Frank P. Ramsey
Encyclopedia
Frank Plumpton Ramsey was a British
mathematician
who, in addition to mathematics
, made significant and precocious contributions in philosophy
and economics
before his death at the age of 26. He was a close friend of Ludwig Wittgenstein
, and was instrumental in translating Wittgenstein's Tractatus Logico-Philosophicus
into English, and in persuading Wittgenstein to return to philosophy and Cambridge.
where his father Arthur, also a mathematician
, was President of Magdalene College
. 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
. He entered Winchester College
in 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:
Ramsey suffered mildly from depression
, and was intellectually interested in psychoanalysis
. While writing his dissertation he went to Vienna
to be psychoanalysed by Theodor Reik
, a disciple of Freud. As one of the justifications for undertaking therapy, he asserted in a letter to his mother that unconscious impulses might even affect the work of a mathematician.
In September 1925 he married Lettice Baker, the wedding taking place in a Register Office since Ramsey was, as his wife described him, a ‘militant atheist’. (She subsequently ran a photography practice in Cambridge for many years ("Ramsey and Muspratt").) The marriage produced two daughters. Despite his atheism
, Ramsey was quite tolerant towards his brother when the latter decided to become a priest in the Church of England
.
'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. Ramsey and 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 the Tractatus Logico-Philosophicus
as his doctoral thesis
. G.E. Moore and Bertrand 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
with Piero Sraffa
, an Italian economist who had been brought to Cambridge by Keynes after Sraffa had aroused Benito Mussolini
’s ire by publishing an article critical of the Fascist regime in the Manchester Guardian. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work.
, 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 took before that 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 Wittgenstein’s Tractatus Logico Philosophicus. Ramsey was impressed by Wittgenstein’s work and after graduating as a Wrangler in the Mathematical Tripos
of 1923 he made a journey to Austria
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.
.
One of the theorem
s 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
, namely the decidability of (what is now called) Bernays–Schönfinkel–Ramsey class of first-order logic, as well as a characterization 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 is unsolvable (see Church's theorem). 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). Wittgenstein mentions him in the introduction to his Philosophical Investigations
as an influence (but not as great an influence as Piero Sraffa
).
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 and utility
(1926), optimal taxation (1927) and optimal one-sector economic growth
(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."
" (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 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" (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.
is inversely proportional to the price elasticity of 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 the decrement of utility may be a minimum?" (Ramsey 1927). The problem was suggested to him by the economist Arthur Pigou and the paper was Ramsey’s answer to the problem.
(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 odds
the 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 Behavior
of John von Neumann
and Oskar Morgenstern
in 1944 (1947 2nd ed.)
problems, Ramsey contracted jaundice
after an abdominal operation and died on 19 January 1930 at Guy's Hospital
in London at the age of 26.
The Decision Analysis Society annually awards the Frank P. Ramsey Medal to recognise substantial contributions to decision theory
and its application to important classes of real decision problems. He is buried at the Parish of the Ascension Burial Ground
in Cambridge.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who, in addition to mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, made significant and precocious contributions in philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
before his death at the age of 26. He was a close friend of Ludwig Wittgenstein
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
, and was instrumental in translating Wittgenstein's Tractatus Logico-Philosophicus
Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus is the only book-length philosophical work published by the Austrian philosopher Ludwig Wittgenstein in his lifetime. It was an ambitious project: to identify the relationship between language and reality and to define the limits of science...
into English, and in persuading Wittgenstein to return to philosophy and Cambridge.
Life
He was born on 22 February 1903 in CambridgeCambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
where his father Arthur, also a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, was President of Magdalene College
Magdalene College, Cambridge
Magdalene College is a constituent college of the University of Cambridge, England.The college was founded in 1428 as a Benedictine hostel, in time coming to be known as Buckingham College, before being refounded in 1542 as the College of St Mary Magdalene...
. He was the eldest of two brothers and two sisters, and his brother Michael Ramsey
Michael Ramsey
Arthur Michael Ramsey, Baron Ramsey of Canterbury PC was the 100th Archbishop of Canterbury. He was appointed on 31 May 1961 and was in office from June 1961 to 1974.-Career:...
, the only one of the four siblings who was to remain Christian, later became Archbishop
Archbishop
An archbishop is a bishop of higher rank, but not of higher sacramental order above that of the three orders of deacon, priest , and bishop...
of Canterbury
Canterbury
Canterbury is a historic English cathedral city, which lies at the heart of the City of Canterbury, a district of Kent in South East England. It lies on the River Stour....
. He entered Winchester College
Winchester College
Winchester College is an independent school for boys in the British public school tradition, situated in Winchester, Hampshire, the former capital of England. It has existed in its present location for over 600 years and claims the longest unbroken history of any school in England...
in 1915 and later returned to Cambridge to study mathematics at Trinity College
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
. 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:
Ramsey suffered mildly from depression
Depression (mood)
Depression is a state of low mood and aversion to activity that can affect a person's thoughts, behaviour, feelings and physical well-being. Depressed people may feel sad, anxious, empty, hopeless, helpless, worthless, guilty, irritable, or restless...
