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Intractability Arguments for Massive Modularity

Introduction

In recent years it has become commonplace to argue for a massively modular conception

of our mental architecture on the grounds that the alternative would be computationally

intractable. Such intractability arguments vary considerably in detail, but they all share the

following pair of commitments. First of all, they assume the classical computational theory of

mind1:

CTM: Human cognitive processes are classical computational ones –roughly,

algorithmically specifiable processes defined over syntactically structured mental

representations.

As has been commonly observed, however, the truth of CTM requires more than mere

computability. What it requires is that mental processes are, in some appropriate sense, tractably

computable; and it is on this point that intractability arguments seeks to undermine amodular

views of cognition. That is, they endorse the following Intractability Thesis:

IT: Non-modular cognitive mechanisms –in particular mechanisms for reasoning— are

computationally intractable.

Given these commitments, however, its appears to follow that:

MM: The mind –including those parts responsible for reasoning— is composed of

modular cognitive mechanisms.

And this is, of course, precisely what the massive modularity hypothesis requires.

As one might expect, the above argument is extremely popular among advocates of

massive modularity.2 Indeed, Peter Carruthers goes so far as to claim that it provides “the most

important argument in support of massive modularity" (Carruthers, this volume & forthcoming).

But an appreciation of the argument extends far more widely than this. Jerry Fodor, for example,

both rejects the claim that reasoning is modular and yet maintains that the “real appeal of

massive modularity is that, if it is true, we can either solve these [intractability] problems or at

1 Though sometimes only tacitly and sometimes only for the sake of argument. 2See, for example, Buss (1999), Carruthers (forthcoming), Cosmides & Tooby (1987), Plotkin (2003), Tooby & Cosmides (1992), Gigerenzer (2000), Sperber (1994).

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least deny them center stage pro tem” (Fodor, 2000, p23). Indeed the influence of the argument

can be found in regions of cognitive science that do not even explicitly address issues about the

architecture of the human mind. Variants of the argument are, for example, familiar in robotics

and a-life (Brooks, 1999).

The central aim of this chapter is to assess the adequacy of intractability arguments for

massive modularity. In doing so, I assume for the sake of argument that CTM is true and focus

instead on the Intractability Thesis (IT). With so many advocates, one might be forgiven for

thinking that the arguments for IT are overwhelming. But what are the arguments; and what

might they reasonably be taken to show? I argue that when one explores this issue with

appropriate care and attention, it becomes clear that a commitment to IT is built on shaky

foundations; and this is because all the main arguments for it are deeply unsatisfactory. A

satisfactory argument would (minimally) need to conform to the following three conditions. First

and most obviously, it would need to show that amodular mechanisms are intractable. Second, it

would need to do so in such a way as to render an amodular conception of reasoning untenable.

As we shall see, however, this is no straightforward matter since contrary to appearances there

are plenty of ways for a mechanism to be intractable that in no way undermine the claim that it

constitutes part of our cognitive architecture. Finally, a satisfactory argument for IT needs to

avoid being so strong as to undermine the classical-cum-modular account of cognition as well.

Unless this condition is satisfied, the argument for IT clearly cannot be recruited as part of the

case for MM. What I propose to show is that none of the main extant arguments for IT satisfy all

these conditions and, moreover, that there are reasons for pessimism about the prospects of

providing such an argument any time soon. I conclude, therefore, that the significance of

intractability considerations for the contemporary debate over massive modularity has been

greatly overestimated.

Here’s a sketch of things to come. In section 1, I describe MM and the attendant notion of

a module in a bit more detail; and in section 2 I explain how modularity is supposed to help

resolve intractability worries. I then turn my attention to the arguments for IT. In section 3, I

consider and reject three ‘quick and dirty’ arguments that fail because they attribute (without

serious argument) commitments that the amodularist simply does not accept. In section 4, I

consider at some length a recent and influential argument by Jerry Fodor and show that it is both

unsound and too strong in the sense that, even if sound, it would undermine modular and

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amodular theories alike. In section 5, I consider a rather different kind of argument: an inference

to IT from the pattern of failures in robotics. Finally, in section 6, I conclude by arguing that

there are reasons for pessimism about the prospects of providing a satisfactory argument for IT

any time soon.

1. Massive Modularity

A central theme of the forthcoming discussion is that the arguments for IT frequently turn

on –sometimes egregious— misunderstandings of MM and the attendant notion of a module.

We would do well, then, to get clear on these notions before turning to the arguments

themselves.

1.1 A Sketch

Massive modularity is a hypothesis --or more precisely, a broad class of hypotheses--

which maintain that our minds are largely or perhaps even entirely composed of highly

specialized cognitive mechanisms or modules. Slightly more precisely, it can be divided into two

parts. The first concerns the shear number of modules that there are. According to advocates of

MM, there are a huge number (Tooby and Cosmides, 1995, p. xiii). But second, and more

importantly for our purposes, MM incorporates a thesis about which cognitive mechanisms are

modular. According to MM —and in contrast to an earlier, well-known modularity thesis

defended by Fodor and others— the modular structure of the mind is not restricted to peripheral

systems — that is, input systems (those responsible for perception, including language

perception) and output systems (those responsible for action and language production). Though

advocates of MM invariably endorse this thesis about peripheral systems, they also maintain,

pace Fodor, that central systems —paradigmatically, those responsible for reasoning— can ‘be

divided into domain-specific modules’ as well (Jackendoff, 1992, p.70). So, for example, it has

been suggested that there are modular mechanisms for such central processes as ‘theory of mind’

inference (Leslie, 1994; Baron-Cohen, 1995) social reasoning (Cosmides and Tooby, 1992) and

folk biological taxonomy (Attran, 199?).

Clearly, there are a variety of ways in which the above rough sketch might be elaborated;

and depending on how this is done, we end up with interestingly different versions of MM

(Samuels, 2000). One important distinction is between what I’ll call strong and weak MM. By

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assumption, both are committed to the modularity of peripheral systems; but where strong MM

maintains that all central systems are modular, weak MM claims merely that many though not all

are. Both theses are thus more radical than the version of modularity defended by Fodor (1983)

in that they posit the existence of modular central systems. But whereas weak MM is entirely

compatible with the existence of distinctively –indeed radically-- non-modular reasoning

mechanisms, strong MM is committed to the denial of all such systems.

Which of these versions of MM is the intractability argument supposed to justify? This is

far clear. But since IT maintains that all amodular mechanisms are computationally intractable,

it’s natural to interpret the argument as trying to justify the strong version of MM. It is this

reading of the argument that I’ll be most concerned to rebut. Nevertheless, I suggest that extant

versions of the intractability argument fail even to support weak MM.

1.2. What is a Module?

Another important respect in which versions of MM may differ concerns how they

construe the notion of a module; and clearly I need to say something about this before assessing

the arguments for IT. There is good and bad news here. The bad news is that debate over how to

construe the notion of a module has been a point of considerable confusion in recent years and

has resulted in an enormous proliferation of distinct notions.3 The good news is, however, that

we need not survey these options here since we are concerned only with those properties of

modules that might plausibly contribute to the resolution of intractability worries. And it turns

out that the story about how modularity aids in the production of tractability is quite a standard

one. Indeed, of all the various characteristics that have been ascribed to modular mechanisms,4

there are really only two that get invoked –sometimes in tandem and sometimes individually—

in addressing intractability worries: domain-specificity and informational encapsulation. For

current purposes, then, I adopt the following minimal definition of a cognitive module: A

3 See Segal, 1996; Samuels, 2000 and Fodor, 2000 for discussions of the various notions of modularity currently in play within cognitive science. 4 And the list of putative characteristics really is a rather long one! Usual suspects include: domain specificity, informational encapsulation, task/functional specificity, autonomy, innateness, cognitive impenetrability, limited access of external processes to the module’s internal states, mandatory (or automatic) processing, relative speed, shallow outputs, fixed neural architecture, susceptibility to characteristic breakdown patterns, characteristic patterns in ontogeny, products of natural selection and universality.

