It is often claimed (1) that levels of nature are related by supervenience, and (2) that processes occurring at particular levels of nature should be studied using dynamical systems theory. However, there has been little consideration of how these claims are related. To address the issue, I show how supervenience relations give rise to ‘supervenience functions’, and use these functions to show how dynamical systems at different levels are related to one another. I then use this (...) analysis to describe a graded approach to non-reductive physicalism, and to critically assess Davidson’s arguments for psychological anomaly. I also show how this approach can inform empirical research in cognitive science. (shrink)

Dynamical systems theory (DST) is gaining popularity in cognitive science and philosophy of mind. Recently several authors (e.g. J.A.S. Kelso, 1995; A. Juarrero, 1999; F. Varela and E. Thompson, 2001) offered a DST approach to mental causation as an alternative for models of mental causation in the line of Jaegwon Kim (e.g. 1998). They claim that some dynamical systems exhibit a form of global to local determination or downward causation in that the large-scale, global activity of (...) the system governs or constrains local interactions. This form of downward causation is the key to the DST model of mental causation. In this paper I evaluate the DST approach to mental causation. I will argue that the main problem for current DST approaches to mental causation is that they lack a clear metaphysics. I propose one metaphysical framework (Gillett, 2002a/b/c) that might deal with this deficiency. (shrink)

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. (shrink)

Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘dynamical hypothesis’ (...) claims that cognition is and can be understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase (...) space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed. (shrink)

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task demands (...) of system identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. (shrink)

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes:i) on one hand the cell proliferation under successive divisions ii) on the other hand, the differentiation between cell lineages. We illustrate this new approach in the case of Caenorhabditis elegans by looking at the (...) early stages of embryogenesis, up to several hundreds of cells (lima bean larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of the control parameters with time. (shrink)

Dynamic systems theory is a way of describing the patterns that emerge from relationships in the universe. In the study of interpersonal relationships, within and between species, the scientist is an active and engaged participant in those relationships. Separation between self and other, scientist and subject, runs counter to systems thinking and creates an unnecessary divide between humans and animals.

. Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural (...) networks, logic programs, and evolutionary systems are instances of such interpreted dynamical systems, and thus our results entail that each of them may be described correctly and, in a sense, even completely by qualitative laws that obey the rules of a nonmonotonic logic system. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven (...) to be the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

Current models of speech motor control rely on either trajectory-based control (DIVA, GEPPETO, ACT) or a dynamical systems approach based on feedback control (Task Dynamics, FACTS). While both approaches have provided insights into the speech motor system, it is difficult to connect these findings across models given the distinct theoretical and computational bases of the two approaches. We propose a new extension of the most widely used dynamical systems approach, Task Dynamics, that incorporates many of the (...) strengths of trajectory-based approaches, providing a way to bridge the theoretical divide between what have been two separate approaches to understanding speech motor control. The Task Dynamics (TD) model posits that speech gestures are governed by point attractor dynamics consistent with a critically damped harmonic oscillator. Kinematic trajectories associated with such gestures should therefore be consistent with a second-order dynamical system, possibly modified by blending with temporally overlapping gestures or altering oscillator parameters. This account of observed kinematics is powerful and theoretically appealing, but may be insufficient to account for deviations from predicted kinematics—i.e., changes produced in response to some external perturbations to the jaw, changes in control during acquisition and development, or effects of word/syllable frequency. Optimization, such as would be needed to minimize articulatory effort, is also incompatible with the current TD model, though the idea that the speech production systems economizes effort has a long history and, importantly, also plays a critical role in current theories of domain-general human motor control. To address these issues, we use Dynamic Movement Primitives (DMPs) to expand a dynamical systems framework for speech motor control to allow modification of kinematic trajectories by incorporating a simple, learnable forcing term into existing point attractor dynamics. We show that integration of DMPs with task-based point-attractor dynamics enhances the potential explanatory power of TD in a number of critical ways, including the ability to account for external forces in planning and optimizing both kinematic and dynamic movement costs. At the same time, this approach preserves the successes of Task Dynamics in handling multi-gesture planning and coordination. (shrink)