, and was intellectually interested in psychoanalysis
Psychoanalysis
Psychoanalysis is a psychological theory developed in the late 19th and early 20th centuries by Austrian neurologist Sigmund Freud. Psychoanalysis has expanded, been criticized and developed in different directions, mostly by some of Freud's former students, such as Alfred Adler and Carl Gustav...
. While writing his dissertation he went to Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
to be psychoanalysed by Theodor Reik
Theodor Reik
Theodor Reik was a prominent psychoanalyst who trained as one of Freud's first students in Vienna, Austria. Reik received a Ph.D. degree in psychology from the University of Vienna in 1912. His dissertation, a study of Flaubert's Temptation of Saint Anthony, was the first psychoanalytic...
, a disciple of Freud. As one of the justifications for undertaking therapy, he asserted in a letter to his mother that unconscious impulses might even affect the work of a mathematician.
In September 1925 he married Lettice Baker, the wedding taking place in a Register Office since Ramsey was, as his wife described him, a ‘militant atheist’. (She subsequently ran a photography practice in Cambridge for many years ("Ramsey and Muspratt").) The marriage produced two daughters. Despite his atheism
Atheism
Atheism is, in a broad sense, the rejection of belief in the existence of deities. In a narrower sense, atheism is specifically the position that there are no deities...
, Ramsey was quite tolerant towards his brother when the latter decided to become a priest in the Church of England
Church of England
The Church of England is the officially established Christian church in England and the Mother Church of the worldwide Anglican Communion. The church considers itself within the tradition of Western Christianity and dates its formal establishment principally to the mission to England by St...
.
Academic life
He returned to England in 1924, and with John Maynard KeynesJohn Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...
's support he became a fellow of King's College, Cambridge
King's College, Cambridge
King's College is a constituent college of the University of Cambridge, England. The college's full name is "The King's College of our Lady and Saint Nicholas in Cambridge", but it is usually referred to simply as "King's" within the University....
, 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. Ramsey and 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 the Tractatus Logico-Philosophicus
Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus is the only book-length philosophical work published by the Austrian philosopher Ludwig Wittgenstein in his lifetime. It was an ambitious project: to identify the relationship between language and reality and to define the limits of science...
as his doctoral thesis
Thesis
A dissertation or thesis is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings...
. G.E. Moore and Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
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
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
with Piero Sraffa
Piero Sraffa
Piero Sraffa was an influential Italian economist whose book Production of Commodities by Means of Commodities is taken as founding the Neo-Ricardian school of Economics.- Early life :...
, an Italian economist who had been brought to Cambridge by Keynes after Sraffa had aroused Benito Mussolini
Benito Mussolini
Benito Amilcare Andrea Mussolini was an Italian politician who led the National Fascist Party and is credited with being one of the key figures in the creation of Fascism....
’s ire by publishing an article critical of the Fascist regime 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
When I.A. Richards and C. K. Ogden, both Fellows of MagdaleneMagdalene
Magdalene or Magdalen may refer to:*Mary Magdalene, a disciple of Jesus*Magdalene , a feminine given name *Magdalene , a character in Marvel Comics...
, first met Ramsey, he expressed his interest in learning German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
. According to Richards, he mastered the language "in almost hardly over a week," although other sources show he took before that 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 Wittgenstein’s Tractatus Logico Philosophicus. Ramsey was impressed by Wittgenstein’s work and after graduating as a Wrangler in the Mathematical Tripos
Tripos
The University of Cambridge, England, divides the different kinds of honours bachelor's degree by Tripos , plural Triposes. The word has an obscure etymology, but may be traced to the three-legged stool candidates once used to sit on when taking oral examinations...
of 1923 he made a journey to Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
to visit Wittgenstein, at that time teaching in a primary school in the small community of Puchberg am Schneeberg
Puchberg am Schneeberg
Puchberg am Schneeberg is a town in the south-eastern part of Lower Austria with approx. 2650 inhabitants. It is situated about 80 Kilometres from Vienna. The highest point of Puchberg is the Schneeberg with 2076 m, the highest mountain of Lower Austria....
. 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.
Work
In 1927 Ramsey published the influential article Facts and Propositions, in which he proposed what is sometimes described as a redundancy theory of truthRedundancy theory of truth
According to the redundancy theory of truth, or the disquotational theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is...
.
One of the theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s proved by Ramsey in his 1930 paper On a problem of formal logic now bears his name (Ramsey's theorem
Ramsey's theorem
In combinatorics, Ramsey's theorem states that in any colouring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs...
). While this theorem is the work Ramsey is probably best remembered for, he only proved it in passing, as a minor lemma
Lemma (mathematics)
In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than as a statement in-and-of itself...
along the way to his true goal in the paper, solving a special case of the decision problem for first-order logic
Entscheidungsproblem
In mathematics, the is a challenge posed by David Hilbert in 1928. The asks for an algorithm that will take as input a description of a formal language and a mathematical statement in the language and produce as output either "True" or "False" according to whether the statement is true or false...
