Information and Interaction: On the Specialization of General System Theory

In the natural sciences, there is a prevalent structure: a structure that involves things that interact with each other through time. In classical physics, there is a theory that describes this structure and that is Newtonian mechanics. In quantum physics, the theory that describes interaction between things is quantum mechanics. The theory that describes interaction between organisms is biology; the theory that describes interaction between prices of competing products in a market is economics (\cite{von}). Therefore, in this thesis, we ask the question: If the natural sciences are, abstractly speaking, the study of attaching mathematical models to "systems that involve interaction," how do we describe these systems mathematically and in full generality? In our search for an answer, we argue for the acceptance of several basic assumptions about the nature of "interacting systems," and that the implied similarities to (para-)category theory are indicative that we base our framework for interacting systems in the language of (para-)category theory. We see at the end of the thesis that these systems can be reduced to a paracategory equipped with a set of faithful outgoing functors (with generally distinct codomains)