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cognitive mechanism is modular just in case it is domain-specific, informationally encapsulated

or both.

1.3 Domain-Specificity and Informational Encapsulation

What do cognitive scientists mean by ‘domain specificity” and “informational

encapsulation”? Both notions get used in a variety of ways and, moreover, both are vague in the

sense that they admit of degree. But when applied to cognitive mechanisms, they are almost

invariably intended to indicate architectural constraints on information flow that (partially)

specify what the mechanism can and cannot do.5

Very roughly, a mechanism is domain specific if it can only take as input a highly

restricted range of representations. To put it rather crudely: If we think of cognitive mechanisms

as ‘black boxes’ into which representations sometimes enter and from which they periodically

depart, then a mechanism is domain-specific if there are heavy restrictions on the class of

representations that are permitted to enter. Consider, for example, a natural language parser.

Such a device can only process inputs that represent phonological properties and, moreover,

represents them in the appropriate format. In contrast, it cannot take as input representations of

color or artifacts or mathematical entities and so on. Thus it is plausible to claim that natural

language parsers are, in the present sense, domain-specific. Much the same is true of many of the

modular central systems that have been posited in recent years. A folk biology module is, for

example, naturally construed as domain-specific since it can only take representations of

biological phenomena as input. In contrast, the kind of central systems for reasoning posited by

Fodor and others are not plausibly domain-specific in any interesting sense since they are

supposed to be able to take an extraordinarily broad range of representations as input –roughly

any conceptual representation whatsoever. Such mechanisms are thus invariably construed as

domain-general as opposed to domain-specific.

5 What does ‘architectural’ means in the present context? This is no straightforward matter. (What is?) But for our purposes we will not go far wrong if we assume that the claim that something is an architectural constraint only if a) it is a relatively enduring feature of the human mind; b) it is not a mere product of performance factors such as limitations on time, energy etc. and c) it is cognitively impenetrable in roughly Pylyshyn’s sense. That is: it cannot be changed solely as a result of alterations in ones beliefs, goals, intentions and other representational states.

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Let’s now turn to the notion of informational encapsulation. According to one standard

definition, a cognitive mechanism is informationally encapsulated just in case it has access to

less than all the information available to the mind as a whole (Fodor, 1983). Taken literally this

would be a very uninteresting notion since it is overwhelmingly plausible that no single

mechanism has access to all the information available to the mind as a whole. All cognitive

mechanisms would thus be encapsulated on the present definition. In practice, however, this

matters little since informational encapsulation is treated as a property that admits of degree; and

what researchers who deploy the notion are really interested in the extent to which a

mechanism’s access to information it interestingly constrained by its architecture. Though there

are various ways in which a mechanism might be so constrained, perhaps the most common

suggestion is that encapsulated mechanisms only have access to the information contained within

a restricted, proprietary database. Suppose, for example, that we possess a folk biology

mechanism that can only utilize the information contained within a restricted database. Such a

mechanism would be unable to access large parts of our general encyclopedic knowledge even if

this knowledge were relevant to the task being performed by the module. Such a mechanism

would thus be informationally encapsulated. Contrast this with a cognitive mechanism that has

access to all the information stored in a person’s memory. Suppose, for example, that we possess

a reasoning mechanism of the kind proposed by Fodor (1983) which can access pretty much all

of one’s encyclopedic knowledge. Such a device would presumably be highly unencapsulated.

Though regularly confounded, it really is important to see that domain-specificity and

informational encapsulation are genuinely different properties of a cognitive mechanism. In a

sense, both concern the access that a mechanism has to representations. (This is I suspect the

source of the confusion.) Yet the kind of access that they involve is very different. Domain-

specificity (and generality) concern what we might call input access. They concern the

representations that a mechanism can take as input and process. For this reason, it is not

uncommon to speak of representations that fall within a mechanism's domain as the ones that

'trigger' it or 'turn it on'. More precisely, on the assumption that cognitive mechanisms are

computational --hence characterizable by the function they compute-- the domain of a

mechanism is also, in the technical sense, the domain of the function computed by the

mechanism. In other words, it is the set of representations that the mechanism will map onto

some element in the range of its function. In contrast, the informational (un)encapsulation of a

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mechanism does not concern input access but what we might call resource access. That is,

encapsulation does not concern the class of representations that can 'turn on' a mechanism --the

ones for which it can compute a solution-- but the ones it can use as a resource once it has been

so activated.

2. Modularity and (In)tractability

How are the domain-specificity and encapsulation of modules supposed to help resolve

intractability worries? In this section I address this issue. But first, I need to say something about

the notion of intractability itself.

2.1. Computational (In)tractability6

Very roughly, a process, task, algorithm or problem is computationally tractable (or,

equivalently, easy or feasible) if it can be performed in a reasonable amount of time using a

reasonable amount of salient resources, such as effort, memory space and information.

Conversely, something is computationally intractable (or hard or unfeasible) if it is not tractable.

Presumably, a satisfactory argument for IT needs to show that amodular reasoning mechanisms

are intractable in this way. There are, however, two importantly different sub-notions of

intractability that we would do well to distinguish: in-principle and in-practice intractability

(Millgram, 1991).

A problem is intractable-in-principal if (very roughly) it cannot be rendered tractable by

the mere addition of new resources. If, for example, a computer the size of the Universe with as

many circuits as there are elementary particles running since the Big Bang won't solve the

problem, then it is intractable-in-principal (Millgram, 1991). This is the notion of intractability

that tends to concern computational complexity theorists. In order to render it amenable to

formal treatment, however, they tend (at least for heuristic purposes) to draw the

feasible/unfeasible distinction in terms of which algorithms or tasks are polynomial and which

super-polynomial. Polynomial algorithms are ones where resource requirements are only

polynomial in the size of the input.7 In contrast, superpolynomial algorithms are those where

6 My approach to characterizing the notion of intractability is heavily indebted to Millgram (1991)'s excellent discussion of the issue. 7 .That is, the resources required to compute a solution to some input can be expressed as a polynomial (or better) function of input size --e.g. n2 or n3000000.

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resource requirements increase exponentially (or worse) as a function of input size and can thus

only be expressed as superpolynomial functions, such as 2n or 100n. It is this latter kind of

algorithm that complexity theorists label "intractable". Such algorithms are also said to be

combinatorially explosive because of the dramatic way in which the resources required to solve a

problem increases as the input gets larger.

In contrast to tasks that are unfeasible in-principle, a problem is intractable in-practice if

the addition of new resources –more processing speed, memory, energy and so on— would

resolve the problem. There are many sorts of in-practice intractability. For instance, one kind

relates to space requirements, such as the amount of memory storage that a system has. But the

most commonly discussed sort of in-practice intractability concerns the idea of real-time

performance –roughly, the capacity of a system to undergo state changes as fast as (or almost as

fast as) some salient feature of the world. So, for example, one might say that a visual system

operates in real-time when the representation of the distal environment that the system produces

changes at the same rate –or close to the same rate— as the states of affairs that the system

purports to represent.

