Kurt Ammon
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.