Frank P. Ramsey
British philosopher who died young but left many important ideas: the improvement of Russell's theory of types, the distinction between logical and semantic paradoxes, the subjective analysis of probability, the Ramsey-sentence for eliminating overt reference to theoretical entities, and the theory of truth.
A logical paradox is such that a contradiction can be proved within a (axiomatic) system using logical concepts, inferences and definitions allowed within the system. Thus, Russell's paradox which uses the concept of set and its membership (which Ramsey regarded as a logical concept), the definition of "Russell set" (the set of every set such that it is not a member of itself; see Russell's picture), and standard logic, is reconstructed as a logical paradox, according to Ramsey.
A semantic paradox (Ramsey called "epistemological") involves extra terms in addition to the preceding. Thus the famous liar paradox which can be derived from the statement
This statement is not true
makes an essential use of the (semantic) predicate "true", so that it is not logical but semantic.
Ramsey noticed that by distinguishing these two and excluding the latter from our cosideration, the difficulties of Principia Mathematica can be resolved by a far simpler method than that proposed by Russell's original theory of types.
No less important than this is Ramsey's subjective theory of probability. He revived Thomas Bayes's way of defining probability in terms of betting ratio; and Ramsey deepened the analysis by considering preferences as well as subjective degrees of belief. Although his theory was incomplete, the same idea was taken up and developed into a coherent system by Leonard Savage, and used as the foundations of new Bayesian statistics.
