 A question arises, however, once one realizes that the statements of primitive propositions and theorems in PM such as ∗10·1 are taken to be “typically ambiguous” (i.e., ambiguous with respect to type). These statements are actually schematic and represent all the possible specific assertions which can be derived from them by interpreting types appropriately. But if statements like ∗10·1 are schemata and yet have bound variables, how do we assign types to the entities over which the bound variables range? The answer is to first decide which type of thing the free variables in the statement range over. For example, assuming that the variable \(y\) in ∗10·1 ranges over individuals (of type \(\iota)\), then the variable \(\phi\) must range over functions of type \((\iota)/n\), for some \(n\). Then the bound variable \(x\) will also range over individuals. If, however, we assume that the variable \(y\) in ∗10·1 ranges over functions of type \((\iota)/1\), then the variable \(\phi\) must range over functions of type \(((\iota)/1)/m\), for some \(m\). In this case, the bound variable \(x\) will range over functions of type \((\iota)/1\).