A cognitive system is any real system that has some cognitive property. Therefore, cognitive systems are a special type of K-systems (see chapter 3, section 3). Note that this definition includes both natural systems such as humans and other animals, and artificial devices such as robots, implementations of AI (artificial intelligence) programs, some implementations of neural networks, etc. Focusing on what all cognitive systems have in common, we can state a very general but nonetheless interesting thesis: All cognitive systems are dynamical systems. Section 2 explains what this thesis means and why it is (relatively) uncontroversial. It will become clear that this thesis is a basic methodological assumption that underlies practically all current research in cognitive science. The goal of section 3 is to contrast two styles of scientific explanation of cognition: computational and dynamical. Computational explanations are characterized by the use of concepts drawn from computation theory, while dynamical explanations employ the conceptual apparatus of dynamical systems theory. Further, I will suggest that all scientific explanations of cognition might end up sharing the same dynamical style, for dynamical systems theory may well turn out to be useful in the study of all types of models currently employed in cognitive science. In particular, a dynamical viewpoint might even benefit those scientific explanations of cognition which are based on symbolic models. Computational explanations of cognition, by contrast, can only be based on symbolic models or, more generally, on any other type of computational model. In particular, those scientific explanations of cognition which are based on an important class of connectionist models cannot be computational, for this class of models falls beyond the scope of computation theory. Arguing for this negative conclusion requires the formal explication of the concept of a computational system that I gave in chapter 1 (see definition 3). Finally, section 4 explores the possibility that scientific explanations of cognition might be based on Galilean models of cognitive systems (see chapter 3, section 5). Most cognitive scientists have not yet considered this possibility. The goals of this section are to contrast this proposal with the current modeling practice in cognitive science, to make clear its potential benefits, and to indicate possible ways to implement it.
Some elements for a history of the dynamical systems theory