To some degree, Fodor's claim that Cognitive science divides the mind into modules tells us more about the minds doing the studying than the mind being studied. The knowledge game is played by analyzing an object of study into parts, and then figuring out how those parts are related to each other. This is the method regardless of whether the object being studied is a mind or a solar system. If a module is just another name for a part, then to say that the mind consists of modules is simply to say that it is comprehensible. Fodor comes close to acknowledging this in the following passage.

If this were really as uncondititionally true as Fodor implies in this sentence, Fodor's Modularity of Mind would have been a collection of tautologies. In fact, Fodor goes to great lengths to show that his central claims are not tautologies, but rather reasonable generalizations from what has been discovered in the laboratory at this point. Fodor gets more specific in passages like this one:

Fodor sums up these two conditions with the phrase informationally encapsulated, and adds that modules are by defintion domain specific i.e. they deal only with a certain domain of cognitive problems. He also claims that what we call higher cognitive functions cannot be either informationally encapsulated or domain specific. Instead, these higher processes must be "isotropic", (i.e. every fact we know is in principle relevant to their success) and "Quinean" (they must rely on emergent characteristics of our entire system of knowledge.) Because modular processes are by definition neither Quinian nor isotropic, there is "a principled distinction between cognition and perception" (ibid), and given the conceptual tools of cognitive science, it is not possible to have a science of the higher "Quinian-Isotropic" cognitive functions, such as thought or belief. He admits, however, that this limitation may only be true "of the sorts {of computational models} that cognitive sciences are accustomed to employ"(p.128). An examination of the presuppositions of those computational models may reveal this to be a limitation of only one particular kind of cognitive science.

I believe that these limitations do hold for the paradigm that gave birth to cognitive science, which is often called the symbolic systems hypothesis. It's most fundamental claim is that a mind is a computational device that manipulates symbols according to logical and syntactical rules. All computers and computer languages operate by means of symbolic systems, so another way of phrasing this claim is to say that a mind is a kind of computer. The symbolic systems hypothesis is still basically alive and well, but now that it is no longer universally accepted it is often given disparaging nicknames, like Haugeland's "GOFAI" (for good old fashioned artificial intelligence) or Dennett's "High church computationalism". Fodor remains the most articulate preacher of the gospel of high church computationalism, and when his concept of modularity goes beyond the tautologous claim that minds are analyzable, it almost always brings in strong commitments to the claim that minds are really computers. His modules are really what computer programmers call subroutines, which is why he defines modules in the quote above as "special purpose computers with proprietary data bases." GOFAI scientists model cognitive processes by breaking them down into subroutines by means of block diagrams, then breaking those subroutines down into simpler subroutines and so on until the entire cognitive process has been broken down into subroutines that are simple enough to be written in computer code. ( See Minsky 1985 to see this process in action.). Most of what Fodor says about modules follows from the fact that subroutines are domain specific and informationally encapsulated ( i.e. they are each designed for specific tasks, and only communicate with each other through relatively narrow input-output connections), and the fact that Fodor believed (and apparently still believes) that GOFAI is the only game in town for AI. When Fodor says that it is impossible to model Quinean and isotropic properties, what he really means is that it is impossible to model them with the conceptual tools of GOFAI, and in this narrow sense of "impossible" he is probably right.

This paper will deal with whether there are similar constraints on the new sorts of models currently available to cognitive science, which were not available when Modularity of Mind was written. Fodor probably thinks that these constraints are as unassailable as ever, but one must remember that Fodor also believes (at least some of the time) that all of our concepts are innate. If there is any truth to Fodor's semi-serious claim that everyone's philosophy of mind is true for them{1}, it is not surprising that it would be difficult for him to see any "new" concepts as being genuinely new. So perhaps{2} he might be made more sympathetic by the fact that the concepts I have in mind are not strictly new, although their application to cognitive science is a fairly recent development.

Dynamic systems theory (DST) claims that the same basic laws that govern physical systems also govern the laws of cognitive systems, and that therefore cognitive science should use the math of physics (calculus etc.), rather than rules of syntax and computer programming. Described thusly, the claim may seem ridiculous to some. It seems to imply that there is no significant difference between rocks and people, or at best between clocks and people. As Clark puts it " Many scientists and philosophers believe that certain physical systems (such as the brain) depend on special organizational principles and hence require a vocabulary and an explanatory style very different from those used to explain the the coordination of pendula or the dripping of taps" (Clark 1997 p.115). However, recent developments in what is called non-linear dynamics have made it possible to use physics equations to describe systems which have the kind of flexibility that seems to justify calling them cognitive systems{3}.

Because Fodor's modularity theory reveals both the strengths and the weaknesses of the symbolic systems hypothesis, it provides excellent criteria for the evaluation of DST. In order to be on equal footing with GOFAI, DST must enable us to account for the functions and properties that Fodor calls modular. And if it is also able to account for Quinean and isotropic mental process (or show why the distinction between modular and Quinean-isotropic processes is spurious), it would be clearly superior to GOFAI, for whom these processes are, by Fodor's own admission, a complete mystery. Accounting for the properties that Fodor calls modular does not mean accepting everything he says about them. Whenever a new theory replaces an old one, it does so by contradicting some parts of the old theory and accepting others. If it accepts a substantial part of the old theory, the new theory is called a reduction. If it rejects most of the old theory, we say that the new theory eliminates the old theory. The best contemporary theories of reduction claim that there is a continuum connecting these two extremes of elimination and reduction (see Bickle 1998). We decide where on the continuum a particular theory replacement belongs by comparing the old and the new theory, and seeing how much and what sort of isomorphisms exist between the two. I will not try to answer whether the example I am discussing is an elimination or a reduction, because I have argued elsewhere (Rockwell 1995) that the distinction is more misleading than useful. Hopefully, however, my analysis will give some sense of where on the continuum we might place the relationship between DST and the symbolic system hypotheses.

I am going to start by describing a concept in DST which I think has many significant isomorphisms with the concept of module: the concept of an attractor which is an invariant set . In Port and Van Gelder 1995, an invariant set is defined as "a subset of the state space that contains the whole orbit of each of its points. Often one restricts attention to a given invariant set, such as an attractor, and considers that to be a dynamical system in its own right." (p.574) The second sentence is encouraging for our project, for if an invariant set can be considered as a dynamic system in it's own right, this seems isomorphic with Fodor's claim that modules are domain specific and informationally encapsulated. But what exactly is this term "attractor", and why would it be helpful to consider an attractor as a separate system?

Port and Van Gelder define "attractor" as " the regions of the state space of a dynamical system toward which trajectories tend as time passes. As long as the parameters are unchanged, if the system passes close enough to the attractor, then it will never leave that region." (p.573). The conditional clause of the second sentence holds the key to the cognitive abilities of dynamic systems. For of course the parameters of every dynamic system do change, and these changes cause the system to tend towards another attractor, and thus initiate a different complex pattern of behavior in response to that change.

The simplest example of an attractor is an attractor point, such as the lowest point in the middle of a pendulum swing. The flow of this simple dynamic system is continually drawn to this central attractor point, and after a time determined by a variety of factors (the force of the push, the length of the string, the friction of the air etc.) eventually settles there. Of course, a system this simple could not possibly be called cognitive in any sense. But consider a dynamic system with the following additional complexities.

1) Instead of making the attractor a point, let us have the system return to a repeating complex motion of some sort. This motion need not be only a motion in physical space. Many of the parameters of the system could be varying in measurable ways, and each of those parameters could be seen as a dimension in what is called state space. State space is not limited to the three dimensions of physical space, for it can have a separate dimension for every changeable parameter in the system.

3)The system can contain several different attractor state spaces, which are connected to each other by means of what are called bifurcations. This makes it possible for the system to change from one attractor state space to another by varying one parameter or group of parameters.

One of the most vivid examples of a cognitive dynamic system that uses bifurcations is the ambulatory system of a horse, which divides into four distinct attractor spaces. These are colloquolly referred to as walk, trot, canter and gallop, but each one consists of a set of motions governed by complex input from both the environment and horse's nervous and muscular system. Careful laboratory study has made it possible to map the dynamics of each of these gaits, (see Kelso 1995 p.70) and each map reveals a multidimensional state space that contains a great enough variety of possible states to respond to variations in the terrain, the horse's heart and breathing rate etc., and yet regular enough to be recognizable as only one of these four types of locomotion. There are no hybrid ways for a horse to move that are part trot and part walk; the horse is always definitely doing one or the other. And the primary parameter that determines the horse's utitilization of each of these gaits is how fast the horse is moving. From speed A to B the horse walks, from speed B to C it trots, and so on. There is not an exact speed at which the transition always occurs, for if there were, a horse would wobble erratically between the two gaits whenever it ran anywhere near those speeds. What usually happens, however, is that the horse rarely travels at these borderline speeds (unless it is being used as a laboratory subject). Instead it travels at certain speeds around the middle of each range for each gait, because those are the ones that require the minimum oxygen and/or metabolic energy consumption per unit of distance traveled. This means that a graph correlating the horse's choice of gait with its speed usually consisting of bunches of dots, rather than a straight line, because certain speeds are not efficient with any of the four possible gaits

