Semantic components and conceptual development

3

Semantic

components

and conceptual

JONATHAN McMaster

development*

BARON

University

Abstract Several phenomena in the acquisition of word meanings may be accounted for by a theory of component-by-component acquisition, a mechanism analogous to that proposed for phonological development. By defining a concept as an habitual plan, and a component as a subplan, we may extend this theory to acquisition of concepts in general. This theory may be applied to logical concepts, physical reasoning and moral reasoning as well as verbal concepts. The ideas of component-by-component acquisition and of transfer of learning between concepts sharing components thus provide an alternative to deveIopmenta1 stage theories. Recently several attempts have been made to extend Jakobson’s (1942) theory of phonological development to the development of verbal concepts (e.g., E. V. Clark, 1971, 1973; Donaldson and Wales, 1970; McNeil& 1970; Menyuk, 1971). This work rests on the analogy between semantic features or components (as defined in various ways by Bierwisch, 1967; Chafe, 1970; Goodenough, 1956; Katz and Fodor, 1963; and Lamb, 1964) and phonological features. The essence of this extension is the idea that verbal concepts may be acquired one component at a time, and that in many cases a single component which extends across several concepts will be learned at about the same time for all of them. For example, Donaldson and Wales (1970) found that many young children respond to the word ‘less’ as if it meant ‘more’ in contexts like, ‘Show me which one has less’, and that manyofthese childreninterpreted ‘short’ as ‘tall’, ‘wee’ as ‘big’, and so on. H. Clark (1970) has suggested that * Lee Brooks, Eve Clark, John Gibbs, Betty Ann Levy, Dave Meyer, Dan Osherson, Linda Siegel, the journal referees, and others made valuable comments on earlier drafts. To save space, some of their criticisms are left un-

answered for now. None has so far endorsed the views expressed. Financial support was provided by a grant from the National Research Council of Canada. The author is now at the University of Pennsylvania. Cognition 2( 3). 299-317

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these misinterpretations result from the absence of a single component of the meaning of the terms in question, which I shall call the ‘antonym’ component. The purpose of this paper is to show how this sort of component theory might be extended still further to explain (eventually) all phenomena in which systematic errors are made in the acquisition of concepts, nonverbal concepts as well as verbal ones. Such an extension will require a redefinition of ‘concept’ and ‘component’ as, roughly, ‘habitual plan’ and ‘subplan’ respectively. The range of phenomena that can be explained in this way is similar to that accounted for by developmental stage theories such as that of Piaget (e.g., 1970). While Piaget would argue that cases of systematic error usually exemplify absence of skills or structures, such as understanding the reversability of operations, which could affect areas of intellectual development, component theory would hold that the skills involved are less general. For Piaget, practice at a particular task might strengthen all of the structures involved in the stage that task requires, while for component theory, practice would strengthen only the components used. The idea that a concept is an acquired habitual plan follows from the analogy (see Miller, Galanter and Pribram, 1960) between human information processing and the operation of a digital computer. If we look at concepts in this way, we must define a concept in terms of a task in which the concept is used. This contrasts with the usual view of concepts as categories defined by relations between perceptual attributes and a single response (Bruner, Goodnow and Austin, 1956). However, even artificial concepts may easily be seen in terms of plans; Trabasso, Rollins and Shaughnessy (1971), for example, have shown how classifying a stimulus may require a strategy in which successive decisions are made, each step requiring examination of a perceptual attribute. Concepts are habitual in the sense that they are evoked by a particular stimulus or situation without additional thought about what to do, that is, without the use of plans to construct plans. Further, the same plan will be likely to recur in the same situation. Concepts may be contrasted on the one hand with instinctual plans, which are ‘wired in’, and with ad hoc plans on the other. Ad hoc plans may in fact use concepts as subplans, or use some of the same subplans as concepts use, except that they are created for the situation at hand, possibly with the use of special plans to create plans (which themselves may use acquired concepts). A plan may be analysed into subplans, which may in turn be analysed into other subplans, and so on (perhaps ending at some level of subplans analogous to machinelanguage instructions in computer programs, each of which must occur as an indivisible unit). We shall assume that subplans may be recombined in various ways, and that a given subplan does not change in character when it occurs as part of different concept plans. To pursue our analogy with Jakobson’s theory, the subplans

