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Distinctions without differences:Commentary on Horgan andTienson's connectionism and thephilosophy of psychologyValerie Gray Hardcastle aa Department of Philosophy , Virginia Polytechnic Instituteand State University , Blacksburg, VA, 24061–0126, USA E-mail:Published online: 10 Jun 2008.

To cite this article: Valerie Gray Hardcastle (1997) Distinctions without differences:Commentary on Horgan and Tienson's connectionism and the philosophy of psychology ,Philosophical Psychology, 10:3, 373-384, DOI: 10.1080/09515089708573227

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PHILOSOPHICAL PSYCHOLOGY, VOL. 10, NO. 3, 1997 3 7 3

Distinctions without differences:commentary on Horgan and Tienson'sConnectionism and the Philosophy ofPsychology

VALERIE GRAY HARDCASTLE

ABSTRACT Horgan and Tienson do a wonderful job of explicating the dynamical system perspectiveand contrasting that view with classical AI approaches. However, their arguments for replacing aclassical conception of connectionism with system dynamics rely on philosophical distinctions that donot make a difference. In particular, (1) their generalized version of Man's three levels of analysiscollapses into itself; (2) their description of attractor dynamics works better than their metaphor offorces; and (3) their versions of "soft laws" and physical laws amount to the same thing.

Sometimes advances are made in science when we find a new way to look atsomething old. Bringing nonlinear mathematics to connectionism in psychology usesan old way to look at something relatively new. It is obvious that connectionist netsare dynamic, but it is unclear how we are supposed to analyze them once we havemade that uninspired observation. It is even less obvious how we are supposed toanalyze the mind if the brain is a connectionist machine or a parallel distributedprocessor.

In their recent book Connectionism and the Philosophy of Psychology [1], TerryHorgan and John Tienson articulate one vision of how this might be done. In brief,they argue that we could use nonlinear mathematics to render explicable thedynamic interactions of the mind. Like many others, they embrace connectionism asa way to appreciate the complexities and subtleties of our information processing.But, unlike most, they also believe that adopting connectionism as the centerpiecein psychology requires rethinking how we conceptualize mental states and mentalityin a serious way.

Let me say at the outset (and without defense) that I believe that Horgan andTienson are right: the mind is a connectionist net and should be analyzed as adynamical system. Moreover, I wholeheartedly support their attempts to bringnonlinear dynamics to philosophy of mind and I agree unreservedly with their belief

Valerie Gray Hardcastle, Department of Philosophy, Virginia Polytechnic Institute and StateUniversity, Blacksburg, VA 24061-0126, USA. Email: valerie@vt.edu.

0951-5089/97/030373-12 © 1997 Carfax Publishing Ltd

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that system dynamics has much to offer cognitive science. Hence, I begin this essayfrom the position of complete simpatico.

But, even though I applaud the broad strokes of the book, I also think that someof the moves the authors make are mistaken. My basic complaint is that Horgan andTienson follow the philosophical dictum of making distinctions too well, and, as aresult, they end up distinguishing things that either should not or cannot beseparated. In particular, their new version of Marr's three levels of analysis collapsesinto itself; their pure descriptions of attractor dynamics works better than theirmetaphor of forces; and their version of "soft laws" and traditional physical lawsamount to the same thing. Further, in making these distinctions, Horgan andTienson gloss over some of the more radical claims that they should be making. Insum, I agree with their moral; I quibble with the details. But the details turn out tobe important to our fundamental conception of mentality.

1. The extension of Marr

Fifteen years ago, a young scientist named David Marr offered us a complex view oftheorizing in artificial intelligence. His tripartite division among levels of explanationstill remains an important touchstone in philosophy of psychology. Among otherthings, Marr suggested that "the top level [of explanation] is the abstract computa-tional theory of the device, in which the performance of the device is characterizedas a mapping from one kind of information to another, the abstract properties of thismapping are denned precisely, and its appropriateness and adequacy for the task aredemonstrated" (Marr, 1982, p. 24). Horgan and Tienson call this level the level ofcognitive function. At the center level, Horgan and Tienson?s algorithmic level, we find"the choice of representation for the input and output and algorithm to transformone into the other" (Mars, 1982, p. 24). Finally, at the bottom, there are "the detailsof how the algorithm and representation are realized physically—the detailed com-puter architecture, so to speak" (Marr, 1982, pp. 24-25). This is the level ofimplementation.

Horgan and Tienson adopt Marr's starting position and then expand theMaman conception of the explanatory levels to reflect the recent emphasis incognitive science on system dynamics and nonlinear modeling of informationprocessing. The functions of level one and the algorithms of level two presumetractable and computable relations among variables. However, neither of theseassumptions are warranted (yet) with respect to the mind. Hence, we need togeneralize Marr's original typology. We should now think of the three levels as (1)the level of cognitive-state transitions, instead of cognitive functions; (2) the level ofmathematical-state transitions, instead of algorithms; and (3) the level of (again)implementation (p. 45). Cognitive functions are a subset of all possible cognitive-state transitions, for some cognitive-state transitions will be computationally intract-able; similarly, algorithms form a subset of all possible mathematical-statetransitions, for some mathematical-state transitions are not computable. Neverthe-less, as in Marr's system, each level remains a functional decomposition of the oneabove and is multiply realizable by the level below (cf., p. 23).

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In generalizing Marr, though} Horgan and Tienson still keep his basic concep-tion of explanation in cognitive science. They claim, along with many in AI, thatwhat we care about with respect to the brain and understanding cognition are notthe brain-ish properties of our nervous system. Instead, the "abstract functional/organizational properties" sensitive to or reflective of the intentional aspects ofmental phenomena are where our focus should lie, for it is these "physical statetransitions" that underlie our information processing (p. 46). However, the physicalstate transitions are not, properly speaking, either physical or mental. We shouldthink of them as being purely mathematical descriptions of the processes our brains(or some other machines) go through in dealing with contentful thought. Thismiddle level then "mediates between the other two: cognitive states are realized bymathematical states, which in turn are realized by physical states of the cognizer'shardware or wetware" (p. 46). There are three levels: the lowest one an implemen-tation of the processes the middle level describes; and the middle level a mathemat-ical working-out of the general higher level account of what the processing is.According to Horgan and Tienson, explanation in cognitive science consists indescribing a cognitive system in three different ways, at three different levels oforganization or analysis.

However, I am not confident that the distinctions that Horgan and Tiensonoutline are viable. Consider first their distinction between the so-called"neurobiological properties" and the "functional/organizational" properties of thebrain. Of course, there are going to be neurobiological properties that are notrelevant to determining or defining content. Nevertheless, any abstract organiza-tional property of the brain which is "systematically appropriate" to content will alsobe a neurobiological property, by definition (p. 46). For example, certain patterns ofactivation appear over the rabbit olfactory bulb whenever the animal is presentedwith an odorant that has previously been paired with some stimuli (food, say, or anelectric shock) (Freeman & Schneider, 1982). Electrodes placed around the relevantolfactory neurons can record these patterns. The resultant EEG waveforms index aneurobiological property, since they indicate summed electrical discharges fromgroups of cells. At the same time, these patterns are deeply connected to content,since they appear when and only when the rabbit receives meaningful olfactoryinputs, and they vary as the meaningful stimuli do.

Despite Horgan and Tienson's assumption to the contrary, outlining thegeneral functional organization of our wetware just is another way to describe ourbrain. Whenever we discuss a particular cognitive system, e.g., our brain, the levelof implementation and of mathematical-state transitions amount to the same thing.Even if the mathematical state-transitions can describe more than one physicalsystem—brains and some computers, say—they will still remain an abstract accountof the brains (and the computers). In other words, the mathematical descriptionsthat Horgan and Tienson see as filling the second level of explanation are also oneway to describe the level of "implementation" [2].

What about the level of cognitive-state transitions? Here I think we run into aparallel situation, given how Horgan and Tienson describe the higher levels. Theyclaim that "there might be many different mathematical ways of delineating a certain

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FIG. 1. The Lorenz attractor or butterfly attractor. At any instant, the equations which describe thisattractor fix the location of a point in three-dimensional space; as the system evolves over time, the motionof the point represents the changing variables. This system never repeats itself exactly; instead, the trajectoryloops around forever, confined to a rather small attractor region in 3-space. (Adapted from Gleick, 1987.)

dynamical system or class of dynanical systems" (p. 47) [3]. In other words, theremight be many mathematical realizations of a dynamical system corresponding toone class of trajectories. Here is how I believe we should unpack this idea: everyphysical or mathematical dynamical system has a set of trajectories which corre-spond to it. Some of the sets of trajectories define various sorts of invariantattractors; some of them do not. Horgan and Tienson believe that we can sortdynamical systems by the topologies, or structure, of their attractors.

For example, a Lorenz attractor, also known as a butterfly attractor, can berepresented by a system of differential equations in a three-dimensional space. Theseequations generate trajectories, some of which lie on the attractor (see Figure 1).Another, completely different, mathematical system could be described by a set ofdiscrete transformations in 3-space. This new set of equations, which is unrelated tothe equations for the Lorenz attractor, also defines trajectories, some of which alsolie in the butterfly-shaped region. These two systems, then, have invariant attractorswith the same topology. We could say that they belong to the same topological class.The conjecture—though there is no proof at all of this idea, mathematical orotherwise—is that we can uniquely characterize any dynamical system by its dimen-sionality and the topology of its attractors.

If this hypothesis is true, and I think it is, then Horgan and Tienson are well

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justified in claiming that the mathematical state-transitions of a system are multiplyrealized by the cognitive state-transitions. However, if this hypothesis is true, then itis also the case that the higher level description of "cognitive-state transitions" is justanother description of the "mathematical-state transitions", albeit perhaps moregeneral. To see what I mean, let us return to the trajectories that correspond to theLorenz attractor. We can define this attractor—the trajectories—by any number ofdifferent sets of equations. These would all describe the mathematical-state transi-tions which comprise a butterfly-shaped region in 3-space. Presumably, we can alsocharacterize this very same region by describing its topology. This sort of topologicaldescription should capture what Horgan and Tienson mean by a cognitive-statetransition, for it would articulate the fundamental shape of the relevant "landscape".(A cognitive cognitive-state transition would then be a qualitative topological descrip-tion of the manipulations that could occur in dynamic information processing.) Butregardless whether you use a set of equations or the topology to describe a Lorenzattractor—or any other sort of attractor—you would still be describing the same setof trajectories, namely, the set that define the attractor region in multi-dimensionalspace.

I conclude that there really is not an interesting explanatory or mathematicaldistinction between the three levels of analysis that Horgan and Tienson present.They are all different ways of characterizing exactly the same interaction. Horganand Tienson had hoped that the cognitive-state transitions would somehow give usthe transitions we normally find between contentful mental states, while the math-ematical-state transitions would be a more fine-grained analysis of the interactionsand evolution of contentful states with states without content. However, demon-strating an isomorphism between the folk content of beliefs, say, and a descriptionof a dynamical system (at any level) requires careful argumentation. It is notobvious; it certainly cannot be presumed. But unfortunately, Horgan and Tiensonstop short of explicating any systematic connections between either their mathemat-ical-state transitions or their cognitive-state transitions and what we normally meanby content.

However, even if Horgan and Tienson had spelled out what exactly is content-ful about the various state transitions, I am dubious they would find much ofsignificance to distinguish among their three types of description, for each presentsus with different ways of accounting for the very same set of trajectories which, inturn, describes (probably) a set of neural firing patterns. Marr's three levels, asgeneralized to be applicable to system dynamical descriptions of information pro-cessing, give us distinctions without a difference.

If Horgan and Tienson are correct in emphasizing the centrality of dynamicalsystems in psychology, then the traditional distinctions between descriptions offunction and descriptions of implementation disappear, for they would both amountto the same thing. As a consequence, the need to distinguish higher level contentfulinteractions from lower level mathematical descriptions in explanations of cognitiveactivity also disappears, for all a dynamical systems analysis gives us are information-ally sensitive trajectories in multi-dimensional spaces under different descriptions. Adynamical systems analysis is more radical than even Horgan and Tienson envision.

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2. The metaphor of force

A second place in which Horgan and Tienson overdistinguish concerns theirmetaphor of force to explicate the defeasible causal tendencies of mental states.Horgan and Tienson state that "cognitive states emit forces that tend to move thecognitive system in various cognitive directions" (p. 98). However, because of thecomplexity of the underlying system, any single mental state, a belief or desire, canonly tend the system in some direction. What actually occurs is the product ofnumerous interacting states and events. Connectionist models using multiple con-straint satisfaction or simulated annealing provide a simple analogy for what Horganand Tienson mean (p. 98).

Horgan and Tienson see the defeasible causal tendencies in cognitive systems asposing large problems for the science of cognitive science (more on this below), forthere is no easy way to specify the necessary and sufficient conditions for being adefeater. However, if one cleaves to the notion of mental states as interacting forces,then how to understand the defeaters becomes clear. As Horgan and Tienson say,"they arise naturally" (p. 99) from the structure of mentality.

Sometimes these mental forces compete with one another—they each pushtowards incompatible goals. In this case, either one force will completely overridethe others or a compromise position will be found. Sometimes mental forcescooperate and reinforce each others' influence. In this case, there are no defeaters.We should imagine "mental activity [as involving] ... a variety of intentional states,all present in the cognitive hopper at once, simultaneously exerting causal influenceon one another and simultaneously clamoring for attention" (p. 100). This just is aclear description of the sort of multiple constraint satisfaction for which connection-ism is known.

Horgan and Tienson admit that, though they want to take the metaphor ofcognitive forces "seriously" (p. 99), it is not perfect. They see two difficulties, inparticular. First, multiple simultaneous constraint satisfaction does not appear to bea good way to account for deductive reasoning and other forms of rigorouscognition. Geometrical proofs, for example, require the explicit appeal to rules andto step-wise computations, neither of which relaxing into a final state on the basis ofmany competing states uses. Second, second-order beliefs and desires, which caninform and alter our primary mental states, do not seem possible using the notionof forces. Horgan and Tienson argue that second-order mental states would affectfirst-order mental states by influencing the factors that cause the primary mentalstates.

In both cases I believe that they are mistaken. One good and easy way to modelthe deductive reasoning processes in humans is to use what we write on paper orexplicitly acknowledge as our steps in reasoning. However, this fact does not showby any means that how we actually reason in our heads conforms to recognizablestep-wise functions. Anyone who has taught introductory logic knows first-hand thatpeople do not in fact reason deductively, even when they think they are. Moreover,it is fairly clear that the patterns of errors we make suggest that a much moreaccurate way to describe human cognition with respect to "logical" problem solving

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is in terms of pattern recognition, for which a multiple constraint satisfaction modelworks very well. We need to keep in mind that how we express ourselves on paperor publicly may not accurately reflect what is going on on the inside.

Certainly, given a prior commitment to connectionism as the appropriate modelfor the mind, the burden of proof here is on Horgan and Tienson to show that (1)we do in fact mentally deduce conclusions from premises when reasoning instead ofmerely recognizing common patterns of logical relations in our thoughts, and that(2) connectionist networks cannot perform deductive proofs. I am skeptical aboutboth premises. Certainly the most recent work in rationality indicates that thought—even rational thought—is by and large context-driven and exemplifies previouslylearned connections among stimuli (see discussion in Smith & Osherson, 1995).And no work has shown that it is impossible for connectionist nets to reason in astep-wise and rule-governed fashion. Indeed, natural deduction in PDP machinesseems quite feasible (cf., Bechtel, 1994).

Maybe Horgan and Tienson would say that if it did turn out that we performedrigorous proofs by pattern recognition instead of appealing to explicit rules, then wereally do not reason deductively after all, for they claim that "deductive reasoning ispossible only for a creature whose cognitive states have formal structure. ... [It]proceeds in steps that...attend to the exceptionless relations that are determined bythe structured content of those cognitive states. This is not simply a matter of beingpushed along by cognitive forces" (p. 104). But this just begs the interestingquestion for those interested in modeling actual human cognition. We do somethingthat resembles deductive reasoning in problem solving. The question is how we aresupposed to understand those processes, regardless of whether it turns out to beactual derivation.

In addition, prima facie, it is not clear to me why our second-order beliefs anddesires would influence our first-order beliefs and desires by affecting the causes ofthose beliefs and desires. Mental forces "activate" other mental forces (p. 104).According to Horgan and Tienson's characterization, there simply isn't any roomfor one mental state to change the structure of other mental states.

But there is more than one way to influence cognitive states. Getting them attheir origins is one way, of course, but so is altering their strength or direction oncecreated. There is no reason to suppose that the process of multiple simultaneousconstraint satisfaction could not change the constraints in virtue of the solutions itfinds. It all depends upon how plastic the system is to begin with, and certainlyforces can operate in very gooey environments.

But even though I do think that Horgan and Tienson's analysis of the limita-tions of cognitive forces is incorrect and that there is nothing to rule out theirexplaining deductive reasoning or deliberate cognitive development, I also believethat the forces metaphor is misguided and misleading in very important ways.Consider how we understand forces in the first place. In physics, forces are vectors,which interact by summation. All vector solutions are "comprise" solutions. Horganand Tienson's picture of one force winning out over the others is not consistent withour understanding of how forces operate. That vectors are additive is a fundamentalfact in vector analysis, and that one cognitive "force" could swamp another is a

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fundamental fact about cognition. This difference is important, because it explainswhy we should not think of mathematical vectors as defeasible, but cognitive statesas having potential causal defeaters.

Horgan and Tienson's whole point is that we cannot understand cognition interms of simple linear interactions, like addition. We need something more complex.Even lots of vectors interacting all at the same time would still equal lots ofsummations. It would be better to stay with what Horgan and Tienson already have.They provide a marvelous model for how to understand cognition as a dynamicalsystem. Better to use that and not introduce fundamentally inaccurate metaphors toexplain what a system dynamics account already handles.

We can think of the trajectories in a dynamical system as "defeasible" since inmany instances the path they take is determined by very small changes in initialconditions. If we alter the parameters of the system, we get a different trajectory.Causal defeaters are rampant. Why not just stay with nonlinear dynamics as the bestway to understand human thought?

One might object to this approach because there is no way to specify completelythe range of all the parameters if a system demonstrates extreme sensitivity to initialconditions, consequently any such model would not be a good model of cognitionfor there would be no way to map any actual instance of information processing.However, sensitivity to initial conditions and other indications of chaos are not thesame thing as being an intractable system. It is entirely possible that we could specifythe dynamical system qua model of mentality entirely accurately as a set of solvablenonlinear equations. Of course, retroactively fitting it to some particular piece ofdetailed cognition in the real world might be exceedingly difficult, but as a firstapproximation or a useful abstraction, a dynamical systems approach might be themost accurate. There simply is no need to drag cognitive "forces" into the pictureat all.

Horgan and Tienson's mistake here is a variant on the one above: theydistinguish and explain where additional posits are not warranted. Here, as above,an understanding of system dynamics is enough. And here, too, we find Horgan andTienson trying to cling to an older conception of cognition that no longer appearsresuscitatable. The metaphor of thoughts as interacting forces can only work ifthoughts are additive, or at least linear in their interactions. However, the messagethat Horgan and Tienson are trying to bring home is that cognition is morecomplicated than that; the interaction of thoughts is nonlinear, highly sensitive toinitial conditions, and very complex. If they are correct, then we can no longerconceptualize mental states as forces, for there is nothing force-like about our mentaltrajectories.

3. Soft laws and science

The claim that all we need is system dynamics to understand cognition turns on howone understands the nature of explanation in the social sciences, which brings me tomy third point of disagreement with Horgan and Tienson. I believe that their

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distinction between soft laws in psychology and quasi-exceptionless laws in the hardsciences does not capture a real difference.

Horgan and Tienson define quasi-exceptionless laws as laws for which the onlyexceptions come from outside the domain of inquiry. For example, the medicalregularities that describe the flow of blood in my veins and arteries might not applyto me when I am shot with an Uzi and die from a massive hemorrhage. But such anevent would not count against the proposed law, for gunshot wounds and theirconsequences lay beyond the scope of biological inquiry. This sort of exception canbe blamed on events that interfere with the law's prediction, but do so in virtue of"external" factors.

These sorts of laws contrast with what Horgan and Tienson call "soft laws",otherwise known as ceteris paribus generalizations. They note that physical lawsmight appear soft because there are always things that could interfere with someobservational prediction. However, these putative exceptions are in principle elim-inable: all we have to do is account for all the physical interactions for any event.However, psychological laws, they believe, are genuinely soft. Even if we couldaccount for all the cognitive influences in a system, they hold that we still mightdiscover some exceptions (from within the domain) to our descriptions of infor-mation processing.

Both of these conceptions of laws strike me as erroneous. Neither the laws inpsychology nor those in physics are exceptionless, and neither will they apply to allpossible relevant situations in the real world. Nor should they; that is not howscience functions.

