Frank Ramsey (mathematician)
Frank Plumpton Ramsey (/ˈræmzi/; 22 February 1903 – 19 January 1930) was a British philosopher, mathematician, and economist 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 secret intellectual society, from 1921.
Frank Ramsey
Ramsey and Wittgenstein[edit]
When I. A. Richards and C. K. Ogden, 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",[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 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 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 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, the latter mentioning him in the introduction to his Philosophical Investigations as an influence.
Early death[edit]
Suffering chronic liver problems, Ramsey developed jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital 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.[11]
He is buried in the Parish of the Ascension Burial Ground in Cambridge; his parents are buried in the same plot.[12]
Ramsey's notes and manuscripts were acquired by Nicholas Rescher for the Archives of Scientific Philosophy at the University of Pittsburgh.[13][14] 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[edit]
Mathematical logic[edit]
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 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, 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 is unsolvable and that first-order logic is undecidable (see Church'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 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,[15] Ramsey proposed a simplification of the Theory of Types developed by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica. 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 paradoxes, so removed Russell's and Whitehead's ramified hierarchy, which was meant to elude semantic paradoxes.[16] Ramsey's version of the theory is the one considered by Kurt Gödel in the original proof of his first incompleteness theorem.[17] 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.[18]
Philosophy[edit]
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 reliabilist theory of knowledge.[19] He also produced what philosopher Alan Hájek has described as an "enormously influential version of the subjective interpretation of probability."[20] 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.[21]
Economics[edit]
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 and utility (1926), optimal taxation (1927) and optimal growth in a one-sector economy (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."[22]
Ramsey's economic views were socialist.[23]
Legacy[edit]
Frank P. Ramsey Medal[edit]
The Decision Analysis Society[32] annually awards the Frank P. Ramsey Medal[33] to recognise substantial contributions to decision theory and its application to important classes of real decision problems.
Frank Ramsey Professorships[edit]
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 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.[34]
Ramsey Effect[edit]
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.[35]