2.2. Massive Modularity as a Solution to Intractability Worries

How is modularity supposed to resolve intractability worries? As mentioned earlier, it is

their domain-specificity and/or informational encapsulation that's supposed to do the work. In

particular, both characteristics are supposed to contribute to solving what is sometimes called the

Frame Problem,8 though is perhaps more accurately (and less contentiously) referred to as the

Problem of Relevance. Very roughly, this is the problem of restricting the options and items of

information that need to be considered to those that are relevant to the task at hand.

Domain-specificity is supposed to engender tractability because it imposes restrictions

on the range of representations that a mechanism can process. As a consequence, it becomes

possible to ‘build into’ the device specialized information about the domain in which it operates

either in the form of ‘domain-specific rules of relevance, procedural knowledge, or privileged

hypotheses’ (Cosmides & Tooby, 1994, p.94). This, in turn, permits the mechanism to ‘ignore’

options that are not relevant to the domain in which it operates. For this reason, domain-

8 Fodor, Dennett, Glymour, Haughland and others all appear to think that the Frame Problem just is what, following Eric Lorman, I call the Problem of Relevance. There is a strong case to be made, however, for the claim that this identification is incorrect. See Lormand (199?) for an excellent discussion.

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specificity has seemed to many like a plausible candidate for reducing the threat of combinatorial

explosion without compromising the reliability of cognitive mechanisms (Cosmides & Tooby,

1992; Sperber, 1994).

Encapsulation is supposed to work in a complementary fashion. First, since an

encapsulated device can only access information contained within its proprietary and restricted

database, the range of information it can search is highly constrained. In particular, the option of

searching through the entire system of beliefs –relevant or otherwise—simply does not arise. By

virtue of its architecture, the mechanism is simply incapable of doing so. Second, by limiting the

mechanism’s access to only those representations contained in a proprietary database, the

number of relations between items of information that it can compute is severely reduced as well

(Fodor, 1985). To take a simple example, suppose that a given process requires a pairwise

comparison of every item of information contained in a database. This would require

approximately 2n comparisons and so, by the standard measure, would be unfeasible in-principle.

Moreover, if the database to which the mechanism has access is large, then the task would be

utterly impractical. Suppose, for example, that there were 1000 elements in the database, then the

number of pairwise comparisons is a 302-digit number –considerably larger than the number of

protons in the known universe! (Harel, p.156). In contrast, if the mechanism is sufficiently

encapsulated, it might be able to perform the pairwise comparison even though the task is

combinatorially explosive. In effect, then, informational encapsulation provides a way to render

a task tractable in-practice even when the task in unfeasible in-principle.

Suppose that all the above is correct –that domain-specificity and encapsulation can

engender computational feasibility. Then it should be clear why MM is supposed to address the

threat that intractability poses for CTM. What it does is ensure that cognitive mechanisms are

architecturally constrained with respect to what options and items of information they can

consider. But although I accept that is one way of engendering feasible computation, I deny that

intractability provides us with good reason to reject an amodular conception of central systems.

Specifically, I deny that there are any good arguments for IT. It is to these arguments that I now

turn.

3. Three ‘Quick and Dirty’ Arguments for IT

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Let me start by considering three arguments for IT that are ‘quick and dirty’ in that they

largely turn on attributing (without serious argument) commitments that the amodularist simply

does not accept.

3.1. Argument 1: Informational Impoverishment

The first, and perhaps the most prominent argument that I’ll discuss is one made popular

by the evolutionary psychologists Leda Cosmides and John Tooby (Tooby and Cosmides,1994).

The argument in question proceeds from the assumption that a nonmodular, hence, domain-

general, mechanism “lacks any content, either in the form of domain-specific knowledge or

domain-specific procedures that can guide it towards the solution of problems” (Tooby &

Cosmides, 1994, p.94). As a consequence, it “must evaluate all the alternatives it can define"

(ibid.). But as Cosmides and Tooby observe, such a strategy is subject to serious intractability

problems since even routine cognitive tasks are such that the space of alternative options tends to

increase exponentially. Amodular mechanisms would thus seem to be computationally

intractable: at best, intolerably slow and, at worst, incapable of solving the vast majority of

problems that they confront.

Though frequently presented as an objection to amodular accounts of cognition (Tooby &

Cosmides, 1992; Buss, 2000), this argument is in fact only a criticism of theories which

characterize our cognitive mechanisms as suffering from a particularly extreme form of

informational impoverished. Any appearance to the contrary derives from the stipulation that

domain-general mechanisms possess no specialised knowledge. But while modularity is one way

of building (specialized) knowledge into a system, it is not the only way. Another is for amodular

devices to have access to bodies of specialized knowledge. Indeed, perhaps the standard view

among advocates of amodular theories is that reasoning mechanisms have access to huge

amounts of such information. This is, I take it, pretty obvious from even the most cursory survey

of the relevant literatures. Fodor (1983), for example, maintains explicitly that domain-general

central systems have access to enormous amounts of specialized information. So for that matter

do Anderson, Gopnik, Newell and many other theorists who adopt a nonmodular conception of

central systems (Anderson, 1993; Gopnik & Meltzoff 199?; Newell, 1990). In each of these

cases, what makes the hypothesized system domain-general is not an absence of specialized

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information, but the enormous range of representations that the mechanism is capable of

processing. The argument currently under discussion thus succeeds in only refuting a straw man.

3.2. Argument 2: Optimality

Another possible argument against the tractability of amodular reasoning mechanisms

turns on the claim that that they implement optimization processes. In the present context,

“optimization’ refers to reasoning processes that broadly conform to standards of ideal

rationality, such as those characterized by Bayesian accounts of probabilistic reasoning or

standard approaches to decision theory. Such processes are widely recognized as being

computationally very expensive –as requiring memory, speed and informational access that

human beings could not possibility possess.9 And it is precisely because of these excessive

resource demands that they are commonly termed ideal, unbounded or even demonic

conceptions of reasoning (Simon 1957; Gigerenzer, 2001). Thus it would seem that if advocates

of nonmodular reasoning are committed to optimization, then the view that they endorse is

subject to intractability worries as well.

It is not at all clear to me that anyone explicitly endorses the above line of reasoning. But

it is strongly suggested by recent discussions of nonmodular reasoning architectures. Dietrich

and Fields (1996), for example, maintain that Fodor’s amodular conception of central systems

“tries to explain human intelligence as approximating ideal rationality” (p.23). Similarly,

Gigerenzer and his collaborators have a tendency to present their adaptive toolbox version of

MM as if it were a response to the intractability problems confronting a domain-general,

optimization view of reasoning (Gigerenzer, 2001; Gigerenzer & Todd, 1999).

9 To use one well-known example, on standard Bayesian accounts, the equations for assessing

the impact of new evidence on our current beliefs are such that if one's system of beliefs has n

elements, then computing the new probability of a single belief, B, will require 2n additions. Such

methods thus involve an exponential growth in number of computations as a function of belief

system size. To give you some idea of just how expensive this is, on the hyper-conservative

assumption that we possess 100 beliefs, calculating the probability assignment of a belief B on

the basis of new information, will require the performance of more than 1030 additions, which is

considerably more than the number of microseconds that have elapsed since the Big Bang!

