 The offense comes from attributing orders (r-types) to propositional functions on the basis of the variables with which they are defined, but also to the functions themselves, as simply values of bound higher-order variables. In response, the defender of type theory must say that any semantic intrepretation of the notion of propositional function will have to attribute to functions these distinctions that are marked in linguistic expressions of some of them, and in particular, the variables involved in their definition.