The human mind is reflexive and creative. This means that we can (to an extent) look at our own cognitive processes and change them. Reflexivity means we can form descriptions of ourselves and our thinking; creativity means that we can change ourselves and our thinking processes by changing those description and then activating or executing the changed cognitive structure. Therefore, whatever description we form of our own thinking, we can act differently. So if we would describe thought processes in terms of formal theories or algorithms, we would be able to move out of the scope of validity of those descriptions In this way, reflexivity forms the basis of creativity.
In conventional “artificial intelligence”, researchers are trying to describe cognitive processes in terms of what essentially are algorithms or formal theories (these two terms may be used interchangeably). This has not been very successful. They have failed to understand that creativity is at the core of intelligence and that the real challenge would be to find a way to build a system that cannot be described completely by an algorithm or formal theory but is able to develop out of the scope of applicability of any particular formalization.
Such a system would have the strange property that it would not be understandable completely. Any process in it could be described and the given theory could always be extended to include that case but the resulting theory would be incomplete again because the system can move out of its scope of validity.
Interestingly, the process by which you move out of the scope of a theory of such a system is to put that theory into the system so it can change it and then run the changed “program”. In the case of the human mind this means, if you can describe how you do it (by introspection and self-observation), or, with other words, if you feed a description of yourself back into yourself as something you look at, you can also act differently.
I owe the larger part of these ideas to one of my friends, the mathematician, computer scientist and philosopher Kurt Ammon, who defined creativity as the ability to compute non-Turing-computable functions, i.e. to do what algorithms can’t do. He points out that people are doing such things, e.g. proving theorems or programming computers. These are activities for which it is possible to prove that a complete formalization is not possible.
I believe that human beings and, as a result, human cultures and groups of humans (e.g. scientific communities) , are creative in this sense. This is the deeper reason why methods of natural sciences like physics cannot be transferred to the cultural sciences and humanities and human culture will always remain in the realm of philosophy. Even the attempts made in some schools of psychology and social sciences to introduce at least statistical “laws” should be of limited use since people and cultures can always change in ways causing the preconditions of such analyzes to become invalid. There are simply no fixed laws of thinking and no fixed laws of culture.
The connection between reflexivity and creativity can also be seen in biology. In a living organism, the genome forms a description of the organism. It forms the organism by transcription. At the same time, the organism can change it by processes of “editing” (from point mutations to crossing over between chromosomes, sexual recombination and so on). Although these processes are not conscious and controlled only to a limited extend, they cause the organism to be creative and as a result make it impossible to describe organisms completely in a formal way.