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The argument is not, however, a good one. Though optimal reasoning is (at least in the

general case) intractable,10 it really needs to be stressed that amodularists are in no way

committed to such a view of human reasoning. What is true is that for a mechanism to optimize

it needs to be unencapsulated hence, amodular; and this is because (at least as standardly

construed) optimization demands the updating of all of one’s beliefs in the light of new

information. But the converse is not true: An unencapsulated mechanism need not be an

optimizer. On the contrary, since the inception of AI it has been commonplace to combine an

amodular conception of reasoning with the explicit denial of optimization. Consider, for

example, Newell and Simon’s seminal work on the General Problem Solver. As the name

suggests, GPS was designed to apply across a very wide range of content domains without

architectural constraint on what representations is could use. It is thus not plausibly viewed as

modular. Yet, to use Simon’s famous expression, it was designed to satisfice –to arrive at

solutions that were good enough as opposed to optimal. Much the same could be said of many of

the amodular, classical accounts of reasoning to be found in AI and cognitive science, including

Laird and Newell’s SOAR architecture and Anderson’s ACT theory (Newell, 1990; Anderson,

1993). These are among the paradigm nonmodular approaches to cognition and yet they are in no

way committed to optimization.

3.3. Argument 3: Exhaustive Search

Still, even if optimization as such is not a problem for amodular accounts of reasoning, it

might still be that there are properties of optimal reasoning to which the amodularist is

committed and that these properties are sufficient to generate intractability problems. Exhaustive

search is perhaps the most plausible candidate for this role. The rough idea is that amodular

reasoning mechanisms must perform exhaustive searches over our belief systems. But given even

a conservative estimate of the size of any individual’s belief system, such a search would be

10 Though there is lots of good research which aims to discover tractable methods for applying

ideal standards of rationality to interesting –but restricted—domains. See, for example, the

literature on Bayesian networks (?????)

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unfeasible in practice.11 In which case, it would seem that amodular reasoning mechanisms are

computationally intractable.

Again, it’s not at all clear to me that anyone really endorses this line of argument.

Nevertheless, some prominent theorists have found it hard not to interpret the amodularist as

somehow committed to exhaustive search. Consider, for example, the following passage in

which Clark Glymour discusses Fodor’s conception of central systems:

Is Fodor claiming that when we set about to get evidence pertinent to a hypothesis we are

entertaining we somehow consider every possible domain we could observe? It sounds

very much as though he is saying that, but of course it is not true. (Glymour, 1985, p. 15)

Glymour is surely correct to claim that no such exhaustive search occurs; and though he is not

wholly explicit on the matter, part of his reason for saying so appears to be that such a process

would be computationally unfeasible. Carruthers (forthcoming) is more explicit:

Any processor that had to access the full set of the agent’s background beliefs (or even a

significant subset thereof) would be faced with an unmanageable combinatorial

explosion. We should, therefore, expect the mind to consist of a set of processing systems

which are isolable from one another, and which operate in isolation from most of the

information that is available elsewhere in the mind (Carruthers, forthcoming)

This really does sound like an argument for IT. Moreover, given the reference to what a

processor “had to access” –rather than merely could access— it really does sound as if the

argument assumes that amodular mechanisms engage is (near) exhaustive search. Interpretative

issues to one side, however, the argument as it stands is not a good one.

Once more, the problem is that it’s very hard to see why the amodularist should accept

the claim that central systems engage in exhaustive search. What the amodularist does accept is

the unencapsulation of reasoning mechanisms which, by definition, have access to huge amounts

of information –we may suppose, all the agent’s background beliefs. But the notion of access is a

modal one. It concerns what information –given architectural constraints— a mechanism can

mobilize in solving a problem. In particular, it implies that any background belief can be used.

But it does not follow from this that the mechanism in fact mobilizes the entire set of background

11 Though not necessarily in-principle. Exhaustive search might only involve a worst-case

running time which is on the order of N—i.e. where time grows linearly with the number of

beliefs in the belief system.

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beliefs –i.e. that it engage in exhaustive search. This is simply not a commitment that the

advocate of amodular central systems would be much inclined to accept. Indeed, as Fodor has

pointed out, it would be absurd to hold an amodular view of reasoning if it implied such a

commitment (Fodor, 1985).

Of course, the fact that the amodularist does not endorse the claim that central systems

engage is exhaustive search is perfectly consistent with their being an argument which shows

that such processes would need to occur if the amodular theory were true. In the coming section,

I consider a prominent argument that has been widely interepreted as supporting this conclusion..

4. The Globality Argument

In the Minds Doesn’t Work That Way, Fodor develops an argument which is supposed to

show the inadequacy of classicism as an account of our cognitive processes. Nevertheless, it has

been widely viewed by advocates of MM as a way of defending the Intractability Thesis

(Carruthers, forthcoming; Sperber, 2002). In what follows, I show both that Fodor’s argument is

unsound and that, even if sound, it is too strong to figure in the intractability argument for MM.

4.1. The Argument

Fodor’s argument is a complex one whose structure is far from transparent. But in rough

form, it concerns a tension between two prima facie plausible claims. The first is that classical

computational processes are in some sense (soon to be discussed) local. The second is that our

reasoning processes are global in roughly the sense that they are sensitive to context-dependent

properties of the entire belief system. Slightly more specifically, Fodor claims that abductive

reasoning (or inference to the best explanation) is global because it is sensitive to such properties

as simplicity and conservativism; properties which, he maintains, are both context dependent and

somehow determined by the belief system as a whole. The problem, then, is this: If classical

computational operations are local, how can we provide a computationally tractable account of

abduction? Fodor's claim is that we almost certainly cannot and that this shows the inadequacy of

classicism as an account of human reasoning.

Let’s spell out the argument in a bit more detail. One central feature is that it proceeds

from an analysis of how best to understand the classical thesis that cognitive processes are

syntactically driven. The rough idea is a very familiar one: cognitive processes are

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representational processes in which the representations have their causal role in virtue of their

syntactic properties. But as Fodor observes, there is an ambiguity here between what we might

call an essentialist (or extreme) thesis and a more moderate thesis. According to the essentialist

reading, which Fodor dubs E(CTM): Each mental representation, R, has its causal role solely in

virtue of its essential syntactic properties –i.e. its constituent structure. To put the point in a

slightly different way, on this view, R’s causal role in cognitive processes supervenes12 on R’s

essential syntactic properties. In contrast, according to the more moderate version of classicism,

which Fodor refers to as M(CTM), the causal role of a representation, R, need not depend on its

essential (constituent) syntactic properties. Rather, it need only depend on some set of syntactic

properties. That is, R’s causal role in cognitive processes supervenes on some syntactic facts or

other. Either way, however, Fodor thinks that the classical conception of cognitive processes is

in serious trouble.

First, suppose that E(CTM) is true. Then the syntactic properties that determine R’s

causal role are the essential ones. In which case, the determinants of its casual role must be

context invariant. But this, according to Fodor, is simply not true of representations involved in

abductive reasoning since their causal role is determined, at least in part, by such properties as

simplicity and conservativism; properties which he maintains are context sensitive par

excellence. When deciding between a range of hypotheses one’s selection will be sensitive to

such issues as which of the hypotheses is the simplest or most conservative. And the degree to

which a hypothesis is simple or conservative depends in large measure on what background

beliefs one has –that is, on the relationship between the hypothesis and the theory or epistemic

context in which it is embedded. But facts about R’s relations to other beliefs are not essential to

R’s being the representation that it is. In which case, E(CTM) must false.

