Frank Ramsey

Frank Plumpton Ramsey (1903–1930) accomplished more in his twenty-six years than most scholars achieve in a full career. A philosopher, mathematician, and economist at Cambridge, he made foundational contributions to the theory of subjective probability, decision theory, the foundations of mathematics, and economics. His 1926 essay Truth and Probability was the first rigorous attempt to ground probability in the degrees of belief of rational agents, an approach that would profoundly influence the Bayesian tradition through the later work of de Finetti and Savage.

Early Life and Cambridge

Ramsey was born in Cambridge, the son of a mathematician who was president of Magdalene College. His intellectual precociousness was evident from childhood. At the age of nineteen, he produced the first English translation of Wittgenstein's Tractatus Logico-Philosophicus, and he was elected a Fellow of King's College, Cambridge, at just twenty-one. His circle included Wittgenstein, Keynes, Russell, and Moore, and he engaged substantively with all of them.

Truth and Probability

Ramsey's most significant contribution to the Bayesian tradition is his 1926 paper Truth and Probability, which argued that probabilities should be understood as degrees of belief revealed through a person's willingness to act. He proposed that a rational agent's degrees of belief must obey the axioms of probability, or else the agent could be made to accept a set of bets guaranteeing a sure loss—what is now called a Dutch book argument.

“The degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it.”— Frank Ramsey, Truth and Probability (1926)

Decision Theory and Utility

In the same essay, Ramsey developed an axiomatic theory of utility and subjective probability simultaneously. He showed that if an agent's preferences satisfy certain consistency axioms, one can derive both a unique probability function and a utility function (up to affine transformation) that together represent the agent's choices as maximizing expected utility. This anticipated by more than two decades the celebrated work of von Neumann and Morgenstern on utility theory and Savage's subjective expected utility framework.

Contributions to Mathematics and Economics

Ramsey's range was extraordinary. In mathematics, he founded what is now called Ramsey theory, a branch of combinatorics concerning the conditions under which order must appear in large structures. In economics, his 1928 paper A Mathematical Theory of Saving introduced the Ramsey growth model, which remains central to macroeconomic theory. He also wrote penetrating critiques of Keynes's A Treatise on Probability, which treated probability as an objective logical relation, arguing instead for the subjectivist view.

Tragic Death and Lasting Influence

Ramsey fell ill in January 1930, likely from complications following surgery, and died at the age of just twenty-six. His work on subjective probability was published posthumously and initially attracted limited attention. It was Bruno de Finetti, working independently in Italy, who developed similar ideas in the 1930s, and Leonard Savage who, in the 1950s, synthesized Ramsey's and de Finetti's insights into the foundations of modern Bayesian decision theory. Savage explicitly acknowledged Ramsey as a primary inspiration.