States of Change: Explaining Dynamics by Anticipatory State Properties

In cognitive science, the dynamical systems theory (DST) has recently been advocated as an approach to cognitive modeling 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, alternatively their commonalities can be analyzed and a unifying framework can be sought. In this paper, the possibility of such a unifying perspective on dynamics is analyzed. The analysis covers dynamics in cognitive disciplines, as well as in physics, mathematics and computer science. The unifying perspective warrants the development of integrated approaches covering both DST aspects and symbolic/computational aspects. The concept of a state-determined system, which is based on the assumption that properties of a given state fully determine the properties of future states, lies at the heart of DST. Taking this assumption as a premise, the explanatory problem of dynamics is analyzed in more detail. The analysis of four cases within different disciplines (cognitive science, physics, mathematics, computer science) shows how in history this perspective led to numerous often used concepts within them. 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 formalize the state-determined system assumption [e.g. derivatives (of different orders) of a function, Taylor approximations]. Furthermore, transition systems - a currently popular format for specification of dynamical systems within computer science - can also 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 analyzed 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, 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. © 2005 Taylor & Francis