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WD_348/ 2007
(  Satoshi Kinoshita )
| Series: | Works on paper: Drawings 4 | | Medium: | oilstick on paper | | Size (inches): | 25.6 x 17.7 | | Size (mm): | 650 x 450 | | Catalog #: | WD_0348 | | Description: | Signed, date and copyright in pencil on the reverse.
The Legacies of Operationism and Positivism in Psychology
Theory & Psychology 1992 Vol. 2(3): 363-390
The Misleading Concept of Cognitive Competences
Angus Gellatly, Department of Psychology, School of Human Development, University of Keele, Staffordshire, UK.
Abstract. Descriptions of action/cognition can be given at various different levels. For heuristic purposes, three levels are identified: the behavioural, the information-processing and the level of summarizing what an individual is capable of (competences). In cognitive psychology competences, principles, rules or strategies are commonly attributed to individuals by way of 'explaining' their accomplishments. The present paper argues that such attributions have value mainly as a form of shorthand, but otherwise tend to mislead. Various controversies concerning the attribution of cognitive competences (inference-making, number competence, mnemonic strategies, theory of mind) are analysed and are shown to be empirically unresolvable because they involve the conflating of different levels of description. It is suggested that the temptation to make attributions of cognitive competences follows from three habits of mind; these involve the nominalist fallacy of reifying classificatory terms, and the mistaking of the reified entity for an individual endowment. A similar argument has been made in the case of 'intelligence' by Howe (1988, 1990). The most effective challenge to the idea of attributing competences to individuals comes, in fact, from within cognitive psychology itself, yet the idea persists and even thrives. By citing examples of research which clearly demonstrate the misleading nature of the idea of individual competences, it is intended to encourage future avoidance of it.
Introduction
In recent articles Howe (1988, 1990) has argued that the notion of intelligence, although useful as a descriptive term, has no value as an explanatory concept. We may describe as intelligent an individual who scores highly on an intelligence test, but this does not explain why or how they achieved a high test score. Howe points out, however, that the habit of treating intelligence as an explanatory concept has a long history in psychology. In the present paper the explanatory role accorded to a wide range of so-called cognitive competences will be similarly criticized. It will be argued that wherever an individual is attributed with possessing a [p. 363] competence, a principle, a strategy or a rule, there we are likely to find description masquerading as explanation. What follows is by no mea intended as an indictment of cognitive psychology. On the contrary, the claim will be that the best efforts of cognitive psychologists serve counteract certain habits of thought that are perhaps endemic to language use. Nevertheless, it will be argued that just because these habits are freely available they exert a pernicious influence upon theorizing in cognitive psychology.
The issues to be raised can be clarified by distinguishing three levels which action/cognition is typically discussed. (These levels are introduced only as a heuristic device; they are not exhaustive, nor should they be reified.) The first is the level of actual performance on a task. This is the descriptive level of the behaviourist and frequently includes some elements of quantification. Second is the level of the mechanisms or processes that mediate task performance. This is the information-processing level '' description which is prevalent in cognitive psychology. It can be said that the rise of cognitivism follows from the acceptance that Level 1 descriptions do not suffice on their own; to understand action/cognition we have to be prepared to deal with unobservable processes and representations.
Thirdly, there is a level of summarizing what a person knows or is capable of. This is the level of description for which problems typically arise, with description and explanation tending to become confused. It also the level of competences, principles, rules, etc. which frequently get attributed to individuals. The problems that this third level of description raise are associated with a whole series of interrelated and mutual] implicative cognitive moves. These moves, or habits, derive from the Cartesian individualism that underwrites most of cognitive psychology. For present purposes just three of the habits need be identified.
The first is the nominalist fallacy, which typically consists in reifying classificatory terms so that abstractions such as categories, principles and rules become concretized, and in some cases even attributed with casual powers. The tendency to indulge in nominalism may pose an inevitable problem for any theoretical/linguistic enterprise; and certainly nominalism can sometimes function as a useful form of shorthand, so that merely cataloguing examples of it in the writings of cognitive psychologists would be an unproductive exercise. It is the present contention, however, that nominalism runs much more deeply in cognitive theorizing than a form shorthand ought to do.
The second of the three habits is itself almost another form of the nominalist fallacy. It is the habit of assuming that classificatory terms such as categories, principles and rules are somehow able to legislate their own future applications. The assumption derives from the classical, or objectivist, theory of categories, according to which category membership is an all- or-none affair determined by the presence or absence of criterial attributes [p. 364] (Bloor, 1983; Lakoff, 1987). The philosophical debate concerning objectivism need not detain us here. Because the assumption of self-legislation is so prevalent in our usual habits of thought, however, and because much of what follows hinges upon rejection of that assumption, it will be helpful immediately to provide an example to act as a contradiction of it.