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correspond to the features or components which are recombined in various ways to produce phonemes. This analogy breaks down, however, in two respects: First there are surely many subplans which are used only for one concept, but each phonemic feature is used in several phonemes; second, concepts may be organized into a hierarchy with some concepts acting as subplans of other concepts. I should note that the analogy between components and computer subroutines is also imperfect. First, I do not assume that the component subplans are executed in series, since it is possible that several of them are executed simultaneously. Second, the subplans may take certain forms that are not characteristic of computer programs. For example, one type of component may instruct some mechanism to allow itself to be intluenced only by a certain dimension, such as number, when it could be influenced by other dimensions such as length without such instruction. This kind of component may distinguish concepts of number, for example, from those of general size or ‘bigness’. Thus, subplans may set the parameters of attention as well as carry out acts. Component theory accounts for systematic errors as failures to use a subplan that would be part of the mature use of the concept. Failure may occur for two reasons. The first is that the subplan is not available for use as part of any concept at the time it is required, possibly because it is difficult or poorly learned; I shall call this a strategy error. The second reason is that the learning which associates the subplan in question with a situation or word may be weak, and, even though the subplan may be available, it is not brought into play; I shall call this an attachment error. Often a subplan may be omitted without jeopardizing the completion of the entire plan. In other cases, perhaps most, some inappropriate subplan may be inserted, and each possible subplan of this sort will be chosen with some probability regardless of whether each is appropriate or not, as long as it allows completion of the plan. In many cases, errors resulting from completion of an inappropriate plan will be identical to responses that would be appropriate in some other situation. For example, omission of the change in response-choice required for ‘less’ in Donaldson’s and Wales’ (1970) study would be appropriate for ‘more’. In such cases, I shall speak of assimilation of the first concept to the second. So far, component theory has led to only one prediction of interest; we ought to be able to describe most conceptual errors as omissions of identifiable subplans and retention of others, rather than completely random responding. Other predictions may be generated by adding the simple assumption that practice at using a subplan as part of one concept (such as the antonym component discussed above) transfers to uses of that subplan as part of other concepts. This may occur in two ways, corresponding to the two types of error just described. First, practice at using a subplan may strengthen the subplan itself. Strategy errors would decrease in the early stages

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of such practice, but, even after such errors had disappeared, the use of the subplan could still improve in the sense that it would require less time or attention. Second, practice at attaching a subplan to the appropriate plan could make it easier to attach similar subplans to other plans. (This mechanism is discussed further by Baron, 1974.) One way of looking at this second mechanism of transfer is to assume that each concept has a characteristic executive routine which calls up the various subplans in the right order; each subplan is thus represented in the executive routine. Practice at representing a subplan as part of one executive routine would thus transfer to representing that subplan as part of other routines. In general, then, we would expect transfer of practice between two concepts to the extent to which the two concepts have similar subplans. There are two consequences of this transfer assumption which are of particular interest in the study of development. First, if a number of concepts share a common component, learning to use one will facilitate learning the others. If we examine a set of concepts which have a few such common components, we might see develop mental stages in the acquisition of the set. Each stage would correspond to the acquisition of one or two new components and their generalization across the set. Second, unlike stage theories, component theory makes no particular predictions about the order of acquiring components. Certain subplans will surely be more difficult than others, and in some cases subplans will not be learned until their own components have been acquired. However, in many cases we would expect to see components learned in different orders depending on the particular experiences and capacities of the learner. In the extreme case, people growing up in one culture may not be exposed at all to the opportunity to learn components used frequently in another culture and vice vema (see Greenberg, 1966). Thus individual differences in the acquisition of concepts within a culture may be analogous to differences between modal developmental sequences in different cultures.

1. Development of word concepts

While there is at present little evidence of precisely the sort designed to compare component theory to other theories, there is a great deal of evidence consistent with the theory. Thus, the best way to argue for component theory as a viable approach may be to describe this evidence from the point of view of the theory, trying to show along the way which components may be absent in each case of systematic error. The phenomena most amenable to this sort of description come from studies of the development of word concepts in children. E. Clark (1971) for example, asked children to act out instructions containing ‘before’ or ‘after’ (e.g., ‘Before the boy

