States of change: Explaining dynamics by anticipatory state properties

Abstract

In Cognitive Science, recently Dynamical Systems Theory (DST) has been advocated as an approach to cognitive modelling that is better suited to the dynamics of cognitive processes than the symbolic/computational approaches are. Often the differences between DST and the symbolic/computational approach are emphasized. However, if two approaches are used also their commonalities can be analysed, and a unifying framework can be sought. In this paper the possibility of such a unifying perspective on dynamics is analysed. The analysis does not only cover dynamics in the cognitive discipline, but also in other disciplines: Physics, Mathematics and Computer Science. The unifying perspective warrants the development of integrated approaches covering both DST aspects and symbolic/computational aspects. The notion of a state-determined system lies at the heart of DST. This type of system is based on the assumption that properties of a given state fully determine the properties of future states. Taking this assumption as a premise, in this paper the explanatory problem of dynamics is analysed in more detail. The analysis of four cases within different disciplines (Cognitive Science, Physics, Mathematics, Computer Science) shows how in history this perspective has led to a number of often used concepts within these disciplines. In Cognitive Science the concepts desire and intention were introduced, and in classical mechanics the concepts momentum, energy, and force. Similarly, in Mathematics a number of concepts have been developed to formalise the state-determined system assumption. Derivatives (of different orders) of a function, and Taylor approximations are examples of such concepts. Furthermore, also transition systems, a currently (within Computer Science and related areas) popular format for specification of dynamic systems can be interpreted from this perspective. One of the main contributions of the paper is that the case studies provide a unified view on the explanation of dynamics across the chosen disciplines. All approaches to dynamics analysed in this paper share the state-determined system assumption and the (explicit or implicit) use of anticipatory state properties. Within Cognitive Science realism is one of the problems identified for the symbolic/computational approach, i.e., how do internal states described by symbols relate to the real world in a natural manner. As DST is proposed as an alternative to the symbolic/computational approach, a natural question is whether for DST the realism of the states can be better guaranteed. As a second main contribution the paper provides an evaluation of DST compared to the symbolic/computational approach, which shows that in this respect, i.e., for the realism problem, DST does not provide a better solution than the other approaches. This shows that DST and the symbolic/computational approach not only have the state-determined system assumption and the use of anticipatory state properties in common, but also the realism problem.