Competence and the classical cascade: a reply to Franks.
Marr's distinction between three levels of explanation of a computational system has become a familiar part of the methodology of cognitive science. Marr distinguishes between the top level of computational theory, the middle level of representation and algorithm, and the bottom level of hardware implementation, and claims that we understand an information-processing system completely only when we understand it at all three levels (Marr , p. 24). This ordering from top to bottom reflects his conviction that understanding at the lower levels will be achieved through understanding at the higher levels, a vision Dennett conveys with the image of 'a triumphant cascade through Marr's levels' (Dennett , p. 227).(1) In an article in this journal, Bradley Franks has argued that this cascade of explanation is blocked by various idealizations used in cognitive science. in particular those employed by competence theories of linguistic knowledge (Franks , p. 476). He concludes that cognitive scientists face a dilemma: abandon idealizations (a tall order for any science), or abandon the possibility of achieving the cascade of explanation which would yield full understanding of a cognitive system. If Franks is right, a prominent form of theorizing in cognitive science (especially about language) faces serious methodological problems. In this reply I outline Franks' argument for this conclusion and explain why I believe that it is unsound. Put briefly, my claim is that Franks' argument depends on assimilating Chomsky's distinction between competence and performance to Marr's distinction between the level of computational theory and that of representation and algorithm, and that this assimilation is mistaken.
2 Idealizations and the explanatory cascade
To understand why Franks believes that certain kinds of idealization current in cognitive science block the explanatory cascade, we need to know more about the cascade itself, and hence about Marr's levels of explanation.
Level 1, the level of computational theory, specifies 'what is being computed and why' (Marr , p. 129); Level 2 specifies a 'representation for the input and output and the algorithm to be used to transform one into the other' (Mart , p. 25); and Level 3 provides 'the details of how the algorithm and representation are realized physically' (ibid.). As we move down through these levels, our explanations become progressively more detailed; we understand first what function a system computes, then the procedure by which it computes it, and finally how that procedure is implemented physically in the system. As Franks remarks, a successful cascade of this kind requires what he calls 'inheritance of the superordinate': 'given a particular Level 1 starting point, any algorithm must compute the same function, and any implementation must implement the same algorithm and compute the same function' (Franks , p. 478). In other words, the Level 1 function must map on to the Level 2 algorithm, which must map on to the Level 3 implementation.(2) A mismatch between any two levels will block the cascade of explanation. If a system S is physically unable to implement the algorithm specified at Level 2, we cannot explain S's ability to compute the Level I function in terms of its executing that Level 2 algorithm. If the Level 2 algorithm does not compute the function specified at Level 1, we cannot explain S's ability to compute that function in terms of that algorithm.
It is now easy enough to see how, in principle, idealizations could block the cascade. A successful cascade requires that we map descriptions at higher levels on to descriptions at lower levels. Idealizations involve at least selective description, if not misdescription, and so they have the potential to create mismatches between descriptions at different levels, mismatches which block the cascade of explanation.(3) For example, if we are working with an idealized conception of system S's hardware, we may think that S can implement an algorithm which in fact it cannot. Then our Level 2 algorithm will not map on to S's actual physical structure. Or if we are working with an idealized conception of S's abilities, so that the function specified at Level I is not one which S in fact computes, we will be unable to complete the cascade by mapping that function on to an algorithm which S actually implements.
Presumably some idealizations could block the explanatory cascade in this
way. Franks notes, following Cartwright , that there is a trade-off between idealization and 'facticity': 'the more we idealize, the less directly related to actual phenomena will be our theories' (Franks , p. 490). Idealizations reflect our views of which aspects of a system are theoretically important and which are incidental. These views can be and sometimes are wrong, and this may be revealed by a mismatch between our higher-level picture and the actual detailed workings of the system. Since this can happen in science in general, it can happen in cognitive science, and in particular in attempts to provide cascade explanations of cognitive capacities. But of course this general point does not suggest that cognitive science suffers from particular methodological problems, as Franks contends. Franks wants to argue not just that idealizations could block the explanatory cascade, but that an influential contemporary approach to language, associated with Chomsky, involves a foundational idealization which does block the explanatory cascade. The heart of his paper is an argument that what he calls 'competence theories' in cognitive science, exemplified in the linguistic case, involve idealizations which must block the cascade.(4) This is the argument with which I take issue, and it is the topic of the next section.