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[doll] jumped the gate, he patted the dog’). The youngest children simply ignored the conjunction and performed the actions in the order they were mentioned. A group of older children carried out the instructions correctly when they contained ‘before’, but for ‘after’ they either continued to use an order-of-mention strategy or else treated ‘after’ as if it meant ‘before’. In this example, both the order-of-mention strategy and the ‘before’ strategy may be seen as ways of filling in the plan so that it can be executed. They are both ways of specifying which action to do first. Apparently, the ‘before’ strategy is acquired before the ‘after’ strategy; possibly the ‘after’ strategy is represented as a modification of the ‘before’ strategy, in which the actions are reversed. Clark (1971, 1973) also notes that her findings agree with those of Donaldson and Balfour (1968) concerning the meaning of terms such as ‘more’ and ‘less’. Again, children seem to pass through a stage in which they take ‘less’ to mean ‘more’ in a variety of tasks, such as saying which of two trees has more (less) apples, or making a single tree have more (less). Donaldson and Wales (1970) extended these findings to other pairs of antonyms, such as ‘same-different’ and ‘tall-short’. In no case was the meaning of the negative term learned first. These findings suggest that a component is added to most of the concepts which use it at the same stage of development; most of the distinctions based on the ‘antonym’ component seem to be acquired within a couple of years of the first such acquisition. Similar findings from Russian literature concerning the meaning of spatial prepositions such as ‘over’ and ‘under’ are cited by Clark (1971) and by Menyuk (1971, Ch. 6). Baron and Kaiser (1973) have recently completed a study which illustrates the independence of the acquisition of different components. Children’s knowledge of pronouns was tested in a situation involving an experimenter, a child and two dolls. The children were told to do such things as ‘give (me, yourself, him, her, us, etc.) some pants’, or to ‘show me (my, your, their, etc.) feet’. Most errors involved assimilation of first to third person (e.g., responding to ‘us’ as if it were ‘them’), or of plural to singular. Errors on person thus seem to be due to absence of subplans which direct the required action toward individuals distinguished by certain cues, such as who has just spoken to whom. Errors on number involve the parts of the plan which provide rules for deciding whether to stop or continue the action. Each of these errors tended to occur across several pronouns and tests, and different children tended to make different types of assimilations consistently. This finding supports the prediction that components correspond to ‘factors’ within a semantic field within a language. In all of the cases described so far, the task has involved carrying out some action in response to verbal instructions. The strategies are thus expressed directly in the action, and errors are often categorized according to the stimulus that would have

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been appropriate for the action done. In other cases the task may involve producing a word, or saying whether or not a word is appropriate to a situation. Here the strategy may involve selecting relevant cues from the situation, possibly using information from these to select other cues and ultimately producing or verifying the word. Some. times the ‘situation’ may be provided entirely or in part through verbal description so that a verification task may require attention to purely verbal aspects of the situa. tion. Thus, different strategies may be involved in action tasks like those described above, word-production tasks and verification tasks. The component subplans 01 verbal concepts are not entirely determined by the word but by the task as well. We could not necessarily expect a child who could ‘make it have less’ to be able to ‘tell me whether it has less’, although clearly there may be components common to the two tasks, such as the antonym component. In general, results from production and verification tasks are similar to those from action tasks. Both Clark (1971) and Donaldson and Wales (1970) noted, for example, that terms like ‘after’, ‘less’, and ‘smaller’ are acquired later in spontaneous speech and verification tasks than the corresponding terms without the antonym component. Another example is based on an observation made by Bennett (1969) that words such as ‘over’, ‘through’ and ‘across’ can have two meanings. For example, ‘the tree across the road’ can mean either ‘across the road from someone’ (who may be specified) or ‘lying across the road’. In the first sense, three arguments may be specified (tree, road, specified person), while in the second sense, two (tree, road). The first sense may thus be said to use an additional component which allows specification of what the object is across (over, etc.)from. Reich, Rice and Schneider (1972) asked children to select pictures illustrating such sentences as ‘The tree is across the road’ from a set of distracters. Young children had greater difficulty with pictures illustrating the three-argument form. Thus, the simpler two-argument form seems to be acquired first. The principle governing the growth from two to three arguments may be at work in an earlier transition from a one- to a two-argument interpretation of relational terms. Piaget (Flavell, 1963, pp. 276-278) found that young children could not think of themselves as their brother’s brother, and often asserted that if there were two boys in a family, only one was the brother. These and similar confusions have been interpreted as showing that the child thinks of terms like ‘brother’, ‘left’ and ‘darker’ as defining classes rather than relations. According to component theory, he may be said to lack the subplans used for making inferences from relational statements, for example, knowing that ‘brother’ is a reversible relation, unlike ‘father’. (Haviland and Clark, 1972, have recently proposed a similar, and more extensive, analysis of acquisition of kinship terms in general.) A somewhat more subtle component has been investigated by Asch and Nerlove