This paper proposes a model for implementation of intrinsic natural language sentence meaning in a physical language understanding system, where 'intrinsic' is understood as 'independent of meaning ascription by system-external observers'. The proposal is that intrinsic meaning can be implemented as a point attractor in the state space of a nonlinear dynamical system with feedback which is generated by temporally sequenced inputs. It is motivated by John Searle's well known (Behavioral and Brain Sciences, 3: 417–57, 1980) critique of the (...) then-standard and currently still influential computational theory of mind (CTM), the essence of which was that CTM representations lack intrinsic meaning because that meaning is dependent on ascription by an observer_._ The proposed dynamical model comprises a collection of interacting artificial neural networks, and constitutes a radical simplification of the principle of compositional phrase structure which is at the heart of the current standard view of sentence semantics because it is computationally interpretable as a finite state machine. (shrink)

The problem of the direction of time is reconsidered in the light of a generalized version of the theory of abstract deterministic dynamical systems, thanks to which the mathematical model of time can be provided with an internal dynamics, solely depending on its algebraic structure. This result calls for a reinterpretation of the directional properties of physical time, which have been typically understood in a strictly topological sense, as well as for a reexamination of the theoretical meaning of (...) the widespread time-reversal invariance of classical physical processes. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we (...) prove that such a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

The proposed model is put forward as a template for the dynamical systems approach to embodied cognition. In order to extend this view to cognitive processing in general, however, two limitations must be overcome. First, it must be demonstrated that sensorimotor coordination of the type evident in the A-not-B error is typical of other aspects of cognition. Second, the explanatory utility of dynamical systems models must be clarified.

The theory of dynamical systems allows one to describe the change in a system' 's macroscopic behavior as a bifurcation in the underlying dynamics. We show here, from the example of depressive syndrome, the existence of a correspondence between clinical and electro-physiological dimensions and the association between clinical remission and brain dynamics reorganization. On the basis of this experimental study, we discuss the interest of such results concerning the question of normality versus pathology in psychiatry and the relationship (...) between mind and brain. (shrink)

From birth to 15 months infants and caregivers form a fundamentally intersubjective, dyadic unit within which the infant’s ability to recognize gender/sex in the world develops. Between about 18 and 36 months the infant accumulates an increasingly clear and subjective sense of self as female or male. We know little about how the precursors to gender/sex identity form during the intersubjective period, nor how they transform into an independent sense of self by 3 years of age. In this Theory and (...) Hypothesis article I offer a general framework for thinking about this problem. I propose that through repetition and patterning, the dyadic interactions in which infants and caregivers engage imbue the infant with an embodied, i.e., sensori-motor understanding of gender/sex. During this developmental period (which I label Phase 1) gender/sex is primarily an intersubjective project. From 15 to 18 months (which I label Phase 2) there are few reports of newly appearing gender/sex behavioral differences, and I hypothesize that this absence reflects a period of developmental instability during which there is a transition from gender/sex as primarily inter-subjective to gender/sex as primarily subjective. Beginning at 18 months (i.e., the start of Phase 3), a toddler’s subjective sense of self as having a gender/sex emerges, and it solidifies by 3 years of age. I propose a dynamic systems perspective to track how infants first assimilate gender/sex information during the intersubjective period (birth to 15 months); then explore what changes might occur during a hypothesized phase transition (15 to 18 months), and finally, review the emergence and initial stabilization of individual subjectivity-the period from 18 to 36 months. The critical questions explored focus on how to model and translate data from very different experimental disciplines, especially neuroscience, physiology, developmental psychology and cognitive development. I close by proposing the formation of a research consortium on gender/sex development during the first 3 years after birth. (shrink)

