 Church tells us that there is a relation \(\Delta\) that holds between concepts of each type within a hierarchy and the entities of the type immediately below it, for example between a concept of type \(\iota_2\) and another concept of \(\iota_1\). But something more needs to be said to illuminate the nature of this relationship. This is because although it helps to increase the numerical value of a subscript in order to remove ambiguity from our notation and indicate a corresponding increase in type, this provides little or no insight into the relationships among the concepts themselves, which are neither related by the numerical successor relation, nor dependent for their existence and identity on the notation for them. Moreover, expressing concepts may require adding new expressions to the language, so not everything can be expressed using a fixed vocabulary like the numerals.