The example, previously used by Bloor (1976), concerns the question of whether there are more whole numbers or more even numbers. An educated and numerate adult might reasonably answer that there must be more whole numbers because the set of whole numbers already contains within itself the set of even numbers. In other words, the answer is justified by assimilating the problem to the principle of class inclusion, which seems fair enough. As it happens, however, mathematicians long since resolved that the problem should be assimilated not to class inclusion but to the principle of one-to-one correspondence. In fact, an infinite set is defined as one the whole of which can be placed in one-to-one correspondence with a part of itself.
Naturally, a single example from an abstruse field such as mathematics will carry only so much weight. Yet other examples will confirm what this one demonstrates, namely that 'correct'—by which is meant 'accepted'— application of a principle cannot be derived from analysis of the principle itself. No more can it be a matter of individual choice. Usage of principles, like usage of classificatory terms, is a social matter determined by consensus. This is not to say that either form of usage is arbitrary. To win acceptance usage must serve some worthwhile function, theoretical or practical, as well as being defensible in terms of other criteria such as parsimony, elegance, novelty or consistency with tradition. The important point is that such matters are only ever settled via a consensus that is always liable to future change. In this paper it will be shown that many debates concerning the attribution of cognitive competences are actually disputes about usage of classificatory terms, and that they are not, therefore, susceptible to empirical resolution.
The third undesirable habit is also clearly, if complexly, related to the first two. It is the habit of mistakenly taking concepts that are elaborated in talk and social practice for individual endowments. In other words, there is a tendency not only to reify terms elaborated in psychological discourse, the first habit, but then to attribute the reified entity to individual persons. The individual is assumed to somehow possess a competence, principle or rule, and this is then invoked as the 'explanation' for particular behaviours. the practice of explaining intelligence test scores as due to intelligence is a prime example of this habit (Howe, 1988), but other examples abound. Evidence of logical reasoning may be 'explained' by reference to logical competence, or successful counting behaviour by reference to the possession of certain counting principles. In what follows numerous examples of this type of 'explanation' will be cited. [p. 365]
Again, as a form of Level 3 description the attribution of competences or principles or rules is essential to normal communication. It is often necessary to summarize someone's attainments, and we frequently do this by at least implying a competence, e.g. 'He has learnt to count', 'She can programme in Turbo C'. But while this kind of description is admirably suited to certain practical purposes (see the section on 'Diagnosis an: Competence'), it becomes a hindrance when a competence is treated as an unproblematic theoretical entity and/or mistaken for a Level 2 explanation.
The notion of competences also has appeal when introduced in the context of a competence/performance distinction. The distinction meshes well with certain common experiences, e.g. 'I lost my place in the calculation when you asked me the time', implying that my competence for calculation should remain unimpugned. Givon (1979) points out that it also makes sense in terms of the initial abstraction and simplification require: for the analysis of any complex phenomenon. But, as Givon goes on the argue, when an abstract competence is reified and becomes a principal object of study in its own right, then the notion has become damaging: Givon's comments were directed at the use of the notion of linguistic competence in theoretical linguistics, and this is probably the context most readily brought to mind by the term 'competence'. For reasons of lack of expertise and because arguments paralleling many of those to be made have already been put forward with respect to linguistics (Broadbent, 1973: Givon, 1979, 1989; Lakoff, 1987; Stabler, 1985), this paper eschews discussion of that subject area. It is worth remarking, however, that the distinction becomes problematic in other contexts also. Most notably, as we will see, in the Piagetian literature.
The habit of attributing competences, principles or rules is, however, widespread throughout cognitive psychology. It is seen wherever individuals are assumed to 'have', for example, transitivity, conservation, number competence, an object concept, abstract thinking, principles such as one-to-one correspondence, rules such as logical rules or schemata, or even mnemonic strategies. It is on such topic areas that the present paper will concentrate.
The Case of Transitivity
Any of a number of subject areas in cognitive psychology could serve to provide an introduction to the principal arguments and general outlook to be developed. However, the debate over transitivity provides a particularly: good point of entry because the exhaustively detailed empirical and theoretical treatments of transitive inference-making happen to illustrate with exceptional clarity various features which also characterize other [p. 366] debates in cognitive psychology. One of these is the reiterative structure of the argument: much of the controversy over transitivity since 1971 can be read as a recycling and amplification of ideas already given compressed expression in the earlier writings of Piaget. It also reprises an earlier debate over the age at which children show conservation (Hall & Kaye, 1978). A second feature is the frequent occurrence of nominalist thinking. Adopting what Johnson-Laird (1982, 1983, 1986) has dubbed the doctrine of mental logic, many participants in the debate have written as though 'true' transitive inference-making becomes possible through the acquisition of a mechanism of inference-making, or as a result of the development of understanding about transitivity. (Defenders of Piaget often view this as a mistake due to interpreters of his work—see below.)
A further feature of the transitivity debate which is repeated in other areas of controversy is the appearance of a distinction between implicit and explicit cognitive capabilities. According to Chapman (1988), the distinction is rooted in the difference between being able reliably to solve a problem and having the ability to justify one's solution verbally. Chapman believes these should not be understood simply as implicit and explicit expressions of one underlying competence, as suggested in the work of Braine (1959) and Brainerd (1973). Be that as it may, the distinction is one frequently made, and the position taken in this paper is that it is introduced as part of negotiations over the usage of classificatory terms.