Mainstream forms of psychiatric talk therapy and cognitive behavioral therapy (CBT) do not reliably generate lasting recovery for eating disorders. We discuss widespread assumptions regarding the nature of eating disorders as fundamentally psychological disorders and highlight the problems that underlie these notions, as well as related practical problems in the implementation of mainstream treatments. We then offer a theoretical and practical alternative: a dynamical systems model of eating disorders in which behavioral interventions are foregrounded as powerful mediators between (...) psychological and physical states. We go on to present empirical evidence for behavioral modification specifically of eating speed in the treatment of eating disorders, and a hypothesis accounting for the etiology and progression, as well as the effective treatment, of the full spectrum of eating problems. A dynamical systems approach mandates that in any dietary and lifestyle change as profound as recovery from an eating disorder, acknowledgment must be made of the full range of pragmatic (psychological, cultural, social, etc.) factors involved. However, normalizing eating speed may be necessary if not sufficient for the development of a reliable treatment for the full spectrum of eating disorders, in its role as a mediator in the complex feedback loops that connect the biology and the psychology with the behaviors of eating. (shrink)

Neural organization contains a wealth of facts from all areas of brain research and provides a useful overview of physiological data for those working outside the immediate field. Furthermore, it gives a good example that the approach of dynamical system theory together with the concepts of cooperative and competitive interaction can be fruitful for an interdisciplinary approach to cognition.

Dynamical simulations of male and female mating strategies illustrate how traits such as restrictedness constrain, and are constrained by, local ecology. Such traits cannot be defined solely by genotype or by phenotype, but are better considered as decision rules gauged to ecological inputs. Gangestad & Simpson's work draws attention to the need for additional bridges between evolutionary psychology and dynamical systems theory.

This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of dynamical (...) systems, which I call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories. (shrink)

In this paper we will discuss some basic aspects of the global theory of dynamical systems. Rather than entering in technical derivations, we will try to emphasize the main points of the concept of dynamical systems which lead us to the generalization presented here, as well as some results that are easily generalized. Besides, some considerations of philosophical nature will be made.

This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems.

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. (shrink)

Periodically in science there arrive on the scene what appear to be dramatically new theoretical frameworks (what the philosopher of science Thomas Kuhn has called paradigm shifts). Characteristic of such changes in perspective is the recasting of old problems in new terms. By altering the conceptual vocabulary we use to think about problems, we may discover solutions which were obscured by prior ways of thinking about things. Connectionism, artificial life, and dynamical systems are all approaches to cognition which (...) are relatively new and have been claimed to represent such paradigm shifts. Just how deep the shifts are remains an open question, but each of these approaches certainly seems to offer novel ways of dealing with basic questions in cognitive science. (shrink)

Stocks and flows are building blocks of dynamic systems: Stocks change through inflows and outflows, such as our bank balance changing with withdrawals and deposits, or atmospheric CO2 with absorptions and emissions. However, people make systematic errors when trying to infer the behavior of dynamic systems, termed SF failure, whose cognitive explanations are yet unknown. We argue that SF failure appears when people focus on specific system elements, rather than on the system structure and gestalt. Using a standard (...) SF task, SF failure decreased by a global as opposed to local task format; individual global as opposed to local processing styles; and global as opposed to local perceptual priming. These results converge toward local processing as an explanation for SF failure. We discuss theoretical and practical implications on the connections between the scope of attention and understanding of dynamic systems. (shrink)

Locke & Bogin (L&B) suggest that theoretical principles of ontogenetic development apply to language evolution. If this is the case, then evolutionary theory should utilize epigenetic theories of development to theorize, model, and elucidate the evolution of language wherever possible. In this commentary, I evoke principles of dynamic systems theory to evaluate the evolutionary phenomena presented in the target article.

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.

