  A fundamental question is whether Turing machines can model all reasoning
processes. We introduce an existence principle stating that the perception of
the physical existence of any Turing program can serve as a physical causation
for the application of any Turing-computable function to this Turing program.
The existence principle overcomes the limitation of the outputs of Turing
machines to lists, that is, recursively enumerable sets. The principle is
illustrated by productive partial functions for productive sets such as the set
of the Goedel numbers of the Turing-computable total functions. The existence
principle and productive functions imply the existence of physical systems
whose reasoning processes cannot be modeled by Turing machines. These systems
are called creative. Creative systems can prove the undecidable formula in
Goedel's theorem in another formal system which is constructed at a later point
in time. A hypothesis about creative systems, which is based on computer
experiments, is introduced.
