We believe that live studies in which individuals, organisms, ecosystems and human societies appear are flawed due to the inadequacy of conceptual structures with which their quantitative results should relate in order to generate new hypotheses which can be examined.
The entities that make up systems and the connections between them will be determined by all existing binary relations. These binary relations may in some cases be replaced by functions, for which we may use tools inherent to differential calculus to calculate the dependence and independence relations between entities. Dependence and independence between entities have been developed using a few mathematical tools such as partial derivatives, the Wronskian and the Chain Rule.
From a representation of the entities via mathematical functions we have analysed functional dependence. In this paper, we will present issues relevant to systems, analysing the causal structure of entities (systems, subsystems, variables) from a functional point of view.
This paper is an attempt to approximate the concept of causality to a numerical study of partial derivatives with implications that range from the foundations of the system, in other words entry, state and response variables. We believe that subsequent work may be carried out along these lines.