3 Competence, performance and the explanatory cascade
Franks claims that 'competence theories involve an overextension of function, thereby failing to support a cascade for cognition' (Franks , p. 484). His reason for asserting this is most easily understood by considering his central example of a competence theory, Chomskyan linguistics.
As is well known, Chomsky draws a distinction between competence and performance. In an early discussion, he defines competence as the speaker/hearer's knowledge of his or her language, and performance as the actual use of that knowledge in concrete situations; and he says that performance directly reflects competence only if the speaker/hearer is unaffected by errors, memory limitations, distractions, and shifts of attention and interest in applying his or her knowledge of language in actual performance (Chomsky , p. 4). The notion of a speaker/hearer's competence involves an idealization which abstracts away from so-called performance limitations, and, according to Franks, it is this idealization which creates a mismatch between Level 1 function and Level 2 algorithm in the Chomskyan account. This mismatch is starkly illustrated by the limitations imposed by human finitude. As Franks quite rightly points out, '[w]e do not and cannot process expressions of unrestricted length or complexity' (Franks , p. 487); we do not have enough time or enough memory, for a start. But Chomskyan theory idealizes away from these limitations in describing our linguistic competence, and posits rules of grammar which give rise to an infinite language, 'with no limitation on the length of permissible strings, nor on their degree of internal complexity' (Franks , p. 486). The grammar provides a structural description for expressions that are too long and too complex for any human to process in real time. Hence, Franks argues, there is a mismatch between grammar and algorithm: the description of competence (the grammar) assigns structural descriptions to expressions we cannot process, so the function specified by the grammar cannot be mapped onto any algorithm that we actually execute. Computational function (Level 1) and psychological algorithm (Level 2) are not even extensionally equivalent, so the mapping required by the cascade of explanation is blocked. This is what Franks means by saying that 'competence theories involve an overextension of function' (Franks , p. 484).
The key idea behind this argument is that the very performance limitations which are idealized away in describing competence at Level 1 will have to be taken into account in describing actual algorithmic processing at Level 2. If this is right, it is the distinction between competence and performance itself that creates a mismatch between Level I function and Level 2 algorithm; the details of the linguistic theory are immaterial. Hence Franks draws a general moral: 'the classical cascade is incompatible with linguistic theory employing the competence/performance distinction: competence idealizes the performance function so as to block the cascade' (Franks , p. 488). Indeed, since the competence/performance distinction is not restricted to linguistic theory, this reasoning seems to support the conclusion that 'competence accounts issue in mismatches' (and so block the cascade) in cognitive science generally (Franks , p. 479).
4 A tale of two distinctions
We need to look more closely at Franks's argument that Chomsky's competence/performance distinction blocks the explanatory cascade through Marr's levels. The argument starts from the fact that, given Chomsky's definition of them, competence and performance are guaranteed to diverge for any actual subjects; performance directly reflects competence only in ideal speakers unaffected by the limitations which constrain the performance of real speakers. Granting that we have a divergence between competence and performance in the case of real people, the crucial question is why this should create a mismatch between Marr's Levels 1 and 2, as Franks claims. The answer, according to Franks, is that theories of competence just are theories of the function computed (Level 1), while theories of performance just are theories of the algorithm executed (Level 2) (see, for example, the passage from p. 487 quoted below). If Chomsky's distinction can be assimilated to Marr's in this way, the divergence between competence and performance in the case of real, finite human beings must create (in fact, must be) a divergence between Level I function and Level 2 algorithm. Franks puts it this way: 'the result of accepting what all parties to the debate do accept - that humans are finite entities with finite resources . . . is that the competence/Level 1 function overextends the performance/Level 2 function (qua psychological algorithm)' (Franks , p. 487). This mismatch between competence/Level 1 function and performance/Level 2 algorithm blocks the explanatory' cascade through Marr's levels.
