development of the procedure can be illustrated by the formula

$$L+P_{t}+E\to P_{t+1},$$
L + Pt + E → Pt+1, (5)
where L **is the universal programming language including knowledge about** L itself, Ptis the procedure at time t = 0, 1, 2, ..., P0 is empty, and E **stands**
for experience.

The second hypothesis refers to informal concepts such as the computable functions in Theorems 3 and 4.

Hypothesis 2 (Structure) **The knowledge in a creative machine according** to Hypothesis 1 contains informal concepts that are extensible beyond the limits of any given Turing machine or formal system. The third hypothesis deals with inductive reasoning, that is, the construction of knowledge in a creative system.

Hypothesis 3 (Induction) **In practice the construction of knowledge in a**
creative machine is achieved by informal inductive reasoning that is based on all available knowledge including informal concepts according to Hypothesis 2.

The last two hypotheses say that a creative system can revise all its knowledge and construct any knowledge. Hypothesis 4 (Revision) **A creative machine may revise all its knowledge** but a universal programming language from which it starts according to Hypothesis 1. In principle, all knowledge is fallible and correctable by the machine. Hypothesis 5 (Generality) **A creative machine can in principle construct** and verify any knowledge including all knowledge about itself as far as the knowledge can be constructed and verified.

## 5 Discussion

We discuss creative machines, in particular, in view of the Church-Turing thesis. The next section compares related work, for example, the **Turing**
machine concept.