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(1960). They noted that a number of terms exist which can describe human character, in one sense of their meaning, and inanimate objects in another sense, such as ‘bright’, ‘dull’, ‘hard’, ‘warm’, ‘cold’, etc. The first sense seems to be acquired after the second for all of the terms. There is a rapid increase in proper use and understanding of such character terms between the ages of 7 and 10. A six-year old, for example, is apt to describe a ‘bright’ person as ‘someone who is covered with gold paint’. The use of only terms with double meanings in this study must be considered valuable only as a control for knowing the term itself. It is by no means claimed that the two meanings of ‘bright’ differ only in a single component. But it does seem plausible that the various character terms do share a common component. Once the child learns to attend to cues of character, possibly, he might begin to use all of these terms in this sense. Learning lexical concepts component-by-component occurs in ‘babytalk’ as well as in the acquisiton of adults’ concepts, even when the meanings of words are so idiosyncratic that they are incomprehensible to all but the child’s parents (see Clark, 1973, for a thorough review). Menyuk (1971, Ch. 6) analyses an example of Lewis’ (1963) in which a child’s lexicon grows by addition of features. Initially, the word ‘tee’ is used to refer to all animals (nonhuman, animate). Next, a new word, ‘goggie’, is used to refer only to small dogs and toy dogs (nonhuman, animate, doggy). The next new word ‘hosh’ is applied to large dogs and horses (nonhuman, animate, large). Finally the word ‘biggie-goggie’ is used to refer to large dogs, distinguishing them from horses (nonhuman, animate, large, doggy). Meanwhile, the child has recognized other components which allow him to distinguish between various other animals, such as ‘pushie’ (nonhuman, animate, cat), and so on. Ingram (1971) has provided a component-theoretical account of several reported examples of children’s very first words and gestures. He notes that the small number of components used to define these early words may be responsible for the frequently reported occurrence of ‘over-generalization’ in the use of early words. For example, one child used ‘ba-ba’ to refer to herself, other people and the cat, that is, presumably, animate objects in general. Then ‘dada’ was used for all men, and later for father only. Each new restriction on the use of a word can be accounted for by the addition of a component to its meaning. From the account just given, it might appear that the range of reference of a word must always become smaller when a new component is added to its meaning. This would be true if all concepts were defined by simple logical conjunction of their components (i.e., if the decision were based on a logical ‘and’ relation), but this is not always so, as components may be added disjunctively (a logical and/or relation). For example, ‘food’ may refer first to what is actually eaten, such as pork. Later, ‘food’ may also refer to animals from which the food comes, such as pigs. Here a

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disjunctive component, which we may abbreviate as ‘precursor of’, may be added. To use this new component, a child would have to recall his knowledge that pork comes from pigs. In another sort of case, ‘doctor’ may first be restricted to male physicians. Later, a new concept may be learned in which these particular attributes do not have to be tested to apply the concept. Yet the old concept may remain alongside the new; many holders of Ph.D. degrees have been known to refer to physicians as ‘real doctors’. This is not to say that a concept is never relearned from scratch, but rather that many examples in which texts of certain attributes appear to be dropped (see Saltz, Soller and Siegel, 1972) may result from the addition of components or new concepts. Some of these subplans used in verbal production, such as those which allow us to follow rules of agreement, may require attention to what has already been said or to some representation of what will be said. Other subplans require attention to the representation of intended meaning. It would seem likely that these two kinds of subplan ordinarily operate in parallel. Table 1 shows some selected errors made by children and college students, categorized according to whether the subplan omitted seemed to involve meaning or not; those that do not are often violations of grammatical rules involving selection or subcategorization (Chomsky, 1965). What is of interest here is the appearance that most of these errors may involve a single component, a failure to execute the subplan which directs attention to some aspect of the situation.

Table

1.

Selected errors in child language and essays of college students (correct form in parentheses when needed)

Child language’ Non-semantic

That’s too bigger for you. Me do it. Me do rolls first, Mama. I want many soap. Violin tired. Piano sleeping. A your car. A my pencil. More wet. More outside. Allgone sticky. Semantic examples discussed throughout

text

1. Examples are taken from Menyuk (1971), Brown, Cazden, and Bellugi (1969), Schle-

singer (1971), and unpublished observations A. Kaiser and J. Baron.

of

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Student pupers Non-semantic

Education beings for the child as something adults make them do. . those on which (whom) he depends. . . to make inferences onto (about) the population ..

. .. if a mother may be absence(absent) .. . . .. I have chosen to critically analysis . .. Semantic2

White has refuted (rejected) Watson’s behaviorism . . . . . . as Levinthal has demonstrated (suggested), we must consider . . . This again can be proven (supported) by Cohen’s article . . . In order to prove (test) her theory . . . His subjects had pre-conceived emotions (attitudes) concerning . . . This may infer (imply) that . . . 2. Note that the first three examples here stem to involve a component distinguishing

doubt from presupposed certainty. to be a common sort of error.

This seems

Errors which appear to involve meaning, such as substituting ‘prove’ for ‘support’ may arise in two ways, depending on whether the intended meaning is correct or not. If the intended meaning is correct, the error may simply involve retrieval of the appropriate word. The student may realize that some doubt is involved in the situation he is describing, yet this knowledge will not be sufficient to rule out his choice of ‘prove’. Alternatively, the student may construct an incorrect ‘nonverbal’ representation of the situation and may think that there was in fact no possible doubt. Only other tests could allow us to distinguish these possibilities. Even in the case of an incorrect nonverbal representation, however, training in choosing the correct word may force the student to attend to the relevant features of the situation, and may thus be a useful teaching technique. 2. Development of physical and logical concepts In addition to verbal concepts, component theory may also explain a number of phenomena which have previously been explained by Piaget (e.g., 1970) and his followers as manifestations of stages of intellectual development. A number of these phenomena concern making comparative judgments along various dimensions. Young children are often unable to make such judgments along one dimension when some other dimension is inconsistent. For example, one row of beads may be longer than another, but they might have the same number of beads. A pre-operational child, asked whether both rows have the same number, will answer that the longer row has more. He will do this even if he observes the relative lengths of the rows being manipulated before his eyes. Likewise, given a row of three beads which is longer than a row of four, he might hold that the former has more beads.