This argument is driven by the idea that the competence/performance distinction can be assimilated to the computational/algorithmic distinction. This idea is a tempting one. According to Marr, a computational theory tells us what function a system computes, while an algorithmic theory tells us how it does it; according to Chomsky, a theory of competence tells us what a speaker knows, while a theory of performance tells us how that knowledge is put to use. Furthermore, it seems that a Chomskyan theory of linguistic competence specifies a generative procedure or function which assigns a structural description to linguistic expressions, just as a Martian computational theory specifies the function computed. And it seems that a Chomskyan theory of performance fills in the details of how the mapping from expression to structural description is accomplished in actual practice, just as a Marrian algorithmic theory supplies the details of how the function is actually computed. So it looks as though a performance theory is a detailed specification of the representations and algorithms used in actual processing, while a competence theory is a computational theory, an abstract specification of the overall function computed by these algorithmic means. Indeed, Marr himself says that the distinction between what is computed and how it is computed 'is roughly his [Chomsky's] distinction between competence and performance' (Marr , p. 28).
Furthermore, the assimilation of Chomsky's distinction to Marr's is prominent in discussions of the cascade of explanation. Dennett (, p. 74) suggests that what Chomsky calls a 'competence model' tells us what an information-processing mechanism is able to do, as Marr's computational level does, while a performance model reveals the underlying algorithmic mechanisms, as Marr's second level does. If it turns out that in specifying what the system does we have captured how it does it, we have 'a triumphant cascade through Marr's levels' (, p. 227). Clark (, p. 284) develops the notion of a cascade of explanation by bringing in Peacocke's Level 1.5 (Peacocke ). A Level 1.5 theory is so named because it specifies more than Level 1 but less than Level 2; it defines a class of algorithms by specifying the information drawn on in the computation of the function. Since a Level 1 computational theory specifies merely what function is computed, it defines a large and varied class of mechanisms (all those capable of computing the function in question). A Level 2 theory of representation and algorithm says how that function is computed, and hence defines a far more restricted class of mechanisms. A Level 1.5 theory defines an intermediate class of algorithms (those that draw upon the information in question). Unlike Dennett, Clark identifies Chomskyan competence theories with Level 1.5. But like Dennett, he sees the goal of classical cognitive science as being a triumphant cascade from competence theory to Level 2 implementations. According to this picture, the cognitive scientist's aim is to narrow down the equivalence class of algorithms specified at the competence or computational level until she homes in on the very algorithm which our cognitive system executes in actual performance.
Despite these apparent parallels between Marr's and Chomsky's distinctions, I shall argue that they cannot in fact be assimilated. Since they cannot, Franks's argument that the competence/performance distinction blocks the explanatory cascade fails.
5 Against assimilation
Marr's computational and algorithmic theories are accounts of a single system, couched at different levels of abstraction. The higher level theory says what function the system computes and why, while the lower level theory describes in detail how the system does it. Franks assimilates Chomsky's competence/performance distinction to Marr's computational/algorithmic distinction by depicting theories of competence and theories of performance in the same way - as accounts of a single system, couched at Marr's two levels of abstraction. But that is not Chomsky's distinction. As Chomsky stressed when introducing it, competence models and performance models are theories of different things, not theories of the same thing couched at different levels of description. Competence is the speaker/hearer's knowledge of her language, while performance is the actual use of that language in concrete situations. A theory of competence aims to describe a speaker/hearer's knowledge of language, but it does not aim to describe how that knowledge is put to use in real-time processing, in actually speaking and understanding. That is the task of a theory of performance, which must incorporate an account of how competence - knowledge of language - is put to use by perceptual and production systems. As Chomsky wrote in 1972, 'Competence . . . is one of the many factors that interact to determine performance' (, p. 117). More recently, he distinguishes between a cognitive system that stores information and performance systems that put it to use, as separate components of the language faculty (Chomsky [19951, p. 2).(5)
This understanding of the competence/performance distinction is not an idiosyncratic one, confined to its originator. In a paper which Franks cites as evidence that competence theories are advanced in a realist spirit, Fodor explains the distinction thus:
At heart, the competence/performance distinction is a distinction between kinds of explanations. 'Competence theories' account for facts about the behaviors and capacities of a speaker/hearer by reference to properties of his internalized grammar, whereas 'performance theories' account for facts about the behavior and capacities of a speaker/hearer by reference to interactions between the internally represented grammar and other aspects of the speaker/hearer's psychology. So, to cite the classic example, we explain the speaker/hearer's ability to understand and produce novel forms by reference to the productivity of the grammar he has learned, but we explain the speaker/hearer's inability to understand multiply center-embedded sentences by reference to interactions between the mentally represented grammar and the (short-term) memory he employs in parsing the sentences that the grammar generates (Fodor , p. 154).
Similarly, Stephen Stich explicates a general notion of competence theory in terms of interaction between different mental systems:
Theories that invoke the notion of competence attempt to explain actual behaviour (or performance) in a given domain by appealing to the interaction of a number of underlying mental systems. One of these systems, the one that is identified with the subject's competence in the relevant domain, stores a rich body of information or knowledge about the structure of the domain. The other systems are brought into play when the knowledge is used to accomplish some cognitive task. In the case of language, for example . . . it is hypothesized that speakers have a mentally represented grammar - a complex system of rules that specifies the grammatical properties and relations of sentences in the speaker's language. In making judgments about sentences, the internalized grammar interacts with the attention system, the motivation system, a short-term memory buffer, and other cognitive systems. On certain occasions one or more of these other systems may be responsible for the speaker's reporting a judgment that does not reflect the information encoded in the grammar. For example. the sentence the speaker is being asked to judge may be so long or contain so many levels of embedding that it overtaxes the resources of the short-term memory buffer (Stich , p. 185).
Both these authors fill out the distinction between knowledge of language and its use in terms of an internally represented grammar and other mental systems which interact with it when that knowledge is put to use. Because of the intervention of these systems, my performance or use of language will not always directly reflect my competence or knowledge of language. As Stich and Fodor note, one of the factors that interacts with competence is memory; we cannot process extremely long sentences, presumably because the human parser has limited memory resources. This means that there are sentences which are assigned a structural description by the rules of the language that I know, but are not assigned that (or possibly any) structural description by my parser. Speaking of 'a "parser" that incorporates the l-language along with other elements - certain strategies and procedures, a certain organization of memory, and so on'. Chomsky (, p. 19) says:
The parser associates structural descriptions with expressions; the I-language generates structural descriptions for each expression. But the association provided by the parser and the I-language will not in general be the same, since the parser is assigned other structure, apart from the incorporated I-language. There are many familiar examples of such divergence: garden path sentences, multiple self-embedding, and so on.(6)
This divergence between the mapping generated by the I-language and that provided by the parser is an example of the mismatch which, according to Franks, threatens the explanatory power of Chomskyan linguistics. But Chomsky explains the divergence in terms of the interaction between competence, or I-language, and the structure of the parser, one of the mechanisms involved in putting language to use.(7) According to the Chomskyan view, the divergence is simply an illustration of the fact that the I-language or internalized grammar is only one of the factors contributing to linguistic comprehension.
The distinction between a grammar or I-language and a parser yields a way of capturing the difference between Franks' conception of linguistic theory and that of Chomsky. According to Franks' picture, a grammar (a description of competence) is an idealized description of the mapping computed by the parser when language is put to use in performance. He then goes on to assimilate the mapping generated by the grammar to Marr's computational level, and that computed by the parser to Marr's algorithmic level. The divergence between the mappings provided by grammar and parser then appears as a mismatch between the function specified at the computational level and the procedure executed at the algorithmic level, a mismatch which blocks the explanatory cascade. According to Chomsky, by contrast, a grammar is a non-idealized description of a 'system of knowledge of language attained and internally represented in the mind/brain' (Chomsky , p. 24) which interacts with other factors (such as the memory resources of the parser) when language is actually used. The divergence between the mappings provided by grammar and parser is a result of the fact that a grammar is not a parser.(8)
One further consideration may help to illustrate the difference between Chomsky's and Matt's distinctions. If knowledge of language and the use of that knowledge are distinct, it is at least theoretically possible that a mind/brain could know a language in Chomsky's sense of having competence, but lose the ability to use that knowledge (the most extreme case of performance failing to reflect competence). As Chomsky says in defending the distinction, '[a]bility to use language may improve or decline without any change in knowledge. This ability may also be impaired, selectively or in general, with no loss of knowledge, a fact that would become clear if injury leading to impairment recedes and lost ability is recovered' (, p. 9). What is described by Marr's two levels cannot be dissociated in this way, precisely because they are two levels of description of the same process. It is not possible that a mind/brain could retain the ability to compute the function specified at the computational level while losing the ability to execute any algorithms for computing that function. Theories of performance are theories about the actual process of using linguistic knowledge in speaking and hearing (among other things), a process which is affected by many other factors besides competence. Theories of competence are not theories of a process at all; they are about a speaker/hearer's knowledge of language (which Chomsky takes to be a state of the brain). This knowledge may be specified by giving rules which generate pairings of sentences and structural descriptions; but even if (impossibly, given performance limitations) in actual speech perception the same structural descriptions were constructed for the same sentences by the execution of the rules specified in the grammar, the projects of specifying knowledge of language and of specifying its use in actual performance would be different.
In the penultimate section of his paper Franks considers two rejoinders to his argument, both based on the claim that '[c]ompetence and performance are two separate aspects of the faculty for producing and understanding language' (Franks , p. 597). The second of these rejoinders comes closest to mine, since it takes it that 'the level of abstraction away from performance mechanism and implementation that competence theories demand is not to be properly construed in terms of different levels of description of the kind discussed' (Franks , p. 498). However, this second rejoinder still incorporates the assimilationist assumption that theories of competence are abstract or idealized theories of performance mechanisms. This is evident from Franks' reply to it, which is that the proponent of the rejoinder cannot escape the task of 'determining which aspects of the competence function and algorithm are idealizations of the performance function and algorithm' (Franks , p. 499). In my view this task is an artefact of construing a specification of competence as an idealized description of processing, rather than construing it as a nonidealized description of the speaker/hearer's knowledge of language.
I have been arguing that Chomsky's distinction between competence and performance cannot be assimilated to Marr's distinction between the computational and algorithmic levels in the way required by Franks' argument. A description of competence - a grammar - is a non-idealized description of a speaker's knowledge of language, not an idealized description of the function computed by the speaker's parser or speech perception system when language is used. Since the grammar is not intended as a description of the function computed by the parser. the divergence between the two mappings is not a mismatch between levels 1 and 2, and does not block the explanatory cascade.
If this is right, it is not surprising that idealization away from processing limitations, which plays such a central role in Franks' argument, plays very little part in the Chomskyan distinction between competence as knowledge of language and performance as its use. On Franks' picture, a competence theory presents an idealized description of performance; competence just is the performance of an idealized agent, not subject to processing limitations. But in Knowledge of Language, for example, the only idealizations Chomsky mentions in relation to competence are the positing of 'an idealized "speech community" that is internally consistent in its linguistic practice' (, p. 16), the members of which speak a language that is 'a "pure" instance of UG', ibid., p. 17) and share the same 'property of mind described by UG' (ibid., p. 18). There is no need for idealizations of the processes of speech perception or production, since these are not the concern of the theory of competence. When idealizations away from processing limitations such as 'memory limitations, shifts of interest . . .' (Chomsky , p. 3) are mentioned, the point is that performance directly reflects competence only under such an idealization (ibid., p. 4). Actual linguistic performance is the result of 'the interaction of a variety of factors, of which the underlying competence of the speaker-hearer is only one' (ibid., p. 4). Though linguistic performance is a powerful source of evidence about this underlying competence, competence cannot be read off performance. That is why the linguist must idealize away from the effect of processing limitations in trying to work out what the underlying competence is.
