 In Russell’s hands the paradox applies to predicates, classes, and propositional functions and leads to a new picture of the logico-mathematical universe, which is outlined in a first exposition of the doctrine of types: to each propositional function \(\phi\) is associated a range of significance, i.e., a class of objects to which the given \(\phi\) applies in order to produce a proposition; moreover, precisely the ranges of significance form types. However, there are objects that are not ranges of significance; these are just atoms (i.e., urelemente or individuals) and they form the lowest type. The next type consists of classes or ranges of individuals; then one has classes of classes of objects of the lowest type, and so on (see also the entry on  type theory)..