According to the dominant computational approach in cognitive science, cognitive agents are digital computers; according to the alternative approach, they are dynamical systems. This target article attempts to articulate and support the dynamical hypothesis. The dynamical hypothesis has two major components: the nature hypothesis (cognitive agents are dynamical systems) and the knowledge hypothesis (cognitive agents can be understood dynamically). A wide range of objections to this hypothesis can be rebutted. The conclusion is that cognitive systems may well be dynamical systems, and only sustained empirical research in cognitive science will determine the extent to which that is true.

Van Gelder's characterization of the differences between the dynamical and computational hypotheses, in terms of the contrast between change versus state and geometry versus structure, suggests that the dynamical approach is also at odds with classical mechanism. Dynamical and mechanistic approaches are in fact allies: mechanism can identify components whose properties define the variables that are related in dynamical analyses.

van Gelder argues that computational and dynamical systems are mathematically distinct kinds of systems. Although there are real experimental and theoretical differences between adopting a computational or dynamical perspective on cognition, and the dynamical approach has much to recommend it, the debate cannot be framed this rigorously. Instead, what is needed is careful study of concrete models to improve our intuitions.

Van Gelder presents the dynamical hypothesis as a novel law of qualitative structure to compete with Newell and Simon's (1976) physical symbol systems hypothesis. Unlike Newell and Simon's hypothesis, the dynamical hypothesis fails to provide necessary and sufficient conditions for cognition. Furthermore, imprecision in the statement of the dynamical hypothesis renders it unfalsifiable.

Van Gelder's example of a dynamical model is a Perceptron. The similarity of dynamical models and Perceptrons in turn exemplifies the close relationship between dynamical and algorithmic models. Both are models, not literal descriptions of brains. The brain states of standard modeling are better conceived as processes in the dynamical sense, but algorithmic models remain useful.

The concept of virtual machine allows us to combine the dynamical and computational hypotheses in an investigation of cognition. Van Gelder explicitly rejects this approach, but not only does it allow us to use the modelling technique most appropriate to the task, it also opens up a new range of phenomena where these techniques interact.

Van Gelder's specification of the dynamical hypothesis does not improve on previous notions. All three key attributes of dynamical systems apply to Turing machines and are hence too general. However, when a more restricted definition of a dynamical system is adopted, it becomes clear that the dynamical hypothesis is too underspecified to constitute an interesting cognitive claim.

(1) Van Gelder's concession that the dynamical hypothesis is not in opposition to computation in general does not agree well with his anticomputational stance. (2) There are problems with the claim that dynamic systems allow for nonrepresentational aspects of computation in a way in which digital computation cannot. (3) There are two senses of the “cognition is computation” claim and van Gelder argues against only one of them. (4) Dynamical systems as characterized in the target article share problems of universal realizability with formal notions of computation, but differ in that there is no solution available for them. (5) The dynamical hypothesis cannot tell us what cognition is, because instantiating a particular dynamical system is neither necessary nor sufficient for being a cognitive agent.

Dynamics is not enough for cognition, nor it is a substitute for information-processing aspects of brain behavior. Moreover, dynamics and computation are not at odds, but are quite compatible. They can be synthesized so that any dynamical system can be analyzed in terms of its intrinsic computational components.

For the dynamical hypothesis to be defended as a viable alternative to a computational perspective on natural cognition, the role of biological constraints needs to be considered. This task requires a detailed understanding of the structural organization and function of the dynamic nervous system, as well as a theoretical approach that grounds cognitive activity within the constraints of organism and ecological context.

Van Gelder's hard line against representations is not supported or supportable, and his soft line in favor of dynamical systems thinking as a supplement to representational models of cognition is good advice, but not revolutionary, as he seems to think.

Research in attitudes and social cognition exemplifies van Gelder's distinction between the computational and dynamical approaches. The former emphasizes linear measurement and rational decision-making. The latter considers processes of associative memory and self-organization in attitude formation and social influence. The study of dynamical processes in social cognition has been facilitated by connectionist approaches to computation.

We argue that the dynamical and computational hypotheses are compatible and in fact need each other: they are about different aspects of cognition. However, only computationalism is about the information-processing aspect. We then argue that any form of information processing relying on matching and comparing, as cognition does, must use discrete representations and computations defined over them.

Van Gelder has presented a position that he ties closely to a broad class of models known as dynamical models. One can support many of his broader claims about the importance of this class (as has been argued by connectionists for quite some time), but there are a number of unique characteristics of his brand of dynamicism. These characteristics engender difficulties for his view.

A consideration of underlying neural dynamics and the evolutionary process producing cognitive agents should complement the development of dynamical models of behavior. The geometrical aspects of dynamical systems theory which make it useful in the description of systems acting in an environment are less useful in understanding agents interacting with a range of environments, and may call for supplementation by evolutionary insights.

What new implications does the dynamical hypothesis have for cognitive science? The short answer is: none. The target article is basically an attack on traditional symbolic artificial intelligence (AI) and differs very little from prior connectionist criticisms of it. For the past 10 years, the connectionist community has been well aware of the necessity of using (and understanding) dynamically evolving, recurrent network models of cognition.

Although cognitive psychology is still dominated by computational theories, there is an emerging emphasis on dynamical aspects of cognition. Examples are provided supporting the increased use of dynamically inspired models by psychologists. Despite measurement and model verification problems in the direct use of dynamical system theoretic technology, van Gelder's general approach to cognition is recommended.

Another objection to the dynamical hypothesis is explored. To resolve it completely, one must focus more directly on an area not emphasized in van Gelder's discussion: the contributions of dynamical systems theory to understanding how cognition is neutrally implemented.

What van Gelder calls the dynamical hypothesis is only a special case of what we here dub the general dynamical hypothesis. His terminology makes it easy to overlook important alternative dynamical approaches in cognitive science. Connectionist models typically conform to the general dynamical hypothesis, but not to van Gelder's.

Cognitive systems are wilder than today's dynamical systems theory can handle. Cognitive systems might be tamed in principle, but the very notion of a dynamical system will change in the process.