Mention of this point leads us to one further feature of common structure amongst different debates in cognitive psychology, which is that all of them can be seen to revolve around issues of classification. For example, as represented by participants in the controversy, the debate over transitivity concerns the age at which children can be said to 'have' transitivity, or to 'understand' transitivity, or to 'make' transitive inferences. What it turns out to be about, it will be argued here, are two problems of classification. The first of these is the problem of what are to count as exemplars of transitive inference(TI)-making, and indeed of TI itself. The second concerns the criterion for 'having' or 'understanding' transitivity. Should it be the ability to make some particular TI or should it be something else? Participants to the controversy attempt to adjust the classificatory network and to negotiate criteria in such a manner that empirical findings are made consistent with their own theoretical commitments. Analogous questions of classification lie at the heart of all the disputes to be examined later. For the present, however, it is time to put some flesh on our skeletal argument.
A transitive inference is one in which two pieces of information (A>B, B>C) are combined to yield a conclusion (A>C). Piaget (1921, 1971; Piaget, Inhelder, & Szeminska, 1960) has argued that preoperational children—those below the age of 7 or 8—are unable to make such inferences because they lack the necessary cognitive structures (competence) [p. 367] He demonstrated the deficiency in—amongst others—two way] the first a child was presented with two sticks, A being longer than B. A was then removed and B was shown together with a shorter stick: The child was then asked how A compared with C but was typically un) to answer correctly. In the second, active, test a child was shown a tow~ blocks on a table and was asked to build a second tower of the same height on the floor. A stick equal in length to the first tower from the to] bottom was available, and the purpose of the experiment was to see ii: child would spontaneously use it as a measuring device. In other way would she construct a transitive sequence (A = B, B = C, A = C)] would she, perhaps, rely on an unreliable by-eye comparison of the heights of the two towers.
Although preoperational children do usually fail both of these test: might be that they could still make transitive inferences under other conditions. Bryant and Trabasso (1971) suggested that failure on the passive test might reflect, amongst other sources of difficulty, a failure: remember the premisses (A>B, B>C) rather than inability to draw] correct conclusion. Building on the methodology of Braine (1959) and Youniss and Murray (1970), Bryant and Trabasso gave children intensive training on the premisses of a series of 5 sticks (A>B, B>C, C>D D>E). Only once children had passed a test of memory for the premisses were they asked to make the crucial comparison between B and D, and it turned out that under these conditions even 4-year-olds performed well. Bryant and Trabasso therefore concluded that transitive inferences c: be made a lot earlier than Piaget had asserted to be the case.
This conclusion has, however, been subject to a bewildering variety of criticisms.
Some of the earliest opposition came from Youniss and Furth (193 who made a number of methodological criticisms of the Bryant and Trabasso study. In particular, they proposed that during the training period children formed an ordered mental image of the series of sticks: then read off the comparison of B and D from the image. This procedure they argues, would involve only a ‘sublogical’ or 'fiqurative' inference contrasted with 'true', or 'operative', transitivity such as is called for in the tower construction task. In other words, one way in which Youniss] Furth attempted to protect Piaget's theory against Bryant and Traba: claim was by seeking to establish a definition of TI-making that would rule out the offending case. In this respect they were doing no more than repeat Piaget's (1968) strategy of invoking the figurative/operative distinction grounds for discounting precocious performances. However, in the light the preceding discussion of classification, it is worth noting that the excluded case would be considered by many to constitute a prototypical exemplar of the class of TI-making behaviour.
It is also worth noting how Piaget, and also Youniss and Furth, interpret [p. 368] some performances on the towers test. Children below the age of 6 or 7 are inclined either to make visual comparisons or else to use imprecise measuring tools such as arm span, rather than utilizing the available stick. Piagetians interpret both of these tendencies as evidence for a lack of understanding of transitivity. Yet the attempt to use arm span as a middle term in a series surely suggests some grasp of transitivity (Bryant, 1974), even if coupled with an overoptimistic assessment of the reliability of the technique. Once again, what we observe are theoretically motivated adjustments to the threshold for class membership.
A similar refinement of theoretical terms can also be used to counter the claim that a TI based on an ordered mental image is only a 'sublogical' inference. It can be argued that the propensity to construct such an ordered image already requires that a subject possess an implicit sense of transitivity, even if this may show itself only under specific experimental conditions (Perner, Steiner, & Staehelin, 1981). The move here is to broaden rather than narrow the class of transitive performances. Transitivity is to be signaled not only by inference-making but also by image construction. But this move can, in its turn, be challenged by the claim that ordered images may be constructed on the basis of supposedly non-transitive strategies such as 'labelling' (Breslow, 1981; de Boyson-Bardies & O'Regan, 1973) or the coding of absolute stimulus values (Perner et al., 1981). Halford (1984) opines that the evidence on this point remains ambiguous but the present aim is not to try to settle the issue. On the contrary, the claim will be that such issues cannot in principle be settled on empirical grounds.