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This error may not be ‘strictly verbal’, as similar errors are made when the child is asked to choose the row of candies he would rather have (Mehler and Bever, 1967). Thus the deficit may be to a large extent due to the strategy that is evoked by both the word and the nonverbal task. Component theory can explain this kind of confusion by postulating a primitive concept of ‘bigger’, from which ‘longer’ and ‘more’ are differentiated by the addition of components. Originally, all specific dimensions of the stimuli are relevant to ‘bigness’; this simple strategy of letting all information determine the response works fairly well because usually only one specific dimension is relevant at a time, or else several are correlated. But when dimensions are in conflict, that which happens to b- most salient captures the response mechanisms. The components which must 1-e added to differentiate ‘longer’ and ‘more’ from ‘bigger’ are those which restrict attention only to certain dimensions. These components are analogous to those which distinguish ‘I’ and ‘you’ from ‘someone’ (Baron and Kaiser, 1973). In the case of pronouns, a response mechanism is directed by the specific component; in the case of dimensional concepts, an attention mechanism is directed. While ‘bigness’ will suffice for the young child, eventually the occasional need for specificity will encourage learning new components. Thus, Gelman (1969) was able to teach children to differentiate length and number easily when the two were put into conflict and the child had to attend only to the correct dimension. This account is relevant to a study done by Lawson, Baron and Siegel (1974). Children were asked whether one of two rows of dots was longer and whether one had more dots. For some stimuli, a wrong answer for one dimension might be right for another; for example, a child might say that rows of different number but the same length had the same number. If children assimilated both concepts to ‘bigger’, we would expect children to answer most questions according to the physical dimension of these stimuli that was most salient for their concept of ‘bigger’. If the relative salience of length and number differs for different children, we would expect a negative correlation across children between the tendency to assimilate length to number and the tendency to assimilate number to length; children who were correct on length would tend to treat number questions as length questions, and vice versa. Such a correlation was found. This confusion of length and number might slow down the acquisition of conservation of number. Conservation may depend on the acquisition of a new strategy in which constancy of number is inferred from the observation that nothing was added or taken away. The development of this strategy may depend on experience with transformations of actual arrays; the child would apply number estimation strategies and then the new strategy of inference, and eventually come to realize that the old and new strategies always gave the same answer, so that the new inference strategy

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could be used reliably as a shortcut. But if the child’s strategy for number estimation is based on ‘bigness’, the inference strategy will not work, as the child will ‘find’ that number can be affected even when nothing is added or taken away. If ‘bigness’ involves an ordering of the salience of cues, systematic assimilations of one dimension to another will reflect this salience hierarchy. Thus, such assimilations should be transitive: If questions about dimension A are answered as if it were B, and questions about B as if it were C, then questions about A should be answered as if it were C when the C test is applicable. Osherson (ca. 1971) has tested a number of such predictions of transitivity by searching the experimental literature on preoperational children and has found transitivity to hold in a large number of cases, even though different children were often used for different tasks. For example, preoperational children say that one object moves faster than a second object if the first one finishes in front, regardless of curves in the path of the second which actually make its path much longer. These children also assert that faster objects travel a greater distance than the slower ones, even when information about time is lacking. From these two beliefs, we may infer that these children will also hold that if one object has finished in front of another, then it must have travelled a greater distance, regardless of information about the paths or starting points. This prediction, and others like it, are supported. Thus, questions about speed are answered with respect to position, questions about distance are answered with respect to speed and questions about distance are answered with respect to position. We could infer that the normal hierarchy of cues is position, speed, distance, in that order. The view that such transitivity results from a hierarchy of cues for a single concept (probably not identical to ‘bigness’, but analogous) contrasts with the theory of such transitivity which ascribes it to internal consistency of the child’s logic. Osherson’s conclusions are formally the same as those of a study by Clark (forthcoming) in which children were asked to place one object ‘in’, ‘on’ or ‘under’ another, with two responses possible for each test. Here, when both responses in question were possible, ‘under’ was assimilated to ‘on’, ‘ on’ to ‘in’ and, as predicted, ‘under’ to ‘in’. In this case however, it seems likely that more than one primitive concept may be involved. Several other findings may be explained on the basis of assimilation to primitive concepts without certain critical components which require particular strategies of inference or attention to particular cues. Ervin-Tripp and Foster (1960) found that children tended to treat ‘good’, ‘pretty’ and ‘happy’ as synonyms for the purpose of categorizing faces. The same children also confused physical dimensions such as weight, strength and size. Bruner and Kenney (1966) found that young children assimilate ‘which glass is fuller?’ to ‘which glass has more water?‘, while older children judge fullness as a proportion, Likewise, Piaget, has noted (Flavell, 1963) that pre-

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adolescent children assimilate probability, a proportion, to frequency. In a similar vein, Smedslund (1963) has noted that adults often assimilate the concept of correlation to that of joint-frequency, and Kahneman and Tversky (1972) have described several situations in which adults seem to assimilate probability to ‘representativeness’. Logical reasoning may also be broken down into components which may be acquired independently. Here each component may be a subplan involving a certain kind of inference. Such subplans may be acquired independently of knowledge about their application to particular content areas, and independently of each other. One such subplan might be the ability to make inferences based on transitive relations such as ‘longer than’ or ‘equal to’. In a study done by Osherson (forthcoming), for example, 7 out of 8 children who failed on a task involving transitivity of lengthequality also failed on a task involving transitivity of length-inequality. In the inequality tasks, a child was shown three sticks, with their tops hidden, and told, for example, that the red one was longer than the blue one, and the blue one was longer than the green one. He was then asked whether the red one was longer than the green one. In the length-equality task, he was told that the pairs of length were equal. Like other components, the strategy of making transitive inferences may be transferred from one concept to another, in this case from inference of equality to inequality (or the reverse). An important step in the development of logical thought is the use of hypothetical thinking, which first occurs with the period of formal operations. The formal-operational child is capable of assuming some proposition to be true, and reasoning as if it were, while at the same time suspending judgment about the actual truth of the proposition. Rather than categorizing statements as ‘true’, ‘false’ or ‘indeterminate’ as a younger child might, the formal-operational child now has a richer inventory of concepts for categorizing statements or thoughts. This inventory parallels the achievement of concrete operations in developing an inventory of physical comparative concepts besides ‘bigger’, ‘smaller’ and ‘same’. It is through the use of this richer inventory of concepts for categorizing propositions that the formal operational child gives the impression of being more ‘reflective’, ‘introspective’ and ‘analytical’ in his reasoning. An example of such a new concept is the finding of Osherson and Markman (1973) that pre-adolescents are generally unable to classify statements as tautologically true or false, even though they can classify statements of similar logical form as true or false empirically. For example, a child will consider thesentence, ‘Either this chip (concealed) in my hand is green or it is not green’, as indeterminate. Hypothetical thinking should thus be seen as an example of an enriched set of strategies for ‘thinking about thinking’, for categorizing self-generated propositions. Other categorizations of propositions which seem likely to be learned after the onset of formal operations are ‘true by definition’, ‘true given some assumption’, ‘analytic’,

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etc. Failure of some of the subplans used in ‘synthetic’, ‘valid as an explanation’, this kind of thought might be responsible for some of the college students’ errors shown in Table 1, as well as for actual errors of inference.

3. Moral Concepts A final area where component theory may be applied is that of moral reasoning. Kohlberg (e.g., 1969, 1971) has thoroughly analysed the development of such reasoning in subjects’ responses to moral dilemmas. He has interpreted this development in terms of a sequence of six stages: In stages 1 and 2, judgments are made on the basis of self-interest of the party in the dilemma who is faced with the decision; in stages 3 and 4, judgments are made according to societal conventions; in stages 5 and 6, principles which do not depend on social convention are used. According to component theory, discrete stages would not be found were it not for the use of a domain in which a small number of components are involved in many strategies of thought, and in the principles applied habitually by an individual. Some of the components required for the transition to stage 2 thought are the subplans required for taking the perspective of someone else when that perspective might differ from one’s own. Such a deficit is reflected in various manifestations of ‘egocentrism’ as shown, for example, by the young child’s inability to choose a picture of a scene that would correspond to someone else’s perception of it, or by the inability to take the listener’s lack of knowledge into account in explaining how to do something. One consequence of this deficit might be the inability to make certain judgments when these judgments depend upon the perspective of some individual; for example, judgments of whether something is ‘annoying’ or ‘pretty’, as opposed to ‘wet’ or ‘hot’, depend upon the tastes of the person making the judgment. The young child is able to make only objective judgments. Thus, a person in stage 1 might say it is worse to steal a lot of worthless junk that nobody wants than to steal a small, but treasured, possession. Here, judgment is made in terms of physical concepts only; subjective concepts are not used at all in evaluating action. Likewise, in stage I, the value of human life is determined by such qualities as the size of a person’s house; in stage 2, the subjective value of a person to others determines the value of his life. Acquisition of a ‘moral’ component may be required for the transition to stage 3 (see Hare, 1952, Ch. 9). This component distinguishes moral judgments such as ‘virtuous’ and ‘evil’ from nonmoral value judgments such as ‘seaworthy’ and ‘pleasant’. (Many terms may be used in both moral and nonmoral senses. Only the moral sense would fit in a frame such as, ‘John blamed [praised] him for being .) Moral

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judgments differ from other judgments in that they imply standards on which groups of people must come to agreement (Hare, 1952). When asked whether a given act is right, a stage 2 person will usually answer as if he had been asked whether the act was in the interest of the person responsible for it. In a situation of conflict, the ‘right’ resolution for one person will be different from that for another. In stage 3, conventional moral judgments may be based on a concept of virtue which may be separated from subjective or physical consequences to the person judged, and which may be endorsed by some community. The subplan required for this advance may thus be the evaluation of a situation from several perspectives at once. (Kohlberg might agree that this skill is crucial, but he would regard it as embedded in a broad structure of other skills; component theory would not.) Evaluation from the perspective of an abstract impersonal code, such as the law or a religion, may characterize a component required for stage 4. Such a component may also be required for application of terms like ‘guilty’, ‘innocent’, ‘legal’, ‘homicide’ and ‘criminal’ in their strictly legal sense. While stage 3 components based on shared personal values may be more salient in most children’s environments, component theory, unlike stage theory, would not necessarily predict that the stage 3 components had to be acquired before the stage 4 ones. The transition to stage 5 requires several strategies used in the construction and evaluation of moral principles; at this point the individual cannot depend uncritically on social convention. One component that is clearly required is the ability, described above, to tag one’s thoughts as ‘hypothetical’. Others may be the ability to generate a hypothetical principle that would account for particular belief, the ability to generate other consequences that are logically consistent with such a principle, and some strategy for evaluating the consequence of an hypothetical principle in order to decide whether to retain it. This evaluation strategy might involve deciding whether the consequence would be acceptable to some group of people, possibly (in stage 6) all present and future people. Similar strategies might be involved in moral argument. In trying to persuade someone else, one strategy is finding a principle that would account for many of their beliefs as well as yours, generating consequences from it to get them to accept the principle, and finally showing them that it is inconsistent with their original stand in the argument. Again, while it is easy to see how the complexity of habitual strategies like these could retard their acquisition, there is no theoretical reason why many components of these strategies could not be acquired before components which characterize earlier stages. Further, some of the components used in moral reasoning are specific to this area, such as the ‘evaluation strategy’, so we need not expect a close correspondence between moral development and development of other areas which use different components, such as (possibly) mathematical reasoning.

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4. Comparison with other theories In conclusion, I shall review the relation of component theory to other traditions which try to account for similar ranges of phenomena. In this way, the potential contribution of component theory to psychology and education may be made clear. The major theory which attempts to account for the range of phenomena described here is that of Piaget (1970; see also Flavell, 1970). The essential features of his theory have been incorporated into other theories of particular domains, such as those of Kohlberg (1971) and Perry (1970). Several features of Piaget’s theory are incorporated into component theory as well. Component-theory can be seen as a simple extension of Piaget’s notion of assimilation and some of Jakobson’s (1942) ideas about the development of differentiation, Our assumption that the marked form (with the required component) is replaced by the unmarked (primitive concept) before the former is learned parallels Piaget’s notion of assimilation of novel situations to old schemes. The only difference is that component theory assumes that the scheme (strategy) often ‘accommodates’ by mere addition of new components. A second point of agreement with Piaget’s theory is the notion of horizontal decalage. This is parallel to our assumption that learning a component of one concept does not automatically bring about the attachment of that component to other concepts but rather facilitates such attachment when future opportunities for learning arise (giving rise to the appearance of stages in limited domains). For Piaget, the onset of a new stage is not shown simultaneously in all manifestations of that stage but rather in an increased readiness to acquire such manifestations. There is one major point of difference between component theory and Piagetian theory. This difference concerns the ideas of equilibrium, stage and structure, which are, for Piaget and his followers, closely interrelated. According to these ideas, certain acquisitions (of concept, components, strategies or whatever) are interrelated so as to form a stable, ‘equilibrated’, whole if they are all present. For example, there is held to be a sense in which understanding of commutativity, associativity and identity axioms in algebra ‘hang together’. While it is possible to understand the implications of one without understanding those of the others, such incomplete understanding is unstable. For Piaget, such a set of interrelated acquisitions is said to constitute a structure. There are several alternative, more-or-less all-inclusive, structures, and these structures may be ordered developmentally into stages. Component theory makes no assumption about structures. This question, of course, will not be resolved easily (see Flavell, 1971). Yet there may be some value in a developmental theory which is Piagetian in spirit but without the assumption of stages and structures. Much modern educational theory and practice incorporates the idea of unified stages implicitly. Thus, we often rationalize teaching a certain

