program represents a computable function on the set of natural **numbers, is** impossible.

My theorem and principles about creative systems are compatible with Post's view [6, p. 417]:
... logic must ... in its very operation be informal. Better still, we write The Logical Process is Essentially Creative.

Wegner [11] argues that "interaction is more powerful than algorithms".

My simple incompleteness theorem can be regarded as a mathematical proof of his thesis. Moreover, the theorem and its proof imply the existence of systems "computing" non-computable functions, that is, determining values of non-computable functions for given arguments. In this sense, **they confirm** the view of Wegner and Goldin [12] "that neither logic nor algorithms can completely model computing and human thought."
Wegner [11] writes that the incompleteness of interaction machines **follows**
from the fact that dynamically generated input streams are mathematically modeled by infinite sequences over a finite alphabet, which are not enumerable. The "incompleteness", rather indeterminacy of creative systems follows from their definition, in particular from the fact that no formal theory can
"capture" all computable functions on the set of natural numbers.

My incompleteness theorem implies that there is no general algorithm or formal system for the verification of programs. This result is compatible with Wegner's view "that proving correctness is not merely hard but impossible" because "**open, empirical, falsifiable, or interactive systems are necessarily**
incomplete**" [11, p. 10]. It is also compatible with G¨odel's statement [3, p.**
84] that "one has been able to define them [demonstrability and definability]
only relative to a given language", that is, there is no general definition of formal proofs but such definitions can only be given in particular formal systems.

## References

[1] Ammon, K. The automatic acquisition of proof methods. Proceedings of the Seventh National Conference on Artificial Intelligence, St. **Paul,**
U.S.A, August 1988. Morgan Kaufmann, San Mateo, Calif., USA.