1. Carnap's continuum of inductive methods for a family of monadic predicates, the so-called ?-continuum or ?-system, is restricted by the as sumption that the size of the family is known at the start of the learning process. In the proper inductive situation we do not have this information. In this article a two-dimensional system will be constructed that is appropriate to deal with the proper inductive situation. This system describes a learning process both for relative frequencies of properties and for the size of the family; it may therefore be called a generalization of Carnap's continuum.