 Carnap’s general strategy was first to identify a broad class of confirmation functions, as subjectivists Ramsay and de Finetti were also to do, and then find a natural way of limiting this class still further. The confirmation functions have to meet some basic mathematical conditions. The axioms that state these conditions partially define a function, and this function can be interpreted in a number of ways. Carnap himself lists three in Carnap 1950. In (1955), John Kemeny (one of Carnap’s collaborators and later a co-inventor of BASIC programming language and still later president of Dartmouth College) gave an argument that persuaded Carnap that it was more fruitful to think of the function as indicating fair betting quotients rather than evidential support. This took Carnap even closer in conception to the work of such subjectivists as Ramsey and de Finetti. Indeed, the discussion of fair betting quotients, and related issues of Dutch book arguments had been initiated by de Finetti.