As Fodor notes, the above argument does not undermine M(CTM): the thesis that a

mental representation’s casual role is determined by some syntactic facts or other. Even so, he

maintains that this should be of little solace to classical cognitive scientists. First, according to

Fodor, M(CTM) is not in fact a classical view at all since “by definition, which Classical

computations apply to a representation is determined not just by some of its syntactic properties

or other but, in particular, by its constituent structure, that is by how the representation is

12 Terminological note: To say that causal roles supervene on constituent structure means (very roughly) that representations cannot differ in their casual roles unless they differ in their

16

constructed from its parts”[p.30]. In short: according to Fodor the classicist is committed to

E(CTM).

Second, Fodor claims that M(CTM) only avoids the above objection to E(CTM) “at the

price of ruinous holism”: of “assuming that the units of thought are much bigger than in fact they

could possibly be” [Fodor, p.33]. Indeed, Fodor appears to think that if M(CTM) is true, then the

units of thought will be total theories –entire corpuses of epistemic commitments [p.33]. Though

the argument for this claim is far from transparent, the following strikes me as a charitable

reconstruction. First, suppose, that the conclusions of Fodor’s previous arguments are in force.

That is:

1. E(CTM) is false because the causal role of a representation in abductive reasoning is at

least partially determined by its relation to an embedding theory T (i.e. background

beliefs).

2. The classical computations that apply to a representation are determined solely by its

essential (i.e. constituent) structure. Very crudely: classical processes can only ‘see’ the

internal syntactic structure of the representations that are being processed.

Now as Fodor points out, M(CTM) is compatible with (1) since the relation between a

representation and its embedding theory might be a relational syntactic property S (or at least

depend on S). Nonetheless, if (2) is true, then a classical computational system is only sensitive

to the essential –i.e. constituent-- syntactic properties of a representation and not to relational

properties like S. In which case, a classical system cannot be influenced by S merely as a

consequence of having access to R. Nevertheless, as Fodor points out, it is straightforward to

transform R so that S can have a causal influence: The mechanism might simply rewrite R as the

conjunction of R and whatever parts of T are relevant to determining S. In the worst case, the

shortest expression to which the computer needs access in order to be sensitive to S is the entire

theory –i.e. T including R.

All the above is compatible with classicism. But according to Fodor a serious dilemma

looms large. On one hand the representations over which cognitive processes are typically

defined are much shorter than whole theories [p.31]. But on the other hand, Fodor maintains that

“the only guaranteed way of Classically computing a syntactic-but-global property” is to take

constituent structure as well.

17

‘whole theories as computational domains”; and this clearly threatens to render abduction

computationally intractable. The problem, then, is this:

Reliable abduction may require, in the limit, that the whole background of epistemic

commitments be somehow brought to bear on planning and belief fixation. But feasible

abduction requires in practice that not more than a small subset of even the relevant

background beliefs are actually consulted. [p.37]

Thus it would seem that if Classicism is true, abduction cannot be reliable. But since abduction

presumably is reliable, Classicism is false.

4.2 Problems with the Globality Argument

Though I accept Fodor’s objection to E(CTM), I have three worries about his case against

the more moderate M(CTM). A first and relatively minor concern is that, contrary to what Fodor

appears to think, the classicist in not committed to E(CTM). The reason is that there are two

importantly different versions of M(CTM); and the classicist need only deny one of them.

According to the first version:

M(CTM)1: Though R’s causal role is determined by some syntactic fact or other,

essential syntactic properties need make no determinative contribution

whatsoever.

Classicists are committed to the denial of M(CTM)1 because of the conditions that need to be

satisfied in order for different representations to have distinct casual roles within a classical

system. In brief, a representation, R, can have a causal role that is distinct from those of other

representations only if the mechanism can distinguish it from other representations. But a

classical, Turing-style computational device can distinguish R from R* only if they differ in their

essential syntactic/formal properties. So, a necessary condition on R and R* possessing different

causal roles is that they differ in their essential syntactic properties. In which case, on the

assumption that mental representations do differ in their causal roles, it follows that the causal

role of any representation is at least partially determined by its essential --i.e. constituent—

syntactic properties.

All this is, however, entirely compatible with an alternative version of M(CTM):

M(CTM)2: Though R’s causal role is partially determined by its essential

syntactic properties, other syntactic facts may be partially determinative as well.

18

Since this thesis requires that the causal role of R be partially determined by its essential

syntactic properties it does not conflict with the fact that classical systems distinguish between

representations in virtue of their essential syntactic properties. But M(CTM)2 also permits that

R’s causal role partially depend on inessential or relational syntactic properties. And this is just

as well since many paradigmatic classical systems conform to M(CTM)2 not E(CTM). For

example, programmable Turing machines are organized in such a way that R's causal role is

jointly determined by its essential syntactic properties and the program. (Change the program

and you change R’s causal role as well.) But the program just is a series of representations that

influence the causal role of R in virtue of syntactic properties. So, M(CTM)2 and not E(CTM) is

true of a programmable Turing machine.13 Though I won’t go into the issue here, much the same

is true of pretty much every system from the classical AI literature.

A second problem with Fodor’s argument against M(CTM) is that, in order to go through,

it is not enough that abduction is context sensitive, it must be global as well. Without this

assumption, no intractability worries arise since there is no reason to suppose that abductive

reasoning within a classical system would require (near) exhaustive search of background

beliefs. The problem, however, is that there is no reason whatsoever to accept the claim that

abduction is global in the relevant sense. Recall: on Fodor’s view, abduction is a global process

because it depends on such properties as simplicity and conservativism which, on his view, are

somehow determined by the belief system as a whole. But claims about the globality of these

properties may be given either a normative or a descriptive-psychological reading. On the

normative reading, assessments of simplicity and conservativism ought to be global: that is, a

normatively correct (or at any rate ideal) assessment of the simplicity or conservativism of a

hypothesis ought to take into consideration one’s entire background epistemic commitments. But

of course it is not enough for Fodor’s purposes that such assessments ought to be global. Rather,

13 Nor is the present point especially about programmes as opposed to (other) data-structures. For

the sake of illustration, consider a system that incorporates a semantic network (Quinlan). Such

systems are standard fair in classical AI. Nonetheless, what inferences can be drawn from a

representation within such a system depend not only on its essential syntactic properties of but

also on the arcs that link it to other representations –which are, by assumption, non-essential

syntactic relations.

19

it needs to be the case that our assessments of simplicity and conservatvism are, in fact, global.

And to my knowledge, there is no reason to suppose that this is true.

A comparison with the notion of consistency may help make the point clearer.

Consistency is frequently construed as a normative standard against which to assess our beliefs

(Dennett, 1987). Roughly: all else being equal, our beliefs ought to be consistent with each other.

When construed in this manner, however, it is natural to think that consistency should be a

global property in the sense that a belief system in its entirety ought to be consistent. But there is

absolutely no reason whatsoever to suppose –and indeed some reason to deny-- that human

beings conform to this norm. Moreover, this is so in spite of the fact that consistency really does

play a role in our inferential practices. What I am suggesting is that much the same may be true

of simplicity and conservativism. When construed in a normative manner, it is natural14 to think

of them as global properties –i.e. that assessments of simplicity and conservativism ought to be

made in the light of our total epistemic commitments. But when construed as properties of actual

human reasoning processes, there is little reason to suppose that they accord with this normative

characterization.

