 Note that \(f\) has to be interpreted as a higher-order function which is predicated of the function \(\phi \bang \hat{z}\). In the modern notation used above, the language has to be a typed language in which \(\lambda\) expressions are allowed in argument position. As was pointed out later (Chwistek 1924, Gödel 1944, and Carnap 1947) there should be scope indicators for class expressions just as there are for definite descriptions. (The possibility of scope ambiguities in propositions about classes is mentioned in the final sentences of the Introduction (PM I, 84)). Chwistek, for example, proposed copying the notation for definite descriptions, thus replacing ∗20·01 with: