Dynamical Systems

Cognitive science is, more than anything else, a pursuit of cognitive mechanisms. To make headway towards a mechanistic account of any particular cognitive phenomenon, a researcher must choose among the many architectures available to guide and constrain the account. It is thus fitting that this volume on contemporary debates in cognitive science includes two issues of architecture, each articulated in the 1980s but still unresolved: " • Just how modular is the mind? – a debate initially pitting encapsulated mechanisms against (...) highly interactive ones. • Does the mind process language-like representations according to formal rules? – a debate initially pitting symbolic architectures against less language-like architectures. " Our project here is to consider the second issue within the broader context of where cognitive science has been and where it is headed. The notion that cognition in general—not just language processing—involves rules operating on language-like representations actually predates cognitive science. In traditional philosophy of mind, mental life is construed as involving propositional attitudes—that is, such attitudes towards propositions as believing, fearing, and desiring that they be true—and logical inferences from them. On this view, if a person desires that a proposition be true and believes that if she performs a certain action it will become true, she will make the inference and perform the action. (shrink)

One of the most foundational and continually contested questions in the cognitive sciences is the degree to which the functional organization of the brain can be understood as modular. In its classic formulation, a module was defined as a cognitive sub-system with nine specific properties; the classic module is, among other things, domain specific, encapsulated, and implemented in dedicated neural substrates. Most of the examinations—and especially the criticisms—of the modularity thesis have focused on these properties individually, for instance by finding (...) counterexamples in which otherwise good candidates for cognitive modules are shown to lack domain specificity or encapsulation. The current paper goes beyond the usual approach by asking what some of the broad architectural implications of the modularity thesis might be, and attempting to test for these. The evidence does not favor a modular architecture for the cortex. Moreover, the evidence suggests that best way to approach the understanding of cognition is not by analyzing and modelling different functional domains in isolation from the others, but rather by looking for points of overlap in their neural implementations, and exploiting these to guide the analysis and decomposition of the functions in question. This has significant implications for the question of how to approach the design and implementation of intelligent artifacts in general, and language-using robots in particular. (shrink)

The study of instabilities in perception has attracted much interest in recent decades. The presented investigations focus on electrophysiological correlates of orientation reversals of both ambiguous visual stimuli and alternating non-ambiguous stimuli, representing the two options of the ambiguous version. Based on a refined experimental setup, significant features in the event-related potentials associated with the perception of orientation reversal were found in both cases. Their occipital location, their early occurence (200–250 ms), and their latency difference (50 ms) offer interesting perspectives (...) for an understanding of unstable brain states in terms of basic concepts of dynamical systems. (shrink)

Advocates of dynamical systems theory (DST) sometimes employ revolutionary rhetoric. In an attempt to clarify how DST models differ from others in cognitive science, I focus on two issues raised by DST: the role for representations in mental models and the conception of explanation invoked. Two features of representations are their role in standing-in for features external to the system and their format. DST advocates sometimes claim to have repudiated the need for stand-ins in DST models, but I argue that (...) they are mistaken. Nonetheless, DST does offer new ideas as to the format of representations employed in cognitive systems. With respect to explanation, I argue that some DST models are better seen as conforming to the covering-law conception of explanation than to the mechanistic conception of explanation implicit in most cognitive science research. But even here, I argue, DST models are a valuable complement to more mechanistic cognitive explanations. (shrink)

Much of cognitive neuroscience as well as traditional cognitive science is engaged in a quest for mechanisms through a project of decomposition and localization of cognitive functions. Some advocates of the emerging dynamical systems approach to cognition construe it as in opposition to the attempt to decompose and localize functions. I argue that this case is not established and rather explore how dynamical systems tools can be used to analyze and model cognitive functions without abandoning the use of decomposition and (...) localization to understand mechanisms of cognition. (shrink)

The dynamical patterns in mental phenomena have a characteristic suppleness&emdash;a looseness or softness that persistently resists precise formulation&emdash;which apparently underlies the frame problem of artificial intelligence. This suppleness also undermines contemporary philosophical functionalist attempts to define mental capacities. Living systems display an analogous form of supple dynamics. However, the supple dynamics of living systems have been captured in recent artificial life models, due to the emergent architecture of those models. This suggests that analogous emergent models might be able to explain (...) supple dynamics of mental phenomena. These emergent models of the supple mind, if successful, would refashion the nature of contemporary functionalism in the philosophy of mind. (shrink)

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.

