Online research in philosophy

Digital computers play a special role in cognitive science—they may actually be instances of the phenomenon they are being used to model. This paper surveys some of the main issues involved in understanding the relationship between digital computers and cognition. It sketches the role of digital computers within orthodox computational cognitive science, in the light of a recently emerging alternative approach based around dynamical systems.

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 pitched; 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.

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.

What new implications does the dynamical hypothesis have for cognitive science? The short answer is: None. The _Behavior and Brain Sciences _target article, “The dynamical hypothesis in cognitive science” by Tim Van Gelder is basically an attack on traditional symbolic AI and differs very little from prior connectionist criticisms of it. For the past ten years, the connectionist community has been well aware of the necessity of using (and understanding) dynamically evolving, recurrent network models of cognition.

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.

(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.

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.

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.

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.

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 keep apart. When this conflation is undone, it becomes apparent that the “computational hypothesis” (CH) is not as dominant in contemporary cognitive science as van Gelder contends; nor has the “dynamical hypothesis” (DH) been neglected.