This article discusses the classical problem of zero probability of universal generalizations in Rudolf Carnap’s inductive logic. A correction rule for updating the inductive method on the basis of evidence will be presented. It will be shown that this rule has the effect that infinite streams of uniform evidence assume a non-zero limit probability. Since Carnap’s inductive logic is based on finite domains of individuals, the probability of the corresponding universal quantification changes accordingly. This implies that universal generalizations can receive (...) positive prior and posterior probabilities, even for (countably) infinite domains. (shrink)

This article discusses the problem of non-zero probabilities for non-tautologous universal generalizations in Rudolf Carnap’s inductive logic when the domain of discourse is infinite. A solution is provided for a generalization of the form “all Xs are Ys”, for example “all ravens all black”. The solution is based on assuming that a significant part of the domain consists of non-Xs. This assumption can often be justified as a kind of ceteris paribus principle.