In order to apply an effective procedure P **according to Theorem 1 in**
Section 2, a creative machine C **according to Definition 1 in Section 3 needs** an effective enumeration of computable functions, say E1**. A simple example** is an enumeration of functions f1, f2, ... defined by fi(n) = i **for all natural**
numbers i and natural numbers n**. By applying the effective procedure** P to E1 the machine C can generate a computable function, say g1**, which** is not contained in E1 according to Theorem 1. The function g1 **can be**
added to E1 which yields an effective enumeration g1, f1, f2**, ..., say** E2. Thus, starting from any effective enumeration E1 **of computable functions a**
creative machine C can, by repeatedly applying P**, generate a sequence** E1, E2, ... of effective enumerations of computable functions where En **has the**
form gn−1, ..., g1, f1, f2, ... for any natural number n **greater than 1. In**
particular, each En contains another computable function gn−1 **that in not** contained in any preceding Ei, where i **is a natural number less than** n.

An effective enumeration E1 **of computable functions can be provided by a**
Turing machine, say T1 generating the functions in E1 **or by a formal system,**
say F1, with a predicate for the computable functions in E1**. By applying**
an effective procedure P according to Theorem 1 a creative machine C can generate a computable function, say g1**. Theorems 1 and 2 in Section 2** imply that the function g1 is neither generated by the Turing machine T1 nor contained in the formal system F1. The incorporation of g1 **into the Turing**
machine T1 and the formal system F1 **yields a more powerful Turing machine**
T2 and a more powerful formal system F2. Thus, a creative machine C **can,** by repeatedly applying P**, generate a sequence of more and more powerful** Turing machines T1, T2**, ... and a sequence of more and more powerful formal** systems F1, F2**, ..., respectively.**
Up to any point in time a creative system C **can only "know" a finite**
description of computable functions which can be represented by a **Turing**
machine, say T1, generating the functions or in a formal system, say F1**, with**
a predicate for the functions. As described above the creative machine C can, by repeatedly applying an effective procedure P **according to Theorem** 1 to T1 or F1, generate more and more powerful Turing machines T1, T2**, ...**
and more and more powerful formal systems F1, F2**, ..., respectively. Thus, a**
creative system C **can generate "knowledge", that is, computable functions**
beyond the limits of its own knowledge in the Turing machine T1 **and the** formal system F1.

According to our considerations preceding Definition 1 in Section 3, the propositional function (predicate), say d, deciding whether or not a com-