 Kleene’s (D) consists of the two arguments mentioned earlier by Church (1936a: section 7). The first argument is that the notion of computation by means of an algorithm does not lead outside the class of recursive functions (cf. Shoenfield [1967: 120] for an argument of the same sort). The second of these concerns the relation between recursive functions and formal systems of “symbolic logic”. Church argues that in any such system whose set of theorems is recursively enumerable, if \(f\) is a unary (“singulary” is Church’s term) function of positive integers and if it is true that