A more accurate rendition of how laws function in explicating the world goes asfollows. Scientific generalizations are only meant to cover a few aspects of the realworld at a time. These aspects are taken from the world and used to define anabstract and simplified version of the world. Suppe (1989) calls this simplifiedpicture a "physical system". We then discover regularities, hypothesize relationships,and create laws about the cartoon world. The hypotheses and laws are intended onlyto apply to the physical system with its few, well-defined parameters, and not to thereal world itself, with all its messy complications. Once we understand the workingof the abstract and relatively simply physical system, we can then use what we havelearned to help us characterize, predict, explain, and understand events occurring inthe laboratory or in the wild.

Consequently, all scientific theorizing happens at least one remove away fromthe actual world. We take the world as giving us some evidence for the appropriate-ness of our hypotheses and predictions, but we do the important theoretical work ofdevising and testing laws with respect to a well-defined abstract system with all therelevant variables specified. As a result, whatever "exceptions" in the real world onemight discover to a law may or may not matter to the law's adequacy, regardless ofwhether the exception appears to fall within the scope of the law's domain. It alldepends on how the physical system is defined.

My contention is that all of science works this way, from quantum mechanicsto molecular biology to economics to sociology. All laws are "ceteris paribus". Noneapply unconditionally to everything, even within a single investigative domain.

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Physicists look at the world in terms of fields and Hubert spaces, while abstractingover macro-sized objects and all their rich interconnections. Molecular biologistsexamine the chemical interactions of large proteins, and though they are sensitive toeach organism as a whole and its immediate environment, they discount the largermilieu in which groups of organisms survive and reproduce. Economists notoriouslyassume that humans are completely rational and totally self-interested, giving nocredence to our tendencies to stupidity and altruism. Sociologists focus on societiesof people and how they influence the individual or other cultures and ignoregeographical facts. All of this is perfectly normal. Indeed, it is probably the only waywe could ever begin to understand our complex world. Divide and simplify toconquer.

Psychology is no different. James examined his phenomenological experiences,but failed to consider the unconscious regulatory aspects of his brain. Piaget studiedthe larger developmental stages of children, while glossing over individual variationwithin a stage itself. Skinner charted the relationships between stimuli and responseand ignored the physiology in between. And today, developmental psychologists plotthe success of facial recognition, for example, and ignore baby's receptivity to music.Clinical psychologists categorize autistic behavior by abstracting over individualdifferences in response. Cognitive psychologists divide memory into three stageswithout considering how emotions affects learning and retention. All of this isperfectly normal, too. Indeed, dividing the project into smaller pieces, generalizingacross individual differences, abstracting over many details, and then simplifying andquantifying one's results is probably the only path to understanding ourselves.

Horgan and Tienson maintain that physical laws are soft in their applicability,but psychological laws are soft in their form (p. 123). A physical law might bedefeated by some hitherto undiscovered force, which is another way of saying thatwe cannot be sure that we know everything there is to know about the physicalstructure of the universe at any particular time. A psychological law, in contrast, hasthe "logical form of ceteris paribus generalizations" (p. 123).

However, given my view of scientific theorizing, this is another distinctionwithout a difference. It is true, as Horgan and Tienson claim, that "not every stateof a cognitive system is a cognitive state", while "every state of a physical system isa physical state" (p. 122), but this is a claim about the relation between the abstractphysical systems and the actual world. A physical system that we create to studyactual cognition will not include every state that a cognitive system might have. Onthe other hand, a physical system designed to capture a quantum mechanical systemmight (though I doubt it) include every state the system might enter. The structureof the laws will be the same; the process of constructing the abstract physical systemswill be the same. How these physical systems are tied to the world might differ interms of scope, but that does not give us a difference between the sorts of laws wemight find in psychology or cognitive science as opposed to physics or chemistry.

Horgan and Tienson see cognition as something that is complicated, messy,and fairly unprincipled, while they view something like chemistry as relativelysimple, neat, and straightforward. PV=nRt, Avagadro's number, covalent bond-ing... all of chemistry seems to fit into tidy packages. They are very suspicious about

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ever getting the rules of cognition to look like that, for too much is going on in thehead all at once to be able to capture all the interactions in simple slogan-likeequations. Perhaps they are right about the differences they see between the physicalsciences and psychology (although much can be said for Thorndike's law of effect,Chomsky's transformational grammars, and Freud's cathecting Q). However, thedifferences they see are differences in the application and scope of defined physicalsystems, not differences in the structure of scientific laws themselves.

