RAMSEY, FRANK PLUMPTON

(b. Cambridge, England, 22 February 1903; d. Cambridge, 19 January 1930), mathematical logic.

Ramsey, the elder son of A. S. Ramsey, president of Magdalene College, Cambridge, was educated at Winchester and Trinity colleges, Cambridge. After graduation in 1923 he was elected a fellow of King’s College, Cambridge, where he spent the rest of his short life. His lectures on the foundations of mathematics impressed young students by their remarkable clarity and enthusiasm, and his untimely death deprived Cambridge of one of its most brilliant thinkers.

Whitehead and Russell, in their system of mathematical logic, Principia Mathematica (1910–1913), had avoided the antinomies (paradoxes) by creating both a theory of types, which dealt with the nature of propositional functions, and an axiom of reducibility. Ramsey accepted the Whitehead-Russell view of mathematics as part of logic but said of the axiom of reducibility that it is “certainly not self-evident and there is no reason to suppose it true.” In his first paper (1926) he took up Wittgenstein’s work on tautologies and truth functions, reinterpreting the concept of propositional functions and thus obviating the need for the axiom of reducibility. He also drew an important distinction between the logical antinomies, for example, that concerning the class of all classes not members of themselves, and those antinomies that cannot be stated in logical terms alone, for example, “I am lying.” For the first class, he accepted Russell’s solution; for the second, which are not formal but involve meaning, he applied his reinterpretation of the Principia Mathematica.

In a paper “On a Problem of Formal Logic” (1930) Ramsey discussed the Entscheidungsproblem—the search for a general method for determining the consistency of a logical formula—using some ingenious combinatorial theorems. To the Oxford meeting of the British Association in 1926, he described the development of mathematical logic subsequent to the publication of Principia Mathematica; this address was printed in the Mathematical Gazette (1926).

Two papers on the mathematical theory of economics appeared in the Economic Journal. In a biographical essay on Ramsey, J. M. Keynes described Ramsey’s interest in economics, the importance of his two papers, and the way in which Cambridge economists made use of his critical powers to test their theories. An interesting, if not altogether convincing, study of the bases of probability theory was published posthumously in a collection of Ramsey’s essays.

BIBLIOGRAPHY

I. Original Works. Ramsey’s works include “The Foundations of Mathematics,” in Proceedings of the London Mathematical Society, 2nd ser., 25 (1926), 338–384; “Mathematical Logic,” in Mathematical Gazette, 13 (1926), 185–194; “A Contribution to the Theory of Taxation,” in Economic Journal (Mar. 1927); “A Mathematical Theory of Saving,” ibid. (Dec. 1928); and “On the Problem of Formal Logic,” in Proceedings of the London Mathematical Society, 2nd ser., 30 (1930), 264–286.

A convenient source is the posthumous volume Foundations of Mathematics and Other Essays, R. B. Braithwaite, ed. (London, 1931); this work contains Ramsey’s published papers, excluding the two on economics, and a number of items from his unpublished manuscripts.

II. Secondary Literature. An obituary notice by Braithwaite is in Journal of the London Mathematical Society, 6 (1931), 75–78. The essay on Ramsey by J. M. Keynes, in Essays in Biography (London, 1933), is valuable for Ramsey’s work in economics and in philosophy.

T. A. A. Broadbent