Publisher Summary Probability theory, epistemically interpreted, provides an excellent account of inductive reasoning. A fundamental reason for the epistemological success of probability theory is that there exists a well-behaved concept of conditional probability. However, still people have, and have reasons for, various concerns over probability theory. One of these is the notion of plain belief. Probability theory, however, offers no formal counterpart to this notion. It seems that the formal representation of plain belief has to take a nonprobabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or by the conjunction of all propositions believed true in it. |However, this does not yet provide a theory of induction—an answer to the question how epistemic states so represented are changed through information or experience. There is a convincing partial answer: If the new information is compatible with the old epistemic state, the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise plain belief would not be represented as corrigible. When epistemic states are represented by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed that provides a complete solution to this problem.