Dynamic systems theory (DS) provides tools for exploring how simpler elements can interact to produce complex psychological configurations. It may, as Lewis demonstrates, provide means for explicating relationships between two reductionist approaches to overlapping sets of phenomena. The result is a description of psychological phenomena at a level that begins to achieve the richness we would hope to achieve in examining psychological life as it is experienced and explored in psychoanalysis.

This book focuses on showing how the ideas central to the new wave oj dynamic systems studies may also form the basis for a new and distinctive theory of human development where both global order and local variability in behaviour emerge together from the same organising dynamical interactions. This also sharpens our understanding of the weaknesses of the traditional formal, structuralist theories. Conversely, dynamical models have their own matching set of problems, many of which are consiously explored (...) here. Less readily acknowledged, the youthfulness of this field means that many of the studies presented here struggle to pass beyond speculative metaphor. Nonetheless, the field is shown to be one of vigour, intelligence and great promise. (shrink)

Economic logic impinges on contemporary political theory through both economic reductionism and economic methodology applied to political decision-making (through game theory). The authors argue that the sort of models used are based on mechanistic and linear methodologies that have now been found wanting in physics. They further argue that complexity based self-organization methods are better suited to model the complexities of economy and polity and their interactions with the overall social system.

Both natural and engineered systems are fundamentally dynamical in nature: their defining properties are causal, and their functional capacities are causally grounded. Among dynamical systems, an interesting and important sub-class are those that are autonomous, anticipative and adaptive (AAA). Living systems, intelligent systems, sophisticated robots and social systems belong to this class, and the use of these terms has recently spread rapidly through the scientific literature. Central to understanding these dynamical systems (...) is their complicated organisation and their consequent capacities for re- and self- organisation. But there is at present no general analysis of these capacities or of the requisite organisation involved. We define what distinguishes AAA systems from other kinds of systems by characterising their central properties in a dynamically interpreted information theory. (shrink)

Lots of things are usefully modelled in science as dynamical systems: growing populations, flocking birds, engineering apparatus, cognitive agents, distant galaxies, Turing machines, neural networks. We argue that relevant logic is ideal for reasoning about dynamical systems, including interactions with the system through perturbations. Thus, dynamical systems provide a new applied interpretation of the abstract Routley-Meyer semantics for relevant logic: the worlds in the model are the states of the system, while the (in)famous ternary (...) relation is a combination of perturbation and evolution in the system. Conversely, the logic of the relevant conditional provides sound and complete laws of dynamical systems. (shrink)

In this paper we prove that the reachability problem is BSS-undecidable for o-minimal dynamical systems.

Context is an important construct in many domains of cognition, including learning, memory, and emotion. We used dynamical systems methods to demonstrate the episodic nature of experience by showing a natural separation between the scales over which within-context and between-context relationships operate. To do this, we represented an individual's emails extending over about 5 years in a high-dimensional semantic space and computed the dimensionalities of the subspaces occupied by these emails. Personal discourse has a two-scaled geometry with smaller (...) within-context dimensionalities than between-context dimensionalities. Prior studies have shown that reading experience and visual experience have a similar two-scaled structure. Furthermore, the recurrence plot of the emails revealed that experience is predictable and hierarchical, supporting the constructs of some influential theories of memory. The results demonstrate that experience is not scale-free and provide an important target for accounts of how experience shapes cognition. (shrink)

Various aspects of the integrability of dynamical systems are discussed with the help of the singular point analysis. In particular the connection with the Painlevé property is described. Several examples will serve as illustrations.

It is argued that the theory of situated cognition together with dynamic systems theory can explain the core of artistic practice and aesthetic experience, and furthermore paves the way for an account of how artist and audience can meet via the artist's work. The production and consumption of art is an embodied practice, firmly based in perception and action, and supported by features of the local, agent-centered and global socio-cultural contexts. Artistic creativity and aesthetic experience equally result from the (...) dynamic interplay between agent and context, allowing for artist and viewer to relate to the artist's work in similar ways. (shrink)