, namely the decidability of (what is now called) Bernays–Schönfinkel–Ramsey class of first-order logic, as well as a characterization of the spectrum of sentences in this fragment of logic. Alonzo Church
Alonzo Church
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...
would go on to show that the general case of the decision problem for first-order logic is unsolvable (see Church's theorem). 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
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, 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
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear...
, 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). Wittgenstein mentions him in the introduction to his Philosophical Investigations
Philosophical Investigations
Philosophical Investigations is, along with the Tractatus Logico-Philosophicus, one of the most influential works by the 20th-century philosopher Ludwig Wittgenstein...
as an influence (but not as great an influence as Piero Sraffa
Piero Sraffa
Piero Sraffa was an influential Italian economist whose book Production of Commodities by Means of Commodities is taken as founding the Neo-Ricardian school of Economics.- Early life :...
).
Work in economics
Keynes and Pigou encouraged Ramsey to work on economicsEconomics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
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 and utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
(1926), optimal taxation (1927) and optimal one-sector economic growth
Ramsey growth model
The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans...
(1928). The economist Paul Samuelson
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...
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
This significant paper was published in The Economic Journal, and involved "a strategically beautiful application of the calculus of variationsCalculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
" (Paul Samuelson
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...
) in order to determine the optimal amount an economy should invest (save) rather than consume so as to maximize future utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
, 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
Mathematical economics
Mathematical economics is the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity...
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" (Keynes 1933). The Ramsey model is today acknowledged as the starting point for optimal accumulation theory
Turnpike theory
Turnpike theory refers to a set of economic theories about the optimal path of accumulation in a system based depending on the initial and final levels...
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
David Cass
David Cass 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 growth model, which is also known as the Ramsey-Cass-Koopmans model.-Biography:David Cass was born in 1937 in...
modified the Ramsey model incorporating the dynamic features of population growth
Population growth
Population growth is the change in a population over time, and can be quantified as the change in the number of individuals of any species in a population using "per unit time" for measurement....
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
Ramsey growth model
The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling 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 theory was the elegant concept of Ramsey pricing. This is applicable in situations where a (regulated) monopolist wants to maximize consumer surplus 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 costMarginal cost
In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good...
is inversely proportional to the price elasticity of 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 the decrement of utility may be a minimum?" (Ramsey 1927). The problem was suggested to him by the economist Arthur Pigou and the paper was Ramsey’s answer to the problem.
Truth and probability
Keynes in his Treatise on ProbabilityJohn Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...
(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
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and in logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
. 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 odds
Odds
The odds in favor of an event or a proposition are expressed as the ratio of a pair of integers, which is the ratio of the probability that an event will happen to the probability that it will not happen...
the 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 Behavior
Theory of Games and Economic Behavior
Theory of Games and Economic Behavior, published in 1944 by Princeton University Press, is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory...
of John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
and Oskar Morgenstern
Oskar Morgenstern
Oskar Morgenstern was a German-born Austrian-School economist. He, along with John von Neumann, helped found the mathematical field of game theory ....
in 1944 (1947 2nd ed.)
Early death
Suffering from chronic liverLiver
The liver is a vital organ present in vertebrates and some other animals. It has a wide range of functions, including detoxification, protein synthesis, and production of biochemicals necessary for digestion...
problems, Ramsey contracted jaundice
Jaundice
Jaundice is a yellowish pigmentation of the skin, the conjunctival membranes over the sclerae , and other mucous membranes caused by hyperbilirubinemia . This hyperbilirubinemia subsequently causes increased levels of bilirubin in the extracellular fluid...
after an abdominal operation and died on 19 January 1930 at Guy's Hospital
Guy's Hospital
Guy's Hospital is a large NHS hospital in the borough of Southwark in south east London, England. It is administratively a part of Guy's and St Thomas' NHS Foundation Trust. It is a large teaching hospital and is home to the King's College London School of Medicine...
in London at the age of 26.
The Decision Analysis Society annually awards the Frank P. Ramsey Medal to recognise substantial contributions to decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
and its application to important classes of real decision problems. He is buried at the Parish of the Ascension Burial Ground
Ascension Parish Burial Ground, Cambridge
The Ascension Parish Burial Ground, formerly St Giles and St Peter's Parish, is a cemetery just off Huntingdon Road near the junction with Storey's Way in the northwest of Cambridge, England. It includes the graves of many Cambridge academics and non-conformists of the 19th and early 20th century...
in Cambridge.
See also
- Ramsey theoryRamsey theoryRamsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear...
- Ramsey–Lewis method
- Ramsey–Dvoretzky–Milman phenomenon
- Ramsey growth modelRamsey growth modelThe Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans...
- Frederick RowbottomFrederick RowbottomFrederick Rowbottom was a British logician and mathematician. The large cardinal notion of Rowbottom cardinals is named after him.-Biography:...
External links
- Appreciation of Frank
- Comprehensive resource on Ramsey
- Short Ramsey biography
- Realaudio BBC profile of Ramsey from 1978, & transcript
- Stanford Encyclopedia of Philosophy: Interpretations of Probability. See 3.5 (3.2) for Ramsey's (Keynes's) views on probability.
- Finding Aid for the Frank P. Ramsey Collection at the University of Pittsburgh's Archive of Scientific Philosophy