If we were to make a computer model of the horse's ability to adapt its gait to its speed, one of the best computer languages for the job would be LISP. LISP models cognitive processes by means of commands that tell the program how to behave when it comes to a branch in the flow of information, which seems isomorphic in this respect to a bifurcation in the flow of a dynamic system from state space to state space. According to Haugeland 1985,(pp.154-5) all LISP programs are built out of six primitive functions.

1) left (x)

If a program contains the command "left(x)" it activates the subroutine on the left side of a branch, if it encounters "right(x)" it activates the subroutine on the the right, and if it encounters "join(x,y)" it activates both subroutines. "Equal(x,y)" returns a special token "true" if if x and y are the same, otherwise it returns a token called "false". "Atom(X)" returns "true" if x is a single atomic token, otherwise it returns "false". Both of these terms are useful when combined with "If (x) then (y) else (z)"{4}, which chooses between y and z depending on whether x is true. (There is also a seventh primitive called "Nil", which Haugeland mentions on the previous page, which is used to plug any empty branches of the program that don't go anywhere.)

We'll start by positing four subroutines we'll call walk, trot, gallop, and canter, as well as a fifth subroutine we'll call "CURRENT SPEED" which measures how fast the horse is moving. Because we are only modeling the decision making process, rather than the entire dynamic system, we will accept those as unexplained primitives. With these five subroutines and two primitives from LISP {"Equal(x,y)" and "If (x), Then (y), else (z)"}, we can create a program that essentially duplicates the decision function of the horse's dynamic ambulatory system. We will posit convenient speeds for each gait of 5,10, 15, and beyond 15, and use the mathematical functions of "greater than" and "less than", because according to Haugeland, all such mathematical functions can be made from LISP primitives. Because LISP must define new words to connect programs together, we will call this program "GO". (see the next footnote for further explanations.)

GO =def

(

(if [ equal(CURRENT SPEED, O), Then 0, else

(if[ CURRENT SPEED <5, then walk, else

(if [CURRENT SPEED<10, then trot, else

(if[ CURRENT SPEED<15,then canter, else gallop]) ]) ]) ])

)

To underscore that this entire program is made from "bifurcating" LISP nodes, we can draw it as a tree diagram.

To some degree, this example{5} is an extension of Tim Van Gelder's "computational governor" thought experiment. Van Gelder's thought experiment showed that if a computer were to duplicate the function performed by the device which controls the speed of a Watt Steam engine, it would require fairly sophisticated computations. Van Gelder claimed that this task was clearly cognitive, that the Watt governor performed this task without computations, and that the same kind of physics which underlies DST was the best explananation for the Watt governor's cognitive abilities. This prompted some to say that the Watt Governor really was computational after all (Bechtel 1996) and others to say that the task was too simple to be called cognitive, and therefore the analogy was spurious. (Eliasmith 1997). Others pointed out that the Watt Governor was merely a feedback loop, and therefore DST must be (in Van Gelder's own words summing up this criticism) "Cybernetics returned from the dead." (Van Gelder 1999) My Horse LISP example is meant to be a partial answer to these last two criticisms. The paradigm cognitive ability in computer science is often considered to be decision making i.e. choosing between alternatives. An If-then-else command is certainly more of a decision making device than a feedback loop, and this example shows that the ambulatory system of a horse is a dynamic system that, among other things, performs the function of an If-then-else command.

In fact, if DST is incapable of emulating symbolic systems in the same ways that human organisms are incapable of emulating them, it would make DST an even more compelling paradigm for organic cognitive science. However, one way to find out the similarities and differences between the two is to search for (and possibly construct{6}) dynamic systems that bifurcate in the same way that LISP trees bifurcate. Given that there are only six LISP primitives, it would be very convenient if we could simply find styles of dynamic bifurcation that corresponded to each of them. Then we would have a perfect reductive identity between LISP and those particular dynamic systems, and our job would be complete. But the chances of things working out exactly that neatly are very slim, for a variety of reasons.

For one thing, it is far more likely that most cognitively effective DST bifurcations will require several lines of code, or even whole programs, to be modeled effectively. Our model of the horse ambulatory system, for example, contains several elements that could not have any parallells in a dynamic system, because they presuppose a computer's need to search and choose before each action. The recursive terms in our horse LISP subroutine made it possible to compare the value of the incoming speed variable to each of the gait subroutines in sequence until the correct one was found. Dynamic systems do not have any need for this kind of comparing function. They shift among different sets of attractors when certain parameters change in value, but in no sense do they "consider" other alternatives before they shift. They do it right the first time. A connectionist net, for example, does need a training period to adjust its weights to perform the proper output. But unlike a computer program, it does not need to reconsider all of the wrong choices after it has been trained.{7} A case could be made that the recursive subroutines are functionally irrelevant when we are considering the abstract similarities between LISP and DST, and that therefore there is a real functional identity between the if-else-then commands and the dynamic bifurcations that control the ambulatory system of the horse. But it will always be a problematic judgement call to decide what is and is not functionally relevant in each case.

The replacement word I like is "material", because it does not imply the physics laboratory, but rather the kind of vulgar "stuff and particles" ontology championed by Hobbes, Democritus, and the more unvisionary breed of man-on-the-street. Physics has not been limited to an ontology of this sort for some time. In fact, a case could be made that even Newton compromised this ontology when he introduced gravity's ability to effect things at a distance{8}. And it became even more compromised as physics progressed to Maxwell's electromagnetic fields, the ghostly incoherencies of relativity and quantum mechanics, and finally to a general sense that you never know what physicists are going say next. Consequently, most philosophical physicalists admit under duress that by "physical" they mean whatever physics believes the world is made of. In the breach, however, they usually return to the materialism of Hobbes and Democritus, which sees the real as being the stuff that we can see and touch and trip over, rather than the abstractions of theoretical physics. My distinction between the "abstract" and the "material" (which subdivides the physical, among other things, if there are other things) is designed to prevent the conflation of these two very different concepts. One can believe that everything is physical, while acknowledging that the material is a subset of the physical.

It may be that connectionist AI was guilty of a kind of misplaced concreteness by conceiving of these state spaces as organlike neural structures, rather than dynamic patterns of motion and change. I am tempted to think of the connectionist modules used in contemporary AI as little dynamic systems imprisoned like birds in cages, so that they can communicate with other modules only by means of input-and-output devices. Computationally, a connectionist net is rather like an AI "toy world" version of a dynamic system. The fundamental computational tool in both is state space transformations. But in a connectionist module, the state spaces are relatively easy to isolate. One can simply measure the inputs and weights of each neuron. Of course, real neurons really do have inputs and outputs with reasonably exact voltages and weight summations. And by replicating those in silicon, it becomes possible to create modules that perform state space transformations on specific inputs. But only a subconscious Cartesian Materialism prompts the assumption that the state space transformations in the cranium are telling the entire cognitive story.

When one measures the dynamics of a complete dynamic organism interacting with a world, there is no reason to doubt, as Kelso puts it, "that both overt behavior and brain behavior, properly construed, obey the same principles." (Kelso 1995 p.28. Quoted in Clark 1997 p.116). Of course, there are too many factors at work in an embodied living system to delineate the state space with the same level of precision that can be done when we are measuring or building a single connectionist network. But this is only an epistemological problem. The fact that it is harder to measure the parameters of the state space and their possible variations does not make any difference to the fundamental nature of the cognitive process.

For this reason, I feel that if we accept Clark's claim that "connectionist approaches. . . are nevertheless both computational and (usually) representational" (p.151), we must also accept that dynamic systems can be computational and representational. If we make a distinction between "representational" and "symbolic", using the latter to refer to the subspecies of representations that constitute symbolic systems, I think that even Van Gelder would accept that neural nets are representational in this narrow sense. If so, DST could conceivably reduce the concept of representation in organic systems to certain kinds of attractor sets, but it would not eliminate the concept altogether. If neural nets are computational and representational, then so are dynamic systems.