A final problem with Fodor’s argument is that even if we suppose that simplicity and

conservativism are, in fact, global properties, the argument still does not go through since it turns

on the implausible assumption that we are guaranteed to make successful assessments of

simplicity and conservativism. Specifically, in arguing for the conclusion that abduction is

computationally unfeasible, Fodor relies on the claim that “the only guaranteed way of

Classically computing a syntactic-but-global property” is to take ‘whole theories as

computational domains” (Fodor, 2000, p.?). But guarantees are beside the point. Why suppose

that we always successfully compute the syntactic-but-global properties on which abduction

relies? Presumably we do not. And one very plausible suggestion is that we fail to do so when

the cognitive demands required are just too great. In particular, for all that is known, we may

well fail under precisely those circumstances the classical view would predict –viz. when too

much of our belief system needs to be consulted in order to compute the simplicity or

conservativism of a belief.

4.3. Does the Globality Argument Support MM?

14 Though by no means mandatory.

20

So far we have seen that Fodor’s argument suffers from a number of deficiencies. But

even if it were sound, the following issue would still arise: Why would anyone think that it

supports MM? After all, if sound, the globality argument appears to show that classical theories

of abduction tout court –not merely amodular ones— are unfeasible. The short answer, I suspect,

is that MM appears to render reasoning sufficiently local to avoid the sorts of feasibility problem

that Fodor raises (Fodor, 2000, p23). But this impression is misleading. Even if sound, the

Fodorian argument would still fail to support MM. In what follows, I argue for this point by

showing how one central premise of the argument— that abduction is a global process— cannot

be squared with both MM and CTM. Hence, there is no stable position which permits the

advocate of a classical-cum-MM account of cognition to claim that Fodor has provided a sound

argument for the IT. Consider the options.

Option 1: Deny Globality. The most obvious strategy would be to deny the globality of

reasoning processes. This is, in fact, pretty much what Fodor takes the advocate of MM to be

doing. Thus he maintains that MM preserves the thesis that mental processes depend on local

properties “by denying –or, anyhow, downplaying—their globality and context sensitivity”

(Fodor, 2000, p.36). In the present context, however, this approach is unsatisfactory. For if one

rejects a central premise of Fodor’s argument, one cannot maintain that it is a sound argument. In

which case, one preserves a commitment to MM only at the cost of giving up the Fodorian

argument for IT.15

Option 2: Explain Globality. An alternative strategy is to accept Fodor’s claim that

abductive reasoning is global in nature and suggest that it can be explained within the massively

modular framework. But it is utterly unclear how this can be done without either compromising

the commitment to MM or rejecting the Fodorian argument for intractability. To see the point,

we need to work through the possible ways in which the modularist might try to explain

globality.

15 I can imagine someone suggesting that the denial of globality is tantamount to a rejection of

nonmodular reasoning mechanisms. But this strikes me as very implausible. Though it may be

true that globality requires nonmodularity, the converse is very obviously untrue. A mechanism

could be radically domain-general and unencapsulated and yet still not be sensitive to global

properties.

21

Version 1: Global Processing Modules. One option would be to claim that some

individual module implements the sorts of global processes allegedly involved in abduction. But

prima facie, this strategy is highly suspect. First, a ‘module’ that implements global processes is

surely no module at all. To speak in such an oxymoronic fashion merely courts confusion and

involves a change of subject matter in which the term ‘module’ is used to describe entities that

would previously have counted as paradigmatically amodular devices. Second, even if we are

prepared to waive such definitional concerns and speak of ‘global processing modules’, it would

seem that the Fodorian argument, if sound, would show such a mechanism to be intractable. The

intractability worries that are allegedly generated by globality are first and foremost worries

about the intractability of abductive processes; and it is only because cognitive mechanisms are

supposed to implement such processes that they too are said to be intractable. But if this is so,

then it’s utterly unclear why globality should pose any less of an intractability problem for the

present suggestion than it does for the explicitly nonmodular alternative. After all, they are just

two approaches to implementing a putatively intractable process. In which case, any mechanism

that implements the process –call it a module, if you like—will be intractable as well. The

present suggestion thus fails to explain how to both preserve a commitment to MM and endorse

the Fodorian argument for IT.

Version 2: Collaborative Activity of Modules. A second way of trying to combine MM

with the acceptance of globality would be to argue that global processes are implemented by

collections of modules acting in concert. Thus while no single module would perform global

operations, the collaborative activity of suites of interconnected modules might subserve global

processes. Here there are two versions that we need to keep an eye on.

Version 2a: Global processes are (classical) computational ones. The idea here is that

the collaborative activity of modules results in a global and context sensitive process that is,

itself, a classical computational one. But, again, it’s hard to see how this could be a solution to

the intractability worries raised by Fodor. To repeat: Fodor’s claims are first and foremost about

the intractability of global computational processes. It is because abductive reasoning

mechanisms implement such processes that they are supposed to succumb to intractability

worries. But if this is so, then whether the process is implemented by a multitude of modular

mechanisms or by a single non-modular device should make no difference to whether or not the

process so implemented is tractable.

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Version 2b: Global processes are noncomputational. This leads us to an alternative view,

recently defended by Dan Sperber (Sperber 2002). Roughly put, the idea is that although

modules are classical devices, the global, context sensitive processes which they collectively

subserve are noncomputational in character. Slightly more precisely, Sperber suggests that

various forms of global, context sensitivity might arise from non-computational interactions

between modules which govern competition for cognitive resources. Thus Sperber claims that

this constitutes a classical, modularist proposal that evades Fodorian worries about the globality

of abduction:

The general point is that a solution to the problems raised for a computational theory of

mind by context-sensitive inference may be found in terms of some "invisible hand"

cumulative effect of non-computational events in the mind/brain, and that Fodor has not

even discussed, let alone ruled out,16 this line of investigation. (Sperber200?)

This is, I think, an ingenious response to Fodor’s argument that surely deserves further

exploration. Nevertheless, as a way of squaring a classical version of MM with Fodor’s argument

for IT, it suffers from three deficiencies.

First, it is not strictly speaking the classical theory of cognition at all. In order to see this

point, we need to distinguish between two claims:

Classical Theory of Mechanisms: Cognitive mechanisms are classical computational

devices.

Classical Theory of Processes: Cognitive processes are classical computational

processes.

As Sperber presents his view it is supposed to preserve a classical conception of cognitive

mechanisms. This is because he endorses both the claim that all cognitive mechanisms are

modular and that all modules are classical devices. This further implies that all intra-modular

processes are classical. Yet the conjunction of these claims is not quite enough to preserve the

classical computational theory as ordinarily construed. This is because on standard

characterizations classicism is a thesis about cognitive processes, not mechanisms; and what is

more, it’s a claim about all cognitive processes and not merely some or even most of them. But

Sperber maintains that inter-modular processes are non-classical –indeed noncomputational. So,

16 This is not quite true. Though Fodor does not explictly consider Sperber's suggestion, he does consider --and reject-- a class of suggestions of which Sperber's is a member (Fodor, 2000, p.??).

23

at best, the proposal is an attenuated version of classicism that cleaves to a classical conception

of cognitive mechanisms and a partially classical view of processes. Yet it’s not clear that even

this much is true. For although I won't press the point too hard, it’s utterly obscure why the

cognitive structure that consists of the non-computationally interacting modules should not count

as a (non-computational) cognitive mechanism in its own right.17 In which case, it’s utterly

unclear why Sperber’s strategy not only relinquishes the classical account of cognitive processes

but a classical account of mechanisms as well.

Still, the above may sound all too much like hairsplitting. Surely a more charitable

interpretation is that, in view of Fodorian concerns about globality, Sperber has tried to push the

classical conception of architecture as far as it can go and then suggest an alternative where the

classical view breaks down. This sounds like good scientific methodology: the most conservative

modification of (what Speber sees as) the current best theory that will accommodate the facts

about globality. The spirit of classicism is thus preserved even if the letter must be rejected… or

so it would appear.

