There's just no such thing as a "solid foundation" in complex systems. Even trying to reason ontologically and create a cardinality of concepts in that way, when you're dealing with non-reducible emergent properties within that system interacting, is a much harder problem than people intuit. In fact, there's a whole field of study on this problem, around complexity and emergence. Santa Fe Institute specializes in this research.
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In fact, going back Leibniz, there's a whole way of thinking about the world in which the only things that are even "real" in a physical sense, are the interactions, themselves.