Abstract

Frank Ramsey in his paper ‘Truth and Probability’ was the first to develop a theory of utility based on a representation theorem, and a theory of partial belief based on utility-valued odds. But his proof of the multiplication theorem, on which in his system the law of addition depends, contains a step for which there seems to be no justification, and Ramsey provided no clue as to how to supply one. I conjecture that the missing justification appeals naturally to a three-valued logic that de Finetti later described in his own discussion of the multiplication theorem. If this is the case then Ramsey’s paper is even more strikingly original than has been thought.