Given that a System is an information structure, we can proceed to analyze the world in terms of its nested information structures or subsystems. All of the dynamics of complex systems can be realized in theory and observation by decomposing natural systems along emergent information flow boundaries. In biological cybernetics and cognitive sciences, we can analyze living organisms as self-producing and maintaining networks of processes that are open to the environment and the other beings coexisting therein. With the development of symbolic language in the homo line, the stage was set for developing extended phenotypes in material culture. With homo sapiens and the Neolithic Age this kicks into high gear, first accellerating slowly but the pace of change is ramping up the whole time.
This is how we find ourselves in the age of disruptive change where we either wise up fast or get kicked off the planet. Much of the change is in the technology of information systems, but even more significant is the evolution of material culture noted above. The ability to not just use tools but to invent them requires an interruption in the normal uses of language that give only the capacity to use language within the given framework. To invent a new tool the individual must first imagine using that tool. A tool might be modified and made better within a space of variation already given, but a new category of tools for a new food source. First the new action including possible invention has to be imagined, the tools fashioned and use attempted. Failure reveals more of the world and now more people engage and play and experiment until sucess. When cognition can go beyond the manipulation of a world given and think about the experience outside the fishbowl of a given life-world embedded necessarily in learned habits of perception and responding active rituals.
The break from life as given to the examined life of awareness is deep and wide and in general not of much survival value within a given way of living. On the other hand, for creating new ways of living and responding adaptively to a changing situation, it is obvious how thinking outside the box might save the day not only for the wise guy with a crazy plan but the whole social group. Inventions of new tools and even ephemeral ways of thinking and doing things almost require trade to develop in parallel with new lingustic modes of dissemination of new tools and culture. Anthropologists can trace the development and dissemination of culture in a number of ways, and one of them is the way that different tools and technique appear and spread over time and place. Many of the sites producing data are relatively recent discoveries, yet another indicator of disruptive change. We now have so many well-educated specialists that all fields are accellerating as more trained field workers spread about the world and are recruited from more diverse places and cultures.
Another aspect that none can ignore is the pace of change in digital technologies. Moore's law will not go on forever, but it has not bottomed out yet. This field was primative when I was born, and at a price that I built a kit computer in high school. Today's youth have what would have been a supercomputer then in the palm of their hands. This means that all the sciences can gather, store and process ever more data. We can also process the data in many ways that seem to magically extract knowledge and use learning processes to teach machines to do what used to require a human.
This brief outline goes a long way to justifying the need for systems theory as a foundational component of any theory of everything (ToE). It should also make clear why any ToE is necessarily incomplete in some very deep ways. The formalities of theory can never fully capture the actuality of emegent systems of natural science. We have special sciences of each level of organization of reductionist models of natural s;ystem dynamics, and they can only be joined into a coherent picture with system theory. To develop a theory, we will need to define the elemental objects and their properties, but we must resist finally settling on particular definitions so that our theory will remain open to modified definitions that better match working practices. Ultimately this work should be grounded in pragmatic philosophy where knowledge is the result of experience in the practices in one or more fields of inquiry. This is also postmodernist in that no tradition is privileged and the truth will be multiple in the sense that some traditions will likely have conflicting truths. We can work to resolve such conflicts, but only by constructing spaces where meanings can be translated and considered outside any traditoin.
The success of the reductionist, objectivist epistemologies is that none can really seriously deny their import whenever their application is successful. The failure is to not recognize that this doesn't complete the picture. Systems theory can be used as a bridge. Understanding that Plato's eternal forms of mathematics are just that, patterns of relating that are independent of time, place and context, but that also leaves an enormous space for the contingent, historical or as the economists say, "path dependent". This is not only the path into the world for meaning and aesthetics, but it is the cure for self-importance. It could have been otherwise. The past does not fully determine the future. This is an informational property of the Universe, information can and is created and destroyed and that is the source of all asymetries in time and the difference between time an space.
I'd have to check this fully with the philosophical physicists, but if your theory has observation and the collapse of the wave function as real and significant to what exists, then information is created and destroyed in time. Therefore, nothing is time reversable, but it leaves open a lot more possibility of significant (meaningful) connections between past, present and future. Consciousness, if essentially quantum based, might be able to navigate time in some causal (intentional?) ways.
-> Integral because integration of parts into wholes is a more important distinction. Of course it is universal. Integral also good in that it refers to wholeness which ties to whole numbers, zero, one and the rest generated from relations of these two.
Principle of threes: refer to Peirce and his demonstrations that two elements are insufficient and any more complex can be build from them. {0, 1, (0, 1)} or maybe this way too: {