I spent some more time thinking about complex adaptive systems being, at their base level, axiomatic systems. As axiomatic systems are defined, this cannot be true. There is no internal application within axiomatic systems. Even though mathematics is n axiomatic system, all applications come from outside the system. Another issue is that axiomatic systems are not adaptive at all. Kinda hurts that I missed out on that big clue.
So a new question: can we enhance axiomatic systems (change their definition) to make them adaptive and make them externally applicable, yet keep their fundamental concepts intact? Can we take them to a new level for both theory and application?