 Individuals would form the lowest type. Attributes or properties of individuals (or what Russell called propositional functions that could be true or false of individuals) would form the next higher type … and so on. In Russell’s type theory, the relation of membership can hold only between objects of different types: if α is a member of β, then α is of lower type than β. In type theory, the variables are typed. That is, a given variable is to be construed as ranging only over objects of a certain type. Thus there will be ‘individual’ variables (of type 0, say) ranging over just the individuals. At the next type up—type 1—there will be ‘property’ and ‘relation’ variables ranging over such properties and relations as hold of, or among, individuals. (0 and 1 here are serving as indices of types.) The idea iterates to cover all types of finite index. Moreover, in Russell’s theory, only the finitely indexed types could be formed. These are the types that can be indexed, from ‘outside’, so to speak, by natural numbers n. There are no transfinite types, i.e., no types that would be indexed by transfinite ordinals such as  ω.[25] 