 ∗30 on “Descriptive Functions” provides Whitehead and Russell’s analysis of mathematical functions in terms of relations and definite descriptions. Frege had used the notion of function, in the mathematical sense, as a basic notion in his logical system. Thus a Fregean “concept” is a function from objects as arguments to one of the two “truth values” as its values. A concept yields the value “True” for each object to which the concept applies, and “False” for all others. Russell, from well before discovering his theory of descriptions, had preferred to analyze functions in terms of the relation between each argument and value, and the notion of “uniqueness”. With modern symbolism, his view would be expressed as follows. For each function \(\lambda x f(x)\), there will be some relation (in extension) \(R\), such that the value of the function for an argument \(a\), that is \(f(a)\), will be the unique individual which bears the relation \(R\) to \(a\). The result is that there are no function symbols in Principia. As Whitehead and Russell say, the familiar mathematical expressions such as “\(\sin \pi/2\)” will be analyzed with a relation and a definite description, as a “descriptive function”. The “descriptive function”, \(R‘y\) (the \(R\) of \(y)\), is defined as follows: 