Another response to the Piagetians' attempted narrowing of the definition of TI-making was given by Trabasso (1975, 1977). He presented evidence that adults, as well as children, use imagery on 5-stick problems. Presaging the arguments of Johnson-Laird (1982, 1983, 1986), Trabasso proposed that the rules of logic do not provide an adequate description of inference-making. If the inferential performances of 4-year-olds were to be judged as 'sublogical', so too would have to be many apparent instances of TI-making by adults. This work by Trabasso constitutes one of the earliest and best demonstrations of how a misleading Level 3 description of behaviour can be replaced by a Level 2 explanation.
Taking a different tack, Bryant and Kopytnyska (1976) met criticisms of the Bryant and Trabasso study by demonstrating that even 4-year-olds are capable of a degree of operative transitivity. They showed that children who failed on the tower construction test would sometimes make spontaneous use of a measuring stick to compare the depths of two holes drilled into blocks of wood. That is, when the temptation to make visual or arm span comparisons was absent some young children revealed a spontaneous understanding of measurement and transitivity. This result can be seen as confirming the interpretation of arm span comparisons as evidence of transitivity. [p. 369]
Between them, therefore, Bryant and Trabasso argued that the stricted definition of TI fails to capture the psychological reality of how inferences are made, that it excludes too much, and that, anyway, it fails to draw an absolute distinction between preoperational and supposedly more advanced children. Yet these varied responses met only some of the criticisms that have been levelled against the original study and theoretical justification.
The initial supposition of Bryant and Trabasso (1971) was that young children tended to fail passive TI problems because their memory the premisses was inadequate. However, Halford and Galloway (1977 were able to show that 54 percent of those young children who could recall the premisses of a TI problem, when asked to do so, did not then draw the correct conclusion. Conversely, Russell (1981) found that 32 percent of those who gave the wrong answer to the test question justified their responses by recalling the premisses correctly, while none did so by incorrectly recalling premisses. These findings are surprising given that Bryant and Trabasso (1971) and others (see Trabasso, 1977) had found good correlations between the retrieval of premisses a: performance on the B-D comparison. (Though see Brainerd and Kingm] 1984.) They may, perhaps, be seen as strengthening the argument that Bryant and Trabasso's training phase served some purpose other than simply ensuring premiss retention (Thayer & Collyer, 1978), name] image construction. However, the argument that image construction itself evidence of implicit transitivity is one means for defusing this objection.
Another line of attack on the original Bryant and Trabasso study and its interpretation has involved the argument that asking children to compare the B and D sticks does not constitute a sufficiently rigorous test transitivity. Jager-Adams (1978) had two groups of children who under went training with sets of sticks that differed in ways which need no concern us here. Both groups did well on the B-D comparison. But when given the verbal description of a sixth stick (6>C, 6>B) only one group of subjects was able accurately to compare its length with that of all other sticks in the series. Jager-Adams appears to have been saying that only the stick insertion test truly identifies transitivity. A not dissimilar claim was forwarded by Chalmers and McGonigle (1984) on the basis of studies employing both 6-year-old children and squirrel monkeys as subjects on five-term problem involving coloured tins of differing weights (see als) below). They found high levels of success on the B-D comparison for both groups of subjects, but poor performance when subjects had to order the set of three items, B, C and D. They concluded that the latter was the true test of transitivity and that the B-D comparison can be done by non-logical means. McGonigle and Chalmers (l 977) had previously proposed that this must be the case since squirrel monkeys succeed on the B-D comparison [p. 370] and squirrel monkeys are, they claim, incapable of logical reasoning. This part of their argument begs all of the questions concerning the psychology of inference-making but it provides nice, clearcut examples of both how preconceptions enter into the debate and how the criterion of transitivity is open to negotiation. The task used by Chalmers and McGonigle also illustrates the problem of determining what is and is not a TI task. As already mentioned, they used coloured tins of differing weight. However, only two absolute weights, heavy (H) and light (L), were employed, the choice of one always being reinforced. When tins A and B were presented A was (H) and B was (L); when B and C were presented B was (H) and C was (L); and so on. Since in the subjects' experience B was sometimes (H) and sometimes (L) —the same being true of D—it could be argued that when B and D were presented together there was no logical grounds for supposing which would be (H) or (L). In other words, one might well deny that this is a TI task at all (see also below).