But –and this is my second concern with the proposal— for all that Sperber says, his positing

of global, noncomputational processes is unmotivated. As Sperber himself admits, his proposal

on the face of it, is no more than "a vague line of investigation" --one that would not "for

instance, impress a grant-giving agency" (Sperber 200?). Nonetheless, he thinks that here

"unexpectedly, Fodor comes to the rescue" (ibid.). In particular, Sperber seems to think that the

Fodorian objections to global computational processes leaves his brand of MM as a line of

investigation that deserves serious attention. But as we have already seen, the globality

argument is unsatisfactory. In which case, for all that Sperber says, the proposal is still a vague

one in search of a motivation for further investigation.

Finally, Sperber’s proposal is not as consonant with the spirit of classicism as it may initially

appear. Among the most fundamental aims of the classical approach is to provide a mechanistic

17 Certainly, there is no problem with the view that cognitive mechanisms can be nested. On the

contrary, this is very much a standard view among cognitive scientists. It looks, then, as if the

issue will boil down to the (rather vexed) question about how to individuate cognitive

mechanisms.

24

account of cognition. Such an account is supposed to explains intelligence in non-mysterious and

manifestly mechanistic terms: to show how intelligence could result from the operations of a

mere machine. And in the service of this objective, the classical theory purports to explain

cognitive activity in terms of processes that are built up from sets of operations that are primitive

in at least two senses. First, they are computationally primitive: they have no other computational

operations as proper parts. Second, they are supposed to be dumb –that is, obviously mechanical

operations whose execution requires no intelligence whatsoever.18 Moreover, part of what

makes these operations appropriately dumb and unmysterious is that they are extremely local.

Consider, for example, the primitive operations of the read-write head on a Turing machine –

move left one square, move right one square, erase symbol etc. Precisely how such operations

are performed depends only on what is detected on the tape and what state the read-write head is

in. And it is, in large measure, because these operations are so local that they are obviously

executable by a mere mechanism. Much the same is also true of all the main mechanistic

alternatives to classicism. So, for example, within connectionist networks, primitive operations

are local interactions between nodes. The dumbness and locality of primitive operations thus

really seem fundamental to the classical paradigm and, more generally, the mechanistic

enterprise in cognitive science.

What does all this have to do with the globality argument? From the standpoint of the

classical theory, Sperber’s global processes are computationally primitive operations in the sense

that they do not have other computational operations are proper parts. Nonetheless, they are not

plausibly viewed as primitive in the other sense of the term --as being executable without

recourse to intelligence. On the contrary, they are a) nonlocal and b) so myterious that we

currently have (virtually) no idea how they might be implemented in a physical system.

5. The Robot Argument

18 This notion of a computational primitive is central to blocking long-standing homunculi

objections to mechanistic theories of cognition. Such arguments purport to show that mechanistic

explanations either assume precisely what they are supposed to explain (viz. the intelligence of

cognitive activity) or else spiral into an infinite regress of nested ‘intelligences’.

25

A rather different sort of argument for IT consists in an inference from the systematic

failure to model central processes, to a conclusion about the unfeasibility of amodular reasoning.

A full dress version of this argument would demand very careful analysis of the history of

computational modeling. To my knowledge, however, no such argument has ever been provided.

Instead, advocates tend to illustrate their general conclusion –the unfeasibility of amodular

architectures— with one of more choice examples for the history of AI. And of these examples,

the most commonly cited –and most plausible— is the failure of an early approach in robotics

that relied heavily on amodular reasoning processes: the so-called Sense-Model-Plan-Act

paradigm (SMPA) (Bonasso et al, 1998; Brooks, 1999).19 In what follows I briefly sketch this

argument and highlight its deficiencies.

The SMPA paradigm was a general approach to robot construction that dominated the

early history of robotics in AI but is now widely viewed as a dead end. On this approach,

information processing is divided into a number of stages, each of which is assumed to depend

on a distinct set of computational mechanisms. The first stage –preprocessing— involves a

mapping of the information received via sensors –typically cameras— onto representations that

can be deployed by central processing. Stage two –a kind of theoretical reasoning— utilizes the

output of preprocessing in order to update a world model –a ‘unified’ representation of the state

of the robot and the environment that it occupies. This model, along with a specification of the

robot’s goals, then serves as input to a third processing stage –a planner which churns through

possible sets of actions in order to fix upon a plan. Finally, the plan is passed onto the control

level of the robot –i.e. to mechanisms that generate movements of the robot itself.20 The cycle of

sensing, modeling, planning and acting then starts all over.

Perhaps the most obvious problem with the SMPA approach was the failure to get the

cycle from perception via modeling and planning to action to run in real time (Bonasso et al.).

As a consequence, robots had an unfortunate tendency to exhibit disastrously maladaptive

behavior. Here is how the editors of one well-known anthology on robotics illustrate the point:

Now the robot is moving. In a few seconds, its cameras detect in its path a large pothole

that is not predicted by its world model. The sensor information is processed; the world

19 The most famous product of the SMPA paradigm was Shakey the Standford Research Institute robot (Nilsson, 1984). 20 It may not have escaped the reader's attention that the SMPA resembles Fodor's account of cognitive architecture to a remarkable degree.

26

model is populated; and at some point while the world model is trying to assert that the

large black blob on the ground is a depression, not a shadow, the robot falls into the

pothole. (Bonasso et al., 1998, p. 5)

For our purposes, the main difficulty is that before the robot can change direction it needs to

complete the modeling and planning stages of the cycle. But these central processes simply could

not be made to run fast enough to keep up with a robot that was moving around the world at the

sort of speed that human beings do. Moreover, despite considerable efforts to address the

difficulty, no satisfactory solution was found: no suitably efficient algorithms for modeling or

planning have been identified and hardware solutions, such as increasing memory size or CPU

speed, only highlight the severity of the problem. In particular, the resulting robots tend to be

laughably slow (Bonnasso, et al, Brooks, Brooks 1999, Gigernezer, 2001, p.43).

What conclusions should be drawn from the failure of SMPA? Given what I have said so

far, it is tempting to conclude that it highlights the unfeasibility of amodular approaches to the

design and understanding of intelligent systems. Rodney Brooks and his collaborators, for

example, famously take it to support the view that “there is no central processor or central

control structure” but instead a large collection of “reactive behaviors” –roughly, modular

devices which generate highly specialized responses to very specific environmental conditions

(Brooks, 1999, p.90). Similarly, Gigerenzer suggests that the failure of SMPA supports the view

that “smart robots need to be … equipped with special-purpose abilities without a centralized

representation and computational control system” (Gigerenzer, 2001, p.43). From this

perspective, then, the failure of SMPA both supports the IT and suggests a more modular

approach to the design of intelligent systems.

But this inference to the intractability of amodular central systems per se is too quick.

One reason is that some of the sources of real-time failure within the SMPA paradigm have little

to do with central processing as such. For example, the preprocessing stage –the perceptual task

of extracting information from the distal environment— was a source of serious combinatorial

problems as well (Bonnasso, et al). But even if we focus exclusively on the difficulties posed by

central processing, I maintain that on closer analysis it's plausible to trace SMPA’s failures not to

amodular processing as such, but to a pair of assumptions about the specific role that such

processes were required to play within the SMPA paradigm: assumptions that the amodularist

need not (and, indeed, should not) endorse.

