Frank P Ramsey

Frank Plumpton Ramsey (February 22, 1903 - January 19, 1930) was an English mathematician and philosopher whose studies and teaching activities took place at the University of Cambridge.

He made important theoretical contributions to mathematics, statistics, and economics. In the midst of his investigations, his main intellectual concerns were of a philosophical nature. In this sense, going against Hilbert's intuitionism and formalism, he sought to continue the logician program of Russell and Whitehead as it was stated in the Principia Mathematica .

Biographical Summary

Ramsey was born in Cambridge and trained at Winchester College, before returning to Cambridge to study mathematics at Trinity College, graduating at the top of his class.

Ramsey's intelligence impressed many Cambridge academics. He showed an interest in numerous branches of learning, He was able to learn German in just one week, using a dictionary and grammar book lent to him by C. K. Ogden. Later, he used that knowledge to read Wittgenstein's Tractatus Logico-Philosophicus . He was so impressed by him that in 1923 he traveled to Puchberg, a small Austrian town, where he worked as a teacher to discuss with him.

Back to England, in 1924, he became a professor at King's College at just 21 years old. He developed a number of works on logic, mathematics, economics, and the philosophy of these disciplines. Unfortunately, he suffered from chronic liver disease and after an operation he died at the age of 26, ending a promising career.

One of the theorems proved by Ramsey in his article On a problem of formal logic now bears his name. It was an important result in combinatorics, supplying the idea that, within a sufficiently large system, despite disorder there must be some order.

He was the origin of the theory that bears his name.

Contributions in economics

Ramsey also made fundamental contributions to economics. For example, the Ramsey price concept, which specifies the optimal trajectory that the price of a regulated monopolist must follow, who wants to maximize consumer welfare. In addition, he also established a theory of the optimal behavior of the public treasury for setting the most appropriate taxation. Finally, the Ramsey model is one of the most used in macroeconomics. In it, consumers are presented as individuals who maximize their utility over an infinite horizon. This is especially suitable for studying the growth of economies, the government's optimal response to shocks, etc. Ramsey developed his model in the late 1920s, but the use of differential equations, the mathematical tool he used to solve it, caused most economists to ignore his work. It was not until 1965 when Cass and Koopmans developed in parallel a very similar model, accepted by economists. It was then found that this model (an improved version of the Solow growth model) was actually equivalent to the one developed almost 40 years earlier by Ramsey.

In addition, Ramsey was a "very good friend"^{[citation needed]} of John Maynard Keynes, whose work on probability stimulated him to develop proposals on subjective probability (Bayesian probability). Again, his work did not become known until similar developments were published in the 1950s by Bruno de Finetti.

Contributions in mathematics

One of the theorems Ramsey proved in his publication On a Problem of Formal Logic in 1928 today bears his name, Ramsey's Theorem. Although this work is the toerema for which Ramsey is primarily remembered in the mathematical discipline, he demonstrated it in a more casual way, since this was a minor lemma in the way of his main goal in publication, which solves a special case. of a decision problem in first-order logic, that is, the decidability of what is now called the Bernays–Schönfinkel–Ramsey class of first-order logic, as well as the characterization of the spectrum of sentences in this fragment of logic. Alonzo Church proceeded to prove that the general case of this decision problem in first-order logic is undecidable and that first-order logic is undecidable (see also Church's Theorem). A great deal of work in mathematics was fruitfully developed from the lemma which was presented as a minor lemma in Ramsey's work on his proof of undecidability: this lemma turned out to be one of the first and most important results in the branch of combinatorics, giving a rigorous background to the idea that in systems that are large enough, regardless of their structure or internal organization, there must be some order. So fruitful was this theorem, in fact, that today at dpia there is an entire branch of mathematics known as Ramsey Theory, dedicated to the study of similar and closely related results.

In 1926, Ramsey proposed a simplification of Type Theory, which was developed by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica. The resulting theory is now known as the Simple Type Theory (TST, or Simple Type Theory in English). Ramsey observed that to deal with mathematical paradoxes, it is enough to determine a hierarchy of types, and therefore removed Russell and Whitehead's branching hierarchy, which was defined to avoid semantic paradoxes. Ramsey's version of this theory is the one that Kurt Gödel considered in the original proof of his First Incompleteness Theorem. Ramsey's Theory of Simple Types continued to be simplified by Willard van Orman Quine in his New Foundations set theory, where any explicit reference to the term type is dropped from the language of the theory.

Philosophical works

• Universal (1925)
• Facts and Propositions (1927)
• Universals of Law and of Facts (1928)
• Knowledge (1929)
• Theories (1929)
• General Propositions and Causality (1929)