Perhaps the most thorough attempts to discredit Bryant and Trabasso's claim that 4-year-olds can make TIs have been those of Halford (1984) and Chapman and Lindenberger (1988). In a series of studies Halford sought to demonstrate that children below the age of 5 (rather than 7 or 8, as Piaget would have claimed) are unable to solve problems in which they must integrate two premisses. Halford gave his subjects extended experience of ordering coloured sticks of differing length, both when these were visible and when they were hidden in coloured cigar tubes of uniform length. But instead of intensive practice on the actual premiss pairs, as given by Bryant and Trabasso, subjects had access to a memory board on which the premiss information was represented. Under these conditions (Experiment IV) 4-year-olds did not exceed chance levels of success on the B-D comparison. Since in other of the experiments 4-year-olds had made successful ordering decisions when only a single premiss had to be considered, or when two premisses could be considered in succession, Halford interpreted their failure on the B-D comparison as demonstrating the hypothesized inability to integrate premisses.
Although it is not possible to do justice to the complexity of Halford's theorizing and his experimental designs in the space available here, three points are worth making about his argument. First, it would appear that the training phases that subjects underwent in all of his experiments could have encouraged the habit of making ordering decisions on the basis of consulting a single premiss on the memory board, or else pairs of premisses
successively. That is, subjects might have learnt that premiss integration was not called for by the tasks being set them, and the youngest subjects may have failed to appreciate that this condition no longer applied when the crucial tests were given to them. Secondly, and following from the previous point, the demonstration that 4-year-olds failed to integrate pairs [p. 371] of premisses in Halford's task does not necessarily mean that they would fail in other circumstances. Cole, Gay, Glick and Sharp (1971) showed that adult subjects who failed one test of premiss integration were able to solve a logically isomorphic version of the task which employed different materials. Reasoning performance, both for children and for adults, is notoriously task-specific. Thirdly, notions of what are to count as examples of premiss integration could become extremely elastic in just the ways that notions of what is to count as TI have.
Rather similar arguments were presented by Chapman and Lindenberger (1988). Following Brainerd and Kingma (1984), they proposed that young children solve Tl problems only when the experimental procedure allows judgements of length to be based on some other variable such as spatial position ('Things get bigger to the right'). They showed that children who succeeded on such tasks did very much worse on 'standard' tasks requiring premiss integration. Again, shortage of space does not allow for doing justice to their paper. But the second and third of the above comments clearly apply once more. And it is also notable that Chapman and Lindenberger report only the number of children who gave both a correct judgement and a valid justification for their judgement on the 'standard' task. The overall picture might be more clear if numbers making only the correct judgement were also reported.
Yet one other defence of the Piagetian position on TI was mounted by Breslow (1981). Following Piaget (1971), Breslow emphasized that being able to solve TI problems is not alone a sufficient criterion for 'having' transitivity. To be credited with the concept the child must appreciate the necessity that the conclusion (A>C) follows from the premisses (A>B, B>C). This further attempt to negotiate the criterion for transitivity will not be scrutinized at this juncture. Appeals to a criterion of necessity are not confined to the identification of transitivity alone and they will be dealt with subsequently in a more general context.
Now that the debate over transitivity has been presented at some length, the relevance to it of the three habits of thought described in the introduction can be assessed. First, it is apparent that nominalism is rampant in the debate. The concepts of TI and TI-making have been unmistakably reified by many of the participants in the debate. Secondly, the range of application of the concepts has, at least on the surface, been treated as unproblematic by many of the participants. Despite the intensive efforts to effect adjustments in the classificatory network pertaining to transitivity, little overt acknowledgement of the real nature of these maneuvers has been forthcoming. The debate over transitivity has been presented as an empirical issue. As a consequence, there has, thirdly, been an attempt to prove that transitivity is a type of competence that an individual either does or does not have. Despite extreme divergence in the . criteria that have been proposed for attribution of the competence, the gap [p. 372] between the actual conduct of the debate and its associated rhetoric has passed almost unremarked.
Transitivity has been debated in terms which reflect the cognitive habits previously identified and the individualistic bias of cognitive psychology. Having established the transitivity debate as a paradigm of how theoretical disputes in cognitive psychology are sometimes conducted, we can now go on to examine the structures of some other disputes within the discipline.
The Doctrine of Mental Logic
The Piagetian position on TI is just one instance of a general tendency to ascribe logically acceptable reasoning performances to the operation of a mental logic. Such accounts of reasoning were explicitly espoused by, amongst others, Kant and Boole. More recent variants have been proposed by Braine and Roumain (1983), Fodor (1980, 1983), Henle (1962, 1981), Rips (1983, 1986), and Sperber and Wilson (1986); and the doctrine crops up also in the writing of developmentalists such as Flavell (1985) and Gelman (1978; Gelman & Baillargeon, 1983).
Once again, Piagetian apologists argue that Piaget's structural analysis of reasoning does not imply commitment to a mental logic (e.g. Chapman, 1988; Overton, 1990). Nevertheless, to see the similarities between the debate on TI and that on the role of logic in adult reasoning, we can begin with questions of definition. Just as attempts have been made to broaden or narrow the definition of TI to suit the diverse requirements of different theorists, so too the definition of what should or should not count as inference has been historically a source of contention (Gellatly, 1988). For example, Mill (1875) claimed that all true inference-making was inductive in character rather than deductive. This led him to argue that what sometimes pass for inferences should not be classed as inferences properly so-called. He provided a number of examples, one of which was the move from' All A are B' to 'Some A are B'. Because the second proposition does not go beyond the first but merely repeats in different words part of what was already asserted, Mill said this should not count as an inference. Similarly, he rejected the following classic textbook example of syllogism:
(1) All men are mortal.