Once we recognize that state spaces can be dynamic, they can be free of many of the limits that Fodor proscribed on modules, even though they are capable of performing the same kinds of functions. Strictly speaking, a dynamic state space is much more like an event than an object. It endures longer than most events, but in this respect it resembles events like tornadoes or waterfalls, which seem object-like because the flow of their constituting processes cohere in a stable pattern. Nevertheless, a state space is a far more volataile entity than an organ, and its boundaries and functions are far more flexible.The concept of organ is certainly a useful one, and will probably continue to be so. But it is based on a possibly misleading assumption: that morphology is always an accurate guide to function, because the body, like a Hi-Fi set, is supposedly divided up into distinct modules with materially delineable borders. Those who accept this assumption acknowledge that it may require microscopes, or sophisticated staining techniques, to find those borders. But the assumption remains that once one has marked out those borders, one has carved the brain or body at it's fundamental joints, and that the purpose of neuroscience is then to answer questions like "what is the hippocampus for?".

We must not discount the possibility that morphology is not the essential factor in determining function. The grey matter of the brain could be seen as primarily a medium through which dynamic ripples eddy and coalesce into state spaces. The fact that people can often relearn skills lost after brain damage, even though the "organs" supposedly responsible for those skills have been surgically removed, could offer support for that possibility. So does the fact that brain scans of different people (or even the same person at different times) often reveal brain functions taking place at radically different locations. On the other hand, we also shouldn't assume that we must make an either/or choice between a dynamic brain and a brain assembled from organs. To continue the ripple metaphor (if it is only a metaphor), even a river's dynamic flow is shaped by the contours of the riverbank. In a similar way, the biological structure of the brain would make it more likely that certain dynamic patterns would stabilize into recurring patterns, just as certain kinds of eddys and tidepools are more likely to form if the river banks contain the appropriately shaped inlets.

The connections between state spaces in embodied dynamic systems are not hard wired the way they are in AI connectionist systems. The bifurcations between attractor spaces are not specific connective neurons, they are only abstract measurements of forces. As the parameters that shape these forces shift, so do the cognitive characteristics of the attractor. For this reason, it is highly implausible that attractor sets in dynamic systems are domain specific and informationally encapsulated in the way that Fodor claimed modules must be. Many of Fodor's arguments for informational encapsulation (for example, the fact that modules must have fast response times), require only that the module be informationally encapsulated at the time it is performing its function. Fodor is correct when he says that "in the rush and scramble of panther identification, there are many things I know about panthers whose bearing on the likely pantherhood of the present stimulus I do not wish to have to consider" (Fodor 1983 p. 71 italics in original). After the rush and scramble have subsided, however, there is no reason that the module which enables us to instantaneously identify panthers shouldn't receive all sorts of input from other sources, and reconfigure itself so as to make more effective responses the next time we see a panther. One could learn, for example, to tell the difference on sight between a male panther and a female panther, and thus learn to initiate two different sets of fast reflexive behaviors. (For example, we could develop one flight strategy designed to avoid hunters, and another to avoid a creature protecting her cubs.) Anyone who has ever learned to sight read music knows that sets of quick responses can be constructed that are very effective for one style of music, but do not yield the necessary speed for another style. Even if one can sight read Bach fluently, it is likely that difficulties will arise the first time one tries to sight read Duke Ellington until one has learned several new pieces in his style. But because the sight reading "module" is not informationally encapsulated, it is possible for it to take in new information the more one studies a new style of music, and thus learn the reflex like speed that makes fluent sight reading possible the next time around.

Dynamic systems have the kind of speed that makes these quick responses possible, and for them, informational interpenetration is probably the rule, rather than the exception. We must remember that "invariant set" is a highly conditional term in DST. "Invariant" really only means that there is a pattern that stays stable long enough to be noticed and (partially) measured. Given the number of parameters that must reach some kind of equilibrium for an invariant set to emerge, it is highly unlikely that they will always remain stable enough to produce anything that could be called informational encapsulation. This is exactly the opposite situation that would arise for modules that were constructed out of fixed neural architecture. As Fodor points out "if you facilitate the flow of information from A to B by hardwiring a connection between them, then you provide B with a kind of access to A that it doesn't have to locations C,D,,E, . . ." (Fodor 1983 p.98). But although this is true for hardwiring, it is not true for bifurcations in a dynamic system. The slightest flicker in the parameters that hold an invariant set stable could bring in information from almost anywhere else in the system, which could change the system (hopefully for the better) when it restabilized{9}.

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