27

The first of these assumptions is that the planner is required to pass its plans directly to

the control level. As a consequence, it needs to micromanage the activities of the robot: to

specify series of actions in an extremely fine-grained fashion, right down to the actuator level

(Bonnasso, et al). So, for example, it is not enough for the plan to specify that the robot should

go to the refrigerator. Rather, it needs to specify precise movements for getting there, such as:

“turn .56 radians”, “move 122.25 cm” and so on (ibid.). But if plans are individuated so finely,

then there are more plans that can be generated and between which a selection needs to be made;

and this means that the computational demands on planning are very extreme indeed.

Second, if the planner is required to pass onto the control level a very fine-grained

specification of actions, then it also becomes necessary to constantly update the world model.

This is because the planner can only produce successful, fine-grained plans, if it is operating on

the basis of sufficiently detailed and accurate information about the world. In which case, the

demand for fine-grained plans more-or-less mandates that the SMPA cycle be completed before

the robot can take any action at all. And this, in turn, means that the advocate of SMPA must

make central processes run in real-time in order that the robot, itself, operate in a suitably rapid

manner.

The above observations suggest an approach to the design of intelligent systems that does

not deny the existence of amodular central systems but merely assigns them a different role from

the one that they play within the SMPA paradigm. Moreover, it is a proposal –widely known as

the hybrid approach– that has dominated the robotics community in AI for more than a decade

(Gat, Kortenkamp et al.).21 In rough outline, the idea is this: If it’s not possible to get a planner to

run fast enough to govern the fine-grained behavior of a mobile robot, then we should decouple

such central processes from the real time task of generating routine behaviors. On this approach

reactive, modular devices of the sort suggested by Brooks can subserve routine tasks, such as the

avoidance of obstacles. The slower, more deliberative central systems then need only be pressed

into service when the reactive mechanisms run out of routine solutions –for example, to specify a

high level objective or to answer specific ‘queries’ posed to it by the reactive modules. In this

way, amodular systems can play a vital role in governing the gross behavior of the robot without

21 It is also plausible to claim that it is the approach that has resulted in the most successful robot systems developed so far (Bonnasso, et al).

28

thereby being required to solve the (apparently) insurmountable task of generating effective,

fine-grained plans for even the most routine of tasks.

To summarize: Though the interpretation of SMPA’s failure is no straightforward matter,

the rejection of amodular central systems is clearly too quick since the current state of robotics –

in particular, the success of the hybrid approach— strongly suggests that such mechanisms can

play a vital role, just not the role assigned to them by the SMPA paradigm.

6. Conclusion: Intractability Arguments Are (Probably) Too Hard To Come By

The burden of this chapter has been to show that the extant arguments for IT are

unsatisfactory. Many of them fail because they impose commitments that the amodularist simply

does not accept. Others make implausible assumptions about the nature of human reasoning and

some of them, even if sound, would still be unsatisfactory since they undermine computational

theories of reasoning tout court and not merely the amodular ones. I maintain, therefore, that we

currently have no good reason to accept a version of IT that can figure in a satisfactory

intractability argument for MM.

Of course, nothing I’ve said so far precludes the possibility that a good argument for IT

will be forthcoming. But I do think that there are grounds for thinking it unlikely to happen any

time soon. As mentioned in section 2, there are two broad categories of intractability: in-

principle intractability and in-practice intractability. So, presumably a satisfactory argument for

IT needs to show that amodular mechanisms are intractable in one or both of these senses and,

moreover, do so in such a way as to render the amodularist position untenable as a conception of

our reasoning architecture. But the prospects of an argument for either kind of intractability

appear bleak.

Consider first the prospects of an argument for in-principle intractability –the sort of

argument that forms the stock-in-trade of computational complexity theory. For a variety of

reasons, there are grounds for pessimism here. First, virtually all extant in-principle, complexity

arguments concern worst-case complexity –i.e. the time and effort that’s required for the worst

possible input to a process. But the relevance of such results is questionable since worst-case

intractability is entirely compatible with the task very frequently --indeed normally-- being

significantly less expensive than the worst case. Thus even if an in-principle argument for the

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worst-case intractability of amodular mechanisms could be had, this alone would not show that

the amodularist view of reasoning should be rejected.

Of course, complexity theorists have good reason to focus primarily on worst-cases,

namely that it readily permits the application of formal methods. But there is an alternative

measure of feasibility sometimes discussed by complexity theorists –viz. what is normally

required for the solution of a task. Such average-case analyses are more plausibly viewed as

relevant to the assessment of claims about cognitive architecture. But now the problem is that in-

principle arguments for average-case intractability are very hard indeed to come by. First, in

order to develop such arguments, one not only needs to specify the possible range of inputs to a

process but their probability of occurrence as well. And this is a kind of information that we

simply do not currently possess for human reasoning processes. A second problem is that the

mathematics of such arguments is extremely complex. As one well-known computer scientist put

it:

Average-case analysis is considerably more difficult to carry out than worst-case

analysis. The mathematics is usually far more sophisticated, and many algorithms exist

for which researchers have not been able to obtain average-case estimates at all. (Harrell,

p.135)

Given that we currently possess few (if any) serious worst-case analyses that bear on the topic of

this chapter, I suspect that the smart money should be firmly against providing relevant average-

case analyses any time soon.

Let's now turn to the prospects of in-practice feasibility arguments. If in-principle

arguments are too much to expect, then perhaps we can hit upon this alternative kind of

argument for IT. But even here the prospects do not seem good. One important feature of in-

practice intractability claims is that they need to be relativized to particular systems (or classes of

systems). This is because what resources it is practical or reasonable to use can differ from one

system to another. In particular, if one system has more resources at its disposal –time,

information, processing power, memory etc.— than another, a task may be intractable-in-

practice for one but not another. This gives rise to a pair of problems for in-practice arguments.

First, a corollary of the relative nature of practical feasibility is that it’s a largely

empirical matter whether a given task or algorithm is practically feasible. One needs to

determine, in particular, whether or not the target system --the system under consideration-- is

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capable of solving the task without incurring, what would be for it, unreasonable resource

demands. In the present context, the target is the human mind and the mechanisms from which it

is composed. And this means that an assessment of practical feasibility requires that we possess

substantial amounts of information about the problems that human beings solve, the mechanisms

which permit their solution and the resource limitations that constrain the operation of these

mechanisms. As of now, it is I think fair to say that the psychology of reasoning simply has not

provided us with detailed answers to these questions. In short: the general state of empirical

research into human reasoning imposes a bottleneck on what plausible in-practice feasibility

arguments we are in a position to make.

A second and related issue is that in order to assess whether or not a given computational

task is unfeasible in-practice, one needs to know quite a bit about the role that it plays within the

overall economy of the human mind. This is a generalization of a point made earlier. Recall: in

assessing the Robot Argument, I argued that the computational expense of planning need not

constitute grounds for rejecting the existence of an amodular planner. In particular, following

advocates of the hybrid approach, I argued that even a computationally expensive planner can

play an important role within cognition is it is suitably decoupled from the real-time production

of routine behavior. But the point can be generalized: In order to show that a process or

mechanism is practically unfeasible, it is not enough that one show how, in some context or other

it makes impractical or unreasonable resource demands. Rather, what one needs to show is that

its resource demands are unreasonable in the contexts it in fact occupies within the cognitive

system. And this is, I take it, a kind of knowledge that our cognitive psychology is unlikely to

deliver any time soon.