It may be that we prune more in psychology than in chemistry or physics todevelop our abstract and simplified models. Certainly, we abstract differently. It mayalso be that our physical laws are designed to capture important regularities that wefind throughout our universe, while our psychological laws are restricted to regular-ities we find in certain phyla, or certain species, or even certain groups within aspecies. But in all cases, we make patently false assumptions about the phenomenawe are seeking to understand: in chemistry, we assume pure substances; in physics,we assume massless, frictionless points, and in psychology we might assume some-thing like an infinite capacity for learning. At the same time, we neglect importantfacts that impact our observational predictions: disregarding certain impurities inchemistry will skew the predicted molecular weight of a substance; neglectingfriction in physics means that projectiles will fall short of their calculated path;ignoring constraints on learning will overestimate our capacity to be open-ended andflexible. In each case, the process—abstraction and simplification—and the prod-ucts—ceteris paribus laws—are the same.

It is easy to get caught up in the deep mysteriousness of human cognition. Howare we supposed to explain my waffling between take-out Chinese and orderingpizza only to eat a salad instead using some sort of useful lawlike regularity? Surely,there are simply too many facts that intervene: my sister called and talked to methrough dinnertime, so I only had time to grab whatever I could from the refriger-ator to satisfy my hunger. But it is equally easy to become immersed in the puzzlesof the physical world as well. How are we supposed to explain the get-away carfailing to start as the robbers jumped in, even though everything had just beeninspected and was in good working condition? Too many facts intervene: the suddenweight of the thieves caused the car to torque slightly, which was enough to force aweakened and stretched belt off its tracks. However, the contingencies of the realworld should not obscure the fact that we can find lawful regularities among theparameters we set in abstract systems that we designed to capture but a few aspectsof our universe, whether we are talking about our own psychology or the behaviorof coils under stress.

Once again, Horgan and Tienson distinguish where they should not. They seea difference between psychology and the other sciences where there is none.Psychology should not be treated as a different way of investigating the world, noris its subject matter particularly distinguishing. Mentality functions just like every-thing else in the universe—according to laws. These laws are simplified, generalized,and abstracted descriptions of some corner of the world, but they are ordinary lawsnonetheless.

Perhaps the most radical implication of their views that Horgan and Tienson

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should embrace is that minds do not require special handling by science after all. Weshould not distinguish cognitive-state transitions from mathematical-state transitionsfrom descriptions of implementation. All we need to define are the appropriatetrajectories in space. We should not analogize mental states to other metaphors inscience. All we need are the mathematics of nonlinear systems. And we should notfundamentally differentiate psychology from the natural sciences. All we need is aproper philosophy of science. I agree with Horgan and Tienson that a systemdynamics approach to cognition is a very good idea. Let us accept it...and what itentails.

Notes[1] All references to Horgan and Tienson's work will be to this book (Horgan & Tienson, 1996).[2] Patricia Kitcher pointed out to me a similar difficulty with Marr several years ago. See also Kitcher

(1988).[3] This section owes much to a discussion of this matter with my father, R. Hugh Walker.

ReferencesBECHTEL, W. (1994). Natural deduction in connectionist systems. Synthese, 101, 433-463.FREEMAN, W.J. & SCHNEIDER, W. (1982). Changes in spatial patterns of rabbit olfactory EEG with

conditioning to odors. Psychophysiology, 19, 44-56.GLEICK, J. (1987). Chaos: making a new science. New York: Viking.HORGAN, T. & TIENSON, J. (1996). Connectionism and the philosophy of psychology. Cambridge, MA: The

MIT Press.KITCHER, P.S. (1988). Marr's computational theory of vision. Philosophy of Science 55, 1-24.MARR, D. (1982) Vision. San Francisco: Freeman.SMITH, E.S. & OSHERSON, D.N. (1995). Thinking: an invitation to cognitive science (2nd edition, vol. 3).

Cambridge, MA: MIT Press.SUPPE, F. (1989). The semantic conception of theories and scientific realism. Chicago: University of Illinois

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