There has been considerable debate in the literature about the relative merits of information processing versus dynamical approaches to understanding cognitive processes. In this article, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information-theoretic analysis reveals how task-relevant information flows through the system to be combined into a (...) categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science. (shrink)

Psychoneural reduction is under attack again, only this time from a former ally: cognitive neuroscience. It has become popular to think of the brain as a complex system whose theoretically important properties emerge from dynamic, non-linear interactions between its component parts. ``Emergence'' is supposed to replace reduction: the latter is thought to be incapable of explaining the brain qua complex system. Rather than engage this issue at the level of theories of reduction versus theories of emergence, I here emphasize a (...) role that reductionism plays – and will continue to play – even if neuroscience adopts this ``complex systems'' view. In detailed investigations into the function of complex neural circuits, certain questions can only be addressed by moving down levels and scales. This role for reduction also finds a place for approaches that dominate mainstream neuroscience, like the widespread use of experimental techniques and theories from molecular biology and biochemistry. These are difficult to reconcile with the anti-reductionist sentiments of the ``complex systems'' branch of cognitive neuroscience. (shrink)

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. (shrink)

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.

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

Tim van Gelder, following Brandom, Collins and others, uses the so‐called wide content of capacities which support social, norm governed activities, such as language, to argue for their anti‐natural, abstract, but socially instituted nature and thence for the failure of the entire traditional mind‐body discussion as ill‐posed. We argue that his former conclusion is wrong, that such properties are naturalisable, complicated organisational properties of the complexly organised, non‐linearly interactive systems that human beings are. This analysis also provides principled support, but (...) on other grounds, for van Gelder’s latter conclusion. We outline a new naturalist approach to the organisational capacities of such systems that is intended to ground their biological, cognitive and social characters. (shrink)

Leading scholars in the fields of philosophy and the sciences of the mind have contributed to this newest volume in the prestigious Pittsburgh-Konstanz series. Among the problem areas discussed are folk psychology, meanings as conceptual structures, functional and qualitative properties of colors, the role of conscious mental states, representation and mental content, the impact of connectionism on the philosophy of the mind, and supervenience, emergence, and realization. Most of the essays are followed by commentaries that reflect ongoing debates in the (...) philosophy of the mind and often develop a counterpoint to the claims of the essayists. (shrink)

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.

Do psychologists and computer/cognitive scientists mean the same thing by the term `information'? In this essay, I answer this question by comparing information as understood by Gibsonian, ecological psychologists with information as understood in Barwise and Perry's situation semantics. I argue that, with suitable massaging, these views of information can be brought into line. I end by discussing some issues in (the philosophy of) cognitive science and artificial intelligence.

Arguments in favor of anti-representationalism in cognitive science often suffer from a lack of attention to detail. The purpose of this paper is to fill in the gaps in these arguments, and in so doing show that at least one form of anti- representationalism is potentially viable. After giving a teleological definition of representation and applying it to a few models that have inspired anti- representationalist claims, I argue that anti-representationalism must be divided into two distinct theses, one ontological, one (...) epistemological. Given the assumptions that define the debate, I give reason to think that the ontological thesis is false. I then argue that the epistemological thesis might, in the end, turn out to be true, despite a potentially serious difficulty. Along the way, there will be a brief detour to discuss a controversy from early twentieth century physics. (shrink)

Scientific and Philosophical Studies of Mind Franklin and Marshall College Lancaster, PA 17604-3003 USA .

