powerful Turing machines or formal systems each of which forms the basis for the generation of its successor (see Theorems 3 and 4). In a comparable process Ammon [1988] **generates programs on the basis of elementary functions that form the components of the final programs. Starting from scratch,**
compositions of the elementary functions are used to construct a **sequence of** more and more powerful partial programs each of which forms the **basis for** the construction of its successor until a complete program is generated (see Section 4).

According to Hypothesis 2 a creative machine contains informal concepts such as computable functions. These concepts are processed by **effective** procedures such as an effective procedure according to Theorem **1. But**
according to Theorems 3 and 4 they are extensible beyond the limits of any given Turing machine or formal system. This means that informal concepts are processed by effective (finite) procedures although there is no complete formal (finite) description of these concepts.

According to Hypothesis 3 knowledge is constructed by informal inductive reasoning that is based on all available knowledge. As described in Section 4 a model of such reasoning processes is the development of computer programs which are empirically verified in tests and then used in practice. **Such**
an empirical verification requires only limited resources such as time. **This**
means that informal inductive reasoning is regarded as more efficient in practice than sophisticated formal procedures. Because all available knowledge can be used there is no sophisticated formal method for the construction of knowledge that can specified in advance.

The fourth hypothesis implies that a creative machine may start from scratch, that is, from any programming language and any input. Thus, it can revise any knowledge that proves to be false in a specific case.

The last hypothesis says that a creative machine can construct and verify any knowledge including knowledge about itself. Here, "any knowledge" includes any knowledge that can be constructed by a human and is finitely describable.

According to Definition 1 in Section 3 a creative machine is capable of evaluating functions beyond the limits of any given Turing machine or formal system. This means that it is capable of evaluating uncomputable functions.

Hypotheses 3 and 4 imply that this evaluation ordinarily involves empirical inductive reasoning that is fallible and correctable, that is, the values f(x) of uncomputable functions f **a creative machine assigns to arguments** x may be false but can be corrected by the machine. An example of an uncom-