Socrates is a man.
---------------------------------
Therefore Socrates is mortal.
His grounds were that the first premiss already includes the proposition asserted in the conclusion. For if there were any doubt as to the mortality of Socrates, or any other man, the same degree of uncertainty would hang [p. 373] over the assertion that 'All men are mortal', acceptance of which forms the basis on which the syllogism proceeds. We have here, then, an excellent example of a theoretically motivated attempt to exclude exemplars from a class of which they are usually considered prototypical. Similar maneuvers occur, as we will see, in relation to the broadening or narrowing of the definition of inference-making itself.
Psychologists engaged in studying reasoning performance frequently make use of formal logic problems such as syllogisms. However, as judged by conventional criteria of correctness, performance on such tests is often extremely poor. Non-literate and unschooled subjects almost invariably fail to adopt the appropriate attitude to such problems (Scribner, 1977), and even highly schooled subjects may draw invalid conclusions or else fail to draw conclusions that are warranted by the premisses given to them (e.g. Henle, 1962). Such behaviour is not usually interpreted as proof of an inability to make inferences. If the reasoning of the subjects is examined carefully, it is generally found to be valid for the problem-as-tackled if not for the problem-as-intended-by-the-experimenter (Henle, 1962; Scribner, 1977). Similarly, the informal speech of both unschooled subjects (Scribner, 1977) and schooled subjects (Braine & Rumain, 1983) may be taken to exhibit exactly the forms of inference that formal tests are intended to elicit. A problem arises, however, when mental logicians like Henle or Braine and Rumain wish to explain such informal reasoning—or, indeed, reasoning on formal problems—by appeal to the operation of a mental logic. What the mental logician does is to cite a performance that can be judged to have the form of a particular inference schema, then attribute to the individual a representation of that schema which is itself then held to explain the very same performance from which it was adduced.
Clearly this is a circular argument. Refutation is impossible because failure to exhibit schema-consistent behaviour when it might be hoped for can always be explained as some kind of performance failure rather than as lack of competence, as in the above case of formal problems. At the same time, there are cases where a mental logician may wish to withhold an ascription of inference-making even when schema-consistent behaviour has been exhibited. For example, where a subject appears to have solved a problem by remembering the answer, or guessing. Again, where an animal's behaviour can be characterized in terms of an inference schema (Gillan, Premack, & Woodruff, 1981), mental logicians might wish to argue that the behaviour was mediated by supposedly non-logical processes. As mentioned earlier, this was precisely the position of Chalmers and McGonigle (1984) in respect of squirrel monkeys succeeding in their Tl task. It is also, of course, the position of Piagetians when, still intent on denying logical capabilities to the young child, they introduce a distinction between sublogical processes and supposedly logical processes.
The problem for the mental logicians is that they are unable to come up [p. 374] with truly principled reasons for the demarcations they wish to make. On the one hand, favoured groups, usually human adults, are attributed logical competence (Level 3) on the basis of schema conforming, or schema charakterizable, performances (Level 1) while, on the other hand comparable performances by non-favoured groups, generally children, animals or machines, are discounted on the basis of process analyses (Level 2) demonstrating that rules of mental logic were not employed. The fact is, however, that process analyses are equally destructive of any mental logic account of adult human reasoning. This is the force of Trabasso's (1975) analysis of TI-making and Johnson-Laird's (1983) analysis of syllogistic reasoning. Mental logicians have criticized Johnson-Laird's theory on the grounds that rules of logic are smuggled in through the back door (Braine & Rumain, 1983; Rips, 1986). They point out that operations performed on the models are characterizable as instances of the familiar logical schemata. But this is just that circular argument that if a performance instantiates a schema it must have been generated by the schema. Process (Level 2) analysis of performance dispels this notion just as readily in the case of the programme as for monkeys or children or, indeed, adults.
We can see that in trying to maintain their position, mental logicians unconsciously trade on confusions between a Level 3 account of performance in terms of a classificatory vocabulary of inferences and inference-making and a Level 2 account in terms of processes or mechanisms. Mental logicians—and the rest of us, too, no doubt—are prone to fall into the nominalist habit of talking about inference-making as 'the process of inference-making'. But analyses such as those by Trabasso and Johnson-Laird indicate that inference-making arises out of a number of cognitive processes no one of which can be identified with 'the process of inference-making'.
The material covered so far has shown the operation of the three nominalist habits of thought with respect to the psychology of inference-making of one sort or another. In the next section the scope of the investigation is broadened to include a very different topic area.