What, then, is the relation between a subject's competence, or knowledge of language, and her actual use of language in speaking and comprehending? Or, as Merrill Garrett puts it, 'what relation holds between formal theories of grammatical structure and theories of the real-time computational processes that underlie human language use' (Garrett , p. 139)? This is a very difficult question, being a version of what Franks calls 'the slippery question of grammars' "psychological reality" ' (Franks , p. 486).(9) But we do not need to know what the relation between competence and performance is in order to know that it is not the relation between Marr's computational and algorithmic levels. And if Chomsky's distinction is not Marr's, then Franks' argument fails.
Department of Philosophy Birkbeck College University of London Malet Street London WC1E 7HX
1 Dennett's main concern in the paper cited is classical cognitive science and the Language of Thought hypothesis rather than Marr's levels; this is why he speaks of the classical cascade. But the problem Franks raises for competence theories is, if genuine, so general that it applies to connectionist and classical accounts alike. On Franks' view, competence accounts credit subjects with the ability to compute functions they cannot in fact compute, and no account. connectionist or classical, can explain subjects' possession of an ability they do not have.
2 These mappings will of course be one-many.
3 An idealization which operates at all levels need not cause mismatches, and so need not block the cascade. Then the mismatch is between what the three-level cascade explains and what needs to he explained, as Franks notes (, p. 483). We wanted an explanation of actual human cognitive capacities. and we only have an explanation of idealized human cognitive capacities. I shall concentrate on mismatches between levels, since these are the focus of Franks' discussion of competence theories of language.
4 Franks says that it is 'less a contingency and more a necessity that competence accounts issue in mismatches' (, p. 479). and that 'the idealizations explicit in competence theories render them unable to support a classical cascade of explanation' (ibid., p. 499).
5 These two quotations reveal a shift in Chomsky's conception of performance, from overt linguistic behaviour in the earlier, more 'externalist' (in the sense of E-language: Chomsky , p. 20) works, to inner processes of production and comprehension in the later, explicitly 'internalist' (in the sense of I-language) works. On the earlier conception, performance qua overt behaviour is the product of competence interacting with other factors (such as memory limitations, articulation errors, etc.). On the later conception, the performance and competence systems interact to produce overt behaviour. These differing notions of performance are reflected in the quotations from Fodor and Stich which follow in the text. Stich explicitly reserves 'performance' as a label for overt behaviour, while Fodor's 'performance theories' appeal to interactions between grammar and other psychological factors.
6 The passage continues: 'There is much confusion about this matter. It is sometimes argued that the language (or "grammar") should be identified with the parser, taken as an input system in something like Jerry Fodor's sense' (Chomsky , p. 19). One reason why it is a mistake to identify the grammar with the parser is that knowledge of language is not used only in parsing; it is 'a central resource, with many applications', as Higginbotham puts it (, p. 124). The fact that knowledge of language is a central resource is one of the grounds on which Higginbotham (, p. 360) questions whether competence theories of language are Level 1.5 theories.
7 Chomsky (, p. 11) suggests that differences between grammaticality (which depends on the grammar) and acceptability (which depends on the parser) can shed light on the organization of the parser.
8 The parser is a mechanism which computes representations of the syntactic structure of incoming speech signals. If it is a classical information-processing device, it can presumably be understood at Marr's three levels, as computing a decidable function, specified at level 1, by executing an algorithm, specified at level 2, realized in neural hardware, specified at level 3.
9 Franks says that his arguments about competence theories and the failure of the explanatory cascade 'do not require any particular view of this [sc. question]' (p. 486). However, his arguments do require us to take the view that a grammar aims to specify the function computed by the real-time computational processes of the parser, and this is false, as the quotation from Chomsky (, p. 19) shows.
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|Title Annotation:||response to Bradley Franks, British Journal for the Philosophy of Science, v. 46, p. 475|
|Publication:||The British Journal for the Philosophy of Science|
|Date:||Dec 1, 1998|
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