays in Philosophy, Logic, Mathematics and Economics'', (ed.)
D.H. Mellor, Humanities Press,
*Rescher, Nicholas and Ulrich Majer (eds.) (1991). ''F. P. Ramsey: On Truth '', Dordrecht, Kluwer
*Sahlin, N.-E. (1990), ''The Philosophy of F. P. Ramsey'', Cambridge University Press, Cambridge
*Sahlin, N.-E. (1996), “He is no good for my work”: On the philosophical relations between Ramsey and Wittgenstein, in ''Knowledge and Inquiry: Essays on Jaakko Hintikkas Epistemology and Philosophy of Science'', ed by M. Sintonen, Poznan Studies in the Philosophy of Sciences and the Humanities, Amsterdam, 61–84
*Sahlin, N.-E. (2005),
Ramsey’s Ontology', a special issue of ''Metaphysica'', No. 3
*
Further reading
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*
Reviewby
Simon Blackburn uthor-shared_Eprint.html" ;"title="Eprint.html" ;"title="uthor-shared Eprint">uthor-shared Eprint">Eprint.html" ;"title="uthor-shared Eprint">uthor-shared Eprint
* (Reviews
1:by Ray Monk
2:by David Papineau [
Archived])
*
External links
Frank Ramsey ''
Stanford Encyclopedia of Philosophy''.
Frank Plumpton Ramsey PapersBetter than the Stars/Frank Ramsey: a biographya 1978 BBC radio portrait of Ramsey and a 1995 article derived from it, both by
David Hugh Mellor.
Maths and philosophy puzzlesBBC Radio 3 programme discussing the legacy of Ramsey.
A photo of Ramsey's graveat
Findagrave
{{DEFAULTSORT:Ramsey, Frank P.
1903 births
1930 deaths
20th-century atheists
20th-century British economists
20th-century English mathematicians
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Cambridge University Moral Sciences Club
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