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subject matter by saying that its study brings about ‘general intellectual development’. If intellectual development does not occur in general, but rather in isolated areas, independently of other areas, such teaching may bring about development only with respect to the concepts and components of the matter in question. For example, there seems to be little reason for acquisition of length, speed and number concepts to facilitate acquisition of mature moral judgment. Thus, while component theory may be difficult to compare empirically with Piagetian stage theory, its different consequences in education suggest that it is at least worth considering as a possible alternative. Another theoretical tradition which has concerned itself with some of the issues discussed here is learning theory, particularly as developed by GagnC (1968) and Furby (1972). In many ways their approach is similar to that of component theory. The acquisition of conservation, for example, is explained in terms of acquisition of subordinate pieces of knowledge such as the knowledge that equivalence is transitive. This sort of learning theory is entirely consistent with component theory and differs only in emphasis; where Gag&s learning theory concerns itself with behavioral tests of what is known, research based on component theory concerns itself with the strategy used to apply the knowledge. Another difference is that where Gagne emphasizes transfer from simple knowledge to more complex knowledge which relies on the simple knowledge, component theory also emphasizes transfer of components from one concept to another. For Gag& the goal of education seems to be to teach certain specific complex concepts; component theory, on the other hand, is also consistent with the goal of providing a base of components so that future learning will be facilitated even if the specific content of that learning is largely unknown. A number of other theories (McLaughlin, 1963; Pascual-Leone, 1970; Klahr and Wallace, 1970) have attempted to account for conceptual development in terms of various capacities that increase with age such as memory span, ‘central computing space’ or ‘drive’. These theories may deal adequately with deficits in which certain tasks cannot be done at all, such as responding to several stimuli at once or carrying out a complex plan. But their extension to tasks in which errors are systematic, and characterized by assimilation of one concept to another, has been very limited so far. It is not clear what additional assumptions would be required for such extensions besides those made by component theory. Surely, even the most ardent componenttheorist must admit that capacity frequently limits performance, and that it increases with age. He must also admit that acquisition of some components is limited by the capacity to carry out complex strategies. But he need not admit that the growth of capacity is a sufficient principle to explain the pattern of development.

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Clark, H. H. (1970) The primitive nature of children’s relational concepts: A discussion of Donaldson and Wales. In J. R. Hayes (Ed.), Cognition and the development of language. New York, Wiley. Donaldson, M., and Balfour, G. (1968) Less is more: A study of language comprehension in children. Brit. J. Psychol., 59, 461-472. and Wales, R. J. (1970) On the acquisition of some relation terms. In J. R. Hayes (Ed.), Cognition and the development of Language, New York, Wiley. Ervin-Tripp, S. M., and Foster, G. (1960) The development of meaning in children’s descriptive terms. J. abn. sot. Psychol., 61, 271-275.

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Brown, R., Cazden, C. B., and Bellugi, U. (1969) The child’s grammar from I to III. In J. P. Hill (Ed.), Minnesota symposium on child psychology, Minneapolis, University of Minnesota Press. Bruner, J. S., Goodnow, J. J., and Austin, G. A. (1956) A study of thinking. New York, Wiley. and Kenney, H. J. (1966) On relational concepts. In J. S. Bruner, R. R. Oliver and P. M. Greenfield (Eds.), Studies in cognitive growth. New York, Wiley. Chafe, W. L. (1970) Meaning and the structure of language. Chicago, University of Chicago Press. Chomsky, N. (1965) Aspects of the theory of syntax. Cambridge, M.I.T. Press. Clark, E. V. (1971) On the acquisition of the meaning of before and after, J. verb. Learn. verb. Beh., 10, 266-275. (1973) What’s in a word? On the child’s acquisition of semantics in his first language. In T. E. Moore (Ed.), Cognitive development guage. New

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Semuntic components and conceptual development

On peut rendre compte, par une thtorie d’acquisition par addition successive de composants, d’un certain nombre de phenombnes d’apprentissage du sens des mots. Le mecanisme serait analogue a celui propose pour le developpement phonologique. Si I’on definit un concept comme une composition habituelle et un composant comme un element de composition, on peut Btendre cette theorie a I’acquisition des concepts en

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general. En effet elle rend compte du developpement des concepts logiques, des raisonnements physiques ou moraux aussi bien que des concepts verbaux. Le principe d’une acquisition composant par composant inclut un transfert possible d’apprentissage entre les concepts partageant les memes composants et peut se poser en concurrence des theories du developpement par stades.