Combining Bayes and Carnap: An Illustration and a Challenge Dealing with Fairness

Abstract Carnap’s The continuum of inductive methods (University of Chicago Press, 1952) is frequently mentioned as an historical milestone in inductive logic, but seldom used in age old problem situations. In this paper it will be shown that the application of Carnapian distributions may be very plausible in certain cases, in particular in coproduction with the Bayesian way of dealing with problems. This will be illustrated in perhaps the simplest possible way, viz. in the context where the question whether a (i.i.d.) device is fair is at stake.