Van Gelder presents the distinction between dynamical systems and digital computers as the core issue of current developments in cognitive science. We think this distinction is much less important than a reassessment of cognition as a neurally, bodily, and environmentally embedded process. Embedded cognition lines up naturally with dynamical models, but it would also stand if combined with classic computation.

The dynamics/computation debate recalls a similar debate in the evolutionary biology community concerning the relative primacy of theories of structure versus theories of change. A full account of cognition will require a rapprochement between such theories and will include both computational and dynamical notions. The key to making computation relevant to cognition is not making it analog, but rather understanding how functional information-processing structures can emerge in complex dynamical systems.

Technical hitches mar van Gelder's proposed map of the conceptual landscape, particularly with respect to descriptive levels and the trio of instantiation, realisation, and implementation. However, for all the formal quibbles, van Gelder is onto something important; the tension he notes between computationalism and a dynamical alternative threatens to transform the way we conduct cognitive science research.

The dynamical hypothesis is strong in that, for it to be true, every cognitive phenomenon must be best modeled by a dynamical system. Depending on how it is interpreted, however, the hypothesis may be seen as probably false or even unfalsifiable. Strengthening the hypothesis to require unification, or at least coherence, across models in different cognitive domains alleviates this problem.

The distinction at the heart of van Gelder's target article is one between digital computers and dynamical systems, but this distinction conflates two more fundamental distinctions in cognitive science that should be kept apart. When this conflation is undone, it becomes apparent that the computational hypothesis is not as dominant in contemporary cognitive science as van Gelder contends; nor has the dynamical hypothesis been neglected.

After a historical sketch of the dynamical hypothesis, we stress that it is a functionalist hypothesis. We then tackle the point of a dynamical approach to constituent structures and emphasize that dynamical modeling must be coupled with morphological analysis.

Van Gelder seeks to distinguish between the computational and the dynamical hypotheses primarily on the basis of ontic criteria – the kind of systems cognitive agents really are. I suggest that this meets with mixed success. By shifting to epistemic criteria – what kind of explanations we require to understand cognitive agents – I suggest there is an easier and more intuitive way to distinguish between these two competing views of cognitive agents.

In conformity with the dynamical perspective advocated by van Gelder, a more psychological approach can highlight the intrinsic temporality of human cognition, revealing the inadequacies of representationalism as a framework for the modeling of mind.

Van Gelder's clear distinction between the quantitative nature of dynamical systems and the nonquantitative nature of computational processes provides a firm basis for distinguishing between processes that happen in time and processes that happen over time. Symbolic reasoning, the presumed basis of intelligent behavior in robots, happens over time. However, the movements and actions that robots must make to behave intelligently, happen in time. Attempting to connect the two, as classical artificial intelligence and robotics have presumed to be necessary, has produced a tension and an arbitrarily moving interface in the construction of robots. Adopting a robotic version of the dynamical hypothesis offers sound theoretical and scientific justification for those robotics researchers who continue to insist that getting the interaction dynamics of intelligent behavior right is a purely dynamical matter, and never a symbolic computational one.

Cognitive agents are dynamical systems but not quantitative dynamical systems. Quantitative systems are forms of analogue computation, which is physically too unreliable as a basis for cognition. Instead, cognitive agents are dynamical systems that implement discrete forms of computation. Only such a synthesis of discrete computation and dynamical systems can provide the mathematical basis for modeling cognitive behavior.

Van Gelder identifies the notion of a dynamical system with that of a quantitative system. According to an alternative view, a dynamical system is a state-determined system. This suggests a more profitable way to understand the roles of computation and dynamics in cognitive explanation.

The nature of the dynamical hypothesis in cognitive science (the DH) is further clarified in responding to various criticisms and objections raised in commentaries. Major topics addressed include the definitions of “dynamical system” and “digital computer”; the DH as Law of Qualitative Structure; the DH as an ontological claim; the multiple-realizability of dynamical models; the level at which the DH is formulated; the nature of dynamics; the role of representations in dynamical cognitive science; the falsifiability of the DH; the extent to which the DH is open; the role of temporal and implementation considerations; and the novelty or importance of the DH. The basic formulation and defense of the DH in the target article survives intact, though some refinements are recommended.

To explain social learning without invoking the cognitively complex concept of imitation, many learning mechanisms have been proposed. Borrowing an idea used routinely in cognitive psychology, we argue that most of these alternatives can be subsumed under a single process, priming, in which input increases the activation of stored internal representations. Imitation itself has generally been seen as a “special faculty.” This has diverted much research towards the all-or-none question of whether an animal can imitate, with disappointingly inconclusive results. In the great apes, however, voluntary, learned behaviour is organized hierarchically. This means that imitation can occur at various levels, of which we single out two clearly distinct ones: the “action level,” a rather detailed and linear specification of sequential acts, and the “program level,” a broader description of subroutine structure and the hierarchical layout of a behavioural “program.” Program level imitation is a high-level, constructive mechanism, adapted for the efficient learning of complex skills and thus not evident in the simple manipulations used to test for imitation in the laboratory. As examples, we describe the food-preparation techniques of wild mountain gorillas and the imitative behaviour of orangutans undergoing “rehabilitation” to the wild. Representing and manipulating relations between objects seems to be one basic building block in their hierarchical programs. There is evidence that great apes suffer from a stricter capacity limit than humans in the hierarchical depth of planning. We re-interpret some chimpanzee behaviour previously described as “emulation” and suggest that all great apes may be able to imitate at the program level. Action level imitation is seldom observed in great ape skill learning, and may have a largely social role, even in humans.

Byrne & Russon provide illustrative examples of imitative abilities in nonhuman primates. The convincing aspects of the examples are not, however, their hierarchical or structured nature: Such organization may be inevitable and hence, does not require explanation via imitation. Rather, examples of imitation are derived from reproduction of behaviors and sequences that, from the organism's perspective, are arbitrary.

The radical nub of Byrne & Russon's argument is that passive priming effects can produce much of the evidence of higher-order cognition in nonhuman primates. In support of their position we review evidence of similar behavioral priming effects n humans. However, that evidence further suggests that even program-level imitative behavior can be produced through priming.

A significant increase in the probability of an action resulting from observing that action performed by another agent cannot, on its own, provide persuasive evidence of imitation. Simple models of social influence based on two-person sequential games suggest that both imitation and pseudo-imitation can be explained by a process more fundamental than priming, namely, subjective utility maximization.

Certain recurring themes have emerged from research on intelligent behavior from literatures as diverse as developmental psychology, artificial intelligence, human reasoning and problem solving, and primatology. These themes include the importance of sensitivity to goal structure rather than action sequences in intelligent learning, the capacity to construct and manipulate hierarchically embedded mental representations, and a troubling domain specificity in the manifestation of each.

We cannot solve questions about imitative learning without knowing what motivates animals to copy others. Imitative capacities can be expected to be most pronounced in relation to situations and models of great social significance. Experimental research on nonhuman primates has thus far made little effort to present such situations and models.

To explore the neural mechanisms engaged by the perception of action with the intent to imitate, positron emission tomographic activation studies were performed in healthy human subjects. We discuss the results in light of the framework proposed by Byrne & Russon, especially the distinction between mechanisms subserving action-level and program-level imitation.

Byrne & Russon argue that the action and program levels of imitation form two discrete categories, with no intermediate steps. A Piagetian view enlarges our understanding of human and ape imitation by showing the developmental paths that imitation takes in the sensory-motor period of intelligence. It is clear from Piaget's (1945/1962) analysis that the action level of imitation is richly varied and that intermediate steps do occur between the action and program levels.