Counting and Understanding of Number
Just as in the case of transitivity, Piaget argued that preoperational children do not have, or understand, the principles of number, including that of one-to-one correspondence. His assertion was based on their characteristic failure on tests of number conservation, seriation and class inclusion. The fact that preschool children are sometimes observed verbally counting small numbers of items (protocounting) was explained as being due to no more than rote recitation of a string of number names together with coordinated tagging of objects. This is a move reminiscent of [p. 375] the introduction of the distinction between operative (true) and figurative (sublogical) transitivity.
In the course of their elegant investigations of numerical skills in children, Gelman and Gallistel (1978) formulated a list of 5 counting principles:
1. One-to-one correspondence (one item, one tag word).
2. Cardinality (last tag gives number of the set).
3. Stable order (of tag words).
4. Abstraction (any set can be counted).
5. Order irrelevance (count items in any order).
They argued that the protocounting of preschool children, though it might involve non-standard (but consistently used) word sequences, already indicates an implicit understanding of at least the first three of these principles. On the basis of performance on a variety of other tests also, they further went on to claim that young children have some grasp of all the principles. They can, for example, adapt to unusual demands such as making the second item from the left in a line 'One', thus evidencing some grasp of the order irrelevance principle. In other words, where Piaget set conservative criteria for attribution of the understanding of number, or counting, Gelman and Gallistel opted for a more liberal position. By calling upon the implicit/explicit distinction they were following a precedent set, as we have seen, in the debate over transitivity.
Not content simply to descry their five principles in the performances of young subjects, Gelman and Gallistel went on to claim that implicit understanding of those principles 'guides performance in counting as well as in the acquisitions of skill in applying the counting procedure'. That is, children are able to count because they contain within themselves counting principles. In this respect, of course, Gelman and Gallistel were following the tradition of making Level 3 attributions. Greeno, Riley and Gelman (1984) pursued the topic further. They argued that a child's understanding of the one-to-one principle improves as it becomes more explicit, not in the sense that the principle necessarily becomes verbalizable but in the sense that it increasingly underlies what the child does. They developed a model in which 'counting principles are specified explicitly and give rise to suitable procedures that are consistent with the principles' (p. 96, emphasis added). They also said: 'The claim that children have this competence says that they have mental representations of the principles characterized in the analysis, and the principles are used in the children's thought and behaviour' (p. 138, emphasis added).
Greeno et al. have many worthwhile things to say about children's understanding of number, yet the pull to think in nominalist terms remains strong enough for them to develop an implementable model of counting in which explicit principles are employed, these principles having the same [p. 376] kind of status as the putative mental schemata of Braine and Rumain (1983) or Rips (1983). Part of the problem seems to be that Greeno et al. are committed to Rozin's (1976) view of cognitive development as consisting of increasing access to, and understanding of, principles that are initially implicit.
The problem with Rozin's positing of internal principles, whether implicit or explicit, can be illustrated by considering that there is a sense in which a mechanical device such as a turnstile clicker can be said to exhibit all of Gelman and Gallistel's five principles. The clicker clearly shows one to-one correspondence, stable order and cardinality. Since it is oblivious to the nature of the items going through the turnstile, so long only as they trip the mechanism, and equally to the order in which they go through, it also exhibits abstraction and order irrelevance. Indeed, the clicker is built in such a way that it exemplifies the principles, and if it did not it would not be up to its job. Yet one surely would not want to say that the clicker was 'guided' by the principles.
Naturally, it is possible to construct scenarios in which the clicker would fail, e.g. when two small people slip through together, or to argue that there are senses in which the clicker does not have the principles, or has them only implicitly rather than operatively. But this is equally the case for attributing principles to animals, children or adults. As we have seen repeatedly with TI and other forms of inference-making, every exemplar of an inference type or of inference-making is only so when understood in a particular sense, participants in these debates making their cases by offering different senses in which candidate instances can be interpreted.
The second objection to Rozin's view is that, with its individualistic bias, the accessing account totally misses the component of socialization in learning such skills as how to count. Surely children neither invent nor 'give birth to' counting principles (the practice of enumeration) for themselves. They are taught and encouraged to enumerate: 'One block, two blocks, three blocks.' It seems unlikely that counting (enumeration) was ever something devised by a single embryonic mathematician running pebbles through his or her fingers; or that it can be the making overt of existing covert habits. In whatever way it happens, enumeration most likely develops as a social practice elaborated by individuals squabbling over fair shares or trying to agree whether they have brought in all the sheep or not. The universality of counting practices should no more be seen as indicative of something immanent within each child than is the universality of cooking practices. It seems more likely that children learn to count not by gaining access to principles within themselves but by being taught 'That's how we do it'. None of which need be taken as a denial of some innate sensitivity to certain aspects of numerosity (Starkey, Spelke, & Gelman, 1983).
A third objection to the accessing account of development—and to [p. 377] mental logic approaches in general—concerns the presumption that principles, even those one can verbally formulate to oneself, somehow define their own future applications. That this is not so was argued earlier on basis of the whole-numbers/even-numbers example. Since then we seen that concepts such as transitivity and inference-making have anything but fixed and pre-existent ranges of application. What the initial example showed is that the occasion for invoking a particular principle is neither self-evident nor a matter for individual choice but a matter of accepted practice. Individuals do not elaborate, or gain greater access to, principles rather they discover what is accepted procedure in particular circumstances: and, perhaps, what principles to invoke as justification (Barnes, Bloor, 1983).
One reaction to this argument could be to claim that the learning of ever more accepted practices in which a principle can be descried is ex] what increased access, or explicitness, consists in. In this case, however is hard to see what gain follows from positing mentally represented principles over and above the learning of the accepted practices themselves. For this is but one more instance of the circular argument by which supposed competence is diagnosed on the basis of behaviour characterizable in terms of that competence.
Twin Myths of Diagnosis and Competence
We have seen that attempts to characterize action/cognition in tern) competences, principles, schemata or rules have their basis in the nominalist habits previously identified. These attempts always result in a form debate that revolves around elisions of Level 2 and Level 3 accounts, with participants constantly seeking to redefine the criteria for Level 3 attributions. The notion that reified competences can be attributed to individuals itself closely linked to a further idea, that of cognitive diagnosis.
The term 'cognitive diagnosis' has become especially associated with Piagetian literature on development but the basic idea has a much provenance. In fact any attempt—as, for example, in mental logic acc: of inference-making—to explain a Level 1 performance by reference to a Level 3 competence, principle or rule will almost certainly involve the assumption of diagnosis. Flavell (1985), after devoting several pages to the problems and complexities of cognitive diagnosis and its supposed theoretical and educational implications, concluded: 'Finally, diagnosis is central to all psychological study, cognitive development or other' (p. 281). The present argument will be that the central role accorded to diagnosis much of psychology is a mistake.
In Piaget's original scheme of things, the classical tests of conservation, transitivity, and so on were supposed to identify types of thinking exhibited by the idealized epistemic subject at a particular stage of psychogenesis. [p. 378] Chapman (1988) argues that it is interpreters such as Braine (1959), Brainerd (1973) and others who have taken the tests to be diagnostic of competences possessed by individual psychological subjects. Their motivation was to translate the purely descriptive stages of Piaget's structuralist theory into functional explanatory constructs typical of cognitive psychology in general. Certainly this interpretation has been the one which has informed various debates in the psychology of cognitive development, and caused them to resemble those in other areas of cognition.
Paradoxically, however, although the classical tests were assimilated to notion of diagnosing individual competences, in practice the diagnosticity of any particular test had to be hedged, it being found necessary to invoke contrasts such as that between conservation and pseudo-conservation. Right from the start, then, the rules of diagnosis were blurred and, as we have seen, subsequent debate has served only to increase this fuzziness. Yet despite the challenge to the diagnostic status of classical tests, the notion of diagnosis itself has usually emerged scathed. Often attributions of competence to younger children are urged the basis of different (more liberal) diagnostic tests, but the idea of diagnosis itself is retained.
There have been three related responses to perceived shortcomings in classical tests viewed as diagnostic tools (Gellatly, 1989). However, in s paper it is argued that, whatever the area of cognition, attributions of competences can never be a wholly empirical matter since the choice of empirical criteria must be theoretically motivated. There can be no fixed criteria for the diagnosis of competences, the having of concepts, rules, principles, and so on. Now this claim could be taken as an indictment of cognitive psychology. It might be thought that any worthwhile discipline ought to be able to establish absolute diagnostic criteria. Yet it turns out that diagnostic criteria in medicine—on which the notion of cognitive diagnosis is modelled—are no less dependent upon convention than are those in psychology.
The basis for this claim is to be found in the study by Fleck (1979) of the emergence of the modern concept of syphilis. Briefly stated, Fleck shows that the concepts of the disease and its diagnosis evolved over several centuries and that, most importantly, they are still evolving. By drawing r attention to the negotiability of diagnostic criteria in medicine, Fleck reveals the usually obscured theoretical complexities that underlie them. Gellatly (1989) suggests two reasons as to why these complexities are ally so obscured. The first resides in the epistemological assumption t scientific facts and concepts just ought to display stability and finality. e second reason is to be found in the fact that with medical diagnosis the emphasis is usually at least as much practical as theoretical. For most people for most of the time what matters is the efficacy of diagnosis and treatment not the neatness and consistency of the theoretical base. This [p. 379] position contrasts sharply with that to be found in cognitive psychology] where the focus of interest in diagnosis is overwhelmingly theoretical rather than practical, even allowing that psychologists are sometimes asked to make, for example, educational recommendations.
To summarize this section: the notion of cognitive diagnosis grounded in absolute criteria is, and always will be, a myth. By its nature diagnosis is a pragmatic affair, whether in medicine or in cognitive psychology. It follows, for reasons which should be apparent, that the notion of absolute cognitive competences must be likewise discredited.
Note: Continued on the following "page" as "WD_349".
-psychology.ucalgary.ca/thpsyc/VOLUMES.SI/
1992/2.3.Gelaty.html
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