Markman and Dietrich¹ recently recommended extending our understanding of representation to incorporate insights from some “alternative” theories of cognition: perceptual symbol systems, situated action, embodied cognition, and dynamical systems. In particular, they suggest that allowances be made for new types of representation which had been previously under-emphasized in cognitive science. The amendments they recommend are based upon the assumption that the alternative positions each agree with the classical view that cognition requires representations, internal mediating states that bear information.² In the (...) case of one of the alternatives, dynamical systems³, this is simply false: many dynamically-oriented cognitive scientists are anti-representationalists.^4,5,6. (shrink)

(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. (shrink)

1. Throughout the paper, and especially in the section called "LISP vs. DST", I worried that there was not enough focus on EXPLANATION. For the real question, it seems to me, is not whether some dynamical system can implement human cognition, but whether the dynamical description of the system is more explanatorily potent than a computational/representational one. Thus we know, for example, that a purely physical specification can fix a system capable of computing any LISP function. But from this it (...) doesn't follow that the physical description is the one we need to understand the power of the system considered as an information processing device. In the same way, I don't think your demonstration that bifurcating attractor sets can yield the same behavior as a LISP program goes any way towards showing that we should not PREFER the LISP description. To reduce symbolic stories to a subset of DST (as hinted in that section) requires MORE than showing this kind of equivalence: it requires showing that there is explanatory gain, or at the very least, no explanatory loss, at that level. I append an extract from a recent paper of mine that touches on these issues, in case it helps clarify what I am after here. (shrink)

Beer’s (2003) paper is a tour de force of detailed comments on the more general notion of “situated- dynamical modeling, and provides a concrete sample ness”, Beer suggests that “on this view, situated action of the kinds of understanding dynamicists may realis- is the fundamental concern and cognition is … one tically hope to achieve. The analysis is thus, as Beer resource among many that can be brought to bear as an states, a “tool for building intuition”, and in this (...) it suc- agent encounters its world”. In the worked example of ceeds brilliantly. But it is also an attempt to show that an agent that approaches circles and avoids diamonds, dynamical approaches can get a foothold in the expla- we see direct evidence of this in the claim that a certain nation of “minimally cognitive behaviors”; that is to three-dimensional projection provides a potent analytic say, behaviors that seem, on the surface at least, good tool. For this projection happens to be one that involves contenders for more traditional forms of problem de- one environmental state variable (vertical object posi- composition and analysis. In these brief comments, I tion), one body state variable (horizontal position rela- want to focus on one important question that I think tive to the object) and one neuronal state variable remains unanswered, and that bears rather directly on (output of interneuron 9). By dispensing with talk of this enterprise of “scaling up”. representations and their contents, and restricting the The question concerns the notion of an integrated depiction of the inner realm to a depiction of inner state dynamical explanation itself. The point about such alone (section 9.3), the dynamicist makes it easy to.. (shrink)

Mind, it has recently been argued1, is a thoroughly temporal phenomenon: so temporal, indeed, as to defy description and analysis using the traditional computational tools of cognitive scientific understanding. The proper explanatory tools, so the suggestion goes, are instead the geometric constructs and differential equations of Dynamical Systems Theory. I consider various aspects of the putative temporal challenge to computational understanding, and show that the root problem turns on the presence of a certain kind of causal web: a web that (...) involves multiple components (both inner and outer) linked by chains of continuous and reciprocal causal influence. There is, however, no compelling route from such facts about causal and temporal complexity to the radical anti- computationalist conclusion. This is because, interactive complexities notwithstanding, the computational approach provides a kind of explanatory understanding that cannot (I suggest) be recreated using the alternative resources of pure Dynamical Systems Theory. In particular, it provides a means of mapping information flow onto causal structure -- a mapping that is crucial to understanding the distinctive kinds of flexibility and control characteristic of truly mindful engagements with the world. Where we confront especially complex interactive causal webs, however, it does indeed become harder to isolate the syntactic vehicles required by the computational approach. Dynamical Systems Theory, I conclude, may play a vital role in recovering such vehicles from the burgeoning mass of real-time interactive complexity. (shrink)

Recent studies such as Thelen and Smith (1994), Kelso (1995), Van Gelder (1995), Beer (1995), and others have presented a forceful case for a dynamical systems approach to understanding cognition and adaptive behavior. These studies call into question some foundational assumptions concerning the nature of cognitive scientific explanation and (in particular) the role of notions such as internal representation and computation. These are exciting and important challenges. But they must be handled with care. It is all to easy in this (...) debate to lose sight of the explanatorily important issues and to talk at cross purposes, courtesy of the (suprisingly) various ways in which different theorists often concieve key terms. (shrink)

In Robert West’s talk last week, dynamical systems theory (DST) was applied to a specific problem involving interacting symbolic systems, without much reference to how those systems are embodied or related to other types of systems. Despite this level of abstraction, DST can yield interesting results, though one might be left wondering if it really leads to understanding, or what it all means. In particular, Robert noted problems he has in convincing referees that the sort of explanation he gave can (...) give a useful understanding, and that it doesn’t invoke dubious notions with its references to emergence, holism, and mathematical openness. (shrink)

The subject of this chapter is the identity of individual dynamical objects and properties. Two problems have dominated the literature: transtemporal identity and the relation between composition and identity. Most traditional approaches to identity rely on some version of classification via essential or typical properties, whether nominal or real. Nominal properties have the disadvantage of producing unnatural classifications, and have several other problems. Real properties, however, are often inaccessible or hard to define (strict definition would make them nominal). I suggest (...) that classification should be in terms of dynamical properties of systems, starting with individual systems rather than classes, and working up by abstractions that fit causal generalities. The advantage of this approach is that individuality is testable and revisable as we come to know more about systems. Another advantage is that if anything is real, then it is the dynamical. Once I have presented this approach in general, I will show that the central concept of dynamical cohesion (the "dividing glue") is amenable to giving a principled account of individuation as a process, at the same time explaining the origin of diversity. Some other advantages of this approach are presented, including how it can be used as a basis for testable classifications. This last has moral implications, since cohesion at the individual and the social levels, and their interactions, can impinge on proper moral decisions. (shrink)

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)

The term cybernetics was first used in 1947 by Norbert Wiener with reference to the centrifugal governor that James Watt had fitted to his steam engine, and above all to Clerk Maxwell, who had subjected governors to a general mathematical treatment in 1868. Wiener used the word “governor” in the sense of the Latin corruption of the Greek term kubernetes, or “steersman.” Wiener defined cybernetics as the study of “control and communication in the animal and the machine” (Wiener 1948). This (...) definition captures the original ambition of cybernetics to appear as a unified theory of the behavior of living organisms and machines, viewed as systems governed by the same physical laws. The initial phase of cybernetics involved disciplines more or less directly related to the study of such systems, like communication and control engineering, biology, psychology, logic, and neurophysiology. Very soon, a number of attempts were made to place the concept of control at the focus of analysis also in other fields, such as economics, sociology, and anthropology. The original ambition of “classical” cybernetics thus seemed to involve also several human sciences, as it developed in a highly interdisciplinary approach, aimed at seeking common concepts and methods in rather different disciplines. In classical cybernetics, this ambition did not produce the desired results and new approaches had to be attempted in order to achieve them, at least partially. In this chapter, we shall focus our attention in the first place on the specific topics and key concepts of the original program in cybernetics and their significance for some classical philosophic problems (those related to ethics are dealt with in Chapter 5, COMPUTER ETHICS, and Chapter 6, COMPUTER-MEDIATED COMMUNICATION AND HUMAN–COMPUTER INTERACTION). We shall then examine the various limitations of cybernetics. This will enable us to assess different, more recent, research programs that are either ideally related to cybernetics or that claim, more strongly, to represent an actual reappraisal of it on a completely new basis. (shrink)

Since the early eighties, computationalism in the study of the mind has been “under attack” by several critics of the so-called “classic” or “symbolic” approaches in AI and cognitive science. Computationalism was generically identified with such approaches. For example, it was identified with both Allen Newell and Herbert Simon’s Physical Symbol System Hypothesis and Jerry Fodor’s theory of Language of Thought, usually without taking into account the fact ,that such approaches are very different as to their methods and aims. Zenon (...) Pylyshyn, in his influential book Computation and Cognition, claimed that both Newell and Fodor deeply influenced his ideas on cognition as computation. This probably added to the confusion, as many people still consider Pylyshyn’s book as paradigmatic of the computational approach in the study of the mind. Since then, cognitive scientists, AI researchers and also philosophers of the mind have been asked to take sides on different “paradigms” that have from time to time been proposed as opponents of (classic or symbolic) computationalism. Examples of such oppositions are: -/- computationalism vs. connectionism, computationalism vs. dynamical systems, computationalism vs. situated and embodied cognition, computationalism vs. behavioural and evolutionary robotics. -/- Our preliminary claim in section 1 is that computationalism should not be identified with what we would call the “paradigm (based on the metaphor) of the computer” (in the following, PoC). PoC is the (rather vague) statement that the mind functions “as a digital computer”. Actually, PoC is a restrictive version of computationalism, and nobody ever seriously upheld it, except in some rough versions of the computational approach and in some popular discussions about it. Usually, PoC is used as a straw man in many arguments against computationalism. In section 1 we look in some detail at PoC’s claims and argue that computationalism cannot be identified with PoC. In section 2 we point out that certain anticomputationalist arguments are based on this misleading identification. In section 3 we suggest that the view of the levels of explanation proposed by David Marr could clarify certain points of the debate on computationalism. In section 4 we touch on a controversial issue, namely the possibility of developing a notion of analog computation, similar to the notion of digital computation. A short conclusion follows in section 5. (shrink)

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.

I find myself ambivalent with respect to the line of argument that Schonbein offers. I certainly want to acknowledge and emphasize at the outset that Schonbein’s discussion has brought to the fore a number of central, compelling and intriguing issues regarding the nature of the dynamical approach to cognition. Though there is much that seems right in this essay, perhaps my view is that the paper invites more questions than it answers. My remarks here then are in the spirit of (...) scouting some of the surrounding terrain in order to see just what Schonbein’s claim is and what arguments or options may be open to the dynamicist. (shrink)

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.

Years ago, when I was an undergraduate math major at the University of Wyoming, I came across an interesting book in our library. It was a book of counterexamples t o propositions in real analysis (the mathematics of the real numbers). Mathematicians work more or less like the rest of us. They consider propositions. If one seems to them to be plausibly true, then they set about to prove it, to establish the proposition as a theorem. Instead o f setting (...) out to prove propositions, the psychologists, neuroscientists, and other empirical types among us, set out to show that a proposition is supported by the data, and that it is the best such proposition so supported. The philosophers among us, when they are not causing trouble by arguing that AI is a dead end or that cognitive science can get along without representations, work pretty much like the mathematicians: we set out to prove certain propositions true on the basis of logic, first principles, plausible assumptions, and others' data. But, back to the book of real analysis counterexamples. If some mathematician happened t o think that some proposition about continuity, say, was plausibly true, he or she would then set out to prove it. If the proposition was in fact not a theorem, then a lot of precious time would be wasted trying to prove it. Wouldn't it be great to have a book that listed plausibly true propositions that were in fact not true, and listed with each such proposition a counterexample to it? Of course it would. (shrink)