Online research in philosophy

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.

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.

(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.

Clark and Chalmers (2002) advance two hypotheses that both cognition and the mind extend into the environment. Both hypotheses are grounded in active externalism about mental content and the Parity Principle. Active externalism proposes that the external features of the environment in the present directly influence our mental contents and behavior. The Parity Principle states that a process or state in the environment is cognitive if it is functionally equivalent to a comparable intracranial cognitive process. This paper reviews two of the strongest replies to the hypotheses, namely that arguments for them commit the coupling-constitution fallacy and that the hypothesis of extended cognition is incompatible with any satisfactory criteria that distinguishes between cognitive and non-cognitive processes. This paper argues that a dynamical systems approach avoids both objections and offers a conceptual and methodological framework for an extended cognitive science. Lastly, an account of collective intentionality will be considered to show how groups of individuals can be the bearers of mental states.

The question whether cognition is subserved by internal processes in the brain (internalism) or extends in to the world (active externalism) has been vigorously debated in recent years. I show how internalist and externalist ideas can be pursued in a common framework, using (1) open dynamical systems, which allow for separate analysis of an agent's intrinsic and embodied dynamics, and (2) supervenience functions, which can be used to study how low-level dynamical systems give rise to higher-level dynamical structures.

The dynamical systems approach in cognitive science offers a potentially useful perspective on both brain and behavior. Indeed, the importation of formal tools from dynamical systems research has already paid off for our field in many ways. However, like some other theoretical perspectives in cognitive science, the dynamical systems approach comes in both moderate or pragmatic and “fundamentalist” varieties (Jones & Love, 2011). In the latter form, dynamical systems theory can rise to some stirring rhetorical heights. However, as argued here, it also triggers a number of serious and specific reservations.

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.

Cognitive science's basic premises are under attack. In particular, its focus on internal cognitive processes is a target. Intelligence is increasingly interpreted, not as a matter of reclusive thought, but as successful agent-environment interaction. The critics claim that a major reorientation of the field is necessary. However, this will only occur when there is a distinct alternative conceptual framework to replace the old one. Whether or not a serious alternative is provided is not clear. Among the critics there is some consensus, however, that this role could be fulfilled by the concept of a 'behavioral system'. This integrates agent and environment into one encompassing general system. We will discuss two contexts in which the behavioral systems idea is being developed. Autonomous Agents Research is the enterprise of building behavior-based robots. Dynamical Systems Theory provides a mathematical framework well suited for describing the interactions between complex systems. We will conclude that both enterprises provide important contributions to the behavioral systems idea. But neither turns it into a full conceptual alternative which will initiate a major paradigm switch in cognitive science. The concept will need a lot of fleshing